The Way of the Wizard
"I have learned something else from the theory of gravitation. no collection of empirical facts however comprehensive can ever lead to the setting up of such complicated equations. A theory can be tested by experience, but there is no way from experience to the construction of a theory. Equations of such complexity as are the equations of the gravitational field can be found only through the discovery of a logically simple mathematical condition that determines the equations completely or almost completely. Once one has obtained these sufficiently strong formal conditions, one requires only little knowledge of facts for the construction of the theory."
Causality
"Hume saw clearly that certain concepts, as for example that of causality, cannot be deduced from the material of experience by logical methods."
Objectivity
"It is quite clear to me that the religious paradise of youth which was lost, was a first attempt to free myself from the chains of the "merely personal," from an existence dominated by wishes, hopes and primitive feelings. Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned as a liberation, and I soon noticed that many a man whom I had learned to esteem and to admire had found inner freedom and security in its pursuit. The mental grasp of this extra-personal world within the frame of our capabilities presented itself to my mind, half consciously, half unconsciously, as a supreme goal.
Similarly motivated men of the present and of the past, as well as the insights they have achieved, were the friends who could not be lost. The road to this paradise was not as comfortable and alluring as the road to religious paradise; but it has shown itself reliable, and I have never regretted having chosen it. ... In a man of my type, the turning point ... lies in the fact that gradually the major interest disengages itself to a far-reaching degree from the momentary and the merely personal and turns inward toward the striving for a conceptual grasp of things."
"The great variety of the external situations and the narrowness of the momentary content of consciousness bring about a sort of atomizing of the life of every human being."
The bandwidth of conscious attention is small compared to the sentient subconscious processing.
Thinking
"When, on the reception of sense impressions, memory pictures emerge, this is not yet 'thinking.' And when such pictures form sequences, each member of which calls forth another, this too is not yet 'thinking.' When, however, a certain picture turns up in many such sequences, then - precisely by such a return- it becomes an organizing element for such sequences, in that it connects sequences in themselves unrelated to each other. Such an element becomes a tool, a concept. I think that the transition from free association or 'dreaming' to thinking is characterized by the more or less preeminent role played by the 'concept'. It is by no means necessary that a concept be tied to a sensorial cognizable and reproducible sign (word); but when this is the case, then thinking becomes thereby capable of being communicated. ...
With what right--the reader will ask--does this man operate so carelessly and primitively with ideas in such a problematic realm without making even the least effort to prove anything? My defense: all our thinking is of this nature of free play with concepts; the justification for this play lies in the degree of comprehension of our sensations that we are able to achieve with its aid. The concept of 'truth' can not yet be applied to such a structure; to my thinking this concept becomes applicable only when a far-reaching agreement (convention) concerning the elements and rules of the game is already at hand.
.... our thinking goes on for the most part without the use of signs (words) and beyond that to a considerable degree unconsciously. For how, otherwise, should it happen that sometimes we 'wonder' quite spontaneously about some experience? This 'wondering' appears to occur when an experience comes into conflict with a world of concepts already sufficiently fixed within us. Whenever such a conflict is experienced sharply and intensively it reacts back upon our world of thought in a decisive way. The development of this world of thought is in a certain sense a continuous flight from wonder."
Distinguish conscious attention. That is both subconscious thinking and conscious attention depend on back-action. The subconscious thinking is the motion of the system point before capture.
"I see on the one side the totality of sense experiences and, on the other, the totality of the concepts and propositions that are laid down in books. The relations between the concepts and propositions among themselves are of a logical nature, and the business of logical thinking is strictly limited to the achievement of the connections between concepts and propositions according to firmly laid down rules, which are the concern of logic. The concepts and propositions get 'meaning,' or 'content,' only through their connection with sense experiences. The connection of the latter (sense experiences) with the former (concepts and propositions) is purely intuitive, not itself of a logical nature. The degree of certainty with which this connection, or intuitive linkage, can be undertaken, and nothing else, differentiates empty fantasy from scientific 'truth'."
Bohm uses "informal language" similarly to Einstein's "intuitive linkage".
Classical physics
"...dogmatic rigidity prevailed in matters of principle: In the beginning (if there was such a thing), God created Newton's laws of motion together with the necessary masses and forces... the more sophisticated development of the mechanics of discrete masses as the basis of all physics, was the achievement of the nineteenth century. What made the greatest impression ,,, was not so much the technical development of mechanics or the solution of complicated problems as the achievements of [classical Newtonian] mechanics in areas that apparently had nothing to do with mechanics: the mechanical theory of light, which conceived of light as the wave motion of a quasi-rigid elastic ether; and above all the kinetic theory of gases: the independence of the specific heat of monatomic gases from the atomic weight, the derivation of the equation of the state of a gas and its relation to the specific heat, the kinetic theory of the dissociation of gases, and above all the quantitative relationship between viscosity, heat conduction, and diffusion of gases which also furnished the absolute magnitude of the atom. ... In chemistry, however, only the ratios of the atomic masses played any role, not their absolute magnitudes, so the atomic theory [of the chemists] could be viewed more as a visualizing symbol than as knowledge concerning the actual composition of matter. ... it was also of profound interest that the statistical theory of classical mechanics was able to deduce the basic laws of thermodynamics, something ... already accomplished by Boltzmann. ... all physicists of the [19th] century saw in classical mechanics a firm and definitive foundation for all physics, indeed for the whole of natural science ... I see Mach's greatness in his incorruptible skepticism and independence ... Mach's epistemological position ... today appears to me to be essentially untenable. For he did not place in the correct light the essentially constructive and speculative nature of all thinking and more especially of scientific thinking. ... As far as the laws of mathematics refer to reality, they are not certain; and so far as they are certain, they do not refer to reality,"
Mach rejected the kinetic theory of atoms on positivistic grounds. This was before scanning tunneling microscopes that can see individual atoms.
Einstein says that theories must be judged both by "inner perfection" and "external confirmation."
The classical mechanical ether rejected
" .. the incorporation of wave optics into the mechanical picture of the world was bound to arouse serious misgivings. If light was to be interpreted as undulatory motion in an elastic body (ether), this had to be a medium that permeates everything, because of the transversality of the light waves, in the main resembling a solid body, yet incompressible, so that longitudinal waves did not exist. This ether had to lead to a ghostly existence alongside the rest of matter, inasmuch as it seemed to offer no resistance whatever to the motion of ponderable bodies. In order to explain the indices of refraction of transparent bodies as well as the processes of emission and absorption of radiation, one would have to assume complicated interactions between the two types of matter, something that was not even seriously tried, let alone achieved."
There was no natural way to explain Maxwell classical electromagnetic field in terms of Newtonian classical particle mechanics.
".. thus mechanics as the basis of physics was being abandoned, almost imperceptibly, because its adaptation to the facts presented itself finally as a hopeless task. Since then, there exist two [classical] types of conceptual elements [in classical rocklike physics]: on the one hand, material points with forces at a distance between them and, on the other hand, the continuous field."
Inertial frames of reference not preferred
"From the standpoint of purely geometrical description, all 'rigid' coordinate systems are logically equivalent. The equations of mechanics (for example the law of inertia) claim validity only when referred to a specific class of such systems, i.e., the 'inertial systems'. In this connection the coordinate system as a material object is without any significance. Hence to justify the need for this specific choice one must search for something that exists beyond the objects (masses, distances) with which the theory deals. For this reason 'absolute space' as originally determinative was quite explicitly introduced by Newton as the omnipresent active participant in all mechanical events; by 'absolute' [Newton] obviously means: uninfluenced by the masses and by their motion."
Einstein rejects the preferential selection of inertial frames of reference as special. In other words, the use of non-inertial frames should be equally valid, if not equally useful. Using an image reminiscent of Abbott's "Flatland" and Plato's Allegory of the Cave, people who live in a small area and never see the stars ascribe a special physical attribute to the vertical direction of acceleration of falling bodies. Einstein concludes:
"The preference given to the vertical over all other spatial directions is precisely analogous to the preference given to inertial systems over other rigid coordinate systems."
Note Einstein's use of the qualifier "rigid". He also points out that these poor fools, with chains around their necks that make it difficult to look upward to the stars and beyond,
"They might not let themselves be influenced by the argument that in its geometrical properties space is isotropic and that it is therefore unsatisfactory to postulate basic physical laws according to which there is to be a preferential direction..."
Einstein replaces Newton's action at a distance with Maxwell's field.
Does Einstein's argument of non preference apply to time as well as space? Is there to be no preferential direction for time? What about time's arrow of irreversible processes? This would seem to be an argument for the Wheeler-Feynman model which uses exactly 1Ú2 each of the retarded electromagnetic potential from the past light cone to here-now plus the advanced electromagnetic potential from the future to here-now to get the correct radiation reaction for a point charge in motion. Feynman also pointed out that the essential classical requirement to get far field transverse radiation energy emitted is not the acceleration of the charge, but its time derivative, i.e., third time derivative of the charge displacement. This gives a third order in time dynamical equation of motion for the charge. One can see that this is required by the equivalence principle of general relativity which says that a charge at rest in a uniform gravitational field does not radiate. Therefore, by the equivalence principle, a uniformly accelerating charge cannot radiate transversely into the far field. However, Einstein denied the kind of action-at-a-distance that Wheeler and Feynman were to use later on. Einstein was in love with the field, Wheeler and Feynman, like Marc Antony at Caesar's Funeral, wished to bury it along with other "honorable" ideas. Remember these are the rocklike intensity-dependent form-independent classical force fields that are locally acting in ordinary three-dimensional relative space at each moment in relative time. "Relative" means "frame-dependent". Einstein, at that time, had no inkling that his "spooky telepathic" thoughtlike quantum fields that are local in higher-dimensional configuration space, but nonlocally-acting in ordinary three-dimensional space and time, and are form-dependent and intensity-independent, were thoughtlike. Indeed, spooky telepathic nonlocality and form-dependence are highly non-classical, i.e., not rocklike, but, rather, nonmaterial properties of thought. In other words, that the quantum wave properties of source matter and the quantum particle properties of their classical wave force fields, are the products of the action of a cosmic thoughtlike fundamental pattern in the universe forming a Sleeping God, were too much for him to admit to -- even though he was a mystical realist. My post-quantum back-action awakens this Sleeping God into The Conscious God. Here is the New Creation Mythematick for The Third Millennium.
Thus, Einstein attacks rocklike classical action-at-a-distance with: "If one accepts the concepts of space (including geometry) and time without critical doubts, then there exists no reason to object to the idea of action at a distance, even though such a concept is unsuited to the ideas one forms on the basis of the raw experience of daily life."
Einstein remarks that the requirement that "forces depend only on the coordinates (and not, for example on their derivatives with respect to time) ... is not very natural..." Phenomenological friction forces with the irreversible arrow of time depend on the first time derivative. Also look at the force of radiation reaction.
Einstein adds a second argument against the kind of intensity-dependent form-independent classical action at a distance as it is found in Newton's law of gravitational force which practically speaking is very useful and accurate for travel between the planets, for airplanes, ships, boats, cars, machinery of all kinds etc.
"Within the framework of [Newton's] theory alone it is entirely arbitrary that the forces of gravitation (and electricity), which come from one point, are governed by the potential function 1/r ... it has long been known that this function is the spherically symmetric solution of the simplest (rotation-invariant) differential equation Laplacian of the potential = 0; it would therefore not be far-fetched to regard this as a clue that this function was to be considered as resulting from a spatial law, an approach that would have eliminated the arbitrariness in the force law. This is really the first insight that suggests a turning away from the theory of action at a distance, a development that - prepared by Faraday, Maxwell, and Hertz-- really begins only later in response to the external pressure of experimental data. ... What made [Maxwell's] theory appear revolutionary was the transition from [classical Newtonian] action at a distance to [local] fields as the fundamental variables. "
Note here that there are three really different ideas of action at a distance -- the classical version, the quantum version, and the post-quantum version. Einstein above, and also Wheeler and Feynman in their classical delayed action at a distance both to the future and to the past light cones, are talking about classical form-independent but intensity-dependent classical action at a distance. In contrast, Bohm is talking about quantum form-dependent but intensity-independent action at a distance. Eberhard's theorem asserts that conservation of quantum probability current densities in configuration space precludes the use of quantum action at a distance, nonlocal in ordinary 3D space and time as a direct communication channel. In contrast, post-quantum action at a distance informed by a direct back-action from the rocklike classical beable to its attached thoughtlike quantum pilot-wave, violates Eberhard's theorem because the quantum currents are no longer conserved in configuration space. That is, the quantum analog to the classical Liouville theorem in classical statistical mechanics is violated. Indeed, this post-quantum friction provides the arrow of time and is the dynamo of creative thought driving the advance of civilization.
To summarize:
Einstein attacks the classical rocklike action at a distance that Wheeler and Feynman embraced.
Einstein: Field? Yes! Instantaneous Newtonian action-at-a-distance? No!
Wheeler and Feynman: Local field? No! Delayed advanced action-at-a-distance from the future? Yes!
"I would also like to mention , as one internal asymmetry of this [Newtonian] theory, that the inertial mass that occurs in the law of motion also appears in the law of gravitational force, but not in the expressions for the other forces."
More on classical mechanics
Einstein also says that "the division of energy into two essentially different parts, kinetic and potential energy, must be felt to be unnatural." What does he mean by that? Why does he use the word "unnatural"? "H. Hertz felt this to be so disturbing that, in his very last work, he attempted to free mechanics from the concept of potential energy (i.e., from the concept of force).
Einstein did abolish gravitational force in general relativity. He replaced Newton's instantaneous classical action at a distance force by local curved 4D space-time geometry. The test mass simply rolls along a slower than light locally straightest path in space-time called the "timelike geodesic". This geodesic while as straight as it can be in curved 4D space-time, corresponds, counter intuitively, to the motion of a point particle on a closed precessing ellipse when viewed in seemingly flat 3D space. The modern fiber bundle theory of gauge forces partially attempts to do with the electroweak and strong forces what Einstein did with the gravity force. These forces are curvatures in the connection among tiny extra-dimensional hyperspheres attached to each space-time event. This is still classical. All of the gauge forces are intensity-dependent and form-independent rocklike i.e., material things. They must be combined with the intensity-independent and form-dependent thoughtlike nonmaterial, but still physical, quantum superpotential to get the modern theory of relativistic quantum fields that create and destroy quanta and their anti-quanta.
Einstein in a panegyric to Newton says :
"The concepts that you created are even today still guiding our thinking in physics, although we now know that they will have to be replaced by others father removed from the sphere of immediate experience, if we aim at a profounder understanding of relationships."
On Maxwell's Electromagnetic Field
"The incorporation of optics into the theory of electromagnetism, with its relation of the speed of light to the electric and magnetic absolute system of units as well as the relation of the index of refraction to the dielectric constant, the qualitative relation between the reflection coefficient of a body and its metallic conductivity - it was like a revelation ... Maxwell needed only one single hypothetical step -- the introduction of the electrical displacement current in the vacuum and in the dielectrica and its magnetic effect, an innovation that was almost preordained by the formal properties of the differential equations."
The fly in the ointment was the "ether" i.e., "empty space as a special instance of a dielectric body. Matter appeared as the bearer of the field not space. ... It was the great merit of H. A. Lorentz that he brought about a change here in a convincing fashion. In principle a [classical local] field exists, according to him, only in empty [3D] space. Matter [i.e., Bohmian beables in my post-quantum mechanics]-- considered to exist of atoms-- is only the seat of electric charges; between the material particles there is empty space, the seat of the electromagnetic field, which is produced by the position and velocity [also time derivative of the acceleration for radiation reaction] of the point charges located on the material particles. Dielectric behavior, conductivity, etc., are determined exclusively by the type of mechanical bindings between the particles that constitute the bodies. The particle charges create the field, which, on the other hand, exerts forces upon the charges of the particles, thus determining the motion of the latter according to Newton's law of motion.
If one compares this to Newton's system, the charge consists in this: [classical intensity-dependent/form-independent] action at a distance is replaced by the field, which also describes the radiation. ... one is struck by the dualism that lies in the fact that the material point in Newton's sense and the field as continuum are used as elementary concepts side by side. Kinetic energy and field energy appear as essentially different things. This appears all the more unsatisfactory as, according to Maxwell's theory, the magnetic field of a moving electric charge represents inertia. Why not then the whole of inertia? Then only field energy would be left, and the particle would be merely a domain containing an especially high density of field energy. In that case one could hope to deduce the concept of the mass point together with the equations of motion of the particles from the field equations - the disturbing dualism would have been removed. .... However, Maxwell's equations did not permit the derivation of the equilibrium of the electricity that constitutes a particle. Only different, nonlinear field equations could possibly accomplish such a thing. But no method existed for discovering such field equations without deteriorating into adventurous arbitrariness."
Bohm's form-dependent quantum corrections to the classical field equations make the latter highly nonlinear in a qualitatively new non-arbitrary non-classical way. Note Einstein's phrase "disturbing dualism". Einstein's thinking here is pre-quantum. It is too tied to ordinary three-dimensional space. Bohm has highlighted the primacy of configuration space for complex systems of interacting particles. Also note that the classical intensity is also the field energy density. There are four form-independent polarization states of the classical Maxwell field. The classical Maxwell field is a rocklike "beable" in the Bohm hidden-variable theory. Two of them (longitudinal and time like) determine the "near field" like the instantaneous radial static Coulomb electric field whose intensity drops off as the reciprocal fourth power of the radial distance from a point charge. In contrast, the "far field" radiation comes from the two transverse polarizations perpendicular to the direction of propagation of the radiation. This far field intensity drops off only as the square of the radial distance from a point-like non uniformly accelerating point charge whose maximum displacement is small compared to the wavelength of the radiation. Since the surface area of a thin spherical shell centered at this jerking charge is proportional to the square of the radial distance, it follows that a constant amount of total flux energy can escape to infinity. Note that a strictly uniformly accelerating charge does not radiate. If it radiated, it would violate Einstein's equivalence principle of general relativity.
What changes in this classical picture when we add quantum effects? If we have a system of particles, these particles form a single "system point" or "beable" in a classical higher-dimensional configuration space. There is a new kind of form-dependent quantum field at each possible position of the system point in configuration space. The effect of this quantum field on its attached material system point, or beable, does not depend on its intensity only on its form. The intensity does give the probability to observe a definite property or "eigenvalue" under special statistical conditions of preparation of an "ensemble" of identical non interacting systems. The new quantum form field organizes the energy of the matter that is already there. This new form-field is nonlocal in the 3D space of the Maxwell field. It connects separated points in space at the same time in a preferred frame of reference. It even connects points in space at different times. The nonlocal form-field glues the particles together in a stable way together with the classical local intensity electromagnetic field. The classical electromagnetic Maxwell field by itself without the quantum form-field is not enough to keep matter diverse and stable.
Unlike the Maxwell field, the quantum form-field has no charges. The back-action charge of the post-quantum form-field must be a structure in configuration space not ordinary space. The Fock space of second quantized field theory involves a coherent superposition of all configuration spaces for variable particle numbers N. This new form-field is the seat of the mind in post-quantum mechanics.
Mind thus appears as a fundamental physical part of the universe. Mind is nonmaterial, but it is physical. The quantum mind does not awake to post-quantum sentience, subconscious, conscious, and super conscious until it gets charged up by back-action. Like a battery of "elan vital", the sentience of inner immediate felt experience requires the vital jolt of back-action. The ancients called back-action "the breath of God", the "inspiration" etc. :-) It is back-action that enables the mind to receive data from the world. In quantum mechanics the mind exerts a nonlocal form-dependent force on its attached material beable, but it does so blindly, therefore, randomly since it is not receiving any direct data back on the effects of its force. Therefore, it cannot correct errors to achieve its purpose. There is no cybernetic feedback-control loop in ordinary quantum physics.
Planck discovers the quantum of action in 1900.
Einstein wrote that the first fundamental revolution in modern physics was Maxwell's replacement of Newton's classical rocklike nonlocal action at a distance by the local action of the classical field. This really has nothing to do with the thoughtlike quantum action at a distance of Bohm's quantum potential. "Rocklike" means "intensity-dependent" and "form-independent". "Rocklike" is the same as "material". "Thoughtlike" means just the opposite of "rocklike" i.e., intensity-independent and form-dependent. "Thoughtlike" means "nonmaterial". But both "rocklike" and "thoughtlike" are "physical". We now continue with Planck's second fundamental revolution which was the introduction of thoughtlike things into physics that was independent of the introduction of the rocklike classical local field intensities.
"... a second fundamental crisis set in ... owing to Max Planck's investigations into heat radiation (1900) ... all the more remarkable because ... in its first phase, it was not in any way influenced by any surprising discoveries of an experimental nature."
At this point let me stop and say something about the premature rush to have me justify the postmodern physics of consciousness with an immediate appeal to experimental test. Einstein's own words testify to the historical fact that at least two of the major revolutions of modern physics, the quantum and relativity, were not, in their first early phases "influenced by any surprising discoveries of an experimental nature". The Michelson-Morley experiment that could not measure the absolute speed of the earth through the Newtonian mechanical ether did not motivate Einstein's creation of the theory of special relativity which, of course, was later on, confirmed by many experiments. Note today, however, we can measure the absolute speed of the earth through the general relativistic ether called the "Hubble flow" of our expanding universe in terms of departure from isotropy of the cosmic black body radiation that Planck explained in 1900. Einstein died before this cosmic blackbody radiation, left over from the big bang, was discovered by microwave engineers at Bell Labs near Princeton.
"On thermodynamic grounds Kirchoff had concluded that the energy density and the spectral composition of radiation in a cavity enclosed by impervious walls of the temperature T, must be independent of the nature of the walls. ... the monochromatic density of radiation rho is a universal function of the frequency f and of the absolute temperature T. Thus arose the interesting problem of determining this function rho(f,T)... According to Maxwell's theory the radiation had to exert a pressure on the walls, determined by the total energy density. From this Boltzmann concluded, by means of pure thermodynamics, that the entire energy density of the radiation (integral of rho df) is proportional to [the fourth power] of T. In this way he found a theoretical justification of a law that had previously been discovered empirically by Stefan.... Wein found that the universal function rho of the two variables f and T would have to be of the form
rho = f^3 F(f/T)
[i.e., rho proportional to the cube of the radiation frequency f multiplying a function F of a single variable f/T that is the ratio of the frequency f and the absolute temperature T, putting in the fundamental universal Planck constant h of action and Boltzmann's constant k of entropy give the dimensionless variable hf/kT]
... the theoretical determination of this universal function F was of fundamental importance -- this was precisely the task that confronted Planck. Careful measurements had led to a rather precise empirical determination of the function F. Relying on those empirical measurements, he succeeded ... in finding ....
rho = (8pi hf^3/c^3 ) (e^hf/kt - 1)^-1
... Planck actually did find a derivation, the imperfections of which remained at first hidden, which latter fact was most fortunate for the development of physics ... it permitted, with the aid of Maxwell's theory, the calculation of the average energy E of a quasi-monochromatic oscillator within the field of radiation:
E = hf/(e^hf/kt - 1)
..... For high temperatures (with f fixed) it yielded ...
E = kT
This is the same expression obtained in the [classical] kinetic theory of gases for the average [random] energy of a mass point capable of oscillating elastically in one dimension. For in kinetic theory one gets
E = (R/N)T
where R denotes the gas constant, and N the number of molecules per mole, from which constant one can compute the absolute size of the atom. Equating these two expressions one gets
N = R/k
The one constant of Planck's formula consequently furnishes exactly the correct size of the atom. The numerical value agreed satisfactorily with the determinations of N by means of kinetic gas theory, though the latter were not very accurate.
This was a great success, which Planck clearly recognized. But the matter has a serious drawback, which Planck fortunately overlooked at first. For the same considerations demand in fact that the [classical equipartition of energy] relation E = kT [per dynamical degree of freedom] would also have to be valid for low temperatures. In that case... it would be all over for Planck's formula .. with the constant h. From the existing [classical Newtonian-Maxwell] theory ... the correct conclusion would have been: the average [random] kinetic energy of the oscillator is either given incorrectly by the theory of gases, which would imply a refutation of statistical [particle] mechanics; or else the average energy of the oscillator follows incorrectly from Maxwell [field] theory, which would imply a refutation of the latter... If Planck had drawn this conclusion, he probably would not have made his great discovery, because pure deductive reasoning would have been left without a foundation.
Planck derives black body radiation from energy quanta via entropy.
Now back to Planck's reasoning. On the basis of the kinetic [particle] theory of gases Boltzmann had discovered that ... entropy was [proportional] to the logarithm of the "probability" of the state under consideration. Through this insight he recognized the nature of processes that, within the meaning of the thermodynamics, are 'irreversible' [i.e., the arrow of time is caused by the spontaneous tendency of closed systems to evolve to more probable states] Seen from the molecular-mechanical point of view, however, all processes are reversible. ... an immensely large number (Z) of [micro] states belong to a macroscopic condition. Z is then a measure of the probability of a chosen macro-state. ... Planck ... applied Boltzmann's principle to a system consisting of very many resonators of the same frequency f. The macroscopic state is given by the total energy of the oscillation of all resonators, a micro-state by the fixation of the (instantaneous) energy of each individual resonator. In order to express the number of micro-states belonging to a macro-state by means of a finite number, Planck divided the total energy into a large but finite number of identical energy elements epsilon [i.e., "quanta"] and asked: in how many ways can these energy elements be divided among the resonators. The logarithm of this number, then, furnishes the entropy and thus (via thermodynamics) the temperature ... Planck got his radiation formula if he chose his energy elements epsilon to have the magnitude epsilon = hf. The decisive element in this procedure is that the result depends upon taking for epsilon a definite value, i.e., on not going to the limit epsilon = 0. This ... contradicts the [classical] mechanical and electrodynamic basis upon which the derivation otherwise depends ... the derivation presupposes implicitly that energy can be absorbed and emitted by the individual resonator only in 'quanta' of magnitude hf, i.e., that the energy of a mechanical structure capable of oscillations as well as the energy of radiation can be transferred only in such quanta -- in contradiction to the [classical] laws of mechanics and electrodynamics. The contradiction with dynamics was here fundamental; whereas the contradiction with electrodynamics might be less fundamental. For the expression for the density of radiation energy, though compatible with Maxwell's equations, is not a necessary consequence of these equations. ... the Stefan-Boltzmann law and Wein's law, which are based on it, are in agreement with experience.
How Einstein explained the photoelectric effect without a proper theory.
All of this was quite clear to me shortly after the publication of Planck's fundamental work; so that, without having a substitute for classical mechanics, I could nevertheless see to what kind of consequence this law of temperature radiation leads to for the photoelectric effect and for other related phenomena of the transformation of radiation energy, as well as for the specific heat of (especially) solid bodies. All my attempts, however, to adapt the theoretical foundation of physics to this [new type of] knowledge failed completely. It was as if the ground had been pulled out from under one, with no firm foundation to be seen anywhere upon which one could have built. That this insecure and contradictory foundation was sufficient to enable a man of Bohr's unique instinct and sensitivity to discover the principal laws of the spectral lines and of the electron shells of atoms, together with their significance for chemistry, appeared to me as a miracle -- and appears to me a miracle even today. This is the highest form of musicality in the sphere of thought.
Einstein and Planck prove the reality of atoms.
Departures from Brownian motion are important in the modern fractal strange attractor theory of the classical chaos of natural macro-processes like the stock market and nerve excitations in the cortex and the heart. Indeed , Bohm's hidden-variable theory has the strange fractal attractors for the motion of the rocklike hidden-variables constructed from the thoughtlike quantum pilot-wave attached to them. If we throw in a direct self-organizing "back-action" from the rocklike classical hidden-variable to its attached thoughtlike quantum pilot-wave, we have the new, relatively simple and visualizable, universal post-quantum mechanics of individual conscious complex adaptive systems such as our own mind-brains and any other alien extraterrestrial intelligences that the universe may suddenly surprise us with.
"... Brownian motion, and related ... fluctuation phenomena ... in essence rest upon classical molecular mechanics. Not acquainted wirh the investigations of Boltzmann and Gibbs, which had appeared earlier and actually exhausted the subject. I developed the statistical mechanics and the molecular-kinetic theory of thermodynamics based upon it. My principal aim in this was to find facts that would guarantee as much as possible the existence of atoms of definite finite size. ... I discovered that ... there would have to be a movement of suspended microscopic particles capable of being observed, without knowing that observations concerning the Brownian motion were already long familiar. The simplest derivation rested upon the following consideration. If the molecular kinetic theory is essentially correct, a suspension of visible particles must possess the same kind of osmotic pressure satisfying the gas laws as a solution of molecules. This osmotic pressure depends upon the actual magnitude of the molecules, i.e., upon the number of molecules in a gram-equivalent. If the density of the suspension is inhomogeneous, the osmotic pressure is inhomogeneous too and gives rise to a compensating diffusion, which can be calculated from the known mobility of the particles. This diffusion can, on the other hand, also be considered the result of the random displacement -- originally of unknown magnitude -- of the suspended particles owing to thermal agitation. By comparing the amounts obtained for the diffusion current from both types of reasoning, one obtains quantitatively the statistical law for these displacements, i.e., the law of the Brownian motion. The agreement if these considerations with experience together with Planck's determination of the true molecular size from the law of radiation (for high temperatures) convinced the skeptic, who were quite numerous at that time ... of the reality of atoms."
Einstein's gentle warning to naive positivist fundamentalist skeptics.
Einstein also remarks that the hostility of positivists, the secular fundamentalists of science, hindered progress in physics.
"... even scholars of audacious spirit and fine instinct can be hindered in the interpretation of facts by philosophical prejudices. The prejudice -- which has by no means disappeared -- consists in the belief that facts by themselves can and should yield scientific knowledge without free conceptual construction. Such a misconception is possible only because one does not easily become aware of the free choice of such concepts, which, through success and long usage, appear to be immediately connected with the empirical material."
Brownian motion and point like photon shot noise
"The success of the theory of the Brownian motion showed again conclusively that classical mechanics always led to trustworthy results whenever it was applied to motions in which the higher time derivatives of the velocity are negligible."
Feynman has pointed out that the classical mechanical description of the electromagnetic radiation reaction requires higher time derivatives of the velocity of the radiating charge. A uniformly accelerating charge will not radiate transverse waves to the far field. Such radiation would violate Einstein's equivalence principle of general relativity. The time derivative of the acceleration vector of the point charge is responsible for all classical electromagnetic radiation.
"... in a space filled with radiation a freely moving (vertically to its plane), quasi-monochromatically reflecting mirror would have to go through a kind of Brownian movement, the mean kinetic energy of which equals (1/2)(R/N)T ... If radiation were not subject to local fluctuations, the mirror would gradually come to rest because, owing to its motion, it reflects more radiation on its front than on its reverse side. The mirror, however, must experience certain random fluctuations of the pressure exerted upon it because of the fact that the wave packets, constituting the radiation interfere with one another. These can be computed from Maxwell's theory. This calculation then shows that these pressure variations (especially in the case of small radiation densities) are by no means sufficient to impart to the mirror the average kinetic energy (1/2)(R/N)T. In order to get this result one has to assume rather that there exists a second type of pressure variations, not derivable from Maxwell's theory, corresponding to the assumption that radiation energy consists of indivisible point-like localized quanta of energy hf [and of momentum hf/c, c = velocity of light], which are reflected undivided. This way of looking at the problem showed in a drastic and direct way that a type of immediate reality has to be ascribed to Planck's quanta, that radiation must, therefore, possess a kind of molecular structure as far as its energy is concerned, which of course contradicts Maxwell's theory. ... This dual nature of radiation (and of material corpuscles) is a major property of reality, which has been interpreted by quantum mechanics in an ingenious and amazingly successful fashion. This interpretation .. appears to me to be only a temporary expedient ... neither mechanics nor electrodynamics (except in limiting cases) claim exact validity .. Gradually I dispaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and more desperately I tried the more I came to the conclusion that only the discovery of a universal formal principle could lead us to assured results. The example I saw before me was thermodynamics. The general principle was there ... The laws of nature are such that it is impossible to construct a perpetuum mobile (of the first and second kind)...."
The total fluctuation in the black body radiation field, according to Einstein, consists of a classical wave noise, used in Hanbury Brown Twiss intensity radio telescope interferometry to measure the angular size of stars accurately in spite of the turbulent atmosphere, and the quantum particle or photon shot noise. The root mean square fluctuation of the wave noise Fourier component is proportional to the mean photon number in the signal. The root mean square fluctuation of the corresponding shot noise is Poisson proportional to the square root of the mean photon number. The mean photon number is the average energy in the mode divided by hf.
Bohm explains the quantum wavelike behavior of "rocklike" classical point particles as the intensity-independent/form-dependent "thoughtlike" force from an objective nonlocal "quantum potential" emanating, the Cabalistic sense, from Hilbert space to configuration space. He also explains the quantum point like "photon" behavior of "rocklike" classical electromagnetic fields as a similar thoughtlike force from a quantum "superpotential" making the electromagnetic field equation highly nonlinear in a nonlocal form-dependent way. The entire classical field configuration of the Maxwell field tensor Fuv over all 3D space at a given moment, in a given special relativistic frame of reference, is pictured as a single "system point" in an infinite dimensional field configuration space analogous to the classical point particles in a finite dimensional configuration space. The word "super" is used by Bohm in exactly the same way that Wheeler uses it in quantum gravity theory where the domain of the Wheeler-DeWitt quantum wave function of the universe is the configuration space called "superspace". Each point of infinite-dimensional classical Wheeler superspace is an entire field configuration of the 3D metric tensor gij in the ADM canonical formalism augmented by shift and lapse functions to pass from 3D to 4D curved space-time. A given path in Wheeler superspace is a possible history of the universe. It will have a Feynman quantum amplitude.
How Einstein created the theory of relativity.
"After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with velocity c (velocity of light in vaccum ), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations."
In fact, such a phenomenon would correspond to a zero energy tachyon of imaginary invariant mass moving at infinite speed with finite momentum.
"One sees that in this paradox the germ of the special relativity theory is already contained. ... all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious."
Digression: Clearly my post-quantum "back-action" works for the "unconscious" in Einstein's sense. I should use the word "sentience" instead of "consciousness". What Einstein means by "consciousness" is more like "attentive awareness" bringing up an unconscious, but sentient, back-active process into a self-referential Godel loop of focused attention or "awareness". So back-action is required of all sentience including subconscious or unconscious thinking and feeling and attentive awareness.
"To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem. The type of critical thinking required for the discovery of this central point was decisively furthered, in my case, especially by the reading of David Hume's and Ernst Mach's philosophical writings."
Just as Einstein questioned the axiom of absolute simultaneity, I am questioning the axiom of absolute retarded causality i.e., that effects are always in the timelike or lightlike future of their causes. Wheeler and Feynman temporarily suspended this axiom only to try to put it back with their total absorber final condition which does not work in the expanding open universe solution of general relativity. Microwave experiments (published in Nature) so far have failed to notice a violation of the total absorber final condition. This could mean a closed universe with a big crunch, or perhaps the experiments, done years ago, were too crude. Wheeler and Feynman only used classical "rocklike" form-independent and intensity-dependent action at a distance. The quantum "thoughtlike" action at a distance in Bell's theorem is more subtle since it is form-dependent and intensity-independent. Eberhard's theorem assumes zero back-action and concludes that thoughtlike quantum action at a distance cannot be used for faster-than-light an backward-in-time precognitive communication. Post-quantum back-action is an entirely new ball game which overrides this conclusion of Eberhard because the statistical predictions of quantum mechanics are distorted by back-action. We now have a general conceptual basis for claims of "precognitive remote viewing" that only involve a small extension of the fundamental laws of physics in a way already anticipated by David Bohm in 1952. The basic idea of back-action is simply that the thoughtlike quantum field from Hilbert space to configuration space has sources and sinks just like the classical rocklike Maxwell field has in ordinary space-time. The thoughtlike charges are local in configuration space which implies that they are nonlocal in space-time. This is a dramatic change, because in effect the laws of post-quantum mechanics are not rigidly fixed, but adapt to their changing environment. That is, the solutions of the post-quantum equations act back on their generating equations changing their parameters in a globally self-consistent loop that violates the absolute character of the axiom of retarded causality. This is exactly what neural networks do at the classical rocklike level. Back-action literally breathes life into the equations of post-quantum mechanics which purport to universally describe all forms of sentience in this universe and any possible universe. By "sentience" I mean any physical system able to have inner-felt experience of "qualia" the way Stapp means it in his book, Mind, Matter and Quantum Mechanics. Post-quantum mechanics only applies to certain complex adaptive systems which Gell-Mann calls "IGUS" for "information gathering utilization systems" in his book, The Quark and The Jaguar.
"One had to understand clearly what the spatial coordinates and the time fixation of an event signified in physics. The physical interpretation of the spatial coordinates presupposed a rigid body of reference, which moreover, had to be in a more or less definite state of motion (inertial system). In a given inertial system the coordinates denoted the results of certain measurements with rigid (stationary) rods. (One should always be aware that the presupposition of the existence in principle of rigid rods is presupposition suggested by approximate experience but is in principle arbitrary.) With such an interpretation of the spatial coordinates the question of the validity of Euclidean geometry becomes a problem of physics."
Observation: It is a short step from Einstein's recurrent use of the word "arbitrary" and his connected idea of the primacy of intuition and "free invention" for the linking of mathematics to experience to his idea of "covariance" in general relativity. Einstein had to withdraw from naive positivist fundamentalism to reach his deeper conceptions of general relativity. This is why I have little patience for my naive fundamentalist positivist critics (e.g., Sam Harris and the Bulgarian) who try to prematurely pressure me to come up with a crucial experimental test (on the basis of illusory pure experience free from theoretical structuring) to falsify the post-quantum physics of sentience, i.e., subconscious thinking and conscious awareness of inner-felt experience. My fully conscious solid-state Q-nanochip, and my prediction of sentient superfluids, still only in the gedankenexperimental stage, are actually pretty close to crucial experimental tests. Let us not forget that Einstein wrote that he would not have given up on general relativity even if Eddington had failed to find his predicted bending of light by the Sun's gravity during an eclipse which was a factor of 2 larger than the Newtonian prediction.
"If, then, one tries to interpret the time of an event analogously, one needs a means for the measurement of the difference in time (a periodic process, internally determined, and realized by a system of sufficiently small spatial extension). A clock at rest relative to the system of inertia defines a local time. The local times of all space points taken together are the 'time' which belongs to the selected system of inertia [i.e., inertial frame], if a means is given to 'set' these clocks relative to each other. One sees that a priori it is not at all necessary that the 'times' thus defined in different inertial systems agree with one another. One would have noticed this long ago, if, for the practical experience of everyday life, light did not present (because of the large value of c) the means for fixing an absolute simultaneity."
Let us look at Einstein's ideas from 1905 from the perspective of almost 100 years later. Einstein's argument is strictly classical. There is no "measurement problem" in classical physics as there is in quantum physics which was to mature about 20 years later. In particular, there is no problem of different observers measurements of the same event interfering with each other. There is no problem of a particle being in many places at the same time as there is in some of the interpretations of quantum physics. Every thing in special relativity is "rocklike" i.e., "explicate", local, form-independent and intensity-dependent. There is no "active information" here the way Bohm meant it. Let us also look at his use of the word 'set'. The key idea here is that classical light signals operationally define the concept of time. Let's call this classical "rocklike" time. Both David Bohm and Henry Stapp have called for a second kind of "inner", or "process", or "implicate" thoughtlike time. Let us call it "post-quantum time" or "conscious mind time". Is this post-quantum time like the Shaman's mythic time or "dream time" written about by Eliade and others? For example, see Fred Alan Wolf's "The Dreaming Universe" for background information. When we have back-action we have a new kind of "spooky telepathic" thoughtlike substitute for the rocklike light signal to set our clocks by. This is why Bohm's quantum potential must really be instantaneous in a preferred frame of reference e.g., the global cosmological frame of the Hubble flow in a special class of solutions of the Einstein field equations. It is well known that the solutions of the field equations can break the full symmetry of those equations.
"The presuppositions of the existence (in principle) of (ideal, or perfect) measuring rods and clocks are not independent of each other: a light signal that is reflected back and forth between the ends of a rigid rod constitutes an ideal clock, provided that the postulate of the constancy of the light velocity in vacuum does not lead to contradictions. According to the rules of connection, used in [Newtonian] physics, between the spatial coordinates and the time of events in the transition from one inertial system to another, the two assumptions of
(1) the constancy of the light velocity
(2) the independence of the laws (thus especially also of the law of the constancy of the light velocity) from the choice of inertial system (principle of special relativity)
are mutually incompatible (despite the fact that both taken separately are based on experience)."
Einstein is saying that his principle of special relativity i.e., the speed of light in vacuum is the same exact number c = 186,000 miles/sec in all inertial frames moving uniformly relative to each other is incompatible with the Galilean relativity equations of frame transformations based on Newton's axiom of absolute time. These Galilean equations are (in one space dimension)
x' = x - vt
t' = t
where x' is the position of event E at time t' in a frame S' moving with constant relative velocity v relative to frame S where that same event E has position x at time t. Note that t' = t is the mathematical statement that Newtonian time is absolute. It is impossible for the speed of light to be the same number c in both frames S' and S. For example, suppose the light signal is sent to the right at speed c in frame S. Frame S' also moves to the right trying to catch up with the light signal. The speed of the light signal dx'/dt' in frame S' is, according to the Galilean equations
dx'/dt' = dx/dt - v = c - v
which contradicts Einstein's (2). The Michelson-Morley experiment showed that the above Galilean equations were in fact wrong for very sensitive optical interferometric measurements. We do not notice this failure in ordinary experience because c is so big compared to speeds of things relative to the Earth's surface. Even the speeds of the planets and comets around the Sun are very small compared to c. It took almost another 20 years before Einstein explained exactly why they were wrong. Einstein, however, was not initially motivated by the Michelson-Morley experiment, but, rather, by a disturbing asymmetry in Maxwell's equations when forced to conform with Newton's mechanics. It was like trying to force a square block in a round hole.
"The insight fundamental for the special theory of relativity is this: The assumptions (1) and (2) are compatible if relations of new type ("Lorentz transformation") are postulated for the conversion of coordinates and times of events. With the given physical interpretation of coordinates and time, this is by no means merely a conventional step but implies certain hypotheses concerning the actual behavior of moving measuring rods and clocks, which can be experimentally confirmed or disproved."
This last point is important because Poincare and Fitzgerald got fragments of this before Einstein understood the whole, but they tried to interpret it as "merely a conventional step" and so they missed the equivalence of mass to energy. The explosion of the atomic bomb in 1945 was more than a "conventional step", as is the energy production of stars, both of which depend on Einstein's insight here for their proper explanation as well as manipulation and control. Every fundamental discovery in physics has profound technological spin-off unforeseen at the time by the discoverer.
"The universal principle of the special theory of relativity is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations (for the transition from one inertial system to any other arbitrarily chosen inertial system). This is a restricting principle for natural laws, comparable to the restricting principle of the nonexistence of the perpetuum mobile that underlies thermodynamics."
Perplexed by Deep Pockets Chakra's Quantum Healing?
Here is the Right Stuff
Rabbi Jacob Sarfatti's Twelve Step Program to Enlightenment :-)
Note the great weight Einstein gives to the classical second law of thermodynamics. The great principles of physics are IMHO:
1. The action is an extremum.
2. The action is quantized.
3. The classical special and general principles of relativity.
4. The classical second law of thermodynamics.
Note 1 and 4 may be two aspects of a single principle as noted first by De Broglie that thermodynamic entropy is action in Hawking's imaginary time.
5. The classical principle of gauge invariance.
6. Noether's theorem connecting continuous symmetries with conserved observables.
7. The quantum superposition principle.
8. The Dirac-Feynman connection of the quantum amplitude to the classical action of a history.
9. Nonlocal permutation quantum symmetry of identical particles leading to Bose-Einstein condensates and the Pauli-exclusion principle for the diversity and stability of ordinary matter.
10. Bohm's reinterpretation of the quantum principle in terms of a thoughtlike quantum pilot-wave and a rocklike classical hidden variable or "beable" and his discovery of the form-dependent/intensity-independent nonlocal quantum force of thought on classical matter.
11. Bell's theorem, that any theory compatible with the statistical predictions of quantum mechanics must be nonlocal if there is to be a unique objective classical reality.
12. The post-quantum back-action principle which breaks the chains restricting thought and matter to both classical determinism and quantum randomness, unifying them into a sentient self-determining higher-level living whole greater than the reductionist sum of their dead lower-level parts.? (Maybe - let experiment decide, but that will take many years.)
"It is a widespread error that the special theory of relativity is supposed to have .. first discovered ... the four-dimensionality of the physical continuum. This, of course, is not the case. Classical [Newtonian] mechanics, too, is based on the four-dimensional continuum of space and time. But in the four-dimensional continuum of classical [Newtonian] physics the subspaces of constant time value have an absolute reality, independent of the choice of frame of reference. Because of this, the four-dimensional continuum breaks down naturally into a three dimensional and a one-dimensional (time), so that the four-dimensional point of view does not force itself upon one as necessary. The special theory of relativity, on the other hand, creates a formal dependence between the way in which the space coordinates on the one hand, and the time coordinates on the other, must enter into the natural laws."
Minkowski's space-time geometry
"Before Minkowski ,, it was necessary to carry out a Lorentz transformation on a law to test its invariance under such a transformation; but he succeeded in introducing a formalism so that the mathematical form of the law itself guarantees its invariance under Lorentz transformations. ... he achieved the same thing for the four-dimensional space that the ordinary vector calculus achieves for the three spatial dimensions. He also showed that the Lorentz transformation ( apart from a different algebraic sign ...) is nothing but a rotation of the coordinate system in the four-dimensional space. "
An inconsistency, or an incompleteness ? -- Godel's theorem in the special theory.
"... It is striking that the theory .. introduces two kinds of physical things, i.e., (1) measuring rods and clocks, (2) all other things, e.g., the electromagnetic field, the material point, etc. This, in a certain sense, is inconsistent; strictly speaking, measuring rods and clocks should emerge as solutions of the basic equations (objects consisting of moving atomic configurations), not, as it were, as theoretically self-sufficient entities. The procedure justifies itself, however, because it was clear from the very beginning that the postulates of the theory are not strong enough to deduce from them equations for physical events sufficiently complete and sufficiently free from arbitrariness in order to base upon such a foundation a theory of measuring rods and clocks. If one did not wish to forego a physical interpretation of the coordinates in general (something that, in itself, would be possible), it was better to permit such inconsistency -- with the obligation, however, of eliminating it at a later stage of the theory. But one must not legitimize the sin just described so as to imagine that distances are physical entities of special type, intrinsically different from other physical variables ('reducing physics to geometry,' etc.).
New non-Newtonian predictions of the special theory.
"(1) There is no such thing as simultaneity of distant events; consequently, there is also no such thing as immediate action at a distance in the sense of Newtonian mechanics. Although the introduction of actions at a distance, which propagate at the speed of light, remains feasible according to this theory, it appears unnatural; for in such a theory there could be no reasonable expression for the conservation of energy. It therefore appears unavoidable that physical reality must be described in terms of continuous functions in space. The material point, therefore, can hardly be retained as a basic concept of the theory."
For example, the classical Lienard-Wiechert retarded potential solution for a moving charge whose influence is on the frame-invariant forward light cone replaces the Newtonian-type Coulomb potential. When the charge is at rest, there is no operational way to tell the difference between it and the old Newtonian type of potential. It's as if it were instantaneous. On the other hand, when we get to quantum electrodynamics, where the Coulomb force is due to the exchange of virtual longitudinal and timelike polarized photons, Feynman does explicitly write that this non-radiative near-field force is "instantaneous" presumably in the rest frame of the source charge generating the field. The reason for this is that virtual photons can actually move faster than classical light. They are not confined to the classical light cone. Einstein's theory of relativity is a classical theory formulated before quantum mechanics. It is still true, of course, that the instantaneous character of the force is not frame-invariant, but it will be "spacelike invariant" i.e. outside the local light cone in all frames, though not "simultaneous" in all frames as it would be in the Galilean relativity of Newtonian mechanics. That is Einstein's essential idea here. In other words, there is no violation of Einstein's main point here that there is no such thing as absolute simultaneity. But the "virtual photons" that form the quantum fluctuations of the near electromagnetic field extend from the slower-than-light timelike region inside the light cone to the faster-than-light spacelike region outside it. However, it appears that these faster than classical light near-field virtual photons cannot be used to send practical superluminal messages.
Einstein says that one cannot accommodate conservation of energy with delayed action-at-a-distance even on the light cone, yet Wheeler and Feynman, and Fokker and Tetrode, proposed such a theory where the local electromagnetic field was eliminated precisely opposite to Einstein's intuition here.
"(2) The principles of the conservation of linear momentum and of energy are fused into one single principle. The inert mass of an isolated system is identical with its energy, thus eliminating mass as an independent concept."
This is easy to formally deduce using Minkowski's formalism, but that is not how Einstein originally discovered his E = mc^2 which is now a pop-culture icon.
"If .. one introduces as the unit of time, instead of the second, the time in which light travels 1 cm, c no longer occurs in the equations ... introducing, instead of the gram and the centimeter, properly chosen 'natural' units (for example, mass and radius of the electron) ... then only 'dimensionless' constants could occur in the basic equations of physics..."
Today we want to use the Planck units of quantum gravity as the natural units rather than the electron. The basic mass is 10^-5 grams and the basic length is 10^-33 centimeters. That's where the quantum fluctuations in the classical space-time continuum get really big and they completely blow it apart into smithereens i.e., Hawking's "quantum foam" of virtual wormholes and "baby universes".
"For I am Shiva and Shakti, the Destroyer and Creator of All Possible Universes. Fission? Fusion? Small potatoes. You ain't seen nuthin yet, Fat Boy. Here come the controlled zero-point Alpha-Omega Sar Ship Engine. " :-)
The Voice of Him that Singeth From The Future
"Make way for the Final Anthropic Cosmological Principle - The Advanced Information Super Highway of Our God!"
(Music from Handel's "Messiah".)
Now Einstein seems to go into a reverie and makes a very interesting conjecture on the super-determined parameter-uniqueness of the fundamental laws of physics. Thus, after introducing the above notion of "natural units" with "dimensionless constants", he says:
"If one considers this done, then only 'dimensionless' constants could occur in the basic equations of physics. Concerning such, I would like to state a proposition that at present cannot be based upon anything more than upon a faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary constants of this kind."
Einstein here is the modern Moses saying there is only One God, there is only One Actual Objective Universe, there are not Many-Worlds as Murray Gell-Mann would have us believe in The Quark and The Jaguar. Of course, we are now in the realm of faith and conjecture, where one man's "intelligibility" may be another's "gibberish". Exactly, who has "The Story Distorted" with "Flap Doodle"? :-) If Einstein is correct here, then Bell's theorem tells us that this One God is nonlocal, and form-dependent. "The universe appears less and less like a Great Machine and more and more like a Great Thought." Sir James Jeans once said long ago in the heyday of Bohr's idealism. Foucault's Pendulum sits balanced like the Scales of Justice on the edge between the two extremes of chance and necessity. Today, from Bohm, we learn that the Universe is both a Great Quantum Indeterministic Thought and a Great Classical Deterministic Machine unified by Post-Quantum back-action into a self-determining Vast Active Living Information System (VALIS) -- The Sentient Universe!
".. that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory)."
This can only happen with a globally self-consistent loop in time from the Alpha of the Big Bang to the Omega of Penrose's projective infinity, and this requires backward in time communication not on David Deutsch's "rocklike" closed timelike curves, which Hawking says are not stable, but on the "thoughtlike" nonlocal form-dependent quantum connection. Eberhard says this is not possible in quantum mechanics, and he is correct. It is possible, however, in post-quantum mechanics because of back-action. This is the mechanism for the Final Anthropic Cosmological Principle that Einstein was pointing to. In other words, the current superstring theory cannot provide "the theory of everything" (TOE) without a gross violation of the principle of retarded causality which forbids any coherent controlled intentional form-dependent/intensity-independent decoding of Bohm's "active information" from the future.
How Einstein created the classical general theory of relativity of the gravitational field.
"The special theory of relativity owes its origin to Maxwell's equations of the electromagnetic field ... the latter can be grasped formally in a satisfactory fashion only by way of the special theory of relativity. Maxwell's equations ate the simplest Lorentz-invariant field equations that can be postulated for an antisymmetric tensor derived from a vector field. ... we know ... from quantum phenomena that Maxwell's theory does not do justice to the energetic properties of radiation. ... to Mach's question: 'how does it come about that inertial systems are physically distinguished above all other coordinate systems?' this [special] theory offers no answer.
That the special theory of relativity is only a first step ... became completely clear to me only in my efforts to represent gravitation in the framework of this theory. In classical [Newtonian] mechanics, interpreted in terms of the field, the potential of gravitation appears as a scalar field (the simplest theoretical possibility of a field with a single component). Such a scalar theory of the gravitational field can be made invariant under the group of Lorentz transformations. ...
(1) From .... special relativity it was clear that the inertial mass ... increases with the total energy ( ... e.g., with the kinetic energy).
(2) From very accurate experiments (especially from the torsion balance experiments of Eotvos) it was empirically known with very high accuracy that the gravitational mass of a body is exactly equal to its inertial mass.
It followed from (1) and (2) that the weight of a system depends in a precisely known manner on its total energy. ... The acceleration of a system falling freely in a given gravitational field is independent of the nature of the falling system (especially therefore also of its energy content). .. within the structure of the special theory of relativity there is no niche for a satisfactory theory of gravitation."
Einstein's key idea -- the equivalence principle.
"Now it came to me: the fact of the equality of inertial and gravitational mass, i.e., the fact of the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation, if one introduces into it, in place of an "inertial system," a frame of reference accelerated relative to the former.
If then one interprets the behavior of a body with respect to the latter frame of reference as caused by a 'real' (not merely apparent) gravitational field, it is possible to regard this frame as an 'inertial system' with as much justification as the original reference system.
So, if one considers pervasive gravitational fields, not apriori restricted by spatial boundary conditions, physically possible, then the concept of the 'inertial system' becomes completely empty. The concept of 'acceleration relative to space' then loses all meaning and with it the principle of inertia along with the paradox of Mach.
The fact of the equality of inertial and gravitational mass thus leads quite naturally to the recognition that the basic postulate of the special theory of relativity (invariance of the laws under Lorentz transformations) is too narrow, i.e., that an invariance of the laws must be postulated also relative to nonlinear transformations of the coordinates in the four-dimensional continuum.
Good bye to naked coordinates.
This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have a direct metric significance. ...
We start with an empty, field-free space, as it occurs -- related to an inertial system -- within the meaning of the special theory of relativity, as the simplest of all imaginable physical situations. If we now think of a non inertial system introduced by assuming that the new system is uniformly accelerated against the inertial system (in a three-dimensional description) in one direction (conveniently defined), then there exists with reference to this system a static parallel gravitational field. The reference system may be chosen to be rigid, Euclidean in its three-dimensional metric properties. But the time in which the field appears as static is not measured by equally constituted stationary clocks. From this special example one can already recognize that the immediate metric significance of the coordinates is lost once one admits nonlinear transformations of the coordinates. To do the latter is, however, obligatory if one wants to do justice to the equality of gravitational and inertial mass ....
If, then, one must give up the notion of assigning to the coordinates an immediate metric meaning (differences of coordinates = measurable lengths, or times), one cannot but treat as equivalent all coordinate systems that can be created by the continuous transformations of the coordinates.
The general theory of relativity, accordingly proceeds from the following principle: Natural laws are to be expressed by equations that are covariant under the group of continuous coordinate transformations. This group replaces the group of the Lorentz transformations of the special theory of relativity, which forms a subgroup of the former.
... the general principle of relativity .. leads us to ... those systems of equations that in their general covariant formulation the simplest ones possible; among these we shall have to look for the field equations of physical space. Fields that can be transformed into each other by such transformations describe the same real situation."
This is Einstein's classical definition of objective reality. Objective reality is the set of all real situations each one of which is invariant under the group of all nonlinear continuous transformations of coordinates. Objective reality is independent of the knowledge of the observer. Note, that in Bohm's version of quantum mechanics the classical configuration space is more fundamental than physical space. Wheeler's classical superspace is the configuration space for general relativity.
"Of which mathematical type are the variables (functions of the coordinates) that permit the expression of the physical [metric] properties of space ?... Which equations are satisfied by those variables .... we do know with certainty a special case: that of the 'field-free' space in the special theory of relativity. Such a space is characterized by the fact that for a properly chosen coordinate system the expression
ds^2 = dx1^2 + dx2^2 + dx3^2 - dx4^2 (1)
belonging to two neighboring points, represents a measurable quantity (square of distance), and thus has a real physical meaning. Referred to an arbitrary system this quantity is expressed as follows:
ds^2 = gikdxidxk (2)
whereby the indices run from 1 to 4. The gik form a (real) symmetrical tensor. If, after carrying out a transformation on field (1), the first derivatives of the gik with respect to the coordinates do not vanish, there exists a gravitational field with reference to this system of coordinates ... but of a very special type ... this special field can be characterized invariantly:
(1) Riemann's curvature-tensor Riklm, formed from coefficients of the metric (2), vanishes.
(2) The trajectory of a mass-point in reference to the inertial system (relative to which (1) is valid) is a straight line, hence an extremal (geodesic). This last statement, however, is already a characterization of the law of motion based on (2). ...
The universal law of physical space must be a generalization of the law just characterized. I now assumed that there are two steps of generalization:
(a) the pure gravitational field
(b) the general field (which is also to include ... the electromagnetic field).
The case (a) was characterized by the fact that the field can still be represented by Riemann metric (2), i.e., by a symmetric tensor but without a representation of the form (1) (save on an infinitesimal scale). ... This means that in the case (a) the Riemann tensor does not vanish ... a field law must hold that is some generalization (loosening) of this law. If this generalized law also is to be of the second order of differentiation and linear in the second derivatives, then only the equation obtained by a single contraction
0 = Rkl = g^imRiklm
was a prospective field law in the case (a). It appears natural ... to assume .. the geodesic line is still to represent the law of motion of the material point.
It seemed hopeless to me at that time to venture the attempt of representing the total field (b) ...
In Newton's theory one can write the field law of gravitation thus:
Laplacian of the gravitation potential vanishes
valid wherever the density of matter .. vanishes. In general one has Poisson's equation ... In the relativistic theory of the gravitational field, Rik takes the place of Laplacian of the gravitation potential. On the right hand side we shall then have to replace [the density of matter] also by a tensor. Since we know from the special theory of relativity that the inertial mass equals the energy, we shall have to put on the right-hand side the tensor of energy density -- more precisely, of the entire energy density that does not belong to the pure gravitational field. In this way one arrives at the field equation
Rik - (1/2)gikR = -kTik
The second member on the left-hand side is added because of formal reasons; for the left-hand side is written in such a way that its divergence, in the sense of the absolute differential calculus, vanishes identically."
This ensures local conservation of all energy-stress currents in physical space. "Absolute" means objective invariance under all nonlinear continuous coordinate transformations. This is also called tensor calculus. Tensor equations have invariant forms under these generalized transformations. Tensors have "square roots" called "spinors". Penrose has generalized these spinors to "twistors" on a complexified space-time where the different kinds of space-time infinities are represented by finite points.
"Not for a moment ... did I doubt that this formulation was merely a makeshift .... If anything in the theory as sketched ... can possibly be claimed to be definitive, ... it is... the limiting case of a pure gravitational field and its relation to the metric structure of space ...
The peculiarity of these equations likes, on the one hand, in their complicated structure, especially their nonlinear character with respect to the field [gij] variables and their derivatives, and, on the other hand, in the almost compelling necessity with which the transformation group determines this complicated field law. If one had stopped with the special theory of relativity, I.e., with the invariance under the Lorentz group, then the field law Rik = 0 would remain invariant also within the frame of this narrower group. But, from the point of view of the narrower group, there would be no offhand grounds for representing gravitation by a structures involved as the symmetric tensor gik If .. one would find sufficient reasons for it, there would then arise an immense number of field laws out of ... gik, all of which are covariant under Lorentz transformations (not however under the general group)."
Note, in general, as you restore symmetries, going to deeper levels of objective physical reality, i.e., as you "loosen" the structure, you filter out possible field laws. Things get simpler. As you go the opposite way i.e., breaking symmetries, the number of possible field laws increase indicating an increasing diversity and complexity in possible phenomena. This is exactly what happens in the expansion of the universe out of the relatively simple big bang. This is the mathematics of groups and their representations. The thoughtlike quantum pilot-waves of physical reality are representations of rocklike objective invariants of groups of transformations between different frames of reference. This includes frames in "internal spaces" inside of physical space.
"Even if ... one had accidentally guessed precisely the law belonging to the wider group, one would still not have achieved the level of understanding corresponding to the general principle of relativity. For, from the standpoint of the Lorentz group, two solutions would incorrectly have to be viewed as physically different if they can be transformed into each other by a nonlinear transformation of coordinates, i.e., if from the point of view of the wider group they are merely different representations of the same field."
Einstein has here given me the clue on how to proceed in formulating the second more formal step in the construction of post-quantum mechanics. His general relativity is concerned with local form-independent but nonlinear continuous transformations of subjective coordinates in physical space. Bohm taught us that in order to understand quantum mechanics we must go to higher dimensional classical configuration space for the motion of the "beable" system point of a complex system. For general relativity, the entire gik configuration over a spacelike slice of curved space-time is the "beable" or classical hidden variable for a Bohmian pilot-wave theory of quantum gravity. Using the Arnowitt-Deser-Misner "canonical" method, Wheeler constructs a non denumerably infinite dimensional "superspace" where each "super-local" point is a three-dimensional geometry 3G. Note that 3G is not the same as Einstein's gik which is the full four dimensional geometry of curved space-time. 3G must be supplemented with the shift Nj and lapse N functions.
Here is my new idea. What we need is a still wider super-group of continuous nonlinear transformations that are "super-local" and form-dependent in Wheeler superspace which is the proper rocklike configuration space of the 3G "beable". They are form-dependent because there is a super-quantum potential contribution from the super-Hilbert space of all possible thoughtlike states in the "Mind of God". We might as well call this thoughtlike super-Hilbert space "Heaven". Call the rocklike Wheeler superspace "Earth". These objective quantum transformations are highly nonlocal in our ordinary three-dimensional physical space. To paraphrase Einstein:
"For, from the standpoint of the local form-independent group, two solutions would incorrectly have to be viewed as physically different if they can be transformed into each other by a nonlinear transformation of coordinates, i.e., if from the point of view of the wider nonlocal form-dependent post-quantum group they are merely different representations of the same field."
Webs of meaningful synchronistic events acausally connecting widely separated events in ordinary space-time would be objective invariant patterns of active information of the nonlocal form-dependent post-quantum group. They form the beauty in the pattern.
Note that the nonlocal form-dependent group of nonlinear continuous transformations at each possible 3G super-point mixes thoughtlike things with rocklike things in a highly self-referential bootstrapped way. That is, the structure of the nonlocal group and its representations are now linked together in an adaptive back-active way. There is no time here in the ordinary sense. We have only the Nj and the N. This is still pretty vague and probably wrong in some crucial details - or, even "not even wrong" in Pauli's sense. But, to my intuition, I am sniffing up the right Tree of Knowledge. Who is that Snake up there in the branches dropping road apples on my head? Is He trying to make a Monkey out of me - or a God? :-)
The general idea however is clear. The idea is to use Einstein's same method, that he used so well in ordinary space, in the bigger configuration space of the proper beable of general relativity. This wider group will be highly nonlocal and form-dependent in the sense of "active information" in ordinary space.
"One more general remark concerning structure and group. It is clear that in general one will judge a theory to be more nearly perfect the simpler a 'structure' it postulates and the broader the group concerning which field equations are invariant. ... these two desiderata get in each other's way. For example: according to the special theory of relativity (Lorentz group) one can set up a covariant law for the simplest structure imaginable (a scalar field), whereas in the general theory of relativity (wider group of the continuous transformations of coordinates) there is an invariant field law only for the more complicated structure if the symmetric tensor. We have already given physical reasons for the fact that in physics invariance under the wider group has to be required: from a purely mathematical standpoint I can see no necessity for sacrificing the simpler structure to the generality of the group.
"The group of general relativity is the first one requiring that the simplest invariant law be no longer linear and homogeneous in the field variables and their derivatives. This is of fundamental importance for the following reason. If the field le is linear (and homogeneous), then the sum of two solutions is again a solution; so it is, for example, in Maxwell's field equations for the vacuum. In such a theory it is impossible to deduce from the field equations alone an interaction between structures that separately represent solutions of the system."
This also happens in the Schrodinger equation for the quantum waves in configuration space. The linearity of the Schrodinger equation leads to the "measurement problem" in Bohr's Copenhagen interpretation and its several variations on the same theme. The post-quantum back-action should introduce a nonlinearity in the Hilbert space analogous to the nonlinearity in the metric equations of space-time geometry introduced by the curvature signature of nontrivial gravitational fields. Note that effective mean-field equations of many-electron systems like the Hartree-Fock equations are already nonlinear in first-quantization. But that is not a profound nonlinearity of the Einstein type because they become linear again in second-quantization where elementary excitations or "quanta" of collective modes are created and destroyed in Fock-space. The wave function of first quantization itself becomes a second-quantized operator on Fock space. Each oscillator mode of Fock space has different numbers of quanta in it. The quantum state of many modes is an entangled sum of products of single modes with different numbers of quanta. The Landau-Ginzburg semi-phenomenological equations of nonlinear optics, superconductors, etc. are profoundly nonlinear in the order parameters corresponding to second-order phase transitions in materials.
"That is why all theories up to now required, in addition to the field equations, special equations for the motion of material bodies under the influence of the fields."
This is not the case in the Bohr-type interpretations of quantum theory, in the many-worlds type interpretations, and in the statistical ensemble (Ballantine) interpretation that Einstein toyed with and that Vic Stenger embraces in his book The Unconscious Quantum. The not-so-hidden agenda of that book is the debunking of quantum theories of mind in general and of the paranormal in particular. It is the case in Bohm's pilot-wave/hidden variable interpretation of quantum theory. The major difference is that the arena is no longer ordinary three-dimensional space, but the higher dimensional configuration spaces of complex systems of many particles interacting with classical form-independent/intensity-dependent gauge fields like the Maxwell field. The entire spread-out configuration of these rocklike particles and their rocklike gauge fields are represented by a single rocklike, or "beable" ,"system point" in this "material" rocklike classical higher dimensional configuration space. This space is very close to the "state space" used in classical chaos theories with "fractal strange attractors". Classical chaos theory on Newtonian mechanics uses "phase space" whereas quantum mechanics only uses the configurational half of phase space. Bohm then introduces the qualitatively new thoughtlike form-dependent/intensity-independent quantum field reaching down from thoughtlike informational infinite-dimensional Hilbert space to the rocklike material higher-dimensional configuration space in which the beable system points move. The paths of these rocklike material beables are guided by the nonlocal form-dependent/intensity-independent quantum force of thoughtlike pilot-waves. The total thoughtlike quantum pilot wave splits into "branches" or "eigenfunctions". Each "non-material" or "spiritual", but still "physical", thoughtlike branch carves out for itself a region of influence in rocklike material configuration space dominated by an "attractor". This attractor can be a fractal strange attractor just like in classical chaos theory.
What determines the precise way the total wave splits into branches? This is a profound problem in quantum mechanics which does not have a unique solution. In simple cases, it is the total experimental arrangement. For example, if we insert a diffraction grating into a beam we automatically measure the "momentum" observable. Therefore, the total quantum pilot wave splits into branches that are "momentum eigenfunctions". When a measurement is done on a single particle, the observed eigenvalue corresponds to a particular basin of attraction in configuration space that the beable particle got trapped into. This occupied branch encodes the "active information" that organizes the intrinsic energy of the beable. The intrinsic energy includes its total mass and also the quantum vacuum fluctuations that dress its bare mass, charge and wave function normalization.
A crude way to describe this capture of the rocklike material beable system point by the single "active" thoughtlike basin of attraction in a landscape of such attractors is to say that the total wave "collapsed" into that particular branch, but the empty branches are still there. This is how Bohm makes contact with Bohr, Heisenberg, von Neumann et-al. However, in more complex cases, where, for example, the brain measures itself in introspection, there is no way to choose a preferred eigenfunction "basis" or "frame of reference" in Hilbert space within quantum mechanics. Quantum mechanics is Godel-incomplete in this profound sense.
One important virtue of Bohm's theory here is that it describes individual complex systems. It does not need statistical ensembles of simple systems the way Vic Stenger needs it to draw the false conclusions of his book for complex systems. Although Bohm's theory can account for the results of statistical experiments on ensembles of identically prepared simple systems like one gets in neutron beams, electron beams, photon beams etc., it is not restricted to them. Bohm's theory can just as easily, in principle, describe the individual behavior of Vic Stenger's brain as it formulates an incorrect model of the mind. :-)
So far, every thing I have said about Bohm's theory has zero back-action from beable to its pilot-wave. Indeed, Bohm showed that such back-action must be exactly zero in order to reproduce the statistical predictions of quantum mechanics which Stenger, for example, never questions. In one sense, Stenger's book is absolutely correct. If quantum mechanics is the final theory of physical reality, then, neither ordinary consciousness, nor the paranormal, can be explained by it. In fact, if Stenger's thesis is correct, not only is the paranormal a Grand Illusion, not only is free will a delusion, but "consciousness" is a fiction. Stenger provides the quantum defence for Watson's behaviorism, and for Dennett and Churchland. Vic's book is essentially a long version of Eberhard's theorem. On the other hand, with back-action it's a whole new ball game.
"In the relativistic theory of gravitation, it is true, the law of motion (geodesic line) was originally postulated independently in addition to the field law."
There is no analog to this in Bohr's version of quantum theory, but there is in Bohm's. The equation of motion of the hidden-variable (beable) "was originally postulated independently in addition to the field law." That is the significant similarity. The significant difference is that Einstein is talking about a local form-independent/intensity-dependent rocklike metric field gik acting on a "test particle" moving in ordinary 3D space. In contrast, Bohm is talking about a form-dependent/intensity-independent thoughtlike quantum field acting on a rocklike beable system point moving, not in 3D space, but in higher-dimensional configuration space. This thoughtlike quantum field acts locally in configuration space but nonlocally or globally in ordinary 4D space-time cutting across space and time separations between localized parts of the extended whole like a hot knife through butter. With zero back-action these nonlocal "spooky telepathic" influences "faster-than-the-speeding-photon" do not communicate locally decodable intelligible messages. The local observer will only detect meaningless quantum randomness in accord with Eberhard's theorem and the discussion in Heinz Pagels' book The Cosmic Code. On the contrary, when back-action somehow manages to rise above and beyond the noise of the external environment through some sort of protection mechanism like a chemical "cage" for the lone electron Eccles gate in the microtubule protein dimer, for example, the meaningless quantum randomness begins to quiet down and a meaningful message is decoded. Meditation, it is claimed by the Maharishi, enhances this listening to the "inner voice" of enlightenment. Perhaps it does. I wouldn't know. I am only a blue-collared quantum mechanic from Flatbush-- a nonlocal union man! :-)
(Tune from Pinafore Finale)
Chorus line of Sar Ship Troupers
"For he is a union man, yes, he is a nonlocal union man.
For in spite of all temptation to rise far above his station,
He remains a union man, he remains a union man."
Einstein and Bohm show how thought becomes matter: How Christ becomes Man.
"Subsequently, though, it turned out that the law of motion need not (and must not) be assumed independently, but that it is already implicitly contained within the law of the gravitational field."
The quantum analog of this would be that the highly nonlinear "conscious" post-quantum extension of the linear Hilbert space Schrodinger equation of orthodox thoughtlike quantum mechanics will determine the rocklike equation of motion for the hidden-variable (beable) in the configuration space of classical mechanical chaos theory with adaptive post-quantum generated fractal strange attractors. Larry Crowell has some preliminary ideas on exactly how to do this mathematically. Bohm has indeed conjectured that this is the case in his book, The Undivided Universe. This would complete his "implicate order" vision. If indeed, this turns out to be the case, then the pragmatic mind-brain dualism I am using is only an "effective" semi-phenomenological model, and at the deepest level of physical reality, cosmic consciousness does create matter. This is my really new post-quantum . physics It is a completely physical idealism that is consistent with, and enriches, both Eastern and Western mystical traditions. It is the postmodern proper scientific foundation for religion and ends "The Warfare Between Science And Theology" (book by the first President of my Alma Mater, Cornell University, the Victorian contemporary of Darwin and Thomas Huxley, Andrew Dickson White). Capra and Zukav touch on this in only the most superficial and intellectually flim-flammsy manner. Indeed, the key ideas needed were not known to them when they wrote their books with my help over twenty years ago. (For the record, I helped Capra financially at a crucial point in his writing of "The Tao of Physics", and I helped Zukav in many ways including actually writing the first drafts of many of the non-metaphysical physics parts of The Dancing Wu Li Masters.)
"The essence of this truly involved situation can be visualized as follows: A single material point at rest will be represented by a gravitational field that is everywhere finite and regular, except where the material point is located: there the field has a singularity."
Note that much bigger black holes also have these same metric singularities. A singularity in the metric geometry of 4D space-time is where at least some components of the fourth-rank curvature tensor Rijkl explode to infinity.
"If, however, one computes the field belonging to two material points at rest by integrating the field equations, then this field has in addition to the singularities at the positions of the material points a curve of singular points connecting the two points."
This is really interesting. Einstein is saying that there is a singular "string" in 3D space, or "vortex" line connecting the two mass points. This singular "vortex" string with the two point sources at the ends is generated by the nonlinearity of the field equations. Remember this is pure classical general relativity with no quantum corrections. The two point masses have a six-dimensional classical configuration space if we neglect the singular string. If we include it, the configuration space is automatically non-denumerably infinite in dimension in the classical continuum limit. Just like in quantum field theory, there is no truly two-particle problem. Every problem has an infinite number of virtual particles dressing the bare real particles in so far as one can use perturbation theory.
"It is possible, however, to stipulate a motion of the material points so that the gravitational field determined by them does not become singular anywhere except at the singular points."
In other words, Einstein is saying that one can eliminate the string-singularity connecting the two mass point sources (i.e., gravitational charges) generating the curvature in the space-time geometry. How is this done?
"These are precisely those motions described in first approximation by Newton's laws."
This obeys the classical action principle that the action is an extremum along the actual classical path of the system point of the two point masses in six-dimensional configuration space. But we know from Feynman's path-integral quantum mechanics that the quantum fluctuations will correspond to all possible paths connecting a "start" and "finish" in configuration space. Therefore, these quantum fluctuations will have Einstein's "string singularity" in an essential way. Therefore, any general relativistic configuration space that includes quantum fluctuations in the motion of the sources of the gravity field must be infinite-dimensional in order to accommodate the string singularities connecting the mass points. This suggests to me a possible physical interpretation of the extra space dimensions of modern superstring theory in terms of extended sources in the classical limit. Two point sources in 3D space require 6 space dimensions plus time in the slow-speed limit etc. Twenty four space dimensions require 8 point sources and so on. One can also consider confined sources in 2 and 1 dimensions because of a nonlinear self-trapping mechanism analogous to laser filaments. Extending the metric ground form ds^2 to these extra space dimensions means using a larger, i.e., "wider" nonlocal symmetry group the way Einstein has already described above. Indeed, it may be that a nonlocal linear group looks locally nonlinear. This would mean that the source of the "rocklike" classical local gravitational nonlinearity is "thoughtlike" nonlocal quantum Einstein-Podolsky-Rosen "spooky telepathic" connectivity. That is, cosmic thought literally warps space-time the way Q does it in Star Trek, The Next Generation. :-)
"One may say, therefore: The masses move in such a fashion that the solutions of the field equations is nowhere singular except at the mass points. This property of the gravitational equations is intimately connected with their nonlinearity, and this, in turn, results from the wider group of transformations.
... If singularities are permitted at the locations of the material points, what justifications is there for forbidding the occurrence of singularities elsewhere? This objection would be justified if the equations of gravitation were to be considered as equations of the total field. ... this is not the case .. . the field of a material particle will differ the more from a pure gravitational field the closer one comes to the location of the particle. If one had the field equations of the total field, one would be compelled to demand that the particles themselves could be represented as solutions of the complete field equations that are free of irregularities everywhere. Only then would the general theory of relativity be a complete theory."
You know in doing this I feel like Woody Allen in one of his Greenwich Village jazz sessions improvising by following the lead of a great musician. Or another fantasy, like singing with Pavoratti, or playing chamber music with Pablo Casals, or being in Toscanini's orchestra.
So Einstein tells us that singularities in the theory are signals that the theory is seriously incomplete. General relativity is a classical rocklike theory with form-independent local fields in ordinary space and time. Not only does it need the other rocklike electro-weak and strong form-independent local fields to complete it, it also needs the thoughtlike nonlocal form-dependent quantum field in the configuration space of its sources, and finally it needs post-quantum "conscious" back-action. Then we will indeed have a real "theory of everything". That is the "Sarfatti Vision". :-)
Einstein's last stand on the warfare between classical relativity and quantum mechanics.
"... I must take a stand with reference to the most successful physical theory of our period, viz., the statistical quantum theory ... this is the only theory that permits a unitary grasp of experiences concerning ... micro-mechanical events. This theory, on the one hand, and the theory of relativity on the other, are both considered correct ... although all efforts to fuse them so far have not met with success."
The primacy of objective physical reality.
"Physics is an attempt conceptually to grasp reality as something that is considered to be independent of its being observed. In this sense one speaks of 'physical reality.' In pre-quantum physics there was no doubt as to how this was to be understood. In Newton's theory reality was determined by a material point in space and time, in Maxwell's theory by the field in space and time. In quantum mechanics the situation is less transparent. If one asks: does a psi-function of the quantum theory represent a real fact in the same sense as a material system of points or an electromagnetic field? one hesitates to reply with a simple 'yes' or 'no.' Why?"
Fools rush in where Angels fear to tread, nevertheless, Bohm's answer to this is a resounding "yes." Einstein is thinking of the Bohr type intepretations of the meaning of quantum physics. In Bohm's version the psi-function does represent a real fact, but it is a thoughtlike real fact which is qualitatively different from the real rocklike facts of classical material points and electromagnetic fields. Both of these classical rocklike things are "hidden-variables" or "beables" in Bohm's interpretation that move under the influence of form-dependent/intensity-independent objective nonlocal spooky "telepathic" actions at a distance. Einstein, as we shall see, did not like this, but Bell's theorem would have forced him to accept it nevertheless if he had lived to see it. Einstein cannot have his cake and eat it. Nonlocality and objectivity are incompatible quantities. An objective theory must be nonlocal. The many-worlds theory appears to be nonobjective and possibly local. That's what Murray Gell-Mann believes and professes in his book, The Quark and the Jaguar in Chapter 12, "The Story Distorted". I take the opposite view that it is Murray who has distorted the quantum story. He cites a letter I co-wrote which presupposes an objective nonlocal quantum reality. Eberhard's theorem correctly entails that objective nonlocal quantum connections are not paranormal "telepathic" and/or "precognitive" communication channels. However, Eberhard's theorem is overridden in post-quantum mechanics because of direct back-action of the hidden-variables on their quantum psi-functions. This "back-action" is not easily conceived of in Bohr's interpretation where there is no hidden-variable. Stapp has done so however in his paper in Physical Review A, July 1994, p.18. Weinberg's nonlinear post-quantum theory is an example of a back-action theory, as is the GRW theory of objective spontaneous collapse of the psi-function of N-particle complex systems.
Einstein proceeds to describe the "pragmatic" epistemological "Copenhagen interpretation" of quantum mechanics of Niels Bohr. It is qualitatively different from Bohm's version. Einstein wrote all this in 1946. He did not meet Bohm for a few more years. Bohm developed his objective nonlocal ontological interpretation directly because of his meetings with Einstein. Einstein did not like what Bohm came up with because it was nonlocal in ordinary space-time. Einstein wanted an objective-local quantum theory to conform to the spirit of special relativity. This was more than ten years before John Bell's famous theorem proved that what Einstein hoped for was impossible. That is, you can have an objective nonlocal, or a nonobjective local, or a nonobjective nonlocal theory, but you cannot have an objective local version of quantum physics. Murray Gell-Mann thinks that his particular version of the many-worlds interpretation of quantum physics is nonobjective and local and that any objective nonlocal theory like Bohm's is "the story distorted". However, E. J. Squires claims that Gell-Mann's theory is actually nonobjective and nonlocal, so that Gell-Mann is in error if Squires is right. Note, I was in Bohm's group at Birkbeck College in London in 1971. Bohr's pragmatic theory is really tied into statistical samples or "ensembles" of identically prepared simple systems. It cannot really claim to describe complex individuals like a living human brain. In contrast, Bohm's version of quantum physics, which naturally extends to include the universal backactivity of post-quantum physics is not fundamentally wedded to the statistical interpretation, though it can explain why it works in its proper regime.
The close of the nineteenth century saw the discovery of radioactivity. The close of the twentieth century saw the discovery of backactivity. Radioactivity and relativity led to Hiroshima and Nagasaki, Chernobyl, the nuclear arms race and the current problem of nuclear terrorism by rogue nation states and criminal sociopathic organizations. What will backactivity lead to if it really does demystify the role of conscious mind as a fundamental nonlocal form-dependent/intensity-independent physical force of "active information" in the universe?
Bohm's theory is the only theory that can naturally and unambiguously describe individual complex systems. This virtue is conclusive in choosing among the current competing explanations for the meaning of quantum physics. I disagree with John Gribbin who thinks that John Cramer's "transactional interpretation" is the "best buy" (e.g., Schrodinger's Kittens). In fact Cramer's version may not even be mathematically consistent. For the record, John Bell favored Bohm's theory as the best buy. I agree with Bell and disagree with Gribbin and Gell-Mann. The latter, of course, disagree with each other. There is no consensus on this issue of what is the meaning of quantum physics even though every one uses its algorithms in the same way for relatively simple inanimate levels of the organization of matter and electroweak-strong gauge fields. I claim that post-quantum physics is required for living complex adaptive organizations of matter and field. This would imply that Gell-Mann's theory of the "IGUS" is fundamentally wrong because it does not have any backactivity.
"What the psi-function (at a definite time) states, is this: What is the probability for finding a definite physical quantity q (or p) in a definite given interval if I measure it at time t? The probability is here viewed as an empirically determinable, and therefore certainly a 'real' quantity, which I may determine is I create the same psi-function very often and each time perform a q-measurement. But what about the single measured value of q? Did the respective individual system have this q-value even before the measurement? To this question there is no definite answer within the framework of the existing theory, since the measurement is a process that implies a finite disturbance of the system from the outside; ..."
Note that conventional quantum measurement theory does not even consider a "self-measurement" which is what we do when we think, feel, experience and introspect.
"... it would therefore be conceivable that the system obtains a definite numerical value for q (or p), the measured numerical value, only through the measurement itself. ... I shall assume two physicists A and B, who represent different conceptions concerning the real situation as described by the psi-function."
"See how The Fates their gifts alot
For A is objective and B is not."
variation on Mikado by Gilbert and Sullivan
"A. The individual system (before the measurement) has a definite value of q (or p) for all variables of the system, specifically that value which is determined by a measurement of this variable. Proceeding from this conception, he will state: The psi-function is not a complete description of the exact state of the system, but is only an incomplete representation; it expresses only what we know about the system because of previous measurements."
Note Einstein's use of "previous". He totally accepts the principle of retarded causality as an absolute invariant, i.e., that effects are in the timelike or lightlike future of their causes in all frames of reference. Of course, there are solutions of Einstein's own general relativity equations which. because of special warp configurations, have closed timelike curves (CTC's) that violate retarded causality globally while obeying it locally. A good discussion of this is in Kip Thorne's book, Black Holes and Time Warps. Thorne's book, of course, was written more than forty years after Einstein wrote the remarks we are studying and meditating upon. There has been tremendous progress, both theoretically and observationally, in the development and verification of Einstein's general theory of relativity at the classical level. There is even the possibility that we will develop globally faster-than-light warp drives for our spacecraft without any time dilation and without any uncomfortable g-forces to contend with, if we can manufacture or find "exotic-matter" which is negative energy propagating forward in time. This is not to be confused with antimatter which is negative energy propagating backward in time. Again, even for this "Alcubierre" warp drive the local motion is still slower than light and it is "geodesic" i.e. freely floating with no gravity experienced by the crew of the ship. There have been claims that it may be possible to make traversable wormholes that will also achieve effective faster-than-light travel to the stars without the need for exotic-matter. Finally, there are many rumors that our military has captured alien UFOs that already have this super-technology and that we are reverse-engineering them at Wright-Patterson and Area 51 etc. for our own military forces. I have no further comment on the veracity of this particular rumor which may simply be disinformation for more conventional "Black Budget" covert R&D of the next generation of military aircraft. The fact that we are now able to detect planets around other stars has added some stimulus to these sorts of conjectures and wishes that run deep in pop-culture.
On Rumors of the Coming Extraterrestrial War
General Douglas Mac Arthur in his final "Duty, Honor, Country" address to the cadets of West Point has a remarkable warning about cosmic warfare with extra-terrestrials. He says we "must harness the cosmic energy". This speech was only a short time after the alleged Roswell UFO incident when we allegedly shot down several alien "flying saucers" that were attempting to fly over the first U S Army nuclear bomber base in New Mexico. If any one had been privy to what really happened it would be General Mac Arthur. Since that time we have made great progress in physics. NASA has a serious small project to develop a practical warp drive in the near future that I am associated with.
Einstein's famous "EPR" gedankenexperiment (thoughtexperiment).
"A. The individual system (before the measurement) has a definite value of q (or p) for all variables of the system, specifically that value which is determined by a measurement of this variable. Proceeding from this conception, he will state: The psi-function is not a complete description of the exact state of the system, but is only an incomplete representation; it expresses only what we know about the system because of previous measurements.
B. The individual system (before the measurement) has no definite value of q (or p). The measured value is produced by the act of measurement itself consistent with the probability appropriate to the psi-function. Proceeding from this conception, he will (or, t least, he may) state: The psi-function is an exhaustive description of the real situation of the system.
Now we present to these two physicists the following case. There is to be a system that at the time t of our observation consists of two component systems S1 and S2, which at this time are spatially separated and (in the sense of classical physics) interact with each other but slightly. The total system is to be described completely in terms of quantum mechanics by a known psi-function, say psi12. All quantum theoreticians now agree upon the following. If I make a complete measurement of S1, I obtain from the results of the measurement and from psi12 an entirely definite psi-function psi2 of the system S2. The character of psi2 then depends upon what kind of measurement I perform on S1."
Notice that if psi2 were by itself a directly measurable object in the individual case, then this would be a faster-than-light "spooky telepathic" communication channel entirely different from the familiar electromagnetic signaling system. However, this is not the case in orthodox quantum mechanics. That is what Eberhard's theorem is all about. It turns out that there is an odd "Catch 22" here when we are limited to statistical observations on ensembles of simple systems that obey the Born probability calculus, i.e., probability density proportional to the squared modulus of the complex-valued psi-function, we only see random noise at the "receiver" end. We can, however, extract useful messages by correlating the random sequence of data from the sender with that from the receiver. However, this cannot be done faster-than-light. It is, nevertheless, the basis for practical secure untappable "quantum cryptography" and "quantum teleportation" now under active development at IBM research laboratories.
What happens with complex living individuals? Yakir Aharonov et-al now claim that the "protected" quantum wave of an individual can be measured directly. If that is a natural ability of the post-quantum living quantum-mind/classical-brain it would not only explain paranormal and transpersonal experiences, but it would also explain ordinary consciousness. Of course, Einstein would be turning over in his grave if that were indeed to turn out to be the truth.
"Now it appears to me that one may speak of the real state of the partial system S2. To begin with. before performing the measurement on S1, we know even less of this real state than we know of a system described by the psi-function."
Which "psi-function" -- psi12? Yes, that will be made clearer by Einstein below. In fact, we now say that S2 is in a local "reduced density matrix" in which there is a classical probability distribution for different possible psi2 states over the statistical ensemble of a large number of simple systems prepared identically and measured in the same way at the same relative time since their preparation. There appears to be no way, in orthodox quantum physics, to extract useful information from a single quantum event. A possible exception to this, if I recall correctly, has been suggested by N.D. Mermin (Cornell) using three-particle correlations where certain things should happen with certainty if quantum physics is correct and they should not happen with certainty is locality is correct. In such a case, a single observation on an individual in the ensemble would give us useful information. I do not think Einstein, who wrote this in 1946, considered this possibility. Did Vic Stenger consider it in his book, The Unconscious Quantum (Physicist?) :-) Vic emailed me that he is planning a critique of my theory under the title "Physicists Off The Real Axis." :-)
Einstein's axiom of absolute retarded causality.
"But on one assumption we should, in my opinion, insist without qualification: the real state of the system S2, is independent of any manipulation of the system S1, which is spatially separated from the former."
If this were not the case, and indeed, Bell's theorem, which Einstein did not know, says it is not the case if quantum physics is true, and, moreover, if these thoughtlike psi-functions, when protected against thermal noise, really are mental states of brains, then we do have a kind of voodoo magical world of the Shaman to contend with -- not of smoke and mirrors, but of Wheeler's Quantum The Smoky Dragon. Bring in the Ghost Busters and release The Dragon Slayers from the Dungeon! :-)
"According to the type of measurement I perform on S1, I get, however, a very different psi2 for the second partial system (psi2, psi2' ....)."
Yes, and physicists today simply say that these different psi2 functions happen with different classical ensemble probabilities to make the reduced density matrix for S2.
"Now, however, the real state of S2 must be independent of what happens to S1."
This is the statement of classical locality, or absolute retarded causality, which all physicists today who accept Bell's theorem, and who believe in objective reality and counterfactual definiteness (CFD) are willing to reject. These physicists feel prematurely secure in what Abner Shimony calls "passion at a distance" which means that there is no violation of retarded causality in the statistical average over the ensemble. Bohm describes this in great detail in The Undivided Universe. It is not at all obvious that our internal mental processes conform to the statistical predictions of quantum physics. Indeed, in my post-quantum physics they do not. Backactivity lifts the degeneracy between the many-worlds intepretations that aim for local non-objectivity since they do not have CFD, and the objective nonlocal Bohm model. That is, my prediction, for the really new objective nonlocal post-quantum physics with backactivity, is a strong reproducible and controllable violation of Einstein's axiom of absolute retarded causality. It's not the "story" that is "distorted" Murray, it's the "statistics" that is distorted. "It's the statistics -- Stupid!" :-) God does play dice with the universe, but the dice are loaded with a post-quantum backactivity that is much more powerful than nuclear radioactivity.
"For the same real state of S2 it is possible therefore to find (depending on one's choice of the measurement performed on S1) different types of psi-function."
So it is clear, that accepting absolute retarded causality, that there must be different pair functions psi12 for both S1 and S2 for the same fixed state psi2 of S2. Note, that Einstein also implicitly assumes free will.
"One can escape from this conclusion only by either assuming that the measurement of S1 telepathically changes the real state of S2 ...."
This is indeed what Bohm and I do assume. Furthermore, if we go beyond quantum physics to post-quantum physics where psi12 connects different brains, then there is an actual telepathic change in the state of mind of the S2 brain depending on the S1 brain's "choice". However, in ordinary quantum mechanics the choice that the S1-brain makes is not really free. It is random. Therefore, the telepathic link is not controllable, and so, S1 cannot send a useful message to S2 that S2 will be able to recognize immediately without a later correlation with S1 by ordinary means. This is Eberhard's theorem again. Bohm describes this as a fragility or non robustness in the nonlocal quantum potential connecting S1 with S2. Backactivity changes this totally.
We see that Einstein started by replacing Newton's nonlocal classical "rocklike" form-independent/intensity-dependent instantaneous action-at-a-distance with Maxwell's local classical "rocklike" form-independent/intensity-dependent field. Einstein, in 1946, obviously did not place much stock in Wheeler and Feynman's 1941 demonstration of a delayed and advanced relativistic action-at-a-distance classical electrodynamics of sources with the Maxwell field eliminated. This was the basis for Feynman's later triumph of quantum electrodynamics. Einstein actually did attend Feynman's Princeton talk on all this. So it is not at all surprising that Einstein would try to do the same thing with the thoughtlike form-dependent/intensity-independent nonlocal quantum connection that he was the first to discover in the early 1930's. I must check to see if Schrodinger's famous paper on "entanglement" rests on his reading of the EPR paper of 1935? Until Bell came along with his theorem in 1963 there was no way to refute Einstein's position of 1946. Even then, with Eberhard's theorem and Shimony's "passion at a distance" it looked like the uneasy dŽtente of the quantum ghost with the spirit of relativity could be maintained at the cost of renouncing any physical theory of the conscious mind. Backactivity changes all this. It's a new ball game now.
"or by denying altogether that spatially separated entities possess real states."
This is Bohr's position which I find incomprehensible. Einstein also did since he does say:
"Both alternatives appear to me entirely unacceptable."
Only the second one by Bohr is unacceptable to me.
Remember that physicist "B", by which Einstein means "Bohr" thinks that the individual quantum system has no definite properties. The latter are brought into being by the measurement itself. The psi-function is a complete description of the individual. John Archibald Wheeler in his "Law Without Law" and similar essays adopts the position of Einstein's physicist "B". Remember now, that Einstein assumes in what follows that both A i.e., "Albert" for Einstein himself, and B accept locality, i.e., absolute retarded causality, so as not to violate the spirit, if not the letter, of special relativity. They must also both accept that "spatially separated entities possess real states". In fact, Bohr and Wheeler do deny that, whatever it means, and therefore, think themselves consistent on this issue. New York Times science journalists, Scientific American editors et-al all accept this uncritically and, when pressed, will spout the Bohr party line. This is a disservice to critical thinking in the supposedly intelligent media! :-)
"If now the physicists A and B accept this reasoning as valid, then B will have to give up his position that the psi-function constitutes a complete description of a real state. For in this case it would be impossible that two different types of psi-functions could be assigned to the identical state of S2."
Einstein clearly means psi12 i.e., "two different types of psi12-functions ......"
"The statistical character of the present theory would then follow necessarily from the incompleteness of the description of the systems in quantum mechanics, and there would no longer exist any ground for the assumption that a future foundation of physics must be based upon statistics."
We now have to be subtle like the Lord, and make some delicate distinctions that will easily pass you by if you do not pay close attention. In fact, Bohm's theory does exactly what Einstein wants in the above quote. But there is an all-important difference which Einstein did not like about what Bohm did. Einstein wanted to reduce quantum mechanics to a kind of sub-statistical mechanics where classical probability rules did apply. This cannot be done. The relative phases between eigenfunctions of a fixed observable in an expansion of the psi-function really do introduce irreducible nonlocal effects in an objective quantum reality. This is the message of Bell's theorem. Consequently, Bohm's theory of 1952 stimulated by his meetings with Einstein, before Bell's theorem of 1963, requires a nonlocal real quantum potential that does imply exactly that
"that the measurement of S1 telepathically changes the real state of S2 ...." This was anathema to Einstein's way of thinking. Bohm heroically stuck to his guns despite the wrath of his revered Master. Let's see how this works. Suppose systems S1 and S2 can each only be in one of two possible local states S1+ and S1- for S1, and S2+ and S2- for S2. We can prepare a coherent "entangled" state psi12 that looks like
psi12 = psi(S1+)psi(S2+) + psi(S1-)psi(S2-)
In fact, Alan Aspect in his famous photon-pair experiment that tested Bell's locality inequality, for a faster-than-light "spacelike" separation between the measurements on S1 and S2 for individual pairs, used exactly this kind of psi12. However, I will not analyze the photon pair experiment which is much more difficult in Bohm's theory since it involves infinite dimensional classical Maxwell field configurations spaces with a super-quantum potential. Instead, consider an experiment with slow moving massive neutrons in the spin singlet state
Psi12 = psi(S1+)psi(S2-) - psi(S1-)psi(S2+)
Note the difference in sign between the two terms for the photon pair state psi12 and the neutron pair state Psi12. The photons obey Bose-Einstein quantum statistics which means maximal constructive interference of the two alternatives. If you transpose S1 with S2 for the bosonic photons you get exactly the same state psi12 back again. It is this feature, for large numbers of bosons which permits the formation of "superfluid" Bose-Einstein condensates. Such a condensate may play a vital role as the physical substrate of our minds. Similarly, the two neutrons are fermions obeying the Fermi-Dirac quantum statistics and they combine with maximal destructive interference in Psi12.
Suppose you try to change a + to a - in Psi12. You get zero! This is the Pauli exclusion principle responsible for the periodic table of the atomic elements and many more phenomena ranging from quarks to molecules, metals and up to white dwarves and rotating neutron stars shooting out beams in opposite directions or pulsars that radiate nicely detectable classical gravity waves that confirm Einstein's general theory of relativity.
Now how does Bohm's theory explain the Einstein-Podolsky Rosen effect. The neutrons are actual tiny particles or "beables". They form a single nonlocal "system point" which is actually a point in a six-dimensional configuration space. There are two basins of attraction, like two valleys in this six-dimensional space. The system point is like a rolling ball where the nonlocal quantum potential is analogous to the force of gravity if you were to think of a classical Newtonian situation. The analogy is of course not perfect. One valley has S1 with the + property and S2 with the - property. The other valley has S1 with the - property and S2 with the + property. What about S1 with + and S2 also with the same +? Similarly, what about both S1 and S2 having the same - property? Well those possibilities are also there on this "landscape" in six-dimensional configuration space. But they are not valleys for the "ball" to roll into. They are, instead, infinitely high inaccessible mountain peaks! It is the "thoughtlike" Psi12-function that determines the shape of the valleys and peaks. The "rocklike" system point is Bell's beable or Bohm's "hidden variable. That's it! It's beautiful, visualizable, and the mathematics really gives this kind of picture. It's the same picture used by classical chaos theorists when they study stock markets and neural nets. Indeed the valleys and peaks can also have a fractal structure in the quantum case as far as the path of the "ball" is concerned. We then have strange attractors and strange repellors. The forbidden possibilities are repellors not attractors. There is one important difference. The valleys and peaks are rigidly fixed in quantum mechanics. In contrast, they are not rigidly fixed in neural network theory. In fact, the thoughtlike valleys and peaks change as the path of the rolling rocklike system point evolves. It is this change which AI scientists associate with "learning" and "adaptation". This is the "back-action" idea. My post-quantum physics puts this adaptive back-action into the fundamental physics which is where Bohm originally suspected it was anyway way back in 1952 -- when I got my strange telephone call! :-)
Einstein -- A Majority of One
It was Einstein's minority opinion that orthodox quantum mechanics as formulated in Bohr's "Copenhagen interpretation" of physicist "B" "offers no useful point of departure for future development". In this I agree. Bohr managed to construct a closed conceptual system with an impenetrable barrier of verbal vagueness and Dragon smoke that not even John Wheeler's visionary splendid inspired prose in "Law Without Law" et-al can blow away. :-)
Bohr and his followers were "convinced that it is impossible to account for the essential aspects of quantum phenomena (apparently discontinuous and temporally not determined changes of the state of a system, simultaneously corpuscular and undulatory qualities of the elementary carriers of energy) by means of a theory that describes the real state of things [objects] by continuous functions of space for which differential equations are valid."
Differential equations describe "analog processes" in contrast to "digital" apparent discontinuities. What about Einstein's use of "and temporally not determined"? This is a breakdown in his axiom of absolute retarded causality which requires locality for its implementation. If one allows Aristotle's "final causes" (teleology) forming a strong controlled "delayed choice" that imbue actual events with meaning and purpose, then we have solved the mystery of the "temporally not determined" individual quantum event. All of that requires post-quantum backactivity.
Bohm's theory of the quantum "pilot-wave" with its "hidden-variable" that is Einstein's real "object" (without backactivity) goes a long way in achieving Einstein's objective, but it is nonlocal against the spirit of special relativity. Indeed, it requires a preferred frame of absolute rest for the instantaneous form-dependent/intensity-independent organizing quantum force. This preferred frame actually does appear in general relativity as a kind of spontaneous broken symmetry even though general relativity has a larger symmetry (super) group than special relativity. That is, the ground or "vacuum" state solution does not have the full symmetry group that its nonlinear generating equations have. Simple externally broken symmetries like the Zeeman effect in atomic physics where a magnetic field lifts an energy degeneracy correspond to a smaller subgroup rather than the larger i.e., "wider" supergroup. So the symmetry-breaking in classical general relativity seems to run in the wrong direction compared to what we are used to in quantum mechanics.
"They are also of the opinion that in this way one cannot understand the atomic structure of matter and of radiation ... Above everything else, however, they believe that the apparently discontinuous character of elementary processes can be described only by means of an essentially statistical theory, in which the discontinuous changes of the systems are accounted for by continuous changes of the probabilities of the possible states."
Contrast this with Bohm's model where the hidden-variable system point has a continuous path in configuration space and the so-called discontinuous collapse is simply a very fast capture of the system point "ball" as it rolls down into a deep valley attractor of the landscape under the action of the quantum force. The particular attractor that the "ball" falls corresponds to the particular eigenfunction that the total psi-function "collapses" into in Bohr's picture. The shape of the landscape, i.e., its global pattern of valleys, mountain peaks, saddle points et-al corresponds to the particular expansion of the total psi-function into the eigenfunctions of the measured observable. What determines this observable? Each observable forms a frame of reference in the quantum Hilbert space. The measuring process chooses a definite frame. In Bohm's theory, without backactivity, the valleys in the landscape that are not occupied by the system point continue to exist and are able to influence the system point later on under suitable conditions of recombination or "erasure" that usually, but not always, get very hard to meet as the system gets bigger. But the main point here is that, when there is no backactivity, i.e., for simple everyday quantum mechanics, there is no uncertainty and no discontinuity for the individual system. Where the ball falls simply depends on the initial conditions. However, this can be a chaotic situation where a tiny change in the initial conditions in the rigid landscape cause an enormous change in the path of the system point. With post-quantum backactivity it's a whole new ball game because now the shape of the landscape changes as a result of the motion of the system point which in turn depends on the shape of the landscape. This is a highly nonlinear counterintuitive feedback control situation that I call "self-determination". Classical physics has total determinism. Quantum physics has total indeterminism. Post-quantum physics straddles the two, is on the edge between them, and has surprising self-determination.
The meaning of the beable brain ball rolling around the quantum wave mind landscape.
Friday, January 24, 1997 7:54 P.M., Caffe Trieste, North Beach, San Francisco.
Jerry Mincus, a Ph.D. in topology and number theory from Cornell, just showed me a copy of John Baez's book on Gauge Fields, Knots and Gravity which I will get and read cover to cover. Then Paul Zeilinsky walked in and I told him, very excitedly, that our second 3D MAX simulation, the first being the Einstein Box of the Einstein-Bohr debate, would be a metaphoric simulation of the ball rolling around the landscape, with the landscape rigid for ordinary quantum mechanics and then the landscape morphing due to its functional dependence on the actual path of the ball. The latter being post-quantum backactivity. Paul asked some very simple and important questions on exactly how we could visualize this and what we were representing.
First, consider elementary classical Newtonian mechanics for the motion of a particle in one space dimension in a classical form-independent potential V(x). We plot V(x) on the vertical axis and x on the horizontal axis. The total energy E is a horizontal line, and the vertical distance from that E line down to V(x) is the positive kinetic energy. Now we want to make an analogous plot in the above metaphor. This is not the same as the plots Bader makes in his important book "Atoms in Molecules" where the attractors are defined in terms of actual paths of a system point inside the configuration space. The two methods of representation are related, but not identical, and we must be careful not to confute one with the other. In the "potential" plot the horizontal x-axis is the classical configuration space and the vertical axis is beyond it. Now in Bohm's theory we plot the quantum potential Q(x) as the "vertical" axis where x is the configuration space. The quantum force is -gradQ in Newton's second law for the system point d^x/dt^2 = -gradQ where the common mass is absorbed in the definition of Q in our simple toy model. Q is computed from the psi-function as essentially -[(grad)^2 |psi|]/|psi| where psi = psi(x,t) is the solution of the Schrodinger equation. For simplicity we only consider here a "free particle" with zero external classical form-independent potential V and no external form-independent non-conservative forces. We want to make the model as simple as possible without losing the key new idea. Well the first thing to notice is that in general psi is a function of time t, therefore, the quantum potential Q(x,t) is also a function of t. I will call this the unitary Stapp explicit quantum time-dependence. I will call backactivity the nonunitary Sarfatti post-quantum implicit time dependence. When I say that the Q(x,t) landscape is "rigid", I mean modulo the quantum time dependence. That is, we subtract out the unitary quantum time dependence. This is analogous to going from the Schrodinger representation to the interaction representation in perturbation theory. To make the model even simpler, imagine a single particle confined to move in the x,y plane in physical x,y,z space. Suppose its psi function is a superposition of energy degenerate eigenfunctions fk(x,y) all having the same energy eigenvalue E. In this case the quantum potential Q(x,y) will not have any explicit unitary Stapp quantum t-dependence. The landscape is then explicitly t-independent for quantum mechanics in this simple case. Now introduce the all new post-quantum backactivity. This means that Q has a new functional dependence. The quantum Q changes to the post-quantum Q'(x, X(t), y, Y(t)) where {X(t),Y(t)} is the actual path of the hidden-variable system point (rocklike beable) which is the solution of the now nonlocal form-dependent/intensity-independent extension of Newton's second law. That is,
d^2X(t)/dt^2 = - dQ(x, X(t), y,Y(t))/dX(t)
d^2Y(t)/dt^2 = - dQ(x, X(t), y,Y(t))/dY(t)
For this simple toy model. That is the gradient of the thoughtlike form-dependent quantum potential is computed at the actual position of its attached rocklike beable. This is a highly nonlinear self-determining adaptive system capable of learning and remembering. It is the prototype of all living organizations of matter and radiation. The number of valley attractors in the Q landscape will be equal to the number of eigenfunctions in the expansion of the total psi-function. In addition there will be spurious critical points in thoughtlike Q. Bader has classified the topology of some of these in 3D space in his book Atoms in Molecules. Indeed, {X(t),Y(t)} is a toy version of Stapp's classical brain configuration for his "top level control system" in his book Mind, Matter and Quantum Mechanics. It is also a toy version of the configuration of a neural net that can learn from experience. This living sentient adaptivity is built into fundamental post-quantum reality.
What I have in my mind is an intuitive working model from which I write down the equations when I need them. I can almost feel and touch it and play with it like some complex toy. It is a structure in virtual reality. I think Hans Bethe had this ability to a very strong extent as did certainly Feynman. Bethe was able to give perfect lectures without notes like he was describing some inner structure the way one would describe a painting or a statue.
Einstein believed that the equations of general relativity are the key to further progress in physics. Was he wrong? He was wrong about locality, or was he? Maybe he was right, but he was in the wrong space. Bohm's quantum equations for the motion of the beable are local in configuration space. They are nonlocal in ordinary space. Perhaps Einstein is correct if we jump out of ordinary spacetime and go to multiple copies of it, one copy for each continuous dynamical degree of freedom and different branches for each discrete degree of freedom like spin, isospin et-al. The true laws for the beable are not linear in Bohm's quantum theory yet they are totally compatible with the linearity of the beable's attached pilot-wave. They quantum leap in order of nonlinearity in my post-quantum backactivity theory where there is now a nonlinear coupling between the pilot waves that cannot be linearized away with second-quantization. That is, the metric of the configuration space is curved as is also the metric of the Hilbert space beyond it. Yet, because backactivity is a generalized GRW objective collapse theory, the linear superposition still works for simple systems explaining why nuclear, atomic, solid state, chemical and astro, physics work, but it breaks down as the systems get bigger and more complex which is why we have a classical limit. So that is beautiful. The interesting post-quantum self-determined phenomenon of our own living consciousness happens on the mesoscopic edge between linear indeterministic microscopic quantum physics and nonlinear (in sense of breakdown of Schrodinger equation) deterministic macroscopic classical physics.
"... the true laws cannot be linear. Such linear laws fulfill the superposition principle for their solutions; hence they contain no assertions concerning the interactions of elementary bodies."
This is an odd remark as in quantum field theory we have seemingly nonlinear products of second-quantized operator field equations that describe interactions among the field quanta even though these products of field operators continue to act linearly on the Fock occupation number Hilbert space of the quanta created and destroyed by these operators.
"The true laws cannot be linear, nor can they be derived from such. I have learned something else from the theory of gravitation. no collection of empirical facts however comprehensive can ever lead to the setting up of such complicated equations. A theory can be tested by experience, but there is no way from experience to the construction of a theory. Equations of such complexity as are the equations of the gravitational field can be found only through the discovery of a logically simple mathematical condition that determines the equations completely or almost completely. Once one has obtained these sufficiently strong formal conditions, one requires only little knowledge of facts for the construction of the theory; in the case of the equations of gravitation it is the four-dimensionality and the symmetric tensor as expression for the structure of space that, together with the invariance with respect to the continuous transformation group, determine the equations all but completely."
Einstein had it relatively easy. There is no thoughtlike form-dependence in classical general relativity and the dimension is small fixed and finite. Post-quantum mechanics requires a whole denumerably infinite stack of rocklike configuration spaces in addition to non denumerably infinite dimensional thoughtlike Hilbert spaces in which, unlike quantum mechanics, the nonunitary representations are more important than the unitary ones.
Epilogue
Remember when Einstein lived and created relativity 1904 to 1918. It was a time of Freudian repression of the sense of the uncanny made more respectable by his renegade disciple Carl Jung in his "synchronicity theory" that Wolfgang Pauli in his dying years took hope in. Most New Agers, certainly the ones in Big Sur, certainly the masses and the elite in Brazil where I visited, think that magical action at a distance is the norm of daily life. So cultural prejudices intrude into how we choose to formulate theoretical physics. Bohm has set the stage for me to shown that action-at-a-distance, including, but beyond, the classical form-independent/ intensity-dependent Wheeler-Feynman kind, is funda-MENTAL to the post-quantum fabric of physical reality.
Newton's idea of "absolute space" means no direct classical back-action of the motion of masses on the structure of the space in which they move. Einstein's great achievement in the general theory of relativity was to explain gravitation as the warping of space-time by the actual motion of all forms of mass-energy. The warping or bending of space-time, i.e., curvature, is a kind of classical back-action of that creates a feedback loop between mass-energy and space-time geometry making the gravitational field equation highly nonlinear. My idea of post-quantum back-action to explain the mind-matter "hard problem" is analogous to Einstein's classical back-action from the stress-energy tensor distribution directly to the formerly rigid Newtonian 3D space , thus transforming it into a dynamical mutable object morphing its inner spacelike shape while also bending time, e.g., the pinching off of the wormhole. In the same way, the actual motion of the system point (or beable) of the complex self-organizing adaptive post-quantum system exerts a direct post-quantum back-action on the quantum pilot wave guiding the system point's actual motion. There is then a two-way relation between this thoughtlike thing (or mind) and its attached rocklike thing (or brain). The thoughtlike thing and the rocklike thing form a new self-determining nonrandom living post-quantum whole that is greater than the sum of its lower level completely random quantum-indeterministic thoughtlike part and its completely classical-deterministic rocklike part. The post-quantum living system decomposes into its quantum and classical pieces when it dies i.e., when the post-quantum back-action gets too small relative to the non-self Darwinian natural selection pressures. The post-quantum back-action in Nietzschean terms is the Will to Consciousness.
To review: 1) Einstein's classical back-action in general relativity is the two-way relationship between the space-time geometry and its attached stress-energy tensor distribution. The resulting complex adaptive system is our actual expanding classical universe from the big bang.
2) My post-quantum back-action in the really New Physics is the two-way relationship between the thoughtlike quantum-indeterministic pilot-wave and its attached classical-deterministic material system point's actual path, or hidden variable beable, in configuration space. The resulting complex adaptive systems are our living mind-brains. The stream of inner felt attentive waking consciousness, as well as dream-time consciousness, as well as sentient subconscious processing or thinking, corresponds to the successive captures of the brain system point, and its lower level subsystem points, by a sequence of self-similar fractal memetic attractors that are continuously regenerated by the motion of the system point while simultaneously generating the motion of that system point. This is a highly nonlinear non algorithmic globally self-consistent self-organizing strange creative loop -- the dynamo of free will in the face of external Darwinian natural selection pressures on memes.