Quantum Back Action

The world, according to the late David Bohm, divides into objectively real, though mathematically complex-valued, quantum waves and objectively real classical particles and gauge fields. The classical particles and gauge fields always have quantum waves attached to them. For a many-particle system, the quantum wave function's domain is the system’s classical-mechanical configuration space not physical space. This is in contrast to Copenhagen-type interpretations (i.e., Bohr, Heisenberg, von-Neumann, etc. -- all are a wee bit different) in which the quantum wave is fundamental and the classical particle is not. Indeed, Bohm’s actual particle position in physical space has been called the "hidden variable". This is topsy-turvy since most practical measurements in quantum physics involve localized "particle" flashes in a detector. The quantum wave patterns build up in the statistics of the particle detections. It would be more appropriate to say that the wave is the hidden variable.

We restrict this discussion to non-relativistic quantum mechanics. Bohm’s theory appears to violate the Lorentz transformations of Einstein’s theory of special relativity at the individual quantum particle level. However, Lorentz symmetry is restored in the statistical quantum wave patterns. That is, there does appear to be a preferred rest frame in which the new nonlocal quantum forces act instantaneously. This fact is a bit ugly, but we must remember that there is a preferred global frame of reference in the standard cosmological "big bang" solution of Einstein’s general relativity field equations. The "co-moving Hubble flow" provides a new kind of covariant aether in which the cosmic photons from the big-bang are isotropic with a temperature that obeys the Planck blackbody distribution. The isotropy establishes an absolute global "rest frame", and the temperature establishes an absolute measure of global cosmic time from the big bang. Bohm conjectures that the quantum force is instantaneous in this global frame which suggests an interesting connection between a solution to classical general relativity and low-energy quantum mechanics. Special relativity is a local tangent space symmetry in general relativity. Therefore, the big bang Friedmann solution is an example of the spontaneous broken symmetry familiar in solid-state physics and in the standard model of elementary quark-lepton fermion sources and gauge boson forces. On the other hand, if we look at quantum electrodynamics we find the counter-intuitive surprising fact that the near field of virtual longitudinal and timelike photons is also instantaneous in every Lorentz frame of reference. This is because every Lorentz transformation between inertial frames in relative uniform motion induces a compensating internal phase symmetry or "gauge" transformation that re-adjusts the near field to be instantaneous in every frame. Can we impose this feature on the special-relativistic generalization of Bohm’s quantum force? This is a question for further research.

The quantum force is the negative spatial gradient of a context-dependent quantum potential that appears in the Hamilton-Jacobi equation for the particle derived from the linear Schrodinger wave equation. The quantum force’s context-dependence explains the wave-like guidance of the individual particle in the famous double slit experiment which the late Richard Feynman called the "central mystery of quantum mechanics". Context-dependence means that the guiding quantum force only depends on the "form" of the quantum potential and not its intensity or strength. This is because the quantum potential is the Laplacian of the amplitude of the wave function divided by that same amplitude. Therefore, multiplying the wave function by a constant does not change the quantum potential. Bohm calls this quantum force "active information" in which a small expenditure of energy is able to control a much larger expenditure of energy. This feature is dramatically illustrated in the quantum Carnot engine operating between a hot negative temperature and a cold positive temperature. The quantum wave is a kind of information wave. This is the same idea that David Chalmers calls for in his criteria for a post-modern physics of consciousness although he does not appear to be aware of the relevance of Bohm's theory in this context.

There is an actual point-like particle with a well defined position and momentum at each moment. There is also an actual gauge force field configuration, but in this discussion we only discuss the source particles. In fact the momentum of the particle is context-dependent determined as the gradient of the phase of the wavefunction at the actual position of the particle at every moment. This particle passes through only one of the two slits, but its attached objective wave passes through both slits. The recombination of the waves from both slits exerts a quantum force on the particle whose effects exactly reproduce the observed statistical coherent wave patterns for ensembles of particles whose initial positions are postulated to obey the Born probability rule. The conservation of probability current, derived from the linear Schrodinger equation along with the Hamilton-Jacobi equation, then ensures that the Born probability rule holds for all times. There is no conflict with the Heisenberg uncertainty principle since the statistical deviations of position and momentum measurements obey that principle. The actual particle trajectories are classically chaotic so that a small change in an initial position generally will result in an unpredictable and uncontrollable large change in trajectory over a short time. This, the simplest form of Bohm’s theory, is deterministic but not predictable. Bohm and Vigier later added a fundamental stochastic sub-quantal level which, according to Nanopoulos, originates in the virtual blackholes and super-string states of the quantum foam at the Planck scale of 10^-33 cm. In addition, the dependence of the wave of several particles on position in higher dimensional configuration space introduces the kind of "nonlocality" observed in the experiments testing Bell’s locality inequality.

We now come to "back-action" which is the main idea of this paper . The origin of this idea is Newton’s third law that for every action there is an equal and opposite reaction. We now know that this is a consequence of translational symmetry in physical space. Radiation resistance in Maxwell's electrodynamics is a kind of back-action of the field on its source. Wheeler and Feynman showed how this back-action is caused by advanced waves propagating backward in time from the future absorption of the radiation. Retarded causality then depends on the future final boundary condition of total absorption which is actually violated in the same standard big bang solution of general relativity I mentioned earlier -- as shown by Hoyle and Narlikar in the January 1995, Reviews of Modern Physics. It can also be shown that quantum spontaneous emission of real radiation by virtual zero point vacuum fluctuations can be explained as advanced wave effects from the future that are classically associated with radiation resistance. Feynman also used the term "back-action" to explain the generation of quantized vortices in superfluid helium.

The late Eugene Wigner, amplifying on von-Neumann’s "collapse" postulate in the Copenhagen-like interpretations, suggested that "consciousness" is essential for the completion of the quantum measurement. This entails a violation of the linear Schrodinger equation.

Note that the Hartree-Fock mean-field approximation for the spectra of many-electron atoms give an effective cubic nonlinear Schrodinger-like equation. The Heitler-London theory of the simple chemical bond and the Heisenberg model of ferromagnetism demand similar effective cubic nonlinearities which show up, for example, in the exchange integral. The exchange integral in the effective Lagrangian involves two electron densities or four wave function factors.The equation of motion from the action principle involves a functional derivative with respect to the wave function so the resultant nonlinearity is cubic. Cubic nonlinearities also show up in the Landau-Ginzburg equations for coherent macroscopic order parameters or giant effective quantum wavefunctions in second order phase transitions including superfluids, superconductors and lasers. The cubic nonlinearity is also found in the Higgs mechanism for mass generation of particles in the spontaneous breakdown of symmetry of the electro-weak force. The Goldstone modes from the symmetry breakdown add a new polarization component to the massless gauge bosons giving them rest mass. Fermion source particles can also acquire rest mass this way. The symmetry breakdown is from a tachyon field that undergoes Bose-Einstein condensation. The Goldstone modes are small subluminal quantized vibrations in the vacuum expectation value of the tachyon field. These nonlinearities in the Schrodinger equation which are generically induced in mean-field approximations to many-particle effects are swept away by second-quantizing the wavefunction so that it is now a creation and destruction operator of elementary excitations of collective modes in non-relativistic solid state physics. The second-quantized Schrodinger equation is now "linear" in the Fock space whose base states consist of different precise numbers of elementary excitations. Nevertheless, this is only a formal trick and the problems of the first-quantized theory are still there. The creation of antimatter at high energy has led to the idea that second-quantization is really more fundamental for relativistic theories, however, Bohm's theory which does not use second quantization may also be able to explain the creation and destruction of particles. This is also a problem for further research. Indeed Feynman's path integral formulation of relativistic quantum field theory does not use second-quantization and Bohm's picture can readily be integrated into Feynman's. Indeed, Feynman's theory is essentially an incomplete version of Bohm's without the actual trajectories. Therefore, in Bohm's theory as in Feynman's the creation and destruction of particle-antiparticle pairs at high energy correspond to actual particles turning around and moving backward in time. Feynman imposes a boundary condition which is a contour around the poles of the particle propagator in the complex-energy plane such that particles move forward in time with positive energy and backward in time with negative energy. This choice ensures microcausality. We must be prepared for exotic matter in which this boundary condition is violated. The exotic matter keeps star gate traversable wormholes from collapsing and permits the Alcubierre warp drive. One can also imagine new exotic processes in which the actual particles move in Hawking's imaginary time and also temporarily transform into tachyons on spacelike paths. These are all problems for further research. Note that the use of complex energy planes in Feynman's theory also demands the use of complex time planes since the two are related by a Fourier transform.

Wigner invoked the metaphor of Newton’s third law in the new context of the mind-matter interaction. He said that matter affects mind, but there is no corresponding reaction of mind on matter without the collapse of the quantum wave function brought about by consciousness. As shown by John Archibald Wheeler in his classic essay, "Law Without Law", this view leads to "delayed choice" actions backward-in-time (BIT) because we did not exist in the early universe and yet we observe light from the early universe. In effect, it is the future that actualizes the past in the von-Neumann-Wignerean view of quantum reality. Indeed, Roger Penrose and Henry Stapp have physics of consciousness theories based on this approach.

To summarize, Wigner uses the metaphor of back-action to say that mind acts on matter in the collapse of the wave function. Penrose and Stapp say that each qualia-event or moment of awareness requires a collapse in the wavefunction of the brain. It is assumed that there are mechanisms that preserve coherence over a time of the order of one second. The wave function is shielded from ordinary thermal fluctuations which would decohere it in times much shorter than one second.

Bohm’s theory is very different from the von Neumann-Wigner theory. First off, I identify "pre-mind" with the quantum wave attached to the relevant many-particle system. This is a new postulate that the potential for psychological "qualia" is a fundamental physical property of the universe in the sense defined by David Chalmers in his December 1995, Scientific American article. If we grant this postulate that the potential for qualia is as fundamental as charge or mass, and that this potential is identical with the quantum waves of certain particles of matter in biological and possibly other complex systems, then Bohm’s quantum force immediately explains how mind moves matter. Furthermore, in Bohm’s theory it is the quantum force that guides the particle into a given branch of the wave function in a measurement situation. This simulates Wigner’s idea that "consciousness" collapses the wavefunction. Bohm’s theory is one of "collapse without collapse". Therefore, I have given a more detailed explanation of Wigner’s idea in terms of a deeper idea due to a combination of Bohm’s and Chalmers’s views. We now have a new way of looking at the modern theories of quantum consciousness of Penrose and Stapp.

To make more contact with the standard quantum mechanics, we now see why it is that the guidance of the particle by the "mind-like" quantum force into a particular "eigenfunction" of the "observable" is, under usual conditions, unpredictable and uncontrollable. The latter two features are due to the fact that the linear Schrodinger equation has zero back-action in the sense that I mean it. Whereas Wigner’s idea of back-action was that of mind on matter, my idea is the exact reverse. The Bohmian back-action is the direct action of particulate matter on its attached guiding mind-like quantum wave whose support is in the configuration space of classical mechanics, and whose range is in Hilbert space. The result, however, is not incompatible with Wigner’s main idea and it, in fact, explains it in a deeper more elegant way.

The absence of back-action in orthodox quantum mechanics is mentioned by Bohm and Hiley in their book, The Undivided Universe.

"unlike what happens with Maxwell’s equations for example, the Schrodinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the conditions of the particles. This of course constitutes an important difference between quantum fields and other fields that have thus far been used. As we shall see, however, the quantum theory can be understood completely in terms of the assumption that the quantum field has no sources or other forms of dependence on the particles. We shall in chapter 14, section 14.6, go into what it would mean to have such a dependence and we shall see that this would imply that the quantum theory is an approximation with a limited domain of validity." p.30

The relevant particles are probably the electrons whose spatial displacement controls the conformations of the protein dimers in the microtubules. It is their collective, perhaps Frohlich electric-dipole, wave form pumped far from thermal equilibrium which, I conjecture, is the physical substrate of our mental experience. All forms of life must have back-action in the sense defined above. Back-action is a necessary condition for the existence of any form of living matter in this theory.

Having come this far, things really start to get interesting. Going to Bohm and Hiley’s "section 14.6" we find:

"Other changes of this sort that might be considered would be to make the Schrodinger wave equation nonlinear and to introduce terms that would relate the Schrodinger wave function to the particle positions. One way to make Schrodinger’s equation dependent on the particle positions (so that there would be a two-way relationship between wave and particle) can be seen by considering equation (14.1). In this equation, we regard Rn as the actual position of the nth particle. From the same arguments as apply to the GRW (Ghirardi, Rimini and Weber ) approach, it would follow that the overall wavefunction would tend to collapse towards the actual particle positions, so that in a large scale system, the empty wave packets of our interpretation would tend to disappear." pp.345-6.

It is important to realize that the idea of the mind doing a quantum computation requires that there be no collapse or decoherence whilst the computation is in progress. The GRW theories postulate that the decoherence time depends inversely as the number of particles N that form the quantum computing hardware unit. GRW introduce ad hoc two new fundamental constants of Nature of 10^-5 cm or 100 nanometers for the scale of collapse, and 10^16 sec or a billion years which divided by N gives the decoherence time beyond which quantum computing deteriorates. Nanopoulos gives a more fundamental derivations of the decoherence time in terms of the masses of the particles. If we use the Nanopoulos formulae and my hypothesis that the human quantum biocomputing unit is at the electron level rather than the proton level, then the decoherence time for the number of electrons in our bodies is of the order of 100 years or approximately one human lifetime. If we use protons as the basic unit, the decoherence time is a factor of 10^20 shorter for the same number of particles. This means one has to use a much smaller number of protons to get the same decoherence time as one would get for electrons. Using protons and a decoherence time of 1 second gives an estimate for the basic unit of our experience. The numbers for this computed by Nanopoulos and Penrose need to be compared. One can imagine that the continuity of our long-term memory that lasts a lifetime is at the electron level in our microtubules while our more immediate short-term moment-to-moment experiences are at the proton level having to do with hydrogen bonds. The coupling between short-term and long-term memories would then have to do with the interaction of hydrogen bonds with the controlling electrons in the protein dimers of the microtubules.

One last wild idea before ending this rough first draft. Let’s play with a cosmological connection in the GRW model since Nanopoulos has already linked the "quantum friction" of the fundamental decoherence time to the quantum gravity foam. Suppose, the basic decoherence time is the Hubble size of the universe divided by the speed of light of about 10 billion years presently. This means that the basic decoherence time at the big bang before inflation was the Planck time of 10^-43 sec which is not unreasonable. Let us further suppose that the spatial scale of collapse, which does not appear to be in Nanopoulos’s theory is the geometric mean between the Planck distance of 10^-33 cm and the Hubble size of the universe multiplied by the square of the dominating gauge force coupling constant. Why the square of the coupling constant? Because that is what happens in the basic Feynman diagram for any interaction force between two sources via the exchange of a virtual boson. Every thing that happens is a composite of such Feynman diagrams in standard field theory. Well if we do this, we get about 10^-5 cm for the present epoch which agrees with GRW using the fine structure constant for QED and we get the Planck scale of 10^-33 cm at the big bang since all the coupling constants grand-unify to 1 before they get to the Planck scale in the standard ideas on the subject. So first homework problem - is there anything in astronomy which would falsify this idea? Can it explain the missing-mass problem and the apparent presence of stars older than the universe? It makes a very interesting prediction. It says that, in an open universe (e.g. Freeman Dyson’s "Time Without End") things get more and more quantum mechanical as the expanding universe gets older and older. That is larger and larger numbers of particles preserve their nonlocal quantum connections to each other over longer and longer coherence times, and therefore show macroscopic quantum effects over wider and wider spatial separations in the far future of the universe even though the density of particles may be decreasing to zero asymptotically. This is a prediction for the "Mind of God" (e.g. end of Hawking’s book, A Brief History of Time) because, on the basis of my idea that the act of quantum computing requires the suspension of decoherence, eventually all the matter in the universe will be quantum mechanical on the cosmological scale. If back-action is present, direct faster-than-light (FTL) communication between distant regions of matter in the open universe can happen. Eberhard’s theorem prohibiting such communication using nonlocal quantum connectivity only works in the limit of zero back-action. In this wild idea all the matter of the open immortal universe becomes part of a Vast Active Living Intelligence (i.e. Phillip Dick’s VALIS) or cosmological brain whose quantum wave function is the "Mind of God" in Hawking’s sense. This model is different from Frank Tipler’s Omega Point which requires a closed universe. My model is consistent with I.J. Good’s notion of "GOD(D)" that he introduced about fifteen years ago. Good worked with Alan Turing breaking the Nazi War Code.

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