- Fallout from the historic breakthrough AAAS USD "Solvay"-type meeting on Retro-Causality.OK Cramer points out that Hoyle & Narlikar have a Feynman path integral formalism and PCW Davies has an S-Matrix formalism that essentially back up his heuristic TI picture. Let's assume that is so for the time being.It's also clear that we have freedom to impose different phase-matching conditions at each end of a transaction between past and future leading to new physics possibilities.Cramer's Type I has the back-FROM-the-future advanced waves from both past emitter and future absorber prior to the emission canceling in destructive interference (pi radian phase shift) and he has an argument for the matching of the intensities. Similarly for complete cancellation of the retarded waves from both emitter and absorber to future of the absorption event. There is constructive interference of the retarded offer history wave with the advanced echo destiny wave between emitter and absorber giving effective past --> future retarded causality for the actual transaction with propagation of energy-momentum-angular momentum-spin etc. between the two events ON THE CLASSICAL FORWARD LIGHT CONE of the emitter.I did not realize that Cramer has also a dual Type II process that he mistakenly threw away in 1980. It is that Type II process that may explain the low entropy of the early universe that sorely vexes Roger Penrose in "The Road to Reality," Garrett Moddell (U. Colo Boulder) pointed out that reception of advanced signals lowers the entropy of the receiver. This is just what Isador Rabi ordered! The advanced signals seem to shoot right back to the initial Big Bang singularity in Cramer's Type II process in which the above Type I is INVERTED i.e. no transaction between emitter and absorber.Cramer's explanation of EPR seems OK for photon pairs, but it is not obvious that it will work for electron, neutron pairs etc. However, if he is correct about Hoyle-Narlikar's & Davies's independent generalizations of Wheeler-Feynman classical action at a distance electrodynamics to any kind of correlated quantum matter waves in configuration space then that will probably work as well though we need to work through the details.On Jun 30, 2006, at 4:42 PM, Jack Sarfatti wrote:
- John Cramer introduces the retro-causal destiny echo wave FROM the future absorber with the "common sense" history offer wave from the past to form a Novikov-type globally self-consistent loop in time in an actualized "transaction" ("handshake") between future and past in the transfer of a quantum of light energy on the light cone by far-field radiation. The issue of how the electron matter wave moves is not solved in this limited picture of two atoms exchanging light energy. There is no photon in the Wheeler-Feynman picture. It is not clear if the Wheeler-Feynman idea makes any sense in modern gauge theory where, for example, the weak gauge bosons and the strong gluons self-interact e.g. "glue balls" analogous to Wheeler's "geons."What Hoyle and Narlikar do is not the same as what Cramer does however it may be possible to derive the latter from the former.The retarded Feynman propagator isK(Past,Present) = Sum over all paths e^i2pi(Classical Action Past to Present)/(Planck's Constant)ZERO in the time reversed order where we need to use the advanced Feynman propagator K(Future,Present)K(Future,Present) = Sum over all paths e^-i2pi(Classical Action Future to Present)/(Planck's Constant)Note when we have N EPR entangled "point" particles the Classical Action is in configuration space of at least 3N dimensions based on 3+1 foliated space-time if a timelike Killing vector field exists - not guaranteed when gravity is included.The retarded wave function that obeys the NR Schrodinger equation in Galilean relativity without antiparticles isPSI(Present) = Functional Path Integral of K(Past,Present) over all possible retarded paths from the past.We cannot use the light cone simplification here.Similarly the advanced wave function isPSI(Present)* = Functional Path Integral of K(Past,Present) over all possible paths from the future.Now to make this special relativistic is to include particle-antiparticle production and this clean break in which the Present is a sharp boundary between Past and Future is not possible since it assumes Absolute Simultaneity.Therefore we simply must use ALL possible paths from everywhere-when that end in the Present at a particular place where a measurement is made. In this case the Born probability density isPSI*(Present)PSI(Present) = Double Riemann & Double Functionals Sums over X and X' of all possible paths of K*(X,Present)K(X',Present)i.e. Riemann sum over all possible events X & X' of the functional sum of all paths from X & X' to Present Local Event.Aharonov & Vaidman et-al simplify this to Double Sums assuming both a past and future "Cauchy Surface"PSI*(Present)PSI(Present) = Double Functional Sums over all possible paths of K*(Future Cauchy Surface,Present)K(Past Cauchy Surface,Present)This gets further simplified ifPast Cauchy Surface is replaced by a pre-selected ensemble for the History State VectorFuture Cauchy Surface is replaced by a post-selected ensemble for the Destiny State Vectorin doing particle quantum mechanics.On Jul 1, 2006, at 1:47 PM, Jack Sarfatti wrote:Fallout from the historic breakthrough AAAS USD "Solvay"-type meeting on Retro-Causality.OK Cramer points out that Hoyle & Narlikar have a Feynman path integral formalism and PCW Davies has an S-Matrix formalism that essentially back up his heuristic TI picture. Let's assume that is so for the time being.It's also clear that we have freedom to impose different phase-matching conditions at each end of a transaction between past and future leading to new physics possibilities.Cramer's Type I has the back-FROM-the-future advanced waves from both past emitter and future absorber prior to the emission canceling in destructive interference (pi radian phase shift) and he has an argument for the matching of the intensities. Similarly for complete cancellation of the retarded waves from both emitter and absorber to future of the absorption event. There is constructive interference of the retarded offer history wave with the advanced echo destiny wave between emitter and absorber giving effective past --> future retarded causality for the actual transaction with propagation of energy-momentum-angular momentum-spin etc. between the two events ON THE CLASSICAL FORWARD LIGHT CONE of the emitter.I did not realize that Cramer has also a dual Type II process that he mistakenly threw away in 1980. It is that Type II process that may explain the low entropy of the early universe that sorely vexes Roger Penrose in "The Road to Reality," Garrett Moddell (U. Colo Boulder) pointed out that reception of advanced signals lowers the entropy of the receiver. This is just what Isador Rabi ordered! The advanced signals seem to shoot right back to the initial Big Bang singularity in Cramer's Type II process in which the above Type I is INVERTED i.e. no transaction between emitter and absorber.Cramer's explanation of EPR seems OK for photon pairs, but it is not obvious that it will work for electron, neutron pairs etc. However, if he is correct about Hoyle-Narlikar's & Davies's independent generalizations of Wheeler-Feynman classical action at a distance electrodynamics to any kind of correlated quantum matter waves in configuration space then that will probably work as well though we need to work through the details.On Jun 30, 2006, at 4:42 PM, Jack Sarfatti wrote:<Cramer1980.webarchive>
Caveat: Cramer has a large body of published work that I have not yet read. So most of my questions may have already been answered.

On Jun 30, 2006, at 12:22 PM, Paul Zielinski wrote:Jack Sarfatti wrote:

Zoom in for a closer look at a finer scale of resolution:What is the quantum wave below a wave of? Cramer seems to think it is a local wave of a single photon in the simplest case. However to really do the the problem we need an electron at the emitter, and electron at the absorber and also the photon.

$64K question.However, the photon is an illusion in this theory. The transaction handshake is fundamentally a 2-electron problem having at least a 6-Dim configuration space in Galilean relativity if we neglect spin and think of the electrons as point particles. Therefore, what is the PSI wave as a local field, a local field of?In Bohm's theory this is relatively clear. But I mean something technical & formal here.For any quantum field local field operator in Heisenberg picture barring quantum gravity shaking, roughlyPSI(x) = PSI(x+ ) + PSI(x-)particle destruction = anti-particle creation = + frequency partparticle creation = anti-particle destruction = - frequency partSee Penrose The Road to Reality on how this relates to holomorphic complex analytic twistor structure (if I recall correctly) that is BROKEN when PSI*PSI is allowed! Therefore, "collapse" or "actualization" is the BREAKING of HOLOMORPHIC STRUCTURE? This is completing the "transaction".This clean split messes up in orthodox attempts at quantum gravity - not surprising.The photon is its own anti-particle.Particle of positive energy forward in time ~ Antiparticle of negative energy backwards in time of opposite charges etc.Let PSI(x)* be the Hermitian adjointPSI(x+)* creates a particle of positive energy moving forward in time like A(ret) inside or on forward light cone.PSI(x-)* creates a particle of negative energy moving backward in timeThis is equivalent to destroying an anti-particle of positive energy moving forward in time also like A(ret) inside or on past light cone.So think of PSI(x)* like A(ret).Think of PSI(x) like A(adv).Note that PSI(x)*PSI(x')*|VACUUM> is already BOSE SYMMETRIZED or FERMI ANTI-SYMMETRIZED entangled.One needs to make general entangled states using PSI(x+)* & PSI(x-)* separately and carefully.Also it's more complicated for anyons in 2 + 1 space-time. Above is for 3 + 1 space-time.Anyons should live on the boundary of spatial volumes in a world hologram picture. All the quantum gravity information would then be carried by anyons with "braid group" fractional quantum statistics?It seems clear to me that the psi function of orthodox QM has a dual function -- it describes a *physical wave* that propagates through 3D space in the manner of a physical wave, and reflects and refracts and penetrates potential barriers according to an optical analogy, according to Schroedinger's equation; while at the same time, it clearly functions as a probability amplitude generating probability densities that at least in part reflect the state of knowledge of "the observer" and are thus capable of abrupt non-unitary changes.

I am pointing to an important distinction above. Complex c-number wave functions are generally entangled and live in at least 3N + 1 dim configuration space for N real quanta as opposed to the single q-number second quantized field operators that formally live in 3 + 1 spacetime where the former is a sum of N-fold products of the latter on the physical vacuum of all the interacting quantum fields - ideally speaking. Therefore, the wave function, and also the c-number Feynman histories are not generally LOCAL CLASSICAL FIELD objects like A(x) in classical electromagnetic field theory of the 1940 Wheeler-Feynman type toy models.

It is no mystery that a probability density that reflects an observer's state of knowledge can change discontinuously, violating the unitary evolution implied by the Schroedinger equation, and that long-range correlations predicted by such a density can abruptly change probabilities by *logical deduction* from the results of measurements performed on arbitrarily remote separated components of a compound system. This is no different in principle from, say, the probability of a flipped coin showing heads abruptly changing from 1/2 to 1 after the coin is "observed" to come up heads; or, in the case of a correlated classical system of two spinning particles of total angular momentum zero, the probability of one particle being "up" abruptly changing from 1/2 to 1 or 0, depending on the results of observations made on the other particle. In the latter case, it is no surprise that the probability of an angular momentum state of one particle changes abruptly upon observation of the dynamical state of the other particle, and that such changes are completely insensitive to the distance between the particles.Not that simple because the observed violation of Bell's locality inequality demanded by orthodox quantum theory shows that any such change in the observer's knowledge violates local objectivity i.e. the ontology is fundamentally nonlocal as is shown formally by the nonlocal Bohm quantum potential in the generic case.

It is also no mystery that such a density is defined over the higher-dimensional configuration space of a dynamical system, since this is the only way to describe correlations among particles whose relative motion is governed by mutual interactions, in the absence of a fully deterministic description. For example, once the center-of-mass and relative motion of a two-body system are separated, any probabilistic description of motion with respect to the relative coordinate will imply a probability function defined over the configuration space of the system, automatically.Not that simple because the rules of classical statistical mechanics in the above case are incomplete. Classical statistical mechanics is based upon objective locality. Technically, classical statistical mechanics forbids negative phase space densities. The quantum Wigner phase space density goes negative precisely where non-classical entanglements are important and where non-classical quantum superposition for even a single real quantum is important as when the "electron is in two places at the same time" for example.

The mystery arises when these physical and epistemic aspects of the psi function are bundled together in a mathematically

seamless manner, such that it is very difficult to separate the two aspects of the quantum mechanical description. Phase space correlation information can then be tacitly reverse-encoded into the |psi|^2 probability amplitude simply by superposing product states.Note Valentini's theorem that signal locality with no perfect cloning of arbitrary unknown quantum states depends upon the validity of the |psi|^2 Born probability density - note it's "density" not "amplitude" - you misused "amplitude" above. Note also that macro-quantum ODLRO in ground states of complex systems VIOLATES the |psi|^2 rule because of PHASE RIGIDITY. Therefore the macro-quantum ODLRO Bohm potential is NOT FRAGILE - therefore we expect MACRO-QUANTUM SIGNAL NONLOCALITY in contrast to micro-quantum signal locality. This explains how our MACRO-QUANTUM CONSCIOUS MIND FIELDS REMOTE VIEW IMHO. ;-)According to this view, the only way to solve this problem is to "diagonalize the conceptual matrix" and cleanly split the

physical (objective, observer-independent) and epistemic (observer knowledge dependent) components of the theory. Whether this is truly feasible in the case of quantum mechanics is still not clear, due of course to the interference terms in the probability densities derived from a linearly superposable n-body probability amplitude.This metaphor is too vague at present.

Cramer's TI approach does at least appear to represent an attempt at separating these two roles of the psi function, first as

a (localizable) physical description of the objective dynamical evolution of microphysical systems, and second as a probability function that is conditioned by observer-dependent states of knowledge, that is naturally capable of abrupt non-local changes in the light of new information.Bohm has already done that. However, Shelly Goldstein has combined TI with Bohm getting a Lorentz invariant theory.Note even in NRQM of Galilean relativity v/c << 1Bohm Quantum Potential(NOW) ~ [PSI(FUTURE)PSI(PAST)]^-1/2Grad^2[PSI(FUTURE)PSI(PAST)]^1/2

Any solution to the quantum conundrum will have to resolve the issue of what is and what is not an "observer", and how and when a quantum system can be said to have been "observed" (as Feynman once asked, "Is a fly an observer?"), in which respects this can be understood as a physical event, and in which respects it is to be understood as simply reflecting a change in the observer's state of knowledge.

Cramer's TI approach does at least attempt a resolution of this basic conceptual problem.So does Bohm's.If we do quantum field theory, the problem is even more daunting since the configuration space is infinite dimensional.Right.

As a heuristic Cramer's toy model is interesting but what exactly does it mean? One must look at Hoyle and Narlikar who use the Feynman path integral including all possible paths - but paths of what IF the photon field is non-dynamical? It's a direct action at a distance, but must it be limited to the light cone?I think Cramer's idea is that this is an objective physical process, to be sharply distinguished from non-localizable observer

knowledge dependent changes in a probability function.Yes, but so what? That does not address my polnt.Yes, one could say that for the constructive interference in an electromagnetic transition but if one is dealing with matter waves the situation is less clear since the group speed of matter waves is inside the light cone and the phase speed is outside the light cone i.e. there is strong dispersion in low energy atomic physics & chemical bonds.Clearly if the psi-function phase velocity is viewed as a physical propagation speed, you will immediately get a contradiction with SR.

You can't send a signal at the phase speed - which saves the day.However, this should not be confused with instantaneous non-local changes that merely reflect changes in state of knowledge of "the observer" .

Cramer wants to eliminate that as "excess metaphysical baggage" - to be polite. ;-)

Z.

http://www.npl.washington.edu/TI/TI_30.htm3.1 Advanced Waves and Wheeler-Feynman Absorber Theory

The basic element of the transactional interpretation is an emitter-absorber transaction through the exchange of advanced and retarded waves, as first described by Wheeler and Feynman (1945, 1949) [see also (Feynman, 1967b)]. Advanced waves are solutions of the electromagnetic wave equation and other similar wave equations which contain only the second time derivative. Advanced waves have characteristic eigenvalues of negative energy and frequency, and they propagate in the negative time direction. Fig. 2 illustrates the propagation of advanced and retarded waves. The advanced wave solutions of the electromagnetic wave equation are usually ignored as unphysical because they seem to have no counterpart in nature.

The classical electrodynamics described by Wheeler and Feynman (WF) was intended to deal with the problem of the self-energy of the electron in an innovative way. Assuming the time symmetric formalism of Dirac (1938) combined with the ad hoc assumption that an electron does not interact with its own field, WF was able to formally eliminate the self-energy term from their electrodynamics. But along with self energy these assumptions also removed the well observed energy loss and recoil processes (i.e., radiative damping) arising from the interaction of the radiating electron with its own radiation field.

However, WF accounted for these well-known damping effects by allowing the emitting electron to interact with the advanced waves sent by other electrons which would ultimately, at some time future, absorb the retarded radiation. Thus the energy loss and recoil of the emitter were accounted for without having it interact with its own field. Moreover, the calculation succeeded in describing electrodynamic interactions in a completely time-symmetric way. To account for the observed asymmetric dominance of retarded radiation, WF invoked the action of external boundary conditions arising from thermodynamics. They thus avoided resort to the usual ad hoc "causality" condition usually needed to eliminate the advanced radiation solutions.

Regrettably, the WF paper, while mathematically correct, proved be an invalid way of dealing with self-energy. As Feynman (1949) later pointed out, the self-interaction is a necessary part of electrodynamics, needed, for example, to account for the Lamb shift. And it is relevant that the WF ad hoc assumption of non-interaction is not needed in their recoil calculations because, as later authors have pointed out (Pegg, 1975; Cramer, 1980), the electron cannot undergo energy loss or recoil, which are intrinsically time-unsymmetric processes, as a result of interacting with its own (or any other) time-symmetric field.

When the offending assumption of non-interaction is removed from the WF formalism, what remains is a classical self-consistent and time-symmetric electrodynamics which cannot be used to deal with the problem of self energy. Further, this WF formalism is not particularly useful as an alternative method of calculating the electrodynamics of radiative processes because the mathematical description of radiation explicitly involves the interaction of the emitter with the entire future universe. Thus a simple integration over local coordinates in the conventional formalism is replaced by an integral over all future space-time in the light cone of the emitter in the WF formalism.

However, this "difficulty" can be viewed an asset. The WF mathematics can be used to investigate the properties of cosmological models describing the future state of the universe by relating such models to radiative processes. In essence this approach provides a way of linking the cosmological arrow of time (the time direction in which the universe expands) to the electromagnetic arrow of time (the complete dominance of retarded over advanced radiation in all radiative processes). There is a considerable literature in this field which the author has reviewed in a previous publication (Cramer, 1983).

Although the original WF work dealt exclusively with classical electrodynamics, later authors (Hoyle and Narlikar, 1969, 1971; Davies 1970, 1971, 1972) have developed equivalent time-symmetric quantum-electrodynamic (QED) versions of the same approach. The predictions of these QED theories have been shown to be completely consistent with those predictions of conventional QED which can be compared with experimental observation {footnote 4}. It has also been shown (Davies, 1972) that despite this similarity of prediction, the time-symmetric QED provides a qualitatively different description of electromagnetic processes. It is essentially an action-at-a-distance theory with no extra degrees of freedom for the radiation fields and no second quantization. The field in effect becomes a mathematical convenience for describing action-at-a-distance processes.

There may also be another advantage to the WF approach to electrodynamics. Dirac's (1938) work on time-symmetric electrodynamics, on which the WF theory is based, was introduced as a way of dealing with singularities in the radiation field in the conventional theory near a radiating electron. Konopinski (1980) in his Lorentz covariant treatment of the radiating electron has pointed out that this time-symmetric "Lorentz-Dirac" approach eliminates such singularities and therefore amounts to a self-renormalizing theory. This formulation may have applications in eliminating related singularities in QCD and in quantum field theory in curved space-time.

3.2 The Emitter-Absorber Transaction Model

There is a second application of the Wheeler-Feynman approach which was introduced by the author in a previous publication (Cramer, 1980). The WF description of radiative processes can be applied to the microscopic exchange of a single quantum of energy, momentum, etc., between a present emitter and a single future absorber through the medium of a transaction, a Wheeler-Feynman exchange of advanced and retarded waves. Fig. 3 illustrates a simplified form (one space dimension and one time dimension) of the the transaction process.

The emitter, e.g., a vibrating electron or atom in an excited state, attempts to radiate by producing a field. This field, according to the Wheeler-Feynman description, is a time-symmetric combination of a retarded field which propagates into the future and an advanced field which propagates into the past. For simplicity let us first consider the net field to consist of a retarded plane wave of the form F1 ~ exp[i(k.r- t)] for tT1 (T1 is the instant of emission) and an advanced plane wave of the form G1 ~ exp[-i(k.r- t)] for tT1. Since the retarded wave F1 has eigenvalues characteristic of positive energy and momentum k, while the advanced wave G1 has eigenvalues of negative energy - and momentum - k, the net loss of energy and momentum by the emitter in producing the pair of waves (F1 + G1) is zero, as might be expected from the time-symmetry of the composite wave.

Let us for the moment set aside consideration of the advanced wave G1 and follow the retarded wave F1. This wave will propagate in the positive time direction (tT1) until it encounters an absorber. The process of absorption, as is well known, can be described as a movement of the absorbing electron (or atom) in response to the incident retarded field F1 in such a way as to gain energy, recoil, and produce a new retarded field F2=-F1 which exactly cancels the incident field F1. Thus the retarded wave from the absorber exactly cancels the retarded wave from the emitter, and there is no net field present after the instant of absorption T, i.e.:

Fnet = (F1 + F2) = 0 for t>T1. [3]

But the Dirac-Wheeler-Feynman assumption of time-symmetric radiative processes requires that the absorber can only produce the cancelling retarded field F1 for tT1 if it also produces an advanced field G2 for tT2. This field G2 will propagate in the negative time direction (i.e., into the past) from the instant of absorption T2, travelling back down the track of the incident wave F to the instant of emission T1. There it interacts with the radiating electron (or atom) at the instant of emission, causing it to recoil and to lose energy. Further, the advanced wave G2 continues to times such that t>T1, where it is superimposed on the advanced wave from the emitter G1 to produce a net advanced field:

Gnet = (G1 + G2). [4]

But the condition that F2=-F1 at the absorber for t<T2 brings with it a similar condition for the advanced fields, so that G2=-G1 at the emitter and for t<T1, so that Gnet=0 for t<T1. The result of the cancellation of the pre-emission and post-absorption waves is that only in the interval T1tT2 is there a non-zero field:

Fnet = (F1 + G2). [5]

From this we see that even under the Dirac assumption of time symmetric radiation of retarded and advanced waves the advanced field G1 cannot produce "advanced effects" such as backward-in-time signalling and the emission of negative energy radiation because it has been nullified by the absorption process.

This, in a simplified one-dimensional form which will be expanded below, is the emitter-absorber transaction. The emitter can be considered to produce an "offer" wave F1 which travels to the absorber. The absorber then returns a "confirmation" wave to the emitter and the transaction is completed with an "handshake" across space-time. To an observer who had not viewed the process in the pseudo-time sequence {footnote 14} employed in the above discussion, there is no radiation before T1 or after T2 but a wave travelling from emitter to absorber. This wave can be reinterpreted as a purely retarded wave because its advanced component G2, a negative energy wave travelling backwards in time from absorber to emitter, can be reinterpreted as a positive energy wave travelling forward in time from emitter to absorber, in one-to-one correspondence with the usual description {footnote 15}.

Thus the W-F time symmetric description of electrodynamic processes is completely equivalent in all observables to the conventional electrodynamic description. Time-symmetric electrodynamics, in both its classical and quantum mechanical forms, leads to predictions identical with those of conventional electrodynamics. For this reason it is not possible to devise experimental tests which will distinguish between time-symmetric and conventional electrodynamics. The intrinsic untestability of time symmetric electrodynamics reveals that it should be considered an alternative interpretation of the electrodynamic formalism rather than an alternative formulation.

It is this alternative interpretation of the electrodynamic formalism which we have generalized (Cramer, 1980) to include all quantum mechanical processes and which leads to the alternative interpretation of quantum mechanics which is presented here. The fundamental element of this interpretation is the emitter-absorber transaction, a simple plane-wave version of which was described above. The transaction is a "handshake" between the emitter and the absorber participants of a quantum event, occurring through the medium of an exchange of advanced and retarded waves. The description just presented is basically one dimensional (in space) and is not fully applicable to the case of three space dimensions with quantization boundary conditions. Before discussing the applications of the interpretation we will generalize the transaction model from one to three spatial dimensions.

There are two problems with the one dimensional plane wave description employed above: (1) it does not explicitly deal with the attenuation and modification of wave amplitude due to propagation through space or to passage through attenuating media; and (2) it does not explicitly include the quantum conditions on the transfer of energy, angular momentum, charge, etc., which are an important aspect of all quantum mechanical processes. In the case of quantum electrodynamics the photon energy quantization condition E= places an extra constraint on the electromagnetic wave equation, requiring that an integer number of quanta be exchanged between emitter and absorber despite the action of intervening space, filters, mirrors, slits, wave plates, etc., in reducing or modifying the amplitudes of the advanced and retarded waves exchanged between emitter and absorber.

For this reason, the two-step pseudo-time sequence {footnote 14} of Fig. 3 and the associated plane wave description must be replaced by a multi-step sequence allowing for spherical and more complicated wave forms and which proceeds until all relevant quantum conditions are met. In particular, we must view the transaction as occurring in pseudo-sequential form which includes an "offer", a "confirmation" and a completed transaction.

Fig. 4 illustrates this more general form of transaction. In the first pseudo-sequential step (1) the emitter located at (R1,T1), sends out a waves F1(r,tT1) and G1(r,tT ) (which can be of spherical or more complicated form) in all possible spatial directions. In step (2) the absorber located at (R2,T2), receives the attenuated retarded wave front F1(R2,T2) and is stimulated to produce a response wave G2(r,t) which has an initial amplitude proportional to the local amplitude of the incident wave which stimulated it:

G2(r,t) ~ F1(R2,T2)×g2(r,t) [6]

Here g2(r,t) is a unit advanced wave, i.e., the advanced equivalent of the retarded wave F1(r,t) in that g2(r,t-T2)=[F1(r,t-T1)]*.

In step (3) the advanced wave G2 propagates back to the locus of emission, at which it has an amplitude which is proportional to its initial amplitude F1(R2,T2) multiplied by the the attenuation which it has received in propagating from the absorption locus to the emission locus. But the advanced wave G2 travels across the same spatial interval and through the same attenuating media encountered by F1, but in reverse. For this reason, the unit amplitude wave g2(R1,T1) arriving back at the emitter has an amplitude which is proportional to F1*(R2,T2), the time reverse of the retarded wave which reached the absorber. Thus at the emission locus the advanced wave amplitude G2 is:

G2(R1,T1) ~ F1(R2,T2) ×F1*(R2,T2) = |F1(R2,T2)|2. [7]

This means that the advanced "confirmation" or "echo" wave which the emitter receives from the absorber as the first exchange step of the incipient transaction is just the absolute square of the initial "offer" wave, as evaluated at the absorber locus. The significance of this * echo and its relation to Born's probability law will be discussed in Section 3.8 below.

In step (4) the emitter responds to the "echo" and the cycle repeats until the response of the emitter and absorber is sufficient to satisfy all of the quantum boundary conditions [E=h(nu) and various conservation laws], at which point the transaction is completed. Even if many such echoes return to the emitter from potential absorbers, the quantum boundary conditions can usually permit only a single transaction to form. The transaction formation can be considered as analogous to the establishment of a four-vector standing wave across the interval bounded by (R1,T1) and (R2,T2), the two loci forming terminating "walls" outside which the wave amplitude must make no contribution to the process. Note that at the completion of step (4) the local fields in the vicinity of both the emitter and the absorber are real (as opposed to complex) because they are a superposition of an advanced and a retarded wave of equal amplitude and the same phase. The significance of this for the problem of complexity is discussed in Section 3.6 below.

To summarize the transaction model, the emitter produces a retarded offer wave (OW) which travels to the absorber, causing the absorber to produce an advanced confirmation wave (CW) which travels back down the track of the OW to the emitter. There the amplitude is CW1~|OW2|2, where CW1 is evaluated at the emitter locus and OW2 is evaluated at the absorber locus. The exchange then cyclically repeats until the net exchange of energy and other conserved quantities satisfies the quantum boundary conditions of the system, at which point the transaction is complete. Of course the pseudo-time sequence {footnote 14} of the above discussion is only a semantic convenience for describing the onset of the transaction. An observer, as in the simpler plane wave case, would perceive only the completed transaction which he could reinterpret at the passage of a single retarded (i.e., positive energy) photon travelling at the speed of light from emitter to absorber {footnote 15}.

But an equally valid interpretation of the process is that a four-vector standing wave has been established between emitter and absorber. As a familiar 3-space standing wave is a superposition of waves travelling to the right and left, this four-vector standing wave is the superposition of advanced and retarded components. It has been established between the terminating boundaries of the emitter, which blocks passage of the advanced wave further down the time stream, and the absorber, which blocks passage of the retarded wave further up the time stream. This space-time standing wave is the transaction, and which we will it use as a basis for the discussion which follows.

It should be emphasized that the TI is an interpretation of the existing formalism of quantum mechanics rather than a new theory or revision of the quantum mechanical formalism. As such, it makes no predictions which differ from those of conventional quantum mechanics. It is not testable except on the basis of its value in dealing with interpretational problems. The author has found it to be more useful as a guide for deciding which quantum mechanical calculations to perform than to the performance of such calculations. As will be demonstrated in Chapter 4, the main utility of the TI is as a conceptual model which provides the user with a way of clearly visualizing complicated quantum processes and of quickly analyzing seemingly "paradoxical" situations (e.g., Wheeler's delayed choice experiments, Herbert's paradox, the Hanbury-Brown-Twiss effect, and the Albert-Aharonov-D'Amato prediction) which would otherwise require elaborate mathematical analysis. It is a way of thinking rather than a way of calculating. It may have value as a pedagogical tool for the teaching of quantum mechanics to students. It also seems to have considerable value in the development of intuitions and insights into quantum phenomena that up to now have remained mysterious.

On Jun 29, 2006, at 5:44 PM, Jack Sarfatti wrote:Time is vertical space is horizontalHere in the above picture is the key idea of John Cramer's time loop in his TI.Of course it must be done with Feynman path integrals to include all possible paths.The red dot is the past emission event. The blue dot is the future absorption event. The two waves out of phase represent total destructive interference of:1. to lower left of the red dot the red dashed wave is the advanced wave from the past emitter red dot. The blue dashed wave is the advanced wave FROM the future absorber blue dot.2. to the upper right of the blue dot is retarded solid red wave from the past emitter out of phase by pi radians with the retarded solid blue wave from the future absorber.In between the red dot and the blue dot is the solid red retarded wave from the past emitting red dot in phase with the dashed blue advanced wave from the future absorbing blue dot.An actualization AKA "collapse" is when the phase difference to upper right of blue dot is really pi.Now in Wheeler-Feynman classical electrodynamics picture this really does work, but only in a TOY MODEL with very specific dynamics and future boundary condition. In that classical Wheeler-Feynman model the blue dashed wave between the red and blue dots represents(1/2)[Aret - Aadv]i.e. radiation reaction reaction (related to zero point vacuum fluctuation spontaneous emission in which all dark energy/dark matter comes BACK FROM THE FUTURE)The solid red wave between the red and blue dots(1/2)[Aret + Aadv]Therefore, the two terms in (1/2 - 1/2)Aadv cancel out between the red and blue dot to form a retarded signal (1/2 + 1/2)Aret.However, this is very Rube Goldberg adhoc even for Wheeler-Feynman classical electromagnetism and it is far from obvious that the analogy carries over to quantum PSI waves.The Fat Lady has not sung on this TI yet. For more complete details and to investigate for yourself go toAlso go to Feynman's original paper on NR QM in Dover edition of Schwinger's QED in which I seem to recall an idea similar to TI is more rigorously derived using all paths. Feynman sets up both past and future spacelike surfaces for initial and final conditions and then asks what happens in between. In affect the intermediate PSI* comes from the future surface and the intermediate PSI comes from the past surface. This is not precisely the same as JC's TI but it is related to it. It is also related to Aharonov's (Vaidman ...) later history and destiny state vector model of orthodox quantum measurements generalized to non-orthodox "weak measurements".The general idea is that what happens is a clash between what has happened and what has not yet happened in a globally self consistent loop that gives zero probability amplitude for all WANNABE time travel autocidal paradoxes.On Jun 28, 2006, at 3:14 PM, Jack Sarfatti wrote:A careful analysis of John Cramer's TI is needed. I have not done so as yet. Peacock and Hepburn should do it. A few preliminary issuesThe idea is clear in Wheeler-Feynman classical electrodynamics for a local classical EM field confined to the light cone for real processes and a precise classical dynamical model. It's not so clear to me as yet how it works for quantum waves because quantum waves live in higher dimensional configuration space fibers over 4D space-time (not to be confused with hyperspace string M theory). Also the dynamics is not the same at all and the quantum waves are not confined to the light cone by any means. In terms of Hamilton-Jacobi theory the key point Peacock and Hepburn make is that the effective potential for entangled quanta is nonlocal therefore the effective Hamiltonian for the action phase S is nonlocal! The quantum waves must be ontological, i.e. quantum waves can be epistemological as Bohr, Heisenberg, London, von Neuman, Wigner, Wheeler profess, but the hologram mind field whose vibrational modulation is the content of our conscious experiences is itself ontological. Everything epistemological is ontological but not vice versa. There is no Cartesian split.Look at Hoyle and Narlikar on classical local EM Wheeler-Feynman theory:The classical past-to-future causal retarded Green's function propagator to solve the sourced field equation forward on the future light cone t - |r| = 0 in globally flat space-timeWAVE Operator on G ~ 4D Dirac delta functionisGret = (4pi/|r|)Dirac delta function of (t - |r|)Similarly, the classical retro-causal teleological BACK FROM THE FUTURE advanced Green's function propagator backwards on the past light cone t + |r| = 0 isGadv = (4pi/|r|)Dirac delta function of (t + |r|)What a difference a mere sign makes!The curvature of gravity introduces a relative tilt between neighboring light cones that are all parallel to each other in global special relativity. Event horizons correspond to that critical tilt in which no light rays can reach light-like future infinity.The EM vector potential fiber gauge connection field for parallel transport isA ~ Integral of G x source over spacelike 3D volume + 2D surface boundary integral of covariant gradients of A and G, i.e. Kirchoff's theorem.Wheeler-Feynman classical theory starts with the Fokker action CONFINED TO LIGHT CONES both directions. THIS DOES NOT SEEM TO APPLY TO QUANTUM WAVES!AFokker = (1/2)[Aret + Aadv]One then has to compute the "RESPONSE OF THE UNIVERSE". The details are complex with a toy model for refractive dispersion of the EM waves in the electric dipole approximation including radiative reaction, the amazing White Rabbit Out Of The Top Hat result is that the effective radiative reaction field at the moment of past emission including all future absorbers obeying a future boundary condition known to be false in our expanding accelerated universe isA(Reaction of Universe) = (1/2)[Aret - Aadv]Therefore, Aadv cancels out of the problem once radiative reaction( related to ZPF) and future absorbers are included. However, this result rests on very shaky ground even for the classical EM field. It has no obvious relevance to quantum waves and I am not sufficiently versed in the nitty gritty of John Cramer's TI to make a judgment as yet. It seems that the assumption of signal locality is far from obvious in Cramer's interpretation of orthodox QM and is like Euclid's fifth axiom?Nick Herbert's FLASH theorem is that a perfect quantum clone machine of arbitrary unknown quantum states like |c> permits signal nonlocality, i.e. use of EPR quantum entanglement as a stand-alone C^3 system not needing any classical hindsight signal to unlock the nonlocally encoded message. This would almost explain all paranormal phenomena like precognitive remote viewing RV and retro-psychokinesis PK (Helmut Schmidt). Russell Targ says that efficiency of all PK is 10^-2RV all other things being equal.Note Lenny Susskind has a simple proof of no-cloning quantum states in orthox QM based only on linearity and unitarity.To clone a state |c> = |a> + |b> is the mapping|c> -> |c>|c> = (|a>|a> + |b>|b> + 2|a>|b>)The problem is the cross term 2|a>|b>since any linear unitary cloning operator UU*U = UU* = 1U|a> = |a>|a>U|b> = |b>|b>ThereforeU(|a> + |b>) = |a>|a> + |b>|b> =/= |c>|c>Therefore a linear unitary clone operator does not exist.Of course "collapse of the state" is NOT a linear unitary process in the Copenhagen intepretation of quantum measurement. However, conservation of probability even there prohibits signal nonlocality.