Theoretical Implications and Possibilities


This experiment raises two obvious questions: (1) Could we extend the BTQT system to build a true Backwards Time Telegraph (BTT), a system which could transmit a string of bits at one time and receive that same string of bits (with or without noise) at an earlier time?; (2) Should we revise Quantum Electrodynamics (QED) to account for these kinds of effects?

                The answer to the first question is simply “no.” The quantum information transmitted backwards through time cannot be decoded into a useful form until the photon on the longer channel is detected.

As in ordinary quantum teleportation, a classical bit of information must be transmitted and received, and that bit cannot be sent backwards through time in this way.

                More precisely, the behavior of this system is totally consistent with the analysis given for the previous experiment [PRL 1/2000]. The results of that experiment (and this one) were totally consistent

with calculations based on Glauber’s approach, which predicted there that R01+R02 should equal

R03+R04; that prediction in turn, implies that the backwards-time communication channel has a Shannon capacity of zero.

                On the other hand, we do believe that these results do hint at a possible reformulation of QED,

which in turn might well enable a true BTT.

                The original version of QED was essentially a hybrid of two parts: (1) a dynamical model

(a “Schrodinger equation”) totally symmetric with respect to time reversals T; (2) the classical Copenhagen

model of measurement, in which the wave function of the entire universe, across all space, “collapses” at and after a magical moment of time “t.” Glauber’s calculations were based on traditional QED; therefore,

this experiment certainly does not disprove conventional QED.

                Nevertheless, the experiment does raise questions about traditional QED. Many theorists believe

that the laws of measurement should eventually be derived, somehow, from the underlying dynamics,

dynamics which govern observers just as much as they govern the systems being observed. (Everett and Bub, among others, have discussed this point at length.) Yet if the underlying dynamics are all symmetric with respect to time, why should the dynamics of measurement be so totally,  rigidly asymmetric?

Even if one uses modern, more elegant statements of the Copenhagen model of measurement, it still violates the underlying spirit of special relativity. When the results of an experiment suggest that backwards-causal effects may be at work, should we not consider the possibility that a new, more natural formulation of the physics might result in some degree of simplification, and some possibility of a more robust theory? Should we not consider some possibility of alternative models of measurement, and

try to devise ways of testing such alternative models?

                There are three obvious objections to these ideas: (1) the apriori philosophical commitment by many physicists  to the idea of time-forwards causality; (2) the difficulty of actually formulating such alternative models, while still accounting for the huge database of experiments which agree with QED;

(3) the issues of how to test such models, which are related to the issues of how to design a possible BTT.

We will discuss these three in order.

                Many physicists have taken a strong position that “time-forwards causality and dynamics are obvious apriori.” Some have even argued that “The human mind is obviously fundamental; it is the unchanging, unquestionable basis for everything we do. The human mind is hard-wired to try to understand the dynamics of the universe in forwards time. Time-forwards causality is the only kind of causality or

order that we can possibly understand. Therefore, we cannot even consider deviating from that approach.”

But these arguments are all very similar to the deep and serious arguments believed by leading authorities all over Europe when they rejected the ideas of Copernicus! The human body is hard-wired to assume gravity forces with g=1, life on a flat surface, and so on. But our body and our brain are just a small part of

the larger universe. Also, the human brain is perfectly capable of learning to make predictions based on very complex models, which explain our subjective experience as a local phenomenon within a larger

and more complex reality. There is no apriori reason why the local direction of causality that we experience in everyday life must be a governing law of the universe, any more than the local direction of gravity is. 

Common sense suggests that we facing a difficult task, in modeling the interface between a macroscopic

gradient of free energy in our part of the universe and a microscopic time-symmetric domain; there is no reason to believe this interface must be trivial, and no reason to believe that we can never raise the

microscopic effects to the macroscopic level. The recent experiments demonstrating macroscopic “Schrodinger cat” states in superconductors prove that we sometimes can raise the microscopic effects

to a macroscopic level, even if it is difficult and even if it seemed impossible for decades before.

                But how can we devise such alternative models of measurement? How can we avoid being inconsistent with the vast body of information supporting QED, unless we simply produce a new formulation which is absolutely equivalent to QED and therefore not testable?

                There are deep theoretical questions here, which merit long analytical discussion, drawing on important contributions from many physicists and philosophers. However, this paper will try to take a more concrete, empirically-oriented approach. A new formulation of QED could ultimately be built by starting from the regime of quantum optics – the experimental study of light, in a totally bosonic regime, where

higher-order effects like vacuum polarization may be neglected. Almost all of the tests of “Bell’s Theorem” [J.S. Bell book] have occurred in this regime; therefore, it is already a regime rich enough to allow us to revisit the key questions about reality, locality and measurement. This paper will  focus almost entirely on that regime.

                The existing literature on quantum optics is so huge that it may seem very intimidating to the theorist.  Yet the bulk of that literature depends on the dynamical aspects of QED, the aspects which are responsible for the 12-digit accuracy often discussed in introductory courses. Historically, the ultimate measurements used on quantum systems were relatively simple; most often they were simply independent counting rates, at the output end of a more complex apparatus. The first really serious tests of quantum

measurement came with the tests of two-photon counting rates for entangled photons, inspired by Bell’s Theorem. The experimental database which needs to be addressed here is mainly the database of experiments on Bell’s Theorem, and the database of experiments on entangled photons developed by the field of Quantum Information Science (QIS). The major results here have all been achieved or replicated in this laboratory – Bell-state measurements, quantum eraser results, GHZ, standard quantum teleportation and so on.

                Except for the recent GHZ results, these results are all ultimately based on the phenomenon of two-photon entanglement. There are two main theoretical approaches currently used in the design and testing of such systems – the Klyshko approach and the Quantum Trajectory Simulation (QTS) approach.

                Klyshko’s approach was initially inspired by early writings of DeBeauregard related to the backwards-time interpretation of quantum mechanics. To predict the behavior of a completely entangled system of two photons, Klyshko would describe the system as a “biphoton.” He would describe it as a single photon, a single beam of light, which is “emitted”  in the future from the counter at the end

of one of the two channels, and then transmitted backwards in time through that channel, back to

the original “two-photon source” (in our case, a BBO crystal). It is then “reflected” from that source,

both in space and in time (and sometimes in polarization). That same beam of light then propagates forwards in time along the other channel. Klyshko’s approach and its mathematical implementation were

the key to the later development by Shih et al [Kim and Shih] of a system to generate two photons which are entangled to a high degree of precision in position.  Positional entanglement has been crucial to the

unique success of this laboratory in several other experiments, such as experiments in quantum lithography and quantum imaging.

                When Klyshko’s approach is used to analyze Bell’s Theorem experiments, it yields a picture which seems somewhat puzzling at first. Let qL be the angle of the linear polarizer on the left channel of the standard Bell’s Theorem experiment, and qR the angle of the linear polarizer on the right. If we assume that the biphoton is emitted from the left, and we deal with the simplest of the four Bell states

(c(|00>+|11>)), then the picture is as follows: the light has a linear polarization of q=qL on both channels

in the time between the two-photon source and the polarizer; the two-photon counting rate predicted by QED (k cos2(qL-qR)) is also predicted by Klyshko, on a more classical basis, because the light entering the right channel has a polarization of q=qL. (This is not the whole story, of course; see the papers by Klyshko [] and by Strekalov[] for more details.) But in reality, we could have done the same analysis, with the same result, by assuming that the biphoton was emitted by the right-hand side! This seems to beg the question: is

q=qL or is q=qR for the light emitted from the two-photon source? And it raises a larger question: how could this approach be generalized, to consider N-particle interactions and so on?

                After some analysis, we would propose that Klyshko’s picture of the physical situation may in fact be correct, with minor modification. Just as Feynman’s path analysis is ultimately a stochastic theory, and

classical thermodynamics is a stochastic theory, we would propose that a more refined model

of quantum measurement would still retain a stochastic aspect, even if we seek a completely realistic model. Thus we would propose that SOMETIMES q=qL and SOMETIMES q=qR in actuality – but

in the standard Bell experiments we cannot measure the relative probabilities. No matter how we assign

probabilities between these two cases, this picture does provide a “hidden-variables” model capable

of reproducing the predictions of QED for this class of experiment – but it violates the classical

ideas about time-forwards causality, because it allows q to depend on something in the future.

Our next task is to show how this kind of picture may be consistent with a more general model

of optical experiments.

                Let us begin by considering the QTS approach. The QTS approach to optical calculations has a long history,  rooted in research on quantum foundations. It is also a very general approach, equivalent to

traditional QED. In this approach, the state of the light at any time t is described by a (bosonic) wave function. The wave function propagates according to multiphoton Maxwell’s Laws in forwards time, until

it encounters a macroscopic object. Associated with each type of macroscopic object is a kind of classical, macroscopic probability distribution for what might happen to the light at that time; but then, after such

a stochastic “jump,” the light continues on its way. The classic Copenhagen view of measurement can be seen as a special case of such a “jump”  model.

                From an abstract viewpoint, QTS can be seen as a kind of hybrid systems model. The lower level of the model is the usual dynamical part of QED, which is formally time-symmetric. But the upper part is just a traditional time-forwards Markhov process model, governed by classical probability theory.

                We would propose consideration of two extensions to QTS, of a very fundamental nature.

                First, we propose that the upper level part of QTS be replaced by a more general classical model – the Markhov Random Field (MRF) model across space-time. The MRF framework includes the traditional Markhov process as a special case, but it also allows for more general possibilities. MRF models are very common in engineering (especially in signal processing) and in computational intelligence (especially

Bayesian networks). The usual Ising types of lattice model in physics [Zinn-Justin] are a special case of MRF, exhibiting all the features that are really important here.

                The key idea in MRF models is that we can compute the probability of any particular scenario

over space-time (in our case) by simply multiplying partial probability distributions across all nodes of the scenario, and then scaling according to a partition function. This is very similar to the usual Feynman path integral approach, except that it uses probabilities instead of probability amplitudes. For simple time-series models, MRF models can often be reduced to equivalent Markhov process models; however, for spatially extended systems, local MRF models are not reducible, in general, to local Markhov process models.

                Taking this approach, we can justify Klyshko’s picture of the Bell’s Theorem experiment by assuming that each polarizer has two probability distributions, in effect. In the usual QTS, the probability for the polarization q+ of the outgoing time-forwards light is just d(q+-qL), where qL is the orientation

of the polarizer. In the modified polarizer model, we would still assume the same for now, because the

power of time’s arrow over macroscopic objects is very great. But for all scenarios where a photon is

passed through the polarizer, we would multiply this by another partial probability distribution,

c1 cos2(q- - qL) + c2 h(q- - qL), where q- is the polarization of the incoming light, where c2>>c1 and where h is a function “close to a delta function.” (The overall scale of c1 and c2 may not matter, in these

scenarios, because of the subsequent scaling by the overall partition function.) In effect, this model states that polarizers “want” the light to match their own orientation, both in forwards propagation and in

backwards propagation, but are more able to make adjustments on the input side if they cannot get exactly what they want. In the basic Bell’s Theorem experiment (from c(|00>+|11>)),  the overall probability distribution for different scenarios would be overshadowed by the high probability of the scenario where

q=qL and q=qR both if that scenario fit basic circumstances here (i.e. if qL=qR); otherwise, it would be dominated by the two possibilities where q=qL and where q=qR, exactly as Klyshko describes.

In four-photon GHZ experiments, this would predict that three outgoing photons would match

the orientation of the corresponding polarizers, while the fourth would not, leading to a cosine-squared

joint counting rate (as predicted by ordinary QED). The function h is not yet distinguishable from a Dirac delta function, but perhaps someday it will be. In this analysis, we have assumed that the two-photon source produces a uniform distribution for q, at its node; this has the effect of making q determined, in practice, by the more selective partial probability distributions attached to the polarizers.

                It is interesting to consider what the partial probability distribution for the polarizer “means” when viewed in reverse time.

                This first modification to QTS admits a realistic picture of the physics, but does not lead to testable differences with QED in any case we have analyzed yet. But the second modification does appear testable.

                In the second modification, we would treat the propagation of light itself as an additional node(s)

in the scenario with a partial probability distribution attached, which should be multiplied by the other partial probability distributions when we calculate the overall probability of a scenario.

                Strictly speaking, our example with Bell’s Theorem experiments could be seen as

a crude example of this modification as well. We assumed that the polarization of the light

coming out from the two-photon source to the left channel, q, is the same as the polarization

of the light which is incoming later on to the left polarizer. But if we considered these two quantities to be

different variables, like “q” and “s”, we could say that the light propagation node

of the scenario is multiplying the overall probability by a factor of d(q-s). This does not really change

our calculations when polarization is the only relevant attribute of light.

                But our second modification to QTS would take this further, by applying it explicitly to

the position of a light-emission or light-absorption event. Crudely speaking, we would propose that the partial joint probability of a photon being emitted at point q- at time t- and absorbed at point q+ at time t+ would equal the square of the usual probability amplitude at q+ for light emitted from q-. (This could also be given a realistic interpretation, even in the multiphoton case, in the spirit of section 4 of quant-ph 0008036; however, that is not essential for our purposes here.)

                This may not sound like any change at all from traditional QED. However, within the MRF framework, it has major implications. When there is only one photon or biphoton present, it states that Maxwell’s Laws “find” a solution which reconciles q- and q+, even though these boundary conditions occur at different times. It yields a physical picture in which light absorption is often driven down to Angstrom-level localization, even for light with a wavelength of many nanometers, through a process which is the exact time-reversal of the ordinary processes of emission from an atom. And (perhaps because of the important effect of the partition function) it does appear to suggest testable differences from the usual time-forwards assumption.

                The most interesting possibility, so far as we can see right now, would be based on an extension

of the experiment by Kim and Shih [Kim/Shih] testing a theory of Popper.

In the original experiment, two photons were produced and positionally entangled; thus the position qA of photon A as it crossed plane A along the left channel was entangled with the position of photon B as it crossed plane B on the right channel. The planes could be adjusted, such that the arrival times of photons A and B on planes A and B would be simultaneous or delayed, as one chooses. When there was a 150 micron slit in a screen on plane A, and a counter well past that slit in the center of the A channel, then the interference pattern for light detected along a “line” of detectors to the right of plane B

was surprisingly narrow – much narrower than one would expect from a naive application of the uncertainty principle to a single photon system. When a mirror slit was inserted on plane B, also 150 microns wide, the interference pattern broadened; however, QED strongly suggests that it would shrink back again if the slit on plane B were widened to 150 microns plus two times the “error bar” in the positional entanglement.

That experiment, like the one reported here, did depend on two-photon joint counting rates, which appears to limit the possible use as a communications channel; however, by using regular femtosecond pulses in the pump signal entering the BBO, and measuring delayed coincidence rates between the pump and the B-channel detectors, one can eliminate the need to know the results of measurements along channel A. The low probabilities of photons going through the slits would make the counting rates here relatively low, but the goal here is to demonstrate some degree of channel capacity, not a fiber-optic trunk line! 

Even ordinary QED ala Copenhagen predicts a strange result when the counter along channel A is moved up to exactly meet and fill slit A along plane A. According to the Copenhagen model of measurement, the measurement of position qA acts as a “cookie cutter” (150 microns wide) on the wave function y(qA,qB), a wave function whose energy is all concentrated near the “diagonal” on the qA,qB plane,

where qA=qB. The result is that position also becomes localized for photon B, at plane B, and the interference pattern should be widened – a measurable impact of a change at slit A. This already appears to imply an unusual channel of information flow at high speed from channel A to channel B!

                Even in our realistic picture of the physics, this strange prediction of Copenhagen QED seems to make sense. For any solution of Maxwell’s Laws, meeting the boundary conditions of localization at qB and

at some detector to the right of qB, the positional entanglement (if exact) would allow that solution to be extended to a solution which meets the condition of localization at qA; this would allow the light to reach any detector which could have been reached if it had been emitted by an incandescent source at qB!

                But the big difference here comes when the time delay between planes A and B is adjusted. QED predicts that a bit could be transmitted (with noise) from plane A to plane B, very quickly, but that the

channel capacity would drop abruptly and discontinuously to zero exactly when the time gap goes to zero.

(This mirrors the discontinuous and abrupt nature of the Copenhagen measurement operators.) By contrast,

we would tend to expect that the channel capacity would vary in a continuous fashion, such that it would

be nonzero even for a lightly backwards-time situation. There is certainly no claim that this could be made useful in a practical, engineering application; however, such applications are not inconceivable, either,

particularly for computing applications where a few nanoseconds can sometimes seem like a long interval of time. It is far too early to know.

                We can easily imagine many different theoretical views of such experiments. We can easily imagine that other theorists will think of new views we have not even considered. However, when theory is doing its job properly, it helps open the door to a wide variety of possible models and testable predictions. The crucial task for now is to begin testing more of these alternatives, in order to ground the theory more concretely and completely in empirical reality.