Hi Dan, Thanks for asking. Very few things are my field, and none of these are, but I, like you, think they are indeed fascinating. John Cramer is a U of WA physicist who proposed TI, the transactional interpretation of Quantum Mechanics as an alternative to the wave-collapse Copenhagen interpretation. TI claims to be objective and explicitly non-local. From Cramer's 1986 paper, which can be found at http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html, "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. ... 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 F1has 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." And so forth. The idea is that there is a transaction between the emitter and the absorber and that the transaction is "negotiated" "at the instant" (whatever that means given that we have waves traveling backward in time) it is executed. Cramer uses TI when teaching quantum mechanics. In "The Plane of the Present and the New Transactional Paradigm of Time", he claims that TI doesn't imply no free will, but it is hard for me to see how e.g. forward and retarded waves communicating over the time span from the formation of the CMB to today leaves room for non-determinism. http://arxiv.org/abs/quant-ph/0507089 So that's Cramer and Wheeler-Feynman. John Conway and Simon Kochen wrote about their theorem that can be phrased loosely as "If we have free will, then so do electrons". They argue that quantum mechanics has done away with the deterministic universe forever, but that whatever we humans have in us that we can define as free will is also an attribute of fundamental particles. The Free Will Theorem http://arxiv.org/abs/quant-ph/0604079 "On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications." The Strong Free Will Theorem http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will Can't copy/paste here so loosely quoted: If the experimenter is free to choose the orientation of his aparatus, the particle's response (more precisely, the universe's response near the particle's location) is not determined by the entire previous history of the universe. Reitdijk-Putnam-Penrose started with an argument from Reitdijk and Putnam, based upon special relativity, and extended by Penrose in what is called the Andromeda Paradox. From http://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument "If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966)[1] and Putnam (1967).[2] It is sometimes called the Rietdijk–Putnam–Penrose argument.[3] Roger Penrose[4] advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:[5] people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already "fixed"?" After reading about the Andromeda Paradox, I played a bit with the relevant special relativity equation, the Lorentz transformation for time, with which synchronized clocks, if in relative motion to you, cease to be synchronized. Distance, i.e. the amount of space between event A and event B, is a factor in the equation, so the greater the spatial separation, the greater the time dilation. If I recall correctly, t' = (t-vx/c^2)/sqrt(1-v^2/c^2) The distance to Andromeda is about 2.5 x 10^6 light years or about 2.4 x 10^22 meters. Walking speed is about 1.4 m/s. If one person is standing and the other is walking by at a time when Andromeda is directly on the horizon, I calculate a difference of around 373850 seconds, or 4.3 days, between the two people in the time of simultaneity. It would be 8.6 days difference if each were walking past one another. Then, they simply could turn and each walk the other way, past one another once again, and their times of simultaneity would have switched! It's difficult for me to see how special relativity, simultaneity and a non-deterministic universe (and hence free will as most people define it) all survive with their common meanings, given the math. It gets worse, for me. The observable universe is about 4.4 x 10^26 meters away on all sides. The space shuttle travels about 1 x 10^11 m/s. Even at 1 x 10^8 m/s, the equation gives me a difference of around 5 x 10^17 seconds. Not bad for a universe that's 1.4 x 10^17 seconds old! I have no idea what it means to have a time of simultaneity between two observable objects that implies that one of those times is before the Big Bang. (Yes, I know about the Hubble Flow and how we can have a 46 million light-year distance between us and a visible object in only 14 billion years or so. I don't know how the increased distances due to the Hubble Flow play into special relativity.) Well, enough, Dan, about all that. The key point relevant to your inquiry is that the Andromeda Paradox is another nail helping to pin down the evidence I see against free will as I knew it as a child. And regarding the Bohm thing that still stirs .... that was just me, saying something like "Bohm is rolling over in his grave" except in a good way, i.e. Bohm's ideas still have power. I apologize for making you think there was something even more interesting to learn about ... But I'm glad you asked for explanations, thanks! Jeff On Mon, Jun 30, 2014 at 5:22 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Jeff, this sounds ultra-interesting, but my lack of background prevents me from understanding what you've written.
Can you please include some more detail? Like, what are the Cramer thing, the Wheeler-Feynman thing, the Conway-Kochen thing, the Rietdijk–Putnam–Penrose thing, and the Bohm thing that "still stirs" ?
Thanks,
Dan
On Jun 30, 2014, at 2:12 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
I hope to better understand the curious case of the photon. It has no frame of reference and, were it conscious, would perceive itself to be emitted and absorbed simultaneously, i.e. no time passing between the events. With zero time between emission and absorption, whimsy allows me to think of emitter and absorber as in some sense touching, albeit one is an ancient star and the other a cone in my living eye. Zero time means zero distance, in my book, although applying that rule to the no-frame-of-reference photon is probably a category error. Cramer's transactional interpretation, inspired by Wheeler-Feynman time-symmetric theory, has both forward and backward-in-time waves between emitter and absorber, agreeing upon the transaction before (as? timey-wimey words ...) it takes place, which leaves precious little room for the free will electrons have if you or I do, John Conway and Simon Kocken say, and leaving no room at all for deciding whether or not to slide a detector into a photon's path after the photon has been emitted. Emitters, detectors and photons have united, and their agreements will be kept! At least, in this regime, Rietdijk–Putnam–Penrose can be resolved in the affirmative.
And now pilot waves. Bohm still stirs. Rod Sutherland combines pilot waves and the transactional interpretation in "Causally Symmetric Bohm Model", http://arxiv.org/pdf/quant-ph/0601095v2.pdf.
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