Prof. Aharonov and Dr. Tollaksen recently published an article on Time-symmetric Quantum Mechanics. This is a logical physical theory, that treats past and future on an equal footing.
This theory can lead us to better descriptions of reality and maybe to unexpected conclusions. Also recently Prof. Paul Davies published a note in the British magazine, The New Scientist, implying that Aharonov et al.'s theory, makes the past dependent on the future, and maybe explaining why the Universe we inhabit is so bio-friendly.
My interpretation of what these scientists have written is that we wish to stay around, so the Universe is being shaped by us.
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5 comments:
Yakir Aharonov and Jeff Tollaksen have each been prolific in generating papers on TSQM over the last several years. With regards to your post, please note that TSQM inherently renders the "unactualized" past dependent on the future. Please also note that Jeff Tollaksen's 2001 thesis included a speculation on destiny states. This topic is also discussed by Yakir Aharonov and Jeff Tollaksen in their paper "New Insights on Time-Symmetry in Quantum Mechanics" [http://arxiv.org/abs/0706.1232
The following reflects my effort to make TSQM "relevant" to some of the paradoxes that continue to perplex quantum mechanics. It was written to introduce TSQM in the context of the EPR Paradox to less technical audiences and may be one of the "unexpected conclusions" you predicted might arise from TSQM in your post. Your comments on the following would be valued
The EPR Paradox & Time Symmetric Quantum Mechanics
EPR paradox was "a thought experiment" devised by Einstein, Podolsky and Rosen "which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory." (See http://en.wikipedia.org/wiki/EPR_paradox and http://en.wikipedia.org/wiki/Incompleteness_of_quantum_physics)
Although the original EPR thought experiment involved position and momentum measurements, David Bohm reformulated the EPR paradox into a more practical experiment utilizing spin or polarization measurements. Bohm's variant of the EPR paradox is described at: http://en.wikipedia.org/wiki/EPR_paradox#Description_of_the_paradox
Visualize if you will two particles that are quantum entangled moving apart in opposite directions. (See also: http://en.wikipedia.org/wiki/Quantum_entanglement
and http://en.wikipedia.org/wiki/Brief_explanation_of_entanglement_in_terms_of_photons)
At some distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. If Bob were then to measure the spin of the second particle, he will find that its spin is in the down direction. As often as Alice and Bob wish to repeat this experiment, Bob will find that the spin of his particle is always opposite to that found by Alice. How can this be?
Stranger still, it does not matter how far apart Alice and Bob may be from each other or how brief the time-lag between Alice's experiment and Bob's – the results of Alice's experiment always appears to affect Bob's particle instantaneously. Again, how can this be?
"The EPR paradox is a paradox in the following sense: if one takes quantum mechanics and adds some seemingly reasonable conditions (referred to as locality, realism, counter factual definiteness, and completeness), then one obtains a contradiction." … "Either
(1) The result of a measurement performed on one part A (by Alice) of a quantum system has a non-local effect on the physical reality of another distant part B, in the sense that quantum mechanics can predict outcomes of some measurements carried out at B (by Bob); or...
(2) Quantum mechanics is incomplete in the sense that some element of physical reality corresponding to B cannot be accounted for by quantum mechanics (that is, some extra variable is needed to account for it.)"
"The principle of locality states that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems to be a consequence of special relativity, which states that information can never be transmitted faster than the speed of light without violating causality. It is generally believed that any theory which violates causality would also be internally inconsistent, and thus deeply unsatisfactory." …
"In 1964, John Bell showed that the predictions of quantum mechanics in the EPR thought experiment are actually slightly different from the predictions of a very broad class of hidden variable theories. Roughly speaking, quantum mechanics predicts much stronger statistical correlations between the measurement results performed on different axes than the hidden variable theories. These differences, expressed using inequality relations known as "Bell's inequalities", are in principle experimentally detectable." (See also http://en.wikipedia.org/wiki/Bell%27s_theorem)
In essence, Bell's inequality follows from the assumption that local results exist, whether or not anyone measures them.
Experiments have now confirmed that "measurements performed on spatially separated parts of a quantum system have an instantaneous influence on one another. This effect is now known as "nonlocal behavior" (or colloquially as "quantum weirdness" or "spooky action at a distance")."
see:
http://en.wikipedia.org/wiki/Nonlocality
and
http://en.wikipedia.org/wiki/Quantum_weirdness
"The EPR paradox arises generically for any entangled state - any state of macroscopically separated systems that is not a product of states of each system. Any entangled state yields quantum correlations that violate a generalization of Bell's inequality. The EPR claim assumes that Bob and Alice would measure independent physical variables. Einstein, Podolsky and Rosen never anticipated that this reasonable assumption would prove inconsistent with experiment and that we cannot in this context isolate systems in an entangled state from each other."
"Most physicists today believe that quantum mechanics is correct, and that the EPR paradox is only a "paradox" because classical intuitions do not correspond to physical reality. How EPR is interpreted regarding locality depends on the interpretation of quantum mechanics one uses. … (I would recommend that the Wikipedia article on the interpretation of quantum mechanics be reviewed before the reader continues.)
See
http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics
You will note that none of these interpretations provides an intuitively satisfactory explanation of how the results of Alice's experiment instantaneously determines the state of Bob's particle. Ironically, according to Yakir Aharonov and Daniel Rohrlich in their book: Quantum Paradoxes: Quantum Theory for the Perplexed; "the claim that quantum theory is incomplete may well be correct, though not in the EPR sense. Quantum theory does not explain how we go from probability to observation, from possibility to actuality, as a complete theory would.
According to Aharonov and Rohrlich "unitary evolution cannot turn possible results into actual results. Aware of this paradox, von Neumann postulated collapse. But von Neumann's collapse is at best an effective model; it does not resolve the paradox. Attempts to resolve the paradox fall into three classes, corresponding to three statements:
i) Quantum mechanics is incomplete and there is collapse.
ii) Quantum mechanics is incomplete and there is no collapse.
iii) Quantum mechanics is complete."
von Neumann's collapse theory may be seen as consistent with statement i). However, according to Aharonov and Rohrlich, "so far there is no evidence for collapse. To falsify collapse, on the other hand, we must verify that no superposition ever collapses. For example, we must show that Schrödinger's cat remains in an entangled state - and in practice, we have no hope of showing that the state remains entangled."
Bohm's and other hidden variable theories may be seen to be consistent with statement ii).
In one sense, time symmetric quantum mechanics (TSQM) may be seen as a hidden variable theory that non-local in time, but in another sense (which I prefer) TSQM may be seen to be consistent with iii).
Again please visualize two particles that are quantum entangled moving apart in opposite directions. At some distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. In traveling from the point of origin to Alice, we may understand the particle's wave function to have, in a probabilistic sense, taken all possible paths and to possess all possible states consistent with the initial boundary condition of the system at the origin. With TSQM we must now visualize a time-reversed wave function which proceeds backwards in time from the occurrence of Alice's experiment to the time and point of origin for Alice's particle. This backward in time wave function would also, in a probabilistic sense, take all possible paths and possess all possible states consistent with three constraints: (i) the time evolution of the wave function is backward in time; (ii) the time-reversed wave function is bounded by the initial state of the system at the origin and (iii) the time-reversed wave function is also bounded by the spin information arising from Alice's experiment. It should be noted at this point that due to conservation of momentum the direction of spin manifest in Alice's time-reversed wave function will be opposite to the spin direction that Alice measured; and identical to the spin Bob will find when his measurement occurs. In any event, Alice's time-reversed wave function may be understood to carry the spin information arising from Alice's experiment to the time and location of origin for the entangled particles. Here, Alice's time reversed wave function may be understood to "bounce" forward in time in a state that is entangled with Bob's particle. Please note that weak measurements of Bob's and Alice's particles immediately prior to the occurrence of their respective ideal measurements will show that each particle has remained entangled, but do not necessarily show whether that entanglement is spatially remote or proximate.
To coin a new principle of physics, determinacy will trump indeterminacy at the time and place a von Neumann (e.g. ideal) measurement occurs, but not before. Accordingly, when Bob conducts his experiment, he will always find his particle to manifest the same spin orientation as that possessed by Alice's time-reversed wave function, which will always be opposite to the spin orientation that Alice measured.
I believe one implication of TSQM is to reintroduce a classic-like causality and locality to quantum mechanics that may have very broad implications as was indicated in your original post.
Best wishes,
Jon Trevathan
Dear Mr. Trevathan, first an apology for not reading your post before.
I will comment on your thoughtful consideration of my post in a later post, for now suffice it to say that I believe we'll get this thing clarified and will thus find important ways to advance physics.
Thanks again.
Eduardo Cantoral
The ideas I explored in my earlier post have been substantially expanded in the attached:
http://www.mediafire.com/download.php?yzvhgm20tmw
Your critique would be valued.
Best wishes,
Jon Trevathan
I will take a look, thank you.
I'm sorry I waited this long. I did not find your file. Send me the url where it is now.
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