Hello Toru,
Thanks for the wonderful paper!
I love some of the concepts you are getting at.
Indeed, the fourth dimension itself is nonlocal!
Consider a photon emitted from a source. Quantum mechanics describes the photon's propagation as a spherically-symmetric wavefront of probability expanding at c.
Relativity tells us that the photon does not age--it stays at the same place in the fourth dimension.
Ergo the fourth dimension is nonlocal--it is expanding relative to the three spatial dimensions at c. Ergo the spherically-symmetric wavefront of probability expanding at c, which describes the photon's propagation, yet represents a locality in the fourth dimension.
This fits perfectly with Einstein's 1912 paper, where he wrote x4 = ict, or dx4/dt = ic. As you can see, the fourth dimension is expanding relative to the three spatial dimensions at the rate of c.
Now, in light of this (no pun intended), is it no wonder that two intially-interacting photons remain entangled? For even though they propagate in opposite directions, they yet remain ageless, and in the same place in the fourth expanding dimension!
And too, the photons remain in the same place in time, although time is an emergent parameter, that we can measure on watches and clocks, that arises because the fourth dimension is expanding relative to the three spatial dimensions, carrying matter in the fourth dimension at c, which manifests itself as photons. Hence you can see why E=mc^2--energy is but matter caught upon the fourth expanding dimension.
I expound on all this in my paper:
http://fqxi.org/community/forum/topic/238
Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken
Now the amazing thing about the fourth expanding dimension is that it actually distributes locality! Finally we have a *physical* model for nonlocality, which turns out to be the same physical model underlying all of relativity and entropy--underlying time and its arrows, while weaving change into the fundamental fabric of spacetime, unfreezing time and liberating us from teh block universe! O happy day! Moving Dimensions Theory, which postulates that the fourth dimension is expanding relative to the three spatial dimension at c, provides a most powerful *physical* model underlying relativity, quantum mechanics, entropy, entanglement, nonlocality, and time and all its arrows across all realms.
Note how nonlocal entanglement only occurs for two objects that where intially interacting. So it is that all nonlocality must have a local origin. And the expansion of the fourth dimension, which begins as a single point but then distributes locality in a spherically-symmetric manner in our 3D at the rate of c, accounts for this--think Huygens' Principle, which underlies quantum mechanical (Feynman's many paths) and classical wave behavior. And suddenly we see that MDT also offers a *physical* model behind the *why* of Huygens' principle, as well as entropy, and time and all its arrows and assymetries! And as nonlocality walks hand-in-hand with quantum mechanics' probability, we have a *physical* raison d'etre for qm's probabilistic nature!
Now you write a lot about the "Time axis" in your paper, but you need to keep in mind that the time axis is a human construct, and that we do not live in a block universe wherein time is frozen. the block universe is also a human construct, which Godel had problems with. Also, Einsetin never said that time is the fourth dimension in his 1912 paper, but rather he wrote x4=ict, and t and ict are very different things. It is amazing how many physicists have thrown away the ic in front of the t, and gotten tenure while conceiving of time machines they never build, and wormholes they never see, not to mention multiverses and parrallel universes and tiny little vibrating strings in their block universe wherdin funding is an established part of the future which has already happened, but you get the point. All the pop-sci books and texts always have those pictures of light cones, but what they forget is that photons do not travel in straight lines, but rather quantum mechanics tells us that photons travel as expanding spherical wavefronts of probality in our 3D. And in doing so, they maintain a locality in the fourth expanding dimension.
Those who argue with MDT's postulate that the fourth dimension ise expanding relative to the three spatial dimensions are actually arguing with the photon. And yet, the photons keep right on travleing at c--billions upon billions upon billions of them--every second, as they surf the fourth expanding dimension, while yet retaining a locality in time an dthe fourth expanding dimension. I would not be surprised if photons start protesting all the tenured elite who are trying to freeze them and emprison them in their block universe, wherein time and progress in theoretical physics must remain frozen.
Now of course we can forgive Einstein for not noting all this in his 1912 paper, as he never quite accepted quantum mechanics' reality, but for all those of us who passed undergrad and grad quantum, and for all of us who use computers which were built upon nonlocality's reality and wave/particle duality--it is time for all of us to admit that the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, and that this fundamental universal invariant gives rise to the time we measure on our watches, which we we also enjoy designating as an axis in diagrams when writing coffee-table physics books that have frozen time so as to write chapter after chapter about time travel.
Well, thanks for the paper!
My heart lept when I saw the title: Stochastic Time and Temporal Non-locality, and I enjoyed reading it!
Would be curious to know your thoughts regarding MDT.
Best,
Dr. E (The Real McCoy)