I argue in this work http://www.sciforums.com/showthread...ure-unless-they-are-active-in-a-present-frame that there is no such thing as past or future, because all there ever exists is ''snapshots'' of present frames of time. If everything is stuck in the present, then how do we sense a time, why do we think it runs forwards with a specific ''flow'' and ''direction?'' Newtons flow of time doesn't exist in modern physics and there is no true direction of time in the cosmological arrow, there is only a measure of entropy, or change if you like. What we have is a sophisticated memory which records one instant of time to another. To derive that, we can say that the duration of consciousness experience a ''flux'' into the future is \(t_0 + \Delta t = t_2\) That is... \(t_0\) (the present time) added with a small dilation \(\Delta t\) takes the observer into the future frame \(t_2\).. Distinguishing \(t_2\) from \(t_1\) (the past) as it is impossible for asymptoptic local observers in quantum mechanics, but somehow not inside our brain. Fred Wolf asked a question, is the past complimentary to the future? If it is, then we might be able to model the mind into physics somehow by recognizing there to be some ''special line'' which separates the past from the future, even if it is an illusion, can be modeled as the complimentary conjugate \(t_0 - \Delta t = t_1\) We can't reverse time, but the logic of the math says that a dilation taken away from the present moment is hypothetically a ''frame back'' in the past. This won't have drastic implications for physics, unless physics is able to prove that the observer somehow is unique in the sense that consciousness is required for an understanding of time itself and what it actually means. The best understanding of time, is the psychological arrow which is regulated by the brain, these circadian rhythms actually account for our experiencing any kind of time, so this is an indication that a complex mind, one that can record vast amounts of information has to have a sophisticated long-scale memory which gives us a broader experience of these collections of \(t\) as we regulate it in a certain ensemble. This ensemble probably isn't a mistake, it's probably the only way the mind can censor out static reality and bring about the sense of changes around us. Perhaps, this could yet let the observer play a new role, an interesting role at the very least as a sub-system in the universe. Wolf, (Parallel Universes; 1985) Note: factoring the past and future conjugates leads to the commutative ring \(t^2 - \Delta t^2\).

I can maybe hearing some people saying ''how does he propose to make such a leap from the mind into quantum mechanics?'' Not only has the problem got to do with time, but it has a problem because it admits a symmetry to time, which is akin to Minkowski spacetime. Perhaps, it came to me, we could be working with the wrong model, what if to experience time, you first need to violate physics? A 68, 1, 012316 (2003). 200. [Albert-Aharonov-D'Amato 85]: D. Z. Albert,. Y. Aharonov, & S. D'Amato, “Curious new statistical prediction of quantum mechanics.'' In their work, they show that it is possible by violating the uncertainty principle is a measurement on a system is made in the past and then again in the future, if you can recollect this information in the present, it doesn't violate physics because the two measurements have been made at different times, one to make predictions about it's location in space, another in the future to determine it's trajectory. Perhaps the mind works in a similar way: perhaps the timekeeping method of the brain, measures the past and future in complimentary ways suitable in D. Z. Albert,. Y. Aharonov, & S. D'Amato (ADD's) model. It brings about a good question for classical physics as well, in how the future effects the past. It could also explain why sometimes we can never remember everything, because the future and past have to commute in such a way the information can be processed in the present frame. Some might say this has a striking resemblance to the Transactional Interpretation. http://quantmag.ppole.ru/physmag/bibliography/A1.html

A measurement is taken on some observable \(\mathcal{O}\) performed on a system \(S\) separated by an actual preperation probability \(|a><a|\) at time \(t_1\) and the actual observation with a property \(|b><b|\) at time \(t_2\), we therefore have no measurement performed between \(t_1\) or \(t_2\), you will find the observable \(\mathcal{O}\) would have a probability of \(P(\frac{q_j}{(a,b)})\). This is a pre and post-selected system. The uncertainty principle is very much like trying to obtain the information of a system; trying to get an exact value of the position and trajectory of a system has recently sparked some new interest concerning new statistics http://www.sciencedaily.com/releases/2012/09/120907125154.htm

I found a little gem of a quote, which resembles the cognition of our ability to provide the recording of the history; time travel isn't possible in this conjecture, instead time travel happens in the mind H. P. Lovecraft discussed this idea of time travel in a 1930 letter to Clark Ashton Smith, where he wrote:[16] Your idea for a time-voyaging machine is ideal—for in spite of Wells, no really satisfactory thing of this sort has ever been written. The weakness of most tales with this theme is they do not provide for the recording, in history, of those inexplicable events in the past which were caused by the backward time-voyagings of persons of the present and future. It must be remembered that if a man of 1930 travels back to B.C. 400, the strange phenomenon of his appearance actually occurred in B.C. 400, and must have excited notice wherever it took place. Of course, the way to get around this is to have the voyager conceal himself when he reaches the past, conscious of what an abnormality he must seem. Or rather, he ought simply to conceal his identity—hiding the evidences of his "futurity" and mingling with the ancients as best he can on their own plane. It would be excellent to have him know to some extent of his past appearance before making the voyage. Let him, for example, encounter some private document of the past in which a record of the advent of a mysterious stranger—unmistakably himself—is made. This might be the provocation for his voyage—that is, the conscious provocation.

Here is something, Reiku once wrote: some of it is a bit dated, but some nice points on closed curves, it explains it in a simple sort of way. In physics, when we consider a particle and its past, present and future path throughout the universe, we call its definite path a ‘’worldline.’’ A particle will always try to move in straight lines throughout spacetime, but because space and time are curved into each other, most of the time, they follow curved paths through space. This is what we mean by a warped space, or distorted spacetime. We find that these distortions are in fact just gravity, or curved spacetime. And gravity is the presence of matter itself. Even light cannot escape the wrath of gravity at very strong levels, but usually, a tiny photon traveling in empty space will almost definitely travel in straight lines. But there really isn’t just one straight line, or worldline for any particle. We find that according to Feynman’s Sum Over Histories, a particle actually has every possible path to its disposal – these path’s are of both times past and times to come. We find that these paths have themselves a statistical element about them and will variably shape how a particle will end up in any state given upon measurement. Take a photon traveling from the past: It will take every known possible path, even those improbable paths through a black hole (but as you can imagine, the statistics for this are so vanishingly small, we can nearly neglect them, but Hawking shows that it is possible for allowing a particle to travel at superluminal speeds using the uncertainty principle), and upon arrival at Earth, we can measure the photon, and all the paths its could have taken, according to the wave function, suddenly collapses into a single probability! For Feynman’s Sum Over History to apply to physics, one must use imaginary time, rather than the concept of real time. Imaginary time is the same thing as real space, whereas real time is the same thing as imaginary space. The two concepts are pivotal to understanding how we contemplate different ways to look at our universe at large, and even at small scales. Granted, the concepts themselves are purely mathematical, but they play an enormous part in relativity and quantum mechanics. You need to first gather up all the possible path a particle can take, bundle them together so-to-say, and then we need to measure those statistics against real time, and the result is the real conditions of the particles history; but even those results have a slight statistical aura about them. In the case of the universe at large and gravity, Feynman would need to have analyzed all possible histories of a curved spacetime, and this at large affects everything that has a worldline in this universe. There would indeed be a finite number of possible outcomes, but one would need to chose which outcome best fits this universe today. Hawking reminds us, that if this is indeed the case, the class of curved spacetime that determines the universe today (including those spaces and times which are blown into unimaginable proportions, or singularities), the probabilities of such spaces cannot be determined by the theory. However, he says it is possible if we calculate them in some arbitrary way. Dr. Hawking is very cryptic this way, but what he means is that science cannot predict any history for the universe if there is a singular past. So any attempt to learn how a universe with a singularity would result, is really a disaster for science. Now, since this study is about time and space at large, let’s consider CTC’s or ‘’Closed-Timelike-Curves.’’ This is a worldline describing a physical system which is ‘’closed’’. This means something physical in fact returns to original starting point. We call such movements ‘’sinusoidal’’. The idea of CTC’s was in fact developed by Willem Jacob van Stockum in 1937 and later by the infamous Kurt Godel in 1949. There is indeed a lot of controversy over their existence, but if they do, it could revolutionize relativity including our ability to create machines capable of a global causal violation; in other words, a path that twists in space and moves through time. Worldlines and of course Feynman’s Sum Over Histories is best described in terms of ‘’light cones’’, which is really a more specified term that is timelike in nature. It will probably be more recognized than the last two concepts. Light cones describe every possible future of a physical object in spacetime, given a current measurement during the present time. This can seem a bit strange, because not only does one deflate all possibilities of the past events to a single value upon measurement (the collapse of the wave function), but one can now calculate all possible path’s in the future in real time. Because of the standard arrows of time, (there is something like several known, such as the Cosmological, Radiative and even Psychological Arrows), the light cones are always depicted to move forward in time. As explained earlier however, a particle doesn’t move constantly in a straight line. Therego it must also tilt into space, as it does through time in curved spacetime, so it is best to refer to these cones as timespace, or spacetime, depending on how one wished to see it. Because of this, one can have in special conditions, a particle which experiences a timespace and spacetime that is so heavily curved, it can return to place it began. Simple basic rotations through space and through time, which are conveniently called, ‘’closed-timelike-curves’’, so just think of a loop that twists in space and moves through time back into its original starting point. Frank J. Tipler, Prof. of mathematics and physics at Tulane University in New Orleans, developed an ingenious idea involving such closed-timelike-curves. I have read his article… it’s a good read. He explains that classical relativity does in fact predict pathological behavior. The exact nature of the pathology, or, CTC’s, are however very debatable, since the predictive nature of relativity has itself many outcomes. His design is quite old now, but it is still a probability in physics creation of time machines today. His design is to create a huge rapidly rotating cylinder (possibly in space – I assume), and the spacetime around the cylinder will be warped to such an extent, that even time itself becomes sinusoidally warped so that instead of flowing in the correct direction… that is forwards, it in fact varies in an oscillating manner. Of course, one might think that such a spacetime would rip a spacetime traveler apart, but we aren’t talking about black holes here. If this machine, entered carefully, could avoid being turned into spaghetti and experience a dilated time frame. Perhaps this is the time machine of the future?

I have been discussing a closed commutative ring when you factor the equations in the OP. It might indicate there is no past, only a circular ring within the present which interloops the future not the past. The future can be sending messages back to the part in a similar commutative ring which could even explain why a present exists at all, because relative to us, we experience the future as unfolding events made in present time, we can do this with the past if we can understand how future retrocausality effects the present and how the present is interpreted as the future of the past, meaning our present frame is formed in the future present, by sending signals back to early stages of the universe.

The sentence above is a run on sentence and as such completely negates any point you were trying to make.