Thank you very much for the paper, which I enjoyed.
However, instead of forgetting time, perhaps we should forget quantum gravity for a moment? For while time manifests itself throughout classical, relativistic, and quantum mechanical physics and our empirical reality, the graviton has never been seen.
Do we have to quantize gravity? Could it be that nature is as it is, and that God or the Prime Mover/Creator came up with both QM and GR, which seem to coexist perfectly well in their current forms? For instance, this laptop computer is powered by quantum phenonema, and too, it is held on my lap by gravity. Each one has a role, and each seems perfectly content to play it. Perhaps both mathematical predictions and the experimental search for gravitons has fallen short because gravitons do not exist. Now this is no reason to stop looking, but too, it is not exactly a reason to keep looking, and it is certainly not a reason to get rid of time, which does seem to exist, as my laptop's clock tells me I am running late, yet again. :)
A book you would enjoy is Freeman Dyson's THE SCIENTIST AS REBEL. On page 219 Freeman Dyson writes,
"(Brian) Greene takes it for granted, and here the great majority of physicists agree with him, that the division of physics into seperate theories for large and small objects is unacceptable. General relativity is based on the idea that space-time is a flexible structure pulled and pushed by material objects. Quantum mechanics is based on the idea that space-time is a rigid framework within which observations are made. Greene believes there is an urgent need to find a theory of quantum gravity that works for large and small objects alike. . . As a conservative, I do not agree that a division of physics into separate theories for large and small is unacceptable. I am happy with the situation in which we have lived for the last eighty years . . . The question I am asking is if there is conceivable way we could detect the existence of individual gravitons. I propose as an hypothesis that it is impossible in principle to observe the existence of individual gravitons." --Freeman Dyson, THE SCIENTIST AS REBEL, pp 219-220
And yet, it is possible to observe, contemplate, experience, and witness time in multiple manners and ways.
I vote that we keep time. :) All I know is that we never have enough of it.
My simple theory--Moving Dimensions Theory--views time as a phenomenon that naturally emerges because the fourth dimension is expanding relative to the three spatial dimenions. Change is fundamentally woven into the fabric of spacetime via dx4/dt = ic, which makes sense, because change is fundamentally woven into our everyday existence, empirical observations, and all branches of physics! Indeed--it would not be possible to make a measurement without change! A great thing about MDT is that it allows us to keep all of relativity while unfreezing time and liberating us from the block universe, which is yet a meaningful artefact that arises from certain interpretations of relativity. And who knows, perhaps MDT will tell us something about quantum time, which will tell us something about quantum gravity. For MDT also provides a framework for quantum entanglemnt and nonlocality, and thus it provides a *physical* model underlying qm's inherent nonlocal, probabilistic nature.
Think about MDT as a simple *physical* unification of relativity and QM--both entanglement and nonlocality can be accounted for via the same principle that ensures a photon does not age, no matter how far it travels. A photon's timelessness, implied by relativity, represents a nonlocality in time. Both quantum entanglement and the agelessness of a photon descend from a common principle: dx4/dt = ic. A photon is matter that "surfs" the fourth expanding dimension, and thus it remains in one place in it, while traveling through the three spatial dimensions at c. Perhaps this is MDT's simplest proof: The only way to remain stationary in the fourth dimension is to move at c through the three spatial dimensions: egro, the fourth dimension is expanding relative to the three spatial dimensions.
And a great thing about MDT is that it also presents a *physical* model for entropy, as briefly elaborated on in my paper:
MDT represents the kind of tehory we have not seen for awhile--a simple postulate and a simple equation that present a novel aspect of the universe--the fourth dimension is expanding relative to the three spatial dimension: dx4/dt=ic. This fundamental invariance underlies the invariance of the speed of light--both the constant velocity of c meausred by all inertial observers and, the constancy of c that is independent of the source. MDT also underlies relativity's two postulates, and all of relativity may be derived from its simple principle of a fourth expanding dimension.
In your conclusion your write, "It is possible to formulate classical mechanics in a way in which the time variable is treated on equal footings with the other physical variables, and not singled out as the special independent variable. I have argued that this is the natural formalism for describing general relativistic systems."
But when we look at Einstein's 1912 Manuscript, we see that time plays a different role from position. x1, x2, x3 represent the three spatial dimensions, which we generally use to demarcate position. And then along comes x4, which Einstein equates with ict. So as t progresses on our watches, x4 must progress. Time is very, very different from the three spatial dimensions! Perhaps it is not a dimension after all, but a parameter emerges because the fourth dimension is expanding relative to the three spatial dimensions, as suggested by x4=ict.
In your conclusion you also write, "The peculiar properties of the time variable are of thermodynamical origin, and can be captured by the thermal
But what underlies the "thermodynamical origin?"
MDT and dx4/dt=ic underlies time's thermodynamic arrow, and in my paper I account for and unify all of time's arrows and assymetries with MDT's simple postulate and equation. And in addition to this, all of relativity may be derived from MDT, while qm's entanglement and nonlocality are explained with a *physical* model, along with entropy.
Thanks for the paper Carlo!
As I write this, the DOW is down by 777! I have to run, so I apologize for any typos, as I only had time for one quick proofread. And once posted, these posts remain forever frozen in the past. :) There is no way to go back and change them--another proof that time travel into the past is impossible, which MDT agrees with.
Dr. E :)