Kerrie, sorry, if you see it as offtopic, maybe you can split the thread, but I'd really like to continue discussion in this direction.
Originally posted by Eh
Yes. But I don't know of any attempts at quantum gravity that treat time as anything but an evolving set of relations. Maybe you're thinking of discrete space and time, but in such case you've merely got discrete events, and still no independent existence for time.
It occurred to me, that when speaking of space, we first define 3D infinite continuum of axes, and then define measures of distance along them. Then we deal with set of relations between those measures of distance, that are necessarily finite (>0). But with time, we deal only with relations of measures, without speaking about what we really measure. But somehow, we DO measure something finite. Because we can compare it.
Yes, I am thinking about discrete space and time. And I'm thinking about what is meaning of a discrete event without independant concept of time. dX/dT, if dT is 0 this leads to infinite (or fault). For discrete change, there must be finite time.
As I said, "change" seems to be a property of the field (or loops, whatever you want to call fundemental). But the loops or lines do not need it for definition, even if they are inseperable in the real world.
Look, loops or lines do not need time for definition, IF they do not posess property of "change". Time as concept behind change is what makes them applicable to real world. In any formula, you introduce time when you use "for n=1..X evaluate F(n)"
I'm not sure I follow you. How is defining time as change in geometry circular?
We say dX/dT=1. When asked, what is T, we answer, it is change dT=dX. When asked how fast X changes, we say at rate of dX/dT. When asked what is X, we easily say its distance, energy, etc. When asked what is T, we don't have answer, only fud. We measure rate of change dX in terms of dX. Its always 1, ie cannot change.
The whole point is that GR leaves independent time (and space) redundant. Much like space, I have never seen a logical reason why time must have any separate existence, so such notions might as well be discarded when we've got a working model. In this case, I haven't seen any independent time defined at all.
Yes, and that's precisely why I wanted to leave GR alone for awhile. GR does not answer why c is finite and constant. It only postulates it and then uses as a glue to fit all timeless geometry together.
I think I see where the confusion is coming from. This is the same problem you'll find as with continuous space. With continuous time, it is assumed any given event is itself made of a collection of smaller events. Much like how you can always divide any volume into smaller volumes infinitely, you can also break any arbitrary event into a collection of smaller events.
I know. I'm not about divisibility. With continuous space, you don't attribute meaning of distance to 0. You can have meaningful distance only if it is above zero. And when it is above zero, you can always divide it into smaller pieces infintely. And I'm about precisely that. I don't care how divisible time is, but only about the fact that to be divisible there has to be something nonzero first. If you want to tell me that uniform continuous change in anything is measure of time, then you have to admit that variations of change rate are basically variations of timerate and any sinusoidal vibration is variation of time. Then ask what is justification to use uniform timeflow to measure varying changes? Then all changes must be uniform and equal.
Maybe it would help if a theory of discrete spacetime is found. In such a case, I suppose you could have a smallest unit of time possible. In such a case, all other events would be a large but finite collection of these primordial events. I don't think it would make sense to ask about what it fundementally means for "how long" a smallest amount of time lasts for, since duration would be entirely defined by the set of discrete events. In other words, the shortest unit of time would be just that - and could not be broken down into smaller times. Is that at least what you had in mind?
Yes, that's exactly the direction I had in mind! But, I have to makes few corrections. It is true that it makes no sense to ask for the
value of the duration of primordial time unit. It is irrelevant. We are beings dependant on it and can only measure relative durations of events. For that we need the primordial unit to be whatever but it must be finite. Only then can we compare relative rates of otherwise in all sense identical chains of events. Only then can different by a finite measure relative timeflow rates exist.
Now, I go further and speculate that this primordial time unit is NOT constant, but subject to change locally itself. I even dare to think that it is in fact the ONLY thing that has capacity to change. I want you to ponder that if dX were const in dX/dT=1, then variable dT is equivalent to uniform time and variable dX, or change. All our models rely on uniform flow of time locally. I undermine this assumption and think about fluctuating local primordial timeflow that only averages out due to formations of more complex structures that have other levels of interactions.
Imo it is impossible to detect directly fluctuations of timeunit, as it is the very unit that defines rates of events that try to measure it. Therefore, every attempt to measure it would produce constant and uniform timeflow. But, its fluctuations would manifest as uncertainty in spatial properties and energy.
Further, think about spatial distances in real world. The only way to sense them is to travel them (light). Distance is a measure of traveltime. Travel is a series of interactions, chain of changes. If chain of changes occurs at variable rate, then velocity varies. But, if the only means to measure rate is change, there is no means to detect variations in velocity either (const c). The only means to notice anything is by comparing different chains of events (spatial directions) that might produce different traveltimes (space curvature).
Imagine that rate of change was infinite. Then any finite distance would be covered by infinite velocity. But as we can't know rate of change, we take as a measure something universal, c. Then, if rate of change were infinite, any distance would be zero. Therefore, finite primordial time unit also defines meaning for spatial distance by setting limit to change rate that manifests as finite velocity of c.
Now, conglomerate of such primordial time units 'upon' which all events occur forms inertial frame, where all laws of physics hold equally with any other frame, independant of value of their average primordial timeunits. Thus, differing frames can have differing average timeflow. But when chain of changes crosses the frames, velocity of it varies, but each frame measures it at same value (c is same for any inertial frame)
Further, primordial time unit gives obvious explanation to inertia as a limit to a rate of change. From there, mass is effectively measure of that inability, or relative value of primordial time unit. From this follows that change in primordial time unit itself is basically energic interaction. Value of primordial time unit is effectively energy.
I believe that same sort of relations are encoded into claim that energy "can change" and somehow curve spacetime, but there stress is put onto other things that make it difficult to explain things like c, inertia, energy while here they fall out naturally. The only difference is focus, allowing time independant existence.
Vacuum is then sea of nearly equal primordial units with unspecified value. Vacuum interactions produce no effects. But vacuum is subject to change by complex objects whose time rate differs. Matter forms concentric fields of time units where center is measure of highest mass/energy and slowest change rate. Matter evaporates into the vacuum, much like sun evaporates radiation, creating extending fields of varying timeflow, which is basically curvature of empty space.
Single change step through primordial time units with differing values is equivalent to different spatial extents. spherical time field is "bigger inside than outside". Or geometry of space isn't any given either, its also completely determined by timeflow in it. In extreme even that far that nice uniform 3D is merely illusion.
imho quite some stuff to work with.
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