topology of time

[AntonioLao]

Time is a measureable physical quantity. Although the physics of the universe is not known exactly at time zero, the physics at time greater than one millionth of one pico pico picoseconds is equivalent to the quantum mechanics of Planck domain. This domain is only calculated theoretically. Experimentally, there is no accommodation of Planck energy although at the region of the Planck length superstring theories begin to make sense. However, one thing is certain and that is time always flow in one direction. This is the direction of increasing entropy.

It can be conjectured that direction is the same as motion along certain topologies. Since time only moves in one direction, its topology is the same in the past, in the present, and in the future. This topology of time can be changed if and only if the direction of time is changed, say, from a future direction changed into a past direction. There is no physics that can assert the changing direction of time, not even Einstein’s theory of special relativity. At best, special relativity can only assert that time can be slowed down; to the point that time can stop moving in any direction. Wherever and whenever time stops then the entropy of an isolated system stays constant. However, negative entropy indicates that time is flowing in the opposite direction. The only one dimensional topology that accommodates both positive and negative entropy is the Hopf link, whose two dimensional extension is the Möbius strip, and three dimensional extensions is the Klein bottle.

[Bogie]

Time is a measurable physical quantity.

This is strictly theory and is a integral part of general relativity and spacetime geometry. "Time simply passes" is an alternative to time being physical.

Although the physics of the universe is not known exactly at time zero, the physics at time greater than one millionth of one pico pico picoseconds is equivalent to the quantum mechanics of Planck domain. This domain is only calculated theoretically. Experimentally, there is no accommodation of Planck energy although at the region of the Planck length superstring theories begin to make sense. However, one thing is certain and that is time always flow in one direction.

We do agree on some things. I agree 100% with the fact that we cannot do science at the exact instant of t=0, and can only do theoretical physics regarding the earliest pico seconds of time after t=0. I also wholeheartedly agree that time only moves in one direction.

This is the direction of increasing entropy.

But on this point we again part ways. You are endorsing the view that entropy is a continuous result of the passing of time and I am of the position that entropy is reversed and usable energy is renewed by the arena process of expansion, overlap, compression, big crunch, and big bang, playing out across the greater universe that lies beyond and encompasses our known universe.

It can be conjectured that direction is the same as motion along certain topologies. Since time only moves in one direction, its topology is the same in the past, in the present, and in the future. This topology of time can be changed if and only if the direction of time is changed, say, from a future direction changed into a past direction. There is no physics that can assert the changing direction of time, not even Einstein’s theory of special relativity. At best, special relativity can only assert that time can be slowed down; to the point that time can stop moving in any direction. Wherever and whenever time stops then the entropy of an isolated system stays constant. However, negative entropy indicates that time is flowing in the opposite direction. The only one dimensional topology that accommodates both positive and negative entropy is the Hopf link, whose two dimensional extension is the Möbius strip, and three dimensional extensions is the Klein bottle.

That reasoning is the result of a narrow "one big bang" universe that is causally connected to Big Bang Theory. One Big Bang is itself only implied by general relativity.

Two separate Big Bangs (or more eternally, a universe characterized by a potentially infinite number of big bang arenas across infinite space) would result in a entirely different cosmology and topography; one where entropy is not coupled with time, but one where the direction of time is always forward and the presence of useful energy is renewable even as time moves forward.

[SteveA]

In terms of deterministic systems, a fundamentally one-dimensional predetermined sequence appears the only form possible, but that also appears to be something incapable of being experienced as any form of dynamic change.

An extension to a two dimensional surface for spacetime would imply parallel deterministic systems, or a set of different deterministic systems, though if this two dimension space was similarly entirely determined, once again it would appear that no actual experience of change would be possible.

An intermediate form could be similar to the present moment as an intersection of predetermined pathways for which an interactive selection allows for some closed loop form of "real-time" change to occur. A 2 dimensional lattice could be a good analogy, though something closer to the "true" form of this (if such is possible to describe) would appear to be of the present moment being at the intersection of all possible divergent future pathways and if the controllable aspects of that were all related to past experiences, then the present moment could be similar to a focal point or intersection of all past experiences.

Another way of looking at time that's a bit unconventional is to instead of considering the present moment as a singular state, imagine that it's a collection of continuously refined possibilities. If there existed some initial state of all possibilities, then every moment could instead of being seen as a selection of some state, be instead seen as a rejection of a single possibility and the next moment a rejection of another possibility. This would appear to be something closer to what a space of controlled experiences would resemble. (Logically it seems we should only be able to control aspects of experience for which preexisting references are available and that the controlled aspects do not create new qualities of experience but instead can only reference preexisting ones or act as constraints upon information and not be creative of information. If you had to extend the possible volume of spacetime experienciable by adding new properties to it, those additions would seem to not have prior associations with that space and would likely instead be sensed as pervasive and non-local, at least until some associations were constructed with the environment, after which a larger possible space of controlled interactions would appear possible)

So something to consider is the difference between what a comprehensible/controllable/interactive topology might be versus what some more fundamental form might be. The interactive version seems to have lots of interesting possible features.

[AntonioLao]

This is strictly theory and is a integral part of general relativity and spacetime geometry. "Time simply passes" is an alternative to time being physical.

I was hoping you won't make these types of comment unless you are authoritatively one of those PhD's in physics. FYI, time was first measured by the invention of the clock and later Newton defined time as absolute. Time is the independent variable of the calculus and calculus made the advancements of science and technology possible. On the other hand, there are many other concepts of time: philosophical time, personal time, etc. Your definition of entropy does not correspond to the thermodynamic definition. Again, please discuss these terms scientifically and not from your own personal speculations. One area of physics to begin understanding entropy is to understand the Carnot cycle.

[AntonioLao]

we cannot do science at the exact instant of t=0,

. Sorry, I need to rephrase that we do science at t=0 but the equations blow up, the answers are all infinities. The resolution of infinities is renormalization as done in all quantum field theories. Please note that the equations of general relativity cannot be renormalized by the usual process of renormalization. Many theorists tried but a unification of quantum mechanics and general relativity still does not exist.

[Bogie]

In the back of my mind I see you trying to solve cold fusion using suspect theory. My posts that apply my layman view could be taken as helpful cautionary signs to encourage consideration of other possible mechanics that could be necessary to achieve your goal. Good luck.

[SteveA]

I was hoping you won't make these types of comment unless you are authoritatively one of those PhD's in physics. FYI, time was first measured by the invention of the clock and later Newton defined time as absolute.

He's got a point though maybe saying that time can't be verified as a purely physical/external object is better.

Does a clock actually measure change? Notice that it requires a memory that a clock had been in some alternate state in order to determine that the clock currently different than it was in the past.

But if someone wanted solid physical proof that change occurs, there's never any present physical state that proves without doubt that past physical states exist.

Even something like assuming measurement of kinetic energy proves motion exists still requires a belief that such a physical correlation exists. You'd still just be presently witnessing some static measurement.

Also, notice that if a particle was moving through empty space with just inertia, it would seem there would be no manner to determine that any form of change/time/motion was occuring as no relative differences would appear available.

Time is the independent variable of the calculus and calculus made the advancements of science and technology possible. On the other hand, there are many other concepts of time: philosophical time, personal time, etc. Your definition of entropy does not correspond to the thermodynamic definition. Again, please discuss these terms scientifically and not from your own personal speculations. One area of physics to begin understanding entropy is to understand the Carnot cycle.

Where does time fundamentally arise from though? If we're to take a scientific approach then we should be able to observe it and verify some predictable and persistent property of it.

It would seem that 'personal time' would be the foundation of any other form of time. How can someone determine that a physical clock is keeping accurate time? In the end, some correlation to ones own perception of a rate of time has to be made. I don't believe anyone would believe that a supposed "clock" that generates random numbers would be a timekeeping device , yet it could be indicating a frame of reference for time that is correct, but 'non-local' in Relativity. At some point it appears there always has to be a correlation related to ones own conscious perception of a rate of time, even if it's just a 'statistically close' agreement.

Also, one of the problems I've pointed out regarding trying to work with time in a purely rational manner is that there seems to be no form of even abstract mechanism that is fundamentally capable of allowing change to exist, unless it has some form of vague "loose end" and some things are simply allowed to happen without any determinable cause.

That, to me, places time as a property that's beyond even magical fairy tales to describe.

As a better analogy of the problem - someone could write up a game for a PC and have all sorts of fanciful events, or even the equivalent of varying laws of physics in it and yet these could all be explained as precisely determined events that fit in perfectly compatibly together despite however fanciful or unpredictable things appeared, but despite that capability, a program has no ability to measure its own rate of execution relative to any external environment (it always executes one instruction per clock cycle), nor can it compute where its figurative power cord arises from, nor what alterations a programmer might make.

And if we attempt to then say that the programmer is yet another program or the power cord is a serial stream from some other computer etc., then this doesn't fundamentally resolve it as it just changes the shape of the initial computer ... and still no program explains where time/energy comes from.

This does actually agree rather well qualitatively with quantum mechanics and the statistical component present in a wavefunction.

[SteveA]

... despite the general theme of my last post, something to consider is that it's only the new/novel component in time that has such a statistical component though. The framework within which that occurs should be prexisting (relative to the present) and in those aspects we could have coherent and controllable interactions in the present.

It's also interesting to consider that there could be ways of increasing the relative significance of the controllable/determinable aspects and reduce the influence of the statistical components ... ways of working with what's already present more efficiently.

For example, the information content of a single photon would appear to arise from the context of what positions it's known to not have been detected. If the quantity of such detectable locations is increased, the same photon could act informationally (and potentially energetically) as if it was comprised of multiple photons.

I posted a link before regarding what I believe was called a "no-on" in which groups of photons all appeared to act collectively in a manner like a consgle photon. There does appear to be a way in which time/change can be factored into multiple independent statistical entities/energies, or ways in which the correct physical context might be able to even "split" a photon instead of splitting an atom.

[Bogie]

. Sorry, I need to rephrase that we do science at t=0 but the equations blow up, the answers are all infinities. The resolution of infinities is renormalization as done in all quantum field theories. Please note that the equations of general relativity cannot be renormalized by the usual process of renormalization. Many theorists tried but a unification of quantum mechanics and general relativity still does not exist.

OK, I stand corrected.

But the issue between us seems to be whether time is physical as in spacetime, or if it simply passes as in Bogie time. Let me differentiate .

Time dilation is the different rate that measured time passes on identical clocks in relative motion to each other, i.e. one clock in an accelerated frame of reference relative to a clock in the at-rest frame of reference. The accelerated clock measures time as if it passes slower during acceleration than it does in the at-rest frame of reference. Time dilation in special relativity, i.e. far from any gravitational influence, describes this phenomenon with Lorentz transformation.

Lorentz transformation is math that reconciles the dilation in a spacetime coordinate system based on the invariant speed of light and therefore the math must preserve the spacetime interval between any two events in Minkowski spacetime. The spacetime interval means the separation between two events is measured by the interval between the two events, which takes into account not only the spatial separation between the events, but also their time (temporal) separation. Minkowski spacetime in the simplest of terms is the three ordinary dimensions of space combined with a single dimension of time to form a four-dimensional spacetime manifold that is convenient for doing spacetime mathematics.

The Lorentz transformation describes only the transformations in which the spacetime event at the origin is left fixed (referring to the preserved spacetime interval), so they can be considered as a 'hyperbolic rotation of Minkowski space' which displays itself as time dilation, so a hyperbolic rotation of the Minkowski spacetime has a hyperbolic relationship to the preserved spacetime interval. They say it requires only that simple math to make the Lorentz transformation.

This time dilation effect in special relativity is reciprocal meaning that from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. Note: Gravitational time dilation is the other form and is caused by the proximity of a gravitational influence. It is not reciprocal meaning that both viewers will agree that the clock closest to the center of gravity is measuring time slower than the clock situated farther from the center of gravity.

So anyway, that is my layman view of time dilation assisted by some simple Googling . But if we are not doing the math in Minkowski spacetime there can be no spacetime effect and yet obviously the phenomenon of clocks measuring time at different rates when in relative motion will still occur. The cause of that measurement difference is due to the energy density of the environments that the clocks are ticking away in.

The principle involved is that acceleration increases the energy density of the environment and slows the movement of the clock relative to the un-accelerated clock.

[quanta07]

Concerning the topology of time,
The association of time and entropy is well known and I believe is generally accepted.
However, there is another view in which time exists as a result of the behavior of spacetime. Within this behavior function, time exists as a series expansion of the function e to the power of ‘t’. The function e to the ‘t’ has the notable property that it’s integral and it’s derivative are equal to the function itself.
Within spacetime behavior, the series expansion of e to the ‘t’ takes on the coefficients of spatial properties, such as volume, surface area and distance, as well as spatial derivatives velocity, acceleration, impulse and flux.
As a species, we evolved within the behavior function of spacetime, and as such our views of a topology of time itself are biased and skewed. Biased by mankinds thought that time is a concept/tool of man and skewed in the belief that time is strictly linear.
The behavior function of spacetime I am referring to is expansion. The first term in the series expansion of this behavior function is Volume(t). As an observer, I am a fixed volume within this function. While expansion continues, all fixed volumes within this behavior function will experience aging, linear time.
Just a different view of the source of linear time……………Happy Thoughts….Q7