Exploring Time as a Curled-up Dimension

[mjones32]

So, I was just thinking what if the time dimension was a tiny curled up dimension like one of these supposed extra 8 dimensions from string theory ?

If it allowed just enough wiggle room for objects to move the idea has some features that appeal to me.
- time is symmetrical ; no past , no future
- no time travel, no paradoxes
- no preferred direction in time

Everything we experience as time moving in one direction is purely a statistical phenomenon.

I'd be interested in if this has ever been discussed previously or documented anywhere.

 

[weaselman]

Hawking (and some others) believe that the time is symmetrical, and that its direction really is a statistical phenomenon, having to do with the thermodynamics (basically, time flows in the same direction in which entropy grows).
As for everything else, I am not sure I understand how you think having time curled up will prevent time travel for example - if it is small enough that you can't move backward, you should not be able to move forward either. The same goes for your symmetry suggestion.

 

[mjones32]

Thanks weaselman - I think the answer to your point re 'forward' and 'backward' is that in this model 'forward' and 'backward' are merely to do with human perception based on statistical / thermodynamic phenomona.

Basically the circular time just allows things to change but there is no concept of a sort of space-time 'place' that a time traveller could 'go to'.

It's a little hard to get your head round the idea that time is intrinsically directionless and that we perceive it as such because of the statistics of the arrangement of matter and energy.

 

[bapowell]

Sounds like this idea prevents the simplest time travel of all -- time translation into the future. If there's no 'place' for us to go, how do we evolve into the future? Try thinking in terms of a timelike worldline. If the time dimension is periodic, then so would be the worldline. We'd be destined to cycle into the future then back into the past ad infinitum.

 

[DrGreg]

Sounds like this idea prevents the simplest time travel of all -- time translation into the future. If there's no 'place' for us to go, how do we evolve into the future? Try thinking in terms of a timelike worldline. If the time dimension is periodic, then so would be the worldline. We'd be destined to cycle into the future then back into the past ad infinitum.

That's exactly what I thought. We'd be stuck in a Groundhog Day. Except that if it's a tiny curled-up dimension, it wouldn't even be that, it would be a Groundhog Nanosecond. I don't know about anyone else, but all my nanoseconds are different.

 

[Dale]

what if the time dimension was a tiny curled up dimension like one of these supposed extra 8 dimensions from string theory ?

The universe is 13.75 billion years old, so that means that the size of the time dimension is at least 13.75 billion light years. I have a hard time calling that "tiny".

 

[nismaratwork]

The universe is 13.75 billion years old, so that means that the size of the time dimension is at least 13.75 billion light years. I have a hard time calling that "tiny".

That would depend on something to compare it to, so any appellation regarding magnitude would be inappropriate.

I have no issue with the notion of living in a 13.7+ billion ly CTC, but without a reason to believe this, I have an issue with the assertion.

 

[Halcyon-on]

I'd be interested in if this has ever been discussed previously or documented anywhere.

This idea has been recently proposed in terms of compact time. See for instance arXiv:1001.2718 for a short introduction.

 

[bapowell]

I have no issue with the notion of living in a 13.7+ billion ly CTC, but without a reason to believe this, I have an issue with the assertion.

Wait. Are you saying you have no reason to believe that the universe is 13.7 billion years old?

 

[DaveC426913]

Wait. Are you saying you have no reason to believe that the universe is 13.7 billion years old?

No, he's saying he has no reason to believe that - after only 13.7by - it would be closed*, and loop back.

*CTC=closed timelike curve

 

[Dale]

That would depend on something to compare it to, so any appellation regarding magnitude would be inappropriate.

I feel completely safe in saying that 13.75 billion light years is not "tiny" regardless of what else might be even larger.

 

[mjones32]

That's exactly what I thought. We'd be stuck in a Groundhog Day. Except that if it's a tiny curled-up dimension, it wouldn't even be that, it would be a Groundhog Nanosecond. I don't know about anyone else, but all my nanoseconds are different.

Obviously, the concept relies on the idea that the circular time dimension does not mandate a groundhog instant and that at the 'end' of the loop particles do not have to find themselves where they started. Time in this context implies merely the capability of change. Thats why I used the phrase 'wiggle room' in the initial post.

Once you accept that premise I find a lot that about this idea that is appealing because of other points made elsewhere in my post.

 

[Dale]

Obviously, the concept relies on the idea that the circular time dimension does not mandate a groundhog instant and that at the 'end' of the loop particles do not have to find themselves where they started.

That is exactly that the concept implies. If it does not repeat then in what sense is it tiny and curled up? Certainly that is exactly what is meant in string theory.

 

[DaveC426913]

I'm with DaleSpam. If time is a closed loop, then the implication is that events repeat exactly and periodically.

 

[nismaratwork]

No, he's saying he has no reason to believe that - after only 13.7by - it would be closed*, and loop back.

*CTC=closed timelike curve

Yes, thank you very much Dave, I am not in any way claiming that current estimates are not accurate.

Dalespam, any statement about scale requires an objective comparison, and if we're talking about universes in CTCs, we're at a different scale. That said, I would say "huge" as well, and compare it to the notion of Planck-scale CTCs for a single test particle. I am not so into semantics that I need to drag this out, you're not wrong, you're not right, and the wise thing for me is to accept that.

Personally, I wonder, and this is inspired by Dimitry in another thread: what about charge? Would there be the possibility that in fact there would be an accumulation or interaction? If Hawking and Thorne are correct, then such a CTC would be self-destructive on a universal scale. The universe would have to be the ONLY such entity; no branes, no bubble universes, for our (nod to dale) Huge CTC to be free from interaction ad infinitum.

 

[mjones32]

That is exactly that the concept implies. If it does not repeat then in what sense is it tiny and curled up? Certainly that is exactly what is meant in string theory.

Well, I look at this way.

The very definition of a dimension implies orthoganality to every other dimension. But your concept of time states that if you now 'when' some object is you can precisely determine where it is in the other 3 dimensions. Therefore , your concept of time, whatever it may be, is not a dimension at all.

But my model does actually conform to that definition of a dimension and a being living in such a space would perceive time that fits your point of view (which is our common impression of time)...i.e. if you know when something was you can state where it was.

Thats what I find intriguing about the concept.

 

[DaveC426913]

Well, I look at this way.

The very definition of a dimension implies orthoganality to every other dimension. But your concept of time states that if you now 'when' some object is you can precisely determine where it is in the other 3 dimensions. Therefore , your concept of time, whatever it may be, is not a dimension at all.

No, not at all. It's not about orthagonality (we agree with that - it is not in contention).

The trouble is with the curled up part. If a dimension curls back on itself, then you will find yourself in the same place as before.

Spatial dimension wrapping: Start at x=0 and head off in direction x, you will find yourself back at x=0.

Timelike dimension wrapping: Start at t=0 and head off in direction t, you will find yourself back at t=0.

Consider the implication of this last idea: true, you may not be back at x,y,z when time loops back on itself, however there will now be two of you in the universe (and, since they can't move faster than c through xyz, they will be within each other's light cone - they will see each other).

In fact, there will be a new one of you every time that time ticks back to 0 again. You are in a universe where a new (and slightly older) version of you pops into existence at regular intervals (which could be every femto-second, if your time dimension is curled up tightly enough.)

 

[Dale]

The very definition of a dimension implies orthoganality to every other dimension. But your concept of time states that if you now 'when' some object is you can precisely determine where it is in the other 3 dimensions. Therefore , your concept of time, whatever it may be, is not a dimension at all.

I have no idea what you are talking about here or what would have made you believe this. I think you are making some completely unfounded and mistaken assumptions.

But my model does actually conform to that definition of a dimension and a being living in such a space would perceive time that fits your point of view (which is our common impression of time)...i.e. if you know when something was you can state where it was.

Thats what I find intriguing about the concept.

Sure, in your model time is a dimension, but your model simply does not fit observation since the universe is observed to be 13.75 billion years old, not "tiny" in the time dimension. We also don't have any evidence that it is curled up and very large, although we cannot rule it out completely. It is nice to have a model, but the value of a model is always its fit to reality, and this model though intriguing does not fit.

 

[Halcyon-on]

I have no idea what you are talking about here or what would have made you believe this. I think you are making some completely unfounded and mistaken assumptions.

Sure, in your model time is a dimension, but your model simply does not fit observation since the universe is observed to be 13.75 billion years old, not "tiny" in the time dimension. We also don't have any evidence that it is curled up and very large, although we cannot rule it out completely. It is nice to have a model, but the value of a model is always its fit to reality, and this model though intriguing does not fit.

The way out to your concerns seems to be given in the conclusions of the paper that I mentioned before (arXiv:1001.2718):

"Paraphrasing the Newton’s law of inertia and the de Broglie hypothesis we assume that elementary free bosonic fields have intrinsic space-time periodicities T_\mu = h / p^\mu[ where h is the Planck constant and p^\mu is the four momentum, that is time curled up with length T=h/E]. These Periodic Boundary Conditions satisfy the variational principle and the theory is in agreement with SR. As much as the Newton’s law doesn’t imply that every point particle goes in a straight line, our assumption does not mean that the physical world should appear to be periodic. According to Special Relativity, these periodicities can vary through interactions (energy exchange) or by changing the reference system. Furthermore the combination of two or more periodic phenomena with irrational ratio of periodicities results in ergodic (nearly chaotic) evolutions. Remarkably, from this assumption of dynamical intrinsic periodicity the usual Quantum Mechanics emerges under many of its different formulations and for several nontrivial phenomena. This could open a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. After all, the notion of time is strictly related with the assumption of periodicity: our usual -non compact- time axis is defined by counting the number of cycles of phenomena supposed to be periodic, in particular with reference to the Cs-133 atomic clock. “We must assume, by the principle of sufficient reason”,4 periodicity to define a relativistic clock. Indeed, every elementary field can be regarded as having a relativistic de Broglie internal clock. For massless (electromagnetic or gravitational) fields these periodicities can in principle be infinite whereas in massive fields they are bounded by the inverse of their masses. As in a calendar, the combination of the “ticks” of all these different internal clocks is sufficient to fix uniquely events in time and the usual exter- nal time axis can be dropped. In these relativistic internal clocks “all that happens in a given period is identical with all that happens in an arbitrary period”[Einstein 1910] Thus, in a full relativistic generalization of acoustic fields, every field can be regarded as characterized by dinamical compactified space-time dimensions. Massless fields with low frequency provide long space-time scales whereas non-relativistic massive fields can be regarded as localized inside the Compton length, but with nearly infinite spatial period and microscopic time compactification, i.e. as classical 3D point-like particles."

 

[mjones32]

The way out to your concerns seems to be given in the conclusions of the paper that I mentioned before (arXiv:1001.2718):

"Paraphrasing the Newton’s law of inertia and the de Broglie hypothesis we assume that elementary free bosonic fields have intrinsic space-time periodicities T_\mu = h / p^\mu[ where h is the Planck constant and p^\mu is the four momentum, that is time curled up with length T=h/E]. These Periodic Boundary Conditions satisfy the variational principle and the theory is in agreement with SR. As much as the Newton’s law doesn’t imply that every point particle goes in a straight line, our assumption does not mean that the physical world should appear to be periodic. According to Special Relativity, these periodicities can vary through interactions (energy exchange) or by changing the reference system. Furthermore the combination of two or more periodic phenomena with irrational ratio of periodicities results in ergodic (nearly chaotic) evolutions. Remarkably, from this assumption of dynamical intrinsic periodicity the usual Quantum Mechanics emerges under many of its different formulations and for several nontrivial phenomena. This could open a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. After all, the notion of time is strictly related with the assumption of periodicity: our usual -non compact- time axis is defined by counting the number of cycles of phenomena supposed to be periodic, in particular with reference to the Cs-133 atomic clock. “We must assume, by the principle of sufficient reason”,4 periodicity to define a relativistic clock. Indeed, every elementary field can be regarded as having a relativistic de Broglie internal clock. For massless (electromagnetic or gravitational) fields these periodicities can in principle be infinite whereas in massive fields they are bounded by the inverse of their masses. As in a calendar, the combination of the “ticks” of all these different internal clocks is sufficient to fix uniquely events in time and the usual exter- nal time axis can be dropped. In these relativistic internal clocks “all that happens in a given period is identical with all that happens in an arbitrary period”[Einstein 1910] Thus, in a full relativistic generalization of acoustic fields, every field can be regarded as characterized by dinamical compactified space-time dimensions. Massless fields with low frequency provide long space-time scales whereas non-relativistic massive fields can be regarded as localized inside the Compton length, but with nearly infinite spatial period and microscopic time compactification, i.e. as classical 3D point-like particles."

Thank you, much appreciated. I'll try to get my head round this in a bit more detail.

 

[mjones32]

I have no idea what you are talking about here or what would have made you believe this. I think you are making some completely unfounded and mistaken assumptions.

Sure, in your model time is a dimension, but your model simply does not fit observation since the universe is observed to be 13.75 billion years old, not "tiny" in the time dimension. We also don't have any evidence that it is curled up and very large, although we cannot rule it out completely. It is nice to have a model, but the value of a model is always its fit to reality, and this model though intriguing does not fit.

Thats kind of the point of my model, to consider the issues with the extended 13.7 billion year time dimension, which has all these associated problems of implied pre-destiny, time travel and the unsymmetrical relationship of past & future from a human point of view.

My point of regarding orthogonality is I think correct - loop time does not mean repeating events though it does lead to other issues, per Dave C post.

So actually neither model fits our observation of reality. If I can get time to study Halcyon-on posting in more detail, maybe I can get a better handle on what 'wiggle room' amounts to.

 

[Dale]

loop time does not mean repeating events

In what possible sense is it a loop then? When you say "loop time" or "tiny curled time" that is exactly what people think, particularly in reference to string theory. If you mean something else then you need to be very explicit about your meaning.

 

[nismaratwork]

How does a temporal loop (CTC) as a temporal dimension NOT imply what DaveC has said? I'm really quite confused now. If you mean that time has curvature, that's not exactly news, but "loop" isn't really open to many interpretations.

 

[DaveC426913]

In what possible sense is it a loop then? When you say "loop time" or "tiny curled time" that is exactly what people think, particularly in reference to string theory. If you mean something else then you need to be very explicit about your meaning.

Well, if I were on a timeline that looped back to 2009, there would be two of me in 2009. They would be at the same t, but not the same x,y and z. Which means I am not stuck in a Groundhog Day event.

In the same, way, I can loop back to location x, but I won't necessarily be at location y, z and t.

 

[Dale]

Yes, you can go diagonally around a tube. It still does not fit observation.

 

[DaveC426913]

Yes, you can go diagonally around a tube. It still does not fit observation.

Right.

Unless the torus has an inner circumference of 14Gy+...