Hypothetical Shape of a Spacetime and Time Travel

[HuskyNamedNala]

Disclaimer: I am an aeronautical engineer with a background in fluids. My knowledge of cosmology only extends to articles and things I read before I go to sleep.

So, here is my question:
I have though about time travel, as many other people have. Currently we think it may not be possible, as it would require moving faster than the speed of light. But what if we could travel "backward" in time with a manipulation of the geometry of space?

The weird part. Imagine we are in a universe where spacetime is shaped like a cylinder...more specifically a coffee cup. Imagine the z axis represents time, while the radial axis represents space. The future is in the direction of positive Z. If we were to imagine time flowing such that along the main cylinder (the "cup" part of this strange geometry) it is advancing into the future, but when it goes into the handle part, time still advances forward, but in the opposite direction. That is to say, if we were to "travel" through the handle in our coffee cup universe, advancement in our future would result in us ending up in the past. Imagine a sequence of events representing time as a fluid flowing through the cup and recirculating in the handle.

Maybe a more concise question will help:

Can spacetime be flat, but have closed loops which would bring you into another part of space and time. Could "time" in these loops travel in a different direction than the main part of space, but still be advancing into the future? In these sense one could time travel without actually ageing or moving faster than the speed of light, or relying on any other crazy physics except a coffee cup shaped universe.

If this question isn't clear I can draw a sketch and upload it.

 

[DaveC426913]

GR does not explicitly forbid time travel. I can't speak to your specific example but there are hypothetical geometries that seem to result in possible timelike movement.

Look up toroidal black holes.

 

[newjerseyrunner]

Not sure about jumping backwards in time, but it's certainly not possible to reverse the arrow of time. Here is an example:

Imagine a basketball in a position above the Earth with a velocity. The mathematics of classical physics works in two directions, meaning you can calculate the balls position, velocity, momentum for both the future and the past. So in classical physics there is no mathematical reason for time to always point towards the future.

However, in quantum physics, a photon travels as a wave function. Upon an interaction, that wave function completely collapses, leaving no information about it's previous state. Quantum physics can only travel towards the future.
General relativity also gives us some really strange ideas about what time is. If you imagine a ship a billion light years away from us traveling away from us, the lorenz transformation will cause it appear to the ship that Earth is several hundred years in the past (not because of the speed of light, because of change in time.) But if you reverse the ship and have them come towards us, suddenly from their perspective Earth is hundreds of years in the future. So the past, present, and future are all relative and seem to all exist simultaneously while also being discreet.

 

[HuskyNamedNala]

My understanding is that entropy, the arrow of time and the classical formulation of physics are at ends. I read about a proof which suggested special relativity and the statistical mechanical definition of entropy are one in the same.

See http://en.m.wikipedia.org/wiki/Relativistic_heat_conduction

For the reference. My follow up question pertains to the arrow of time. Could it be possible to have an arrow that changes direction relative to some "global" coordinates, but is still positive?

Take a sheet of paper and draw a bunch of arrows in one direction. The arrows represent the direction of time. Now simply take the paper and roll it like a hot dog, just as any good scientist/roach coach operator would. You can clearly see from our "paper coordinates" that the arrow direction has remained unchanged. However, from an outsiders perspective, it is clear that the arrow points both forward and backwards depending on what section you chose go inspect. If time always moved "forward" than wouldn't that imply some absolute metrics exists that defines time such that it cannot be changed under different coordinate transformations or dimensions.

Again, please excuse my incorrect terminology, my understanding of abstract math is intuitive and I only have a degree in lowly aerospace engineering.

 

[wabbit]

Isn't QM just as time symmetric as classical mechanics ? Leaving aside interpretations, aren't the predictions time reversible ? I.e. the probability of a past measurement knowing a future one, follow the same rules as the probability of a future measurement knowing a past one.

What changes between the two. I would think is that usually we know the past and predict the future, but this is true in both cases QM and classical, so in both cases it seems to be a matter of the direction of information increase, from the point of view of the observer.

And when (unusual as it may be) we do know only the present and reconstruct the past the trajectories from present to past have increasing uncertainty and entropy in the past direction.

 

[newjerseyrunner]

According to this, a wave function collapse is irreversible: http://en.wikipedia.org/wiki/Wave_function_collapse

 

[DaveC426913]

So I guess that's two ways GR and QM are incompatible! :)

 

[wabbit]

I think these vague musings of mine were a poorly rendered reminiscence of this :

Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis, Carlo Rovelli

Phenomenological arrows of time can be traced to a past low-entropy state. Does this imply the universe was in an improbable state in the past? I suggest a different possibility: past low-entropy depends on the coarse-graining implicit in our definition of entropy. This, in turn depends on our physical coupling to the rest of the world. I conjecture that any generic motion of a sufficiently rich system satisfies the second law of thermodynamics, in either direction of time, for some choice of macroscopic observables. The low entropy of the past could then be due to the way we couple to the universe (a way needed for us doing what we do), hence to our natural macroscopic variables, rather than to a strange past microstate of the world at large.

 

[wabbit]

According to this, a wave function collapse is irreversible: http://en.wikipedia.org/wiki/Wave_function_collapse

Yes but the collapse is a specific interpretation, I don't think this implies that the process is irreversible by itself if we consider only relations between measurements, which are independent of interpretations.

 

[haael]

Isn't QM just as time symmetric as classical mechanics ? Leaving aside interpretations, aren't the predictions time reversible ? I.e. the probability of a past measurement knowing a future one, follow the same rules as the probability of a future measurement knowing a past one.

No. Standard model at least doesn't admit time-reversal symmetry. This is called T-symmetry breaking, a lesser known cousin of the CP-symmetry breaking.

Yes but the collapse is a specific interpretation, I don't think this implies that the process is irreversible by itself if we consider only relations between measurements, which are independent of interpretations.

Irreversibility of collapse is related to irreversibility of the second law of thermodynamics.

Consider the half-mirror experiment. We have a source of photons (laser), first half-mirror that splits the beam into two, then two mirrors and the second half-mirror that merges the beams. We also have two detectors on each side of the second half-mirror.

If we turn the laser on, we will see photons only on one detector. If we put a heat absorbing brick on the path of one of the beams, we will see photons in both detectors.

Now let's try to play this experiment back in time. We "emit" a photon from the detector, it splits on the second half-mirror, merges on the first half-mirror and gets reabsorbed by the laser. Everything is correct.
But in the case of the bricked version it doesn't work. If this setup were time-reversible, then we would have something of the following: we emit a photon from any of the detectors, then on the second half-mirror it always chooses the path without a brick and on the first half-mirror it always chooses the path leading to the laser. This is not the case.

However, the time symmetry can be restored if we assume that the brick emits back a photon in the correct phase. That means, it retains some information about the original absorbed photon and can send it back. This is in contradiction with the second law of thermodynamics. It it holds true, then the brick can emit only random thermal photons.

 

[wabbit]

Regarding T symmetry violation - Yes, but there is still CPT symmetry if my understanding is correct, which means that the time reversed process is still the same modulo some symmetry which doesn't break entropy symmetry.

About the mirrors, without the brick it seems fine, so the question is what is the brick and how is it modeled as a QM object. I don't understand this yet, nor precisely what the law is relating the measurements at the three emittors/detectors here, it seems interesting though, I'll try...

 

[haael]

what is the brick and how is it modeled as a QM object

It is a heat bath. A device that absorbs particles and forgets their phase. This "forgetting" is crucial in wavefunction collapse. If the information about phases could be restored, there would be no collapse.

Of course, interpretations differ in what exactly causes collapse, but all agree that making phase inaccessible is the necessary condition for it to occur.

 

[wabbit]

OK I think I see that the modelling of the brick is not the issue.

The experiments tells us that the possiblities with the brick present are as follow, noting p1 a photon at 1 (emitter in the direct descriptiom), !p1 no photon,etc, and drawing this with the emitter at the left, the reflections to the down or right directions:

Conditional on no photon arriving at the first half silvered mirror "from the top" and on a photon being emitted at 1, we have both possibilities with almost equal probability (equal if the brick transmits 100% of incoming photons)

p1 p2 !p3
p1 !p2 p3

If we time reverse this, i,e. we start with a state of equal probability of a photon at 2 or at 3, and exclude the cases where a photon escapes upward, we also get the same two cases with equal probability, there is always a photon at 1.

This isn't quite right, it's a little hard to isolate the conditional case implicit in the experiment description and if we want an isolated system I think we need to include an emittor/detector at "0" above the first mirror - then calculating non conditional probabilities is easier, we get a law relating the observations of (0,1) to those of (2,3), from which we can derive the conditional probabilities corresponding to each experiment, and also the time symmetry becomes a left-right symmetry so this should work fine.

If "0" is a perfect absorber (black wall, no laser), should it not also spontaneously emit photons? If not than we may have an asymmetry coming from that.