Can Information Be Preserved on Closed Timelike Curves?

[PeterDonis]

I am curious about the definition of a CTC. Is it sufficient for wordline of a test particle to return to a given coordinate time to qualify as a CTC

My understanding is, no.

or must the particle return to a given coordinate time and location?

My understanding is, yes.

Does the proper time of an observer whose worldline is a CTC always continue to advance

On purely classical assumptions, yes. But this is really tied into your next questions:

Does that observer on a CTC always continue to observe that entropy is increasing locally and that for him the arrow of time still applies?

I don't think these are answerable purely in the context of GR. You would need a model of the possible microstates of the observer and the matter surrounding him.

However, I think it is possible to say that no "ordinary" model of the microstates of the observer and the matter surrounding him are compatible with a CTC, because that would entail the same sort of inconsistency in the local state at a given event as we have been discussing in this thread. That is, if the observer's entropy, for example, continues to increase with his proper time, then when he returns to the same event on the CTC as he was at "before" (i.e., at an earlier value of his proper time), there is no consistent way to assign him an entropy.

So I think that there is at least an apparent contradiction between our normal understanding of things like the second law of thermodynamics, the "arrow of time", etc., and a belief that CTCs are possible.

 

[PeterDonis]

Hypothetically if the signal were sent to the device in the past but the device is incapable of storing that information then the information would dissipate into the atmosphere as if it were being deleted at which point is possible to measure an increase in thermal noise around the device.

Increase relative to what? See my response to yuiop below. Any hypothetical scenario along these lines, it seems to me, would end up having to assign multiple incompatible values for physical quantities such as temperature, entropy, etc., at the same event.

 

[JPBenowitz]

Increase relative to what? See my response to yuiop below. Any hypothetical scenario along these lines, it seems to me, would end up having to assign multiple incompatible values for physical quantities such as temperature, entropy, etc., at the same event.

Keep in mind this hypothetical device would only send a signal back in time from the moment it is turned on. The hypothesis is that no meaningful information can be sent backwards in time because it requires you to send the information down a maximally noisy channel. The information can never reach the device because it is lost by virtue of traveling through the CTC. Whether or not the hypothesis is testable is not known but what I want to know is if it is mathematically possible.

 

[PeterDonis]

Keep in mind this hypothetical device would only send a signal back in time from the moment it is turned on.

I'm not sure how this helps. See below.

Whether or not the hypothesis is testable is not known but what I want to know is if it is mathematically possible.

I'm not sure this question is answerable as it stands. Or rather, I suspect that what you have proposed so far is *not* mathematically possible, but not because of any problems with transmitting signals around a CTC requiring a "noisy channel". I think it's because you don't yet have a consistent formulation of the scenario in question to start with.

You are talking about a device sending signals around a CTC, and asking whether having it do so can "change" the state of a detector in the past of the event of emission. Just formulating the question that way to begin with seems inconsistent to me, because the state of the detector (or the thermal environment, or any other place you want to stash the "information" in the signal) can't be two different things at the same event; it has only one state at a given event, and so the arrival of the signal can't "change" the state; the signal has to already be part of the initial conditions that determine what the state *is*.

I would suggest stepping back and carefully formulating a scenario that is entirely self-consistent, *including* the signal traveling around a CTC, and only assigns one state at any given event to the detector, or the thermal environment, or anything else. Doing that will, I think, help a lot in trying to answer the question you appear to be trying to ask.

 

[JPBenowitz]

I'm not sure how this helps. See below.



I'm not sure this question is answerable as it stands. Or rather, I suspect that what you have proposed so far is *not* mathematically possible, but not because of any problems with transmitting signals around a CTC requiring a "noisy channel". I think it's because you don't yet have a consistent formulation of the scenario in question to start with.

You are talking about a device sending signals around a CTC, and asking whether having it do so can "change" the state of a detector in the past of the event of emission. Just formulating the question that way to begin with seems inconsistent to me, because the state of the detector (or the thermal environment, or any other place you want to stash the "information" in the signal) can't be two different things at the same event; it has only one state at a given event, and so the arrival of the signal can't "change" the state; the signal has to already be part of the initial conditions that determine what the state *is*.

I would suggest stepping back and carefully formulating a scenario that is entirely self-consistent, *including* the signal traveling around a CTC, and only assigns one state at any given event to the detector, or the thermal environment, or anything else. Doing that will, I think, help a lot in trying to answer the question you appear to be trying to ask.

Your're right I definitely need to reformulate it to be entirely self consistent because as it stands it is not entirely self-consistent. But I do suspect that there is a self-consistent solution with the approach I am taking. Thanks for clearing a lot of things up though!

 

[JPBenowitz]

I think a large issue with the hypothetical device we were contemplating is that we did not take into account the signal itself. Suppose we send a single photon with a wavelength λ_{}0 around a CTC, if the device detects a wavelength λ_{}0 + λ then we will represent this as a 1 if the device detects a wavelength λ_{}0 - λ then we will represent this as a 0. Because the proper time of light is zero we are forced to choose a hypothetical observer outside of the CTC that measures the proper time of our photons journey. If the proper time is sufficiently large enough such that the scale factor of the universe caused λ_{}0 = (+/-)λ then the photon was destroyed. The information the photon carried dissipated along the CTC.

 

[PeterDonis]

Suppose we send a single photon with a wavelength λ_{}0 around a CTC, if the device detects a wavelength λ_{}0 + λ then we will represent this as a 1 if the device detects a wavelength λ_{}0 - λ then we will represent this as a 0.

If the photon is emitted with a particular frequency, it must be detected with a particular frequency. There can't be any uncertainty about it. The whole scenario has to be self-consistent, and it can't be if there is a possibility of two different frequencies for the detection.

If the proper time is sufficiently large enough such that the scale factor of the universe caused λ_{}0 = (+/-)λ then the photon was destroyed.

This doesn't make sense. The universe can't be expanding or contracting as seen by an observer going around the CTC; if it did then the size of the universe at a particular event on the CTC would not have a well-defined value.

When I said "step back", I *really* meant step back. Scenarios with CTCs in them are highly counterintuitive; lots of ways we naturally think about scenarios simply don't work. My best recommendation is, draw a spacetime diagram of the scenario; let the "time" axis be vertical, and identify the top and bottom edges of the diagram (to properly model the fact that there are CTCs present). Then place the events of interest, like emission and detection of the photon, on the diagram, and remember that at each event, every physical quantity must have a unique, well-defined value. So far I don't think you've described a scenario for which that can be done; but in any case, doing it should be very helpful in avoiding inconsistencies.

 

[audioloop]

Keep in this hypothetical would only a signal back in time from the it is turned on. The hypothesis is that no meaningful information can be sent backwards in time because it requires you to send the information down a maximally noisy channel. The information can never reach the because it is lost by virtue of traveling through the CTC. Whether or not the hypothesis is testable is not known but what I want to know is if it is mathematically possible.

Perfect state distinguishability and computational speedups with postselected closed timelike curves
http://arxiv.org/pdf/1008.0433.pdf
...Postselection of quantum teleportation in this fashion implies that an entangled state eectively creates a noiseless quantum channel into the past...


read my post
Timelike Curves leads to violation of Heisenberg uncertainty Relation
https://www.physicsforums.com/showthread.php?t=624880

 

[audioloop]

and the inverse, from the past to the future

Extracting past-future correlations using circuit QED
http://arxiv.org/pdf/1202.1230v2.pdf
Physical Review Letters. 109, 033602 (2012)

...We propose a realistic circuit QED experiment to test the extraction of past-future entanglement to a pair of superconducting qubits...Extraction of timelike entanglement from the quantum vacuum
http://arxiv.org/pdf/1101.2565v1.pdf.
Physical Review A 85, 012306 (2012) ...Here, we show that timelike entanglement can be extracted from the Minkowski vacuum and converted into ordinary entanglement between two inertial, two state detectors at the same spatial location | one coupled to the eld in the past and the other coupled to the eld in the future...

 

[phyti]

The arrow of time is globally derived from the global increase of entropy.

There is no arrow of time. Time is only a sequence of events, and the next event to occur cannot precede those that have already occurred!
Those who only see a tired universe ignore the formation of plant, animal, and human life, according to organizing principles of genetic code. Then there's gravity forming galaxies and stars. You might consider materials at or near absolute zero, where the removal of 'random' thermal energy produces very orderly structures!

In an information theory sense as a system evolves in time it becomes more random, the system can be in more possible configurations otherwise known as states.

Try selling that to those who process information in their work, where their system requires order and consistency.

Likewise from the second law of thermodynamics a closed system cannot be reversed.

With radiation permeating the entire universe, a closed system is another one of those idealized non-concepts.

It cannot evolve backwards in time to its initial conditions.

Since there is no arrow, there is no direction in time.
Fundamental particles, atoms, molecules, and compounds return to their original states without going 'backward' because they can transition through a finite number of states, provided there is available energy.

I'll stop here since you don't have enough fuel to light the engine, let alone blast off.

Step outside the box of abstraction occasionally. If you have ideas, try them in real world scenarios to see if they still seem reasonable.



[/QUOTE]

 

[PeterDonis]

Try selling that to those who process information in their work, where their system requires order and consistency.

Are you claiming that the computing devices these people (or the people themselves, for that matter) violate the second law of thermodynamics?

 

[phyti]

Are you claiming that the computing devices these people (or the people themselves, for that matter) violate the second law of thermodynamics?

I checked, and no, I didn't claim that.
What's the penalty for violation?

 

[PeterDonis]

I checked, and no, I didn't claim that.

Then I don't see how what you were saying is in any way inconsistent with what JPBenowitz said. He was talking (at least in the particular passages you quoted) about global properties of globally closed systems (and even if you are right that there are no truly closed systems short of the entire universe, the entire universe itself still counts as a closed system). You are talking about local properties of open systems.