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The Arrow of Time and CTC's.

  1. Aug 13, 2012 #1
    The arrow of time is globally derived from the global increase of entropy. 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. Likewise from the second law of thermodynamics a closed system cannot be reversed. It cannot evolve backwards in time to its initial conditions. However irreversibly of a system is ambiguous in the sense that if enough information is known and enough computational power is available then an observer can reverse the system close to its initial conditions but not precisely.

    The increase of randomness in a system over time is deterministic but tends towards chaos in the sense that the error associated with calculating the initial conditions increases exponentially. So as the arrow of time marches forward it becomes exponentially difficult to calculate the initial conditions of any closed system to the point where it is fundamentally impossible due to a physical computational limit. Therefore, if this fundamental computational limit lies on a closed timelike curve there wouldn't be sufficient enough information to determine causality and thus can said to be preserved.

    In an analogy consider an observer with an infinite amount of memory and records its entire journey. The CTC is so large that eventually its memory starts to decay and break down, conserving information but scrambling it. When it returns to its initial position it would have retained nothing from its journey.

    Is this possible?
     
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  3. Aug 13, 2012 #2

    Simon Bridge

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    Thus what can be said to be "preserved"?
    How would a "computational limit" exist as a space-time event?
    Is what possible?
    These statements are too vague.
     
  4. Aug 13, 2012 #3
    Causality can be preserved.
     
  5. Aug 14, 2012 #4

    Simon Bridge

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    The total causality in a closed system is a constant?
    How would one experimentally verify this?
    How are you defining "causality"?

    What about the other two questions?
     
  6. Aug 14, 2012 #5

    Demystifier

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  7. Aug 14, 2012 #6

    Simon Bridge

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    That kinda implies that you can have coordinate-time travel without paradoxes?
    (reads)

    Anyway - I tried, and failed, to find where the phrase "conservation of causality" is used that is not pseudoscience. That may not mean anything. I still think OP is too vague and would benefit by refining the questions.
     
  8. Aug 14, 2012 #7
    Yes, I am trying to build a closed timelike curve with a chronology protection conjecture using information theory. I never used conservation of causality, I said causality is preserved meaning you can distinguish which event took place first.
     
  9. Aug 14, 2012 #8

    PeterDonis

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    Isn't this false by hypothesis if the two causally connected events lie on a closed timelike curve?
     
  10. Aug 14, 2012 #9
    Not if it is undetectable by an observer.
     
  11. Aug 14, 2012 #10
    Last edited: Aug 14, 2012
  12. Aug 14, 2012 #11

    PeterDonis

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    Your definition of causality didn't say anything about observers, unless I'm misunderstanding it. I took "you can distinguish which event took place first" to mean "there is a definite time ordering to the pair of events", regardless of whether any observer actually detects that ordering. This is false for any pair of events that lie on a CTC, period; it doesn't matter whether any observer detects the events or not.

    If by "you can distinguish..." you meant "there must exist some observer who distinguishes...", then you are saying that, by your definition, "causality" is observer-dependent. Is that the position you are trying to take?
     
  13. Aug 14, 2012 #12
    Essentially yes it is. If two events lie on a CTC sufficiently far enough then no meaningful information can be communicated from either event.
     
    Last edited: Aug 14, 2012
  14. Aug 14, 2012 #13

    PeterDonis

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    Hm. In that case I don't think this is really a GR question; it's more of a thermodynamics/quantum mechanics question. You do need GR to provide a background spacetime with CTCs in it (such as the Godel spacetime), but that's all, and I don't think it's enough to answer the "is it possible?" question you pose.
     
  15. Aug 14, 2012 #14
    The rational is essentially the same as an entangled pair of particles. An observer cannot determine which system collapsed first and thus no information has been sent. I am speculating the reverse must also be true such that if no information is sent then causality cannot be distinguished. What I mean by "no information being sent" is that the channel's thermal noise reached a maximum insofar that the error associated with retrieving such information is physically impossible.
     
  16. Aug 14, 2012 #15
    Right, however it is also necessary to incorporate the holographic principle to construct unique surfaces retaining all the information of the physical system.
     
  17. Aug 15, 2012 #16
    Can something like the Poincaré recurrence theorem help in how a CTC might make sense?

    If an observer where exist at a particular state of the system, and the state is repeated at a later time, obviously, the observer an be aware of the original occurrence, since it is apart of the system, and must have the same observation and memory in both occurrence.

    But, I don't understand CTCs my self at all. I'm curious what determines the recurrence time in a CTC? Is this set by GR? Or is a CTC simply a separate piece of space time?
     
  18. Aug 15, 2012 #17
    The Poincaré recurrence theorem could theoretically be used if and only if information is lost (not destroyed) after every recurrence. There is actually a paper on the Poincaré Recurrence time of the universe which was calculated to be 10^10^10^1.08 years if I remember correctly. However, what I am trying to derive is that information cannot be retained or processed over such time scales due to an increase of entropy. This problem is of a fundamental physical limit of computation, namely how long can a memory space last before it decays? the PRT is apart of ergodic theory which statistically states that if a system evolves over a long enough time is "forgets" its initial state. So yes the PRT would fundamentally be apart of a CTC.
     
  19. Aug 15, 2012 #18
    Interesting, but I guess that number must be very hypothetical given that the size of the universe is unknown. Also, can anybody tell me if it is actually known if the PTR can be applied to the universe? I am assuming it is unknown.

    I guess it all depends on the nature of the memory. But even if you imagine a memory that is immune to decay, the size of the memory will still be limited. The time that the memory space can last would depend on its design. You could imagine an observer that could freeze its self for an arbitrary amount of time, only making extremely rare observations, that might cause recurrence of the entire system to be less frequent.
     
  20. Aug 15, 2012 #19

    Simon Bridge

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    @JPBenowitz: <rereads> oh yes, and I noticed at the time too ... must be the 2am effect :( But notice how being more specific about your terms gets better responses?
     
  21. Aug 15, 2012 #20
    Even if the instrument only took measurements at discrete time intervals I couldn't imagine it would be enough to determine the initial conditions of the system.

    All of it is speculation but they are indeed interesting questions. Also there are fundamental limits on memory space regardless of design http://arxiv.org/pdf/quant-ph/9908043.pdf look at page 6. I guess what I want to do is be bold and redefine the arrow of time in a quantum information theory perspective and thus prove the chronology protection conjecture (maybe prove is a strong too strong of a word). But if someone were to build a time machine and planned on killing there grandfather the second they went back in time there entire memory would be wiped clean and thus could never kill their grandfather.
     
    Last edited: Aug 15, 2012
  22. Aug 15, 2012 #21
    Of course not, but you mentioned the question of how long a memory can last with out decay. How long a memory can last with out decay depends on its accuracy.

    I think the suggestion that the arrow of time can be derived from the global increase in entropy, although often stated, has some issues. I would suggest that it works the other way around. Time between events always moving in the same direction makes a decrease in entropy impossible. I'm not sure that entropy can be a global property of a system, because it is observer dependent. It is about information rather then anything physically real. A system can return to an earlier state, but it is impossible to observe that process from with in the system.

    I think that to start talking about quantum information theory, or entropy, is to actually move further away from the problem, rather then closer to it. Time travel backwards in time on a CTC would allow an event to occur with no detectable cause putting cause an effect in trouble, which would then lead to issues with information.

    When thinking about the possibly of time travel. I like to imagine building a computer that can send a signal to its self to its self in the past. The signal will contain a number. If the machine receives a number from the future, it will add 1 then store it. When choosing what number to send back to its self in the past, it will send the stored number. Such a machine would seem impossible to build under the Novikov self-consistency principle. I suppose there must be no way for information to survive in a time loop with a single time line and cause and effect. But how could the building of such a machine be prevented, where as building a machine that didn't add 1 could work?
     
  23. Aug 15, 2012 #22
    Information is a physical manifestation though. It's simply the physical property of being distinguishable. I do not agree that pursing this from an information theory perspective is moving in the wrong direction but that is besides the point. However your analogy makes a very good comparison to causality and information. A time machine computer generates a 1 and sends it to itself in the past and adds it to 0, however the paradox is that it could never add the 1 to 0 because the 0 became a 1. The moment the machine is turned on you would have essentially added an infinite amount of numbers which requires an infinite amount of memory which does not physically exist. The question is what happens to this machine after you exceed its memory?

    One way to reconcile information theory with the causality paradox is to simply state that because it is impossible to distinguish the initial conditions of the 0 and the 1 then no information is actually stored on the device.
     
    Last edited: Aug 15, 2012
  24. Aug 15, 2012 #23

    PeterDonis

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    The Novikov Self-Consistency Principle would say that such a machine is not physically possible, because a closed timelike loop has to be self-consistent.

    http://en.wikipedia.org/wiki/Novikov_self-consistency_principle
     
  25. Aug 15, 2012 #24
    Right, but if the device were in a state which is physically impossible to distinguish whether or not the loop is self-consistent then why couldn't it be constructed? You cannot send a message back in time but theoretically you could send information. It would just appear to be truly random noise.
     
  26. Aug 16, 2012 #25

    PeterDonis

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    If it's impossible to tell whether or not the loop is self-consistent, then it's not self-consistent as far as the principle is concerned. See below.

    At the microphysical level, "random noise" is just "information" that meets particular statistical tests for randomness.

    For example, consider the simple closed loop you described earlier: a one-bit register that sends a signal through an adder that adds 1 to it, then feeds the result back into the same one-bit register, going around a closed timelike curve. The state of the one-bit register is not consistent: if it's 0, then it's 1, and if it's 1, then it's 0. So the circuit is not physically possible.

    Now consider a huge number of such circuits, where we say that the initial values of the bits are randomly chosen. The whole ensemble is still not physically possible, because there is no possible consistent state for any of the bits. The fact that the ensemble as a whole looks like random noise to us, rather than a discernible pattern, makes no difference.

    Similar remarks apply if we are unable to measure the bits. Say, for example, that to the best of our knowledge, each bit is in some quantum superposition of the "0" state and the "1" state. That still doesn't make any difference to the self-consistency of each bit: the unitary evolution of each bit, passing around the CTC through the adder, is still inconsistent. In quantum terms, this means that there is zero amplitude for a signal to pass through the circuit; the set of possible evolutions of a signal passing through the circuit will destructively interfere, for a net total amplitude of zero.
     
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