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Particles traveling back in time

  1. Jul 9, 2013 #1
    *disclaimer* I am not suggesting any crazy theories here, I am merely examining some of the more extreme situations allowed in relativity!

    ok so first off, lets allow particles to travel in timelike trajectories backwards through time relative to us. Although this does have some strange causal effects, relativity remains perfectly consistent as it is symmetric under time reversal. If we assume these particles have positive rest mass, then in our reference frame they would appear to have negative mass. I stress the word "appear" because the invariant mass remains positive. However, dt/dτ = -γ so you end up with negative signs every place "relativistic mass" appears.

    Now, my question is if there is any conservation law (or any other mechanism to prevent this) broken by the spontaneous "creation" of two particles of equal mass, where one is traveling back in time and one is traveling forward in time. The "creation" point is the space-time point where the particle's worldlines intersect. Before this point space was empty, and afterwards we see two particles moving away from each other, one with positive energy and the other with negative energy. It is pretty trivial to show that both energy and momentum should be conserved in this process, and similarly in the time-reversed process (annihilation).

    However, there is one thing I find very bothersome about this process, and I can't shake the feeling that it shouldn't be allowed on the grounds of conservation laws. If you draw the spacetime diagram of the process, you will see one particle going backwards in time from infinity, and then spontaneously start moving forwards in time back to infinity. How is it possible that momentum is conserved in a process where there is a clear change in direction of the particle!

    The only explanation I can think of is that special relativity is actually degenerate in the sense that for any 4-momentum and initial conditions there are 2 possible worldlines that are "solutions" (the normal one and the time reversal of it). So what we're actually seeing here is a "spontaneous" switch between two intersecting worldlines with identical 4-momenta.
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  3. Jul 9, 2013 #2


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    I'm not sure what you mean by "negative mass" or how you conclude that a particle, moving "backward in time" will have negative mass.

    Richard Feynman once proposed (I'm not sure how seriously. I'm never sure how seriously to take Feynman!) that positron be considered an electron "moving back in time". But he then asserted that its energy, not its mass, would be negative.

    By the way, Newtonian physics also has no "conservation" laws forbidding backward movement in time. There is, in thermal physics, a law about "increasing entropy" but that's a statistical law.
  4. Jul 9, 2013 #3
    I think you should read my post more carefully, because I addressed everything you commented on already..

    I thought I made it clear I wasn't talking about particles with negative rest mass. However, their relativistic mass (i.e. their energy) would be negative. So they would behave similarly (but not necessarily identically) to a particle traveling forward in time with negative mass. The derivation of why a particle with positive rest mass traveling backwards in time would have negative energy is very straightforward from basic SR.

    I'm not asking for a law to forbid backward movement in time. In fact I'm making the assumption that no such law exists! I'm looking for a law that would forbid spontaneous creation of mass/negative "mass" pairs from nothing, if particles were allowed to travel back in time. Basically, if there is no mechanism to stop this spontaneous particle production (which we have never observed), then clearly there must be something preventing backwards time travel! Since relativity is perfectly symmetric under time reversal, it must come from some other theory/domain
  5. Jul 9, 2013 #4
    I have no idea the consequence/meaning of what is said , but the use of dimensions to explain the stuff I don't understand is neat, imo time/length should explain all the mechanics as they apply to matter, and perhaps they do. An interesting read in other words :smile:
    It's a continuum, easily spoiled by semantics, wiki uses the term "quantitative transition", SR usually uses just c.

    so what's backwards in time besides physically meaningless? Not so much a law, and probably circumnavigates your point.

    Geometrically I think math shows the relationship between time & length. so maybe equally; what would it mean to go "backward" in length?

    I wonder if "Foward / Backward" time are used the same as "up / down" in length, which is merely orientation. so forward in time must mean towards me, Backward in time is away from me lol. Or is it orientation of the matter itself is backward/forward in time and ONLY from a casual perspective the WHOLE universe can agree on, less spacetime expansions ect., yea i like that one :rofl:

    Oh and comparative geometric "backward" time is just that; a comparative & in 2D no less, where's the invariance of this metric?(invent can't go at or less than c, which the only thing I can see as being "backwards time/length")?
    Last edited: Jul 9, 2013
  6. Jul 9, 2013 #5


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    Okay, do you have any reason to believe that there are particles with negative mass?

  7. Jul 9, 2013 #6
    Again, see the FIRST thing I said in my thread. I'm not talking about reality here, I'm talking about the world governed by general relativity, classical E&M, and relativistic dynamics. It doesn't matter if negative mass particles DO exist, I'm examining what special relativity predicts IF they existed
  8. Jul 9, 2013 #7
    SR says there is no backwards in time, less you define "backwards in time" in some not backwards in time way :tongue2:. SR isn't independent of reality.

    orientation of the matter itself is backward/forward in time and ONLY from a casual perspective the WHOLE universe can agree on, less spacetime expansions (spoiling the assumed metric) ect.
    Last edited: Jul 9, 2013
  9. Jul 9, 2013 #8
    Well yes if you want to get technical there is no such thing as "backwards" or "forwards" in time in the absolute sense. I implicitly meant with respect to the "laboratory" frame though..

    Ignoring that technicality, SR IS independent of reality. It's a mathematical model, which as far as we can tell accurately depicts reality in all domains. It is the ONLY theory that can make this claim though (arguments can be made for statistical mechanics and E&M but its not as clear cut), which is why I said I wanted to stay away from "reality" in this discussion of macroscopic physics.

    My question is simply about a thought experiment conducted in a universe that follows our macroscopic laws of physics. Let me try to condense it further:

    Is there any mechanism within the general relativistic framework preventing the spontaneous appearance of two identical particles with equal and opposite 4-momenta?
    i.e. is there anything preventing a particle from spontaneously reversing its propagation through time?
  10. Jul 9, 2013 #9
    it's true as far as has been tested the rest is theoretical, what in SR hasn't been validated?

    Its a physical technicality and not semantics and see it being as simple as a geometrical consequence of spacetime as we have measured it.

    I don't know 4-momenta let alone the equal and opposite of it, Im of no use to this thread now :smile:, spectating...
  11. Jul 9, 2013 #10


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    You cannot spontaneously reverse time orientation along a time-like curve if space-time is time orientable. The notion of "future directed" along time-like curves must vary smoothly.
  12. Jul 9, 2013 #11


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    I'm not sure this is actually distinguishable from a single particle existing from t = minus infinity to t = plus infinity. Or, more precisely, I think that for what you are suggesting to be consistent with conservation of energy-momentum, it could not be distinguishable from a single particle.

    This part is OK, but what will the "two" worldlines look like? I don't think they'll look like you think they will.

    I don't think this is how things will look, because as you describe it, to the observer, both particles are moving forward in time, so both of them will have positive energy. Energy is relative to the observer, not the particle. So this process does not conserve energy. (I'm assuming it conserves momentum by hypothesis, with the particles having equal rest mass and velocities of equal magnitude and opposite directions.)

    For the second particle to have negative energy while still having positive rest mass, the time component of its 4-velocity, in the observer's frame, must be negative. But this means that the direction of increasing proper time for the particle is the *negative* time direction. Which means that we really have a single worldline, going from t = minus infinity to t = plus infinity; and the "spontaneous creation" event is just a particular event on the worldline, with the first particle's worldline being the portion to the future of this event, and the second particle's worldline being the portion to the past of the event. (The worldline can't "change direction" at the event because momentum has to be conserved.)
  13. Jul 9, 2013 #12
    Well, SR and GR allow for tachyons, closed timelike curves, time travel, and plenty of other things people rule out as "unphysical". However, there is nothing in the theories themselves that prevents these phenomenon. Also, just because we've validated a theory in all the domains accessible to us doesn't mean its valid in all domains. You can't claim SR and reality are completely compatible because that can never be known for sure. This is exactly why I don't want to bring "reality" into this discussion at all. It's a purely theoretical question about a physical model we have.
  14. Jul 9, 2013 #13
    Sorry, I know exactly what you're thinking and where the confusion is. I just wish I could draw a picture on here more easily to clarify. Hopefully the attached picture will help a little bit.

    The particle to the left is traveling through time in the opposite direction as we are, so in our frame it has negative energy.

    Attached Files:

  15. Jul 9, 2013 #14
    Good point :smile:
  16. Jul 9, 2013 #15


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    But on the diagram the particle on the right has reversed energy but not reversed momentum, i.e. you've drawn it in the wrong direction.
  17. Jul 9, 2013 #16
    No its drawn correctly, I think the arrows are just misleading you. The y axis is the lab time, and the arrows just show the worldlines of the particles. In the lab frame the left particle is moving to the left, and the right particle is moving to the right.
  18. Jul 10, 2013 #17


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    This picture matches what I imagined you to be describing, but I see now that I didn't fully understand how you were imagining the signs of the energy and momentum of the two particles. Basically, you're exploiting the fact that the dispersion relation ##E^2 - p^2 = m^2## only has squares of the energy and momentum in it, so we can switch the signs of either ##E## or ##p## without violating it.

    At first blush, there is nothing in this that violates conservation laws, because the net energy and momentum is zero everywhere! Before the "spontaneous creation" event, there are no particles, for a net energy and momentum of zero; after that event, there are two particles with net energy ##E + (- E ) = 0## and net momentum ##p + ( - p ) = 0##. Classically, nothing at all has changed. But see below for a wrinkle you might not have considered.

    (Quantum mechanically, of course, the Feynman picture of the creation of particle-antiparticle pairs out of the vacuum is similar to what you're describing, as HallsOfIvy mentioned. The difference there is that the particle and antiparticle have to come back together and annihilate each other within the time/space limits of the uncertainty principle, which means that they can't be on the mass shell, i.e., they don't satisfy the dispersion relation I wrote down above. You are describing a classical process where both particles *are* on the mass shell, which guarantees, as I said above, that the net energy and momentum is zero everywhere in the spacetime.)

    The wrinkle, though, is this: what happens if we change frames? Suppose we boost into the rest frame of the positive energy particle. Its 4-momentum in this frame is ##(m, 0)##. What is the 4-momentum of the negative energy particle in this frame? We don't even have to calculate it explicitly; it should be obvious that it's going to be ##m (- \gamma', - \gamma' w)##, where ##- w## is the negative energy particle's ordinary velocity in the new frame and ##\gamma'## is the gamma factor associated with ##w##. This violates conservation of *both* energy and momentum in the new frame, since before the spontaneous creation event the net energy and momentum is zero, and after it the net energy is ##m (1 - \gamma')## and the net momentum is ##- m \gamma' w##, neither of which are zero (in fact, both are negative).

    So it looks like the key issue with your proposal is that it violates 4-momentum conservation in every frame except the center of mass frame.
  19. Jul 10, 2013 #18
    There is nothing in the mathematical toolbox that SR uses to prevent it; however, as a physical theory it is based on such things as effects following causes, and with time defined by means of clock readings that increment only.
  20. Jul 10, 2013 #19


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    Yup... another guy said that, and about the same way. :smile:




  21. Jul 10, 2013 #20
    Causality is really an outdated notion. There are theories that exploit and allow retrocausality. You might just call these mathematical "tricks", but since they are just different interpretations of the same theory, whose to say which is "correct"?

    Feynman and Wheeler's absorber theory
    General Relativity (CTCs)
    Retrocausal interpretation of QM
    QFT! (some off-shell virtual particles, and any anti-matter can be viewed as traveling backwards in time)
    Last edited: Jul 10, 2013
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