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Why is an electron a positron going backwards in time?

  1. Oct 31, 2013 #1
    Hi all, I was wondering how wheeler came to the conclusion that an anti-particle is a particle going backwards through time?
  2. jcsd
  3. Oct 31, 2013 #2


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    I'm pretty sure that's just a neat math solution that is not really believed to represent reality. In other words, it's like epicycles ... it will give you a good answer to calculations but it isn't real.
  4. Oct 31, 2013 #3


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    One way to see it is this: Draw a simple "one space dimension, one time dimension" diagram with "time" on the vertical axis, x on the horizontal axis. Draw a zig-zag line with arrow heads on each leg pointing upwards (the future). If you now cover that with a card with a thin horizontal slit (representing "now") you will see the legs as individual dots. As you move the slit upward, crossing a lower vertex of the zig-zag, you will see two dots suddenly appear- the creation of an "elecron-positron pair". They will move away from each other but other legs of the zig-zag will appear as other dots, until until your slit crosses an upper vertex when two dots merge and disappear- the annihilation of an electron and a positron.

    But removing that "mask", seeing all "time" at once, you see the entire zig-zag. The "dots" that you saw moving to the right are the legs going up and to the right- electrons- while the "dots" you saw moving to the left are legs going up and to the left- positrons, which we can see now are those same electrons, still moving to the right but now going down- back in time.

    I not absolutely sure I would agree with phinds that "it isn't real". To many "mathematical fictions" have been shown to correspond to reality. In fact, I'm not all that clear on what "reality" is in physics anymore!
  5. Oct 31, 2013 #4
    It is as real as anything else in physics. Physics is always done by matching a mathematical model to observations. If the model matches than it is a good model and that's all there is to it. In the Path integral interpretation of QM particles can move backwards in time.
  6. Oct 31, 2013 #5


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    What is interpreted as "time" here? Is it coordinate time, proper time or some other concept? What does the time arrow in Feymann diagrams represent?
  7. Oct 31, 2013 #6
  8. Oct 31, 2013 #7


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    CPT symmetry is the key. At the moment, it is believed that the combination of the 3 operations: charge conjugation, parity transformation and time reversal will cause no change to any system which you apply these operations to. To quote wikipedia: CPT theorem says that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have a CPT symmetry. Also, in 2002 Oscar Greenberg proved that CPT violation implies the breaking of Lorentz symmetry. So CPT violation is a very serious offense indeed! :)

    edit: whoops, I now realise that I have not answered the OP, which was about Wheeler's research specifically. Sorry about that.
  9. Oct 31, 2013 #8
    You just described most of QM. All of it is just meant to be a math solution which gives you the right answer, but doesn't describe actual reality. Unless you think Hilbert space and operators are a real thing.
  10. Oct 31, 2013 #9


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  11. Nov 1, 2013 #10


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    I wouldn't put it that way. As somebody mentioned, you can say this about whole of QM, and it's true to an extent, but more importantly, all we have for descriptions at these levels are the models. And the particular model, RQFT, implies that time-reversed particle and anti-particle are equivalent.

    What you should keep in mind is that propagation of particles backwards in time is very different than propagation of information backwards in time. Think of this as phase velocity vs group velocity. So the time component of the wave 4-vector points in opposite direction in time, but the "group" propagation is forward for particles and anti-particles, so the information is always carried forward without violations in causality.

    Once you are comfortable with this distinction, it shouldn't bother you that anti-particles are traveling backwards in time.
  12. Nov 1, 2013 #11


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    That's an interesting point too. What is the definition of information and causality in this context? If we define causality to go in the direction of positive time (for timelike separated events), then when we do a CPT transform, this 'causality' direction would also swap, since the direction of positive time has also swapped. Sound about right?
  13. Nov 1, 2013 #12
    The particle is just its 1D trajectory in 3+1 dimensional spacetime - there is no point in saying that it propagates forward or backward.
    However, indeed we can ask about the cause - e.g if photon production was caused by past or future event.
    We know how to cause it by a past event: e.g. by stimulated emission in laser.
    The question is if we can make CPT analogue of such stimulated emission (what seems simple for free electron laser below), getting stimulated absorption?
    While stimulated emission causes excitation of the target, shouldn't stimulated absorption cause its deexcitation (target needs to be excited to the corresponding energy)?
    https://dl.dropboxusercontent.com/u/12405967/freeelectron.jpg [Broken]
    Last edited by a moderator: May 6, 2017
  14. Nov 1, 2013 #13
    What math did they derive this from?
  15. Nov 1, 2013 #14
    If it was a question for me: exactly the same math as behind stimulated emission, but transformed through CPT symmetry.
  16. Nov 1, 2013 #15
    I get the intuition of population inversion Einstein coefficients ect. but I don't know stimulated emission math.
  17. Nov 1, 2013 #16
    Indeed, I have also a problem to imagine CPT analogue of a standard laser (population inversion after CPT transformation is the same population inversion) ... but for free electron laser it seems quite simple ...
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