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The destiny of an antiparticle

  1. May 3, 2005 #1
    I'm pretty much a newby to the ins and outs of QED and have a question about antiparticles. First: stop me if I'm wrong... Antiparticles can be thought of as (or simple are?) normal particles moving backwards in time. Experiments have shown photons splitting into electron-positron pairs followed by the positron annihilating with an electron to reproduce a photon leaving only the seemingly brand-spanking new electron.

    QED says what's really going on is an electron is emitting a photon, moving backwards in time, emitting another photon (that itself travels backwards in time) and moving forwards in time again. This view surely necessitates that every antiparticle in the universe is predestined to annihilate with a particle, because travelling backwards in time that annihilation is the very origin of that antiparticle. Is this right?
     
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  3. May 3, 2005 #2

    ZapperZ

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    Whoa! Aren't you having a bit of an accounting issue here?

    1. You have a photon

    2. Photon turns into electron-positron

    3. electron and positron anhilate to produce photon

    4. You are then left with a "brand-spanking new electron"?

    Zz.
     
  4. May 3, 2005 #3

    HallsofIvy

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    No, he didn't say that. Notice that you had to have at least one electron initially to anhilate the electron. In 2 an electron and positron are created, in 3 an electron and positron are anhilated (and you get back the photon you lost in 2). The bookkeeping works. It was Feynman who popularized this idea (although I believe it was not original with him)- if we think of a positron as an electron "moving back in time", then we have no problem with the bookkeeping between 2 and 3. That also explains why all electrons are identical- there's really only one electron in the universe, whizzing back and forth in time!
     
  5. May 3, 2005 #4

    ZapperZ

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    Err... I must be dense. You need an electron to anhilate another electron?

    Unless I misread something (entirely possible), you are saying that an electron anhilate with itself? I can see how an electron moving forward in time anhilate with ANOTHER electron moving backwards in time. This is no different than a particle with positive energy anhilate with its mirror image that has a negative energy. After all, if you look at Dirac equation, you can put the negative sign on the energy quantity also. But these are two different entities that are anhilating each other, not the same entity.

    Zz.
     
  6. May 3, 2005 #5
    I think that the first two paragraphs of the OP are laying out different scenarios, so that's where the disagreement is coming from. But the scenario in his first paragraph does appear to have an accounting issue.
     
  7. May 4, 2005 #6
    Zz: Not an accounting issue - an ambiguity issue. I said "followed by the positron annihilating with an electron"... AN electron, not the same one produced in the pair. Sorry, I didn't break this down clearly.

    Let me try again. 1) You start with an electron and a photon. 2) The photon produces an electron-positron pair. 3) The positron annihilates with the original electron producing a new photon, leaving the (as I said) SEEMINGLY new electron.

    From my understanding, what QED says is that the two electrons and the positron are actually the same particle - the original electron - as it A) moves forwards in time; B) produces a photon and moves backwards in time; C) absorbs a new photon and moves forwards in time. (To keep things simple, I have now assumed all photons are moving forwards in time as the photon is its own antiparticle.) With this approach, the positron only existed at 2) above because the electron emitted a photon at B) some time later. This suggests that all positrons are doomed to annihilate, as its origin is in the future. Is this right?

    As for an electron annihilating with itself - no, this is not right. You have to be consistent. If you are observing that the positron is really the electron moving backwards in time, you have to realise that no annihilation is occurring - the electron is simply emitting photons and changing direction in time. Looking in both directions in time, no annihilation is occurring.
     
  8. May 4, 2005 #7

    ZapperZ

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    1. Why would you need the first electron?

    2. How would you know the anhilation occured with which electron? Why would this make any difference which electron was anhilated?

    In quantum statistics of indistinguishibility, you in fact, have no ability to distinguish between one and the other.

    This is VERY confusing. Would it help if you learn about electron and holes in a conductor? At T=0, the ground state of a Fermi sea of electron (the vacuum state) is full. Upon excitation, an electron can jump above that sea to create an electron in the excited state, but it also leaves behind a hole in the fermi sea. That hole, when compare to the rest of the sea of electrons, has a positive charge. So you have used the energy of excitation to create an electron-hole pair. This is no different than the creation of a electron-positron pair. The positive hole is the antiparticle of that electron in this system. The only difference being that in this case, I tag the "-" sign to the energy of the hole, whereas in the electron-positron pair, I tag the "-" sign to the time factor.

    You should not confuse yourself between the mathematical formulation and physical meaning. As useful as the Feynman diagrams, you cannot lose sight that it is a representation of the mathematics, especially a representation of higher order perturbation.

    Zz.
     
  9. May 4, 2005 #8

    vanesch

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    No, not really. Nothing stops you from having an electron moving backward in time all the way, from T=+infty to T=-infty. That's a free positron.

    cheers,
    Patrick.
     
  10. May 4, 2005 #9

    Chi Meson

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    A tangent to the original question: can we assume that any observed positron must eventually annihilate, regardless of our conceptual reasoning?
     
  11. May 4, 2005 #10
    Zz: apologies, I am not explaining myself clearly. I am reiterating a phenomenon I have read about that is apparently very real and the (or a) QED explanation describing it. There is no question of me 'needing' the original electron - this is the phenomenon I am asking about (otherwise it would be a different question, one that you may have answered).

    The ins and outs of measuring which, what and where can be left aside. My question is specific to the theory in QED that a positron is an electron moving backwards in time, and this change in direction of t coincides with the emission (or, backwards in t, absorption) of a photon. Even if this is bull, within the constraints of this theory, does this necessitate that every positron must eventually annihilate (i.e. does every positron originate from an electron in the future)?

    Patrick: thanks for response. I was unprepared for your answer, as it kind of leads straight into the fate of the universe as a whole. I take it T=-infty refers to the relativistic notion that, if you could travel towards the big bang, you'd never get there. I didn't mean to end up in cosmology, but let's take the big bang as t=0. The expansion of the universe is accelerating, so let's assume no big crunch. At t=0 we have a kind of boundary for matter, with (to us) antiparticles heading straight towards the big bang, going "arrrghhh, it's too hot, it's too hot" and turning around again (I would). I can't really get my head around what happens at the other end, if there is no other end ! Where do these backwards-moving electrons come from?
     
  12. May 4, 2005 #11
    That's the thing - there's no physical reason why a positron, that I am aware of, must annihilate in a universe whose expansion is accelerating. I'm tempted to say balls to Feynman and stick with Zz's explanation of antimatter as the only one. If this ain't the end of the universe, armaged- no, sorry that's just s---.
     
  13. May 4, 2005 #12

    ZapperZ

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    OK, so now I'm confused.

    Are you saying that you have an electron, and then this electron later on travels back in time and transformed itself to a positron? That is what I gather from your description of an electron changing "in direction". I want to reiterate that if you look at the feynman diagram of a pair anhilation, for example, that you have TWO separate entities being zapped together: an electron moving forward in time, and a positron moving forward in time.

    On a related but SEPARATE issue, if you look at the dynamics of the positron and you do a time-reversal symmetry operation, and you play around with where the minus sign should be tagged to, you can get a mirror description of it as an electron moving backwards in time. Whether this is a physical solution or have any physical meaning, I cannot say (it certainly has implications to symmetry operations). I'm just thinking that you are looking into this way too much, much more than what is implied physically.

    Zz.
     
  14. May 4, 2005 #13
    This isn't a separate issue; it's the crux of my question, but now I see why we have our wires crossed. Let me back up. Your description of antimatter is the one I am used to. I am not disputing it, and I am supposing nothing of my own invention. I had heard about the 'positron appears identical to an electron moving backwards in time' thing before - specifically in relation to virtual pair creation which is much like an electron moving in a kind of time-loop, emitting and absorbing photons on the way. Never gave it much thought.

    Now, I'm just an undergraduate and will probably only skim the surface of QED in my degree and won't get into this properly until postgrad studies so I like to skip ahead a lot and I read Feynman's lectures on QED for undergrads like myself. When describing the phenomenon in my OP, Feynman did not say 'it looks just like...' he states it IS a single electron moving forwards and backwards in time. Now this is old material and even Einstein got poo-pooed about some things, so if it's balls then fair enough, but if this theory is true, does this necessitate positron annihilation? Treating positrons as separate, forward-moving particles, there is no reason why they must ever annihilate with anything. They were created in the past and their fate is unknown. Taking Feynman's viewpoint, though, the positron was created in the future (by 'created', I mean it ceased to look like an electron and started to look like a positron) which, Patrick's suggestion aside, sounds like every antiparticle in the universe is going to annihilate. With the big bang behind us, the positron's future (our past) is also set in stone.

    I do get what you mean about not taking Feynman diagrams at face value, but this was a written statement and was fairly unambiguous. I wish I had the book here now but I don't.
     
  15. May 4, 2005 #14

    vanesch

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    I think you read too much in QED :-) Let's not forget that QED is *special relativity* (flat spacetime) and quantum fields, and that (at least the unitary part) of the theory is completely time-symmetric. So, cosmology is not incorporated in QED.
    Your question is: because positrons are electrons going backward in time, do they have to come from an electron going forward in time and then interacting (meaning, an annihilation in the future), right ?
    My answer is that, given the settings of QED (flat Minkowski spacetime, time symmetric theory), there is nothing more mysterious with one single electron going backward in time "all the way" (as a free particle), than it is mysterious, or not, to have a free electron going forward in time "all the way" (as a free particle). It is a symmetry of the theory, that to every particle going "forward in time" there is also a situation of the same particle, going "backward in time". That's why to each particle, there is an antiparticle. It is just dictated by that symmetry. It's even more funny: that same symmetry tells you that you are free to choose which particle is the "anti-particle". So your happy electron going forward in time can be considered as a positron going backward in time ! And now you don't have a conceptual problem anymore with positrons, but you now wonder whether each ELECTRON needs to be annihilated in the future: after all, it is a positron that was bounced back in time....

    The message is: don't take that "forward in time" and "backward in time" too literally. Do as everyone else: consider all particles as going forward in time, and say that there are 2 of them: particles, and anti-particles.
    It is just a nice way of remembering that the fact that to each particle, belongs also an anti-particle, is originally due to the time-symmetry of special relativity.

    cheers,
    patrick.
     
  16. May 4, 2005 #15
    I don't doubt it mate, but once riled I just can't let these things lie. All of my quantum theory conversations end with someone saying STOP ASKING SO MANY DAMN QUESTIONS!
    Oh yes, I get the arbitrari...ness (?) of my assumptions but, as it works both ways, so does my question. I think, though, this is just another way of asking "what happens to all the stuff?!?" I dunno... maybe we'll all end up in black holes and then I'll have an answer. I'm just having difficulty figuring out where in the future a backwards-travelling electron is sourced. The big bang offers a nice, simple boundary by which any backwards-travellers must turn.... forward, or from a more sensible point of view, from which matter-antimatter pairs can be created. The heat death of eternity doesn't seem to offer one, or perhaps (like the big bang) there is an end to time but nothing can ever get there. Yeah, that'll do. I'm gonna post a different question now... one that won't send me insane. :surprised
     
  17. May 4, 2005 #16

    vanesch

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    Yes, and I wanted to make you see that you can also see normal electrons as backwards-travelling positrons, so where in the future are these backwards-travelling positrons sourced (which we observe as normal electrons)?

    cheers,
    Patrick.
     
  18. May 5, 2005 #17
    Yeah, I get you, and the inconsistency of my thinking. My choice of electrons 'going the right way' was based on the prevalence of matter over antimatter. It is not possible for every electron to annihilate in the future (and not reproduce) because there are so many more of them. However it is possible for every positron to annihilate in the future. This pushes me to think that one is going towards the future and the other is heading back. If the high energies of the big bang to provide (or are consequence of) a barrier, it is easy to think of positrons as electrons heading towards it, turning back and becoming electrons as we see them with a high probability of going on forever, hence more electrons (which don't turn back) than positrons (which will in the past). But I see that this is the wrong route - many thanks for altering my mind. I pay my dealer good money to do that. ;o)

    How linked in this respect are energy and time? The way I see it, pair creation and annihilation could be seen either way as a particle emitting more EM energy than it has in one direction in time and, in compensation, heading off itself in the other. If the photon it emitted is done so backwards in time, this would appear to be pair creation. If forwards, it would appear to be annihilation.
     
  19. May 5, 2005 #18

    ZapperZ

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    Draw the feynman diagram for this. The way you described it, it could be intepreted in a dozen ways, besides the fact that I don't quite get what you are trying to say.

    Zz.
     
  20. May 5, 2005 #19
    Or upside down... either way.
     

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  21. May 5, 2005 #20

    ZapperZ

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    See, this is where I will utter the words you probably will not like: "it just doesn't matter!"

    I can look at your feynman diagram and say a particle and its antiparticle partner anhilate to produce a photon.

    Or, I can say that a particle moving forward in time meets the same particle but moving backwards in time and they anhilate each other to produce a photon

    Or, I can say a particle moving forward in time "disappears" and becomes that particle moving backwards in time. When it does this, a photon is emited.

    Or, I can say an antiparticle moving forward in time "disappears" and becomes that antiparticle moving backwards in time. When it does this, a photon is emitted.

    My question to this is: so what's the big deal? The reason why when you look at such a sketch that most people do not bother to label it with arrows, etc. is that such a thing is "redundant" because one description is idential to the other. All 4 of what I've said is a description of the IDENTICAL mathematics!

    I will repeat what I had said earlier that the feynman diagram representing this dynamics is a representation of the MATHEMATICAL operation! We cannot lose sight of that fact. Just because you are seeing different parts of the limbs, it is STILL the same animal.

    Zz.
     
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