The destiny of an antiparticle

[El Hombre Invisible]

But, the Feynman interpretation is basically saying that the Einstein's equations tell you the energy impact of doing a 180 degree turn in the time direction.

Do you mean a particle of given velocity will always produce the same energy photon when it changes direction? I was thinking that as long as the velocity of the antiparticle was, say, less than that of the particle, a smaller photon than twice the energy of the particle may be produced. And likewise if the antiparticle travels faster than the particle, a larger photon may be produced.

Put another way, must annihilating pairs have the same energy? I would have thought not, in which case the photon emitted by the particle determines the antiparticle's velocity.

Thanks again.

 

[ohwilleke]

Good question. Certainly, not all anti-matter is automatically toxic to all matter. If it were, mesons wouldn't exist, as all of them have a quark and an anti-quark. Indeed, the eta-c meson, for example, is composed of a charm and anti-charm quark and opposite color charges, although an eta-c can produce an annihillation. See here: http://pdg.web.cern.ch/pdg/cpep/all_decay.html

I've never heard of a particle annihilating with anything other than its exact anti-particle.

Indeed, if true, that would provide some circumstantial motivation for the Feynman interpretation. (By the way, while the examples of quantum tunnelling and Big Bang were inspired by Feynman's interpretation, I made those up myself).

A pretty deep discussion of the issues of quantum entanglement, special relativity and causality can be found here: http://fergusmurray.members.beeb.net/Causality.html and illustrates the kind of discussion that ZapperZ says that scientists aren't having about the topic.

This explains how quantum entanglement goes to another important and partially philosophical in character debate in quantum mechanics over the Copenhagen interpretation: http://plato.stanford.edu/entries/qt-entangle/

This person takes the popular view that no information is transmitted, even though like results occur, which make the key philosophical distinction of information transmitted between observers and information transmitted between particles (without being very upfront about it): http://www.mtnmath.com/whatrh/node73.html

 

[El Hombre Invisible]

Cool. Will check those out right away. BTW, I wasn't talking about a particle annihilating with anything other than its own antiparticle - I was just asking for clarification that the speeds of annihilating pairs are allowed to be unequal, or to put it the Feynman way, that when an electron backs up and becomes a positron, there is no reason why that positron would have the same speed as the electron, therefore no reason why the emitted photon need be exactly twice the energy of the original electron. It's a question of whether or not the resultant photon's energy is predictable prior to emission without looking at the other particle in the annihilation.

Your Big Bang example is along similar lines to something I talked about earlier, with some major differences. If pair creation occurred shortly after the big bang from photons, it may well be as true to say that electrons traveling towards the bang created those photons (which traveled backwards also), then turned and traveled away from it. In this interpretation, the big bang is a barrier by which all backwards-travelling electrons must turn back. It's a funny way of looking at it, to say the energy was not so much a consequence of the bang itself but of the matter that came later, but I find it strangely more intuitive than spontaneous pair creation. The prevalence of matter over antimatter could still be pure coincidence. There is no reason why each particle in every pair created after the big bang need travel forward very far in time and, likewise, there is no need for every particle now traveling forward to turn back and make it this far back in time. Theoretically, the matter to antimatter ratio need not be fixed.

I'm afraid quantum tunnelling is something I've heard the name of, but know nothing about. Is that related to entanglement? I thought your entanglement example was very interesting, and could not determine why Zz said it would break SR. If the medium by which the information was transferred was a photon, then our view of such a phenomenon would be only the coincidence of both particles absorbing photons at the same time, with each even more coincidentally having the opposite effect. I'm not as learned as Zz, but I have never heard of anything in SR that bans coincidence.

 

[ohwilleke]

Zz said it would not break SR and was making the point (basically along the line of the last link) arguing that informed people never thought that it would.

Quantum tunnelling is an entirely different ball of wax. It basically says that there is a probability that particles can do seemingly impossible thing and that the less far from possible those things are, the more likely it is that they will happen. (Very crude non-technical language there). Every transistor relies on tunnelling to work.

There is, call it a "folk theorem" which says that information can't travel faster than the speed of light either. The questions include (1) whether there is information transfer in entanglement situations, and (2) whether you can properly call a resolution of an entanglement a coincidence.

 

[vanesch]

A pretty deep discussion of the issues of quantum entanglement, special relativity and causality can be found here: http://fergusmurray.members.beeb.net/Causality.html and illustrates the kind of discussion that ZapperZ says that scientists aren't having about the topic.

I'd like to point out that, although the discussion is quite good in that link, it misses (as usual :-) an essential part, which is the relative state view on EPR experiments, and resolves the locality issues.
There seems to be a hypothesis which is never mentionned when one talks about the joint probabilities of events at Alice and at Bob, and that is: one seems to take for granted that Alice made, at a certain event, a definite observation (which has a certain probability of occurring), and that Bob also made a certain observation (which has a certain probability of occurring).
However, that is somehow taking for granted the projection postulate in quantum theory, a postulate which is obviously non-local, and not even Lorentz-invariant.
So one shouldn't be surprised to find, in that view, non-local probability distributions. The miracle resides in fact not in the non-locality, but in the fact that this non-locality is inexploitable to build a faster-than-light telephone. Or so it seems.
In a relative-state (or MWI) view on quantum theory, one sticks however to the unitary evolution (and its associated lorentz invariance). This denies then any objective outcome at Alice's and at Bob's: it just states that Alice interacted with her measuring apparatus (and now her body appears in entangled states), and the same for Bob). The observer associated with Alice however, has to choose to be associated to one of her factorized body states (according to the Born rule) and thus "chooses a branch" which makes Alice-observer get the impression that random things occur. In that branch, whenever she travels to Bob's place, she will interact with a body state of Bob which was entangled with a certain state of HIS measurement apparatus. After this interaction with Bob, she will entangle her bodystates with his (mmm:-) and again the observer associated with Alice's body will have to make a choice. As such, locally, the observer associated with Alice will learn about the result that THAT BODYSTATE "observed". So Alice-observer will then deduce (erroneously) that Bob's body DID OBSERVE that result when he was doing that measurement, back then. Only, all results which were possible to Bob, did occur, and it was Alice's observer herself, by choosing one of the bodystates of Alice, which introduced the particular choice of outcome at Bob's (namely the outcome associated with Bob's bodystate which is in a product state with the chosen Alice body state).

So there WAS NO joint probability of outcomes, but of course for Alice, everything happened AS IF there was such a probability, when she projects back in time what Bob did. However, this is entirely due to two things which are completely local: there are the LOCAL interactions of bodies with measurement apparatus and with the system under study, which just lead to entangled bodystates with the state of the system at hand, and the LOCAL interactions of Alice and Bob when they meet to compare notes. And there is, each time, as a consequence of such an interaction and entanglement, a LOCAL choice that the observer associated with a body must make, according to a probabilistic rule, called the Born rule.

As such, this is also an explanation for the "mysterious conspiration against faster-than-light telephones" that seems to occur in Copenhagen quantum theory: indeed, there is no non-local mechanism at all, so there cannot be any non-local communication. We only erroneously deduce probabilities of space-like separated "measurement outcomes" which weren't outcomes, but just evolving systems, which we seemed to force into an outcome when we interacted locally with them (and hence made us choose again one of our entangled bodystates).

This view resolves all locality issues. The price to pay is a difference between the objective ontology and the subjective experiences, the latter being a single random path of an observer (according to the Born rule) through the objective reality which contains all possibilities, making random choices upon each interaction with "the rest of the world".

One can, or cannot be in favor of this explanation (I am, you guessed it). However, one cannot deny its existence when treating locality issues in EPR. I am of the opinion that it resolves by far in the most elegant way the issue, and this by sticking strictly to as well the formalism of SR as the (unitary) formalism of quantum theory.

This person takes the popular view that no information is transmitted, even though like results occur, which make the key philosophical distinction of information transmitted between observers and information transmitted between particles (without being very upfront about it): http://www.mtnmath.com/whatrh/node73.html

Well, in the MWI view, the information that is transmitted is through the (slower than light) OBSERVER himself, because the "measurement" of Bob wasn't resolved until Alice (her body) contacted him (interacted with his bodystate) and had to make a choice herself (the Alice observer).

cheers,
Patrick.

 

[ohwilleke]

After this interaction with Bob, she will entangle her bodystates with his (mmm:-)

Somebody is way, way too hard up.

More seriously, thanks for bringing the MWI into the discussion. I personally don't like the MWI, but your example does a good job of illustrating its intepretive power.

 

[vanesch]

More seriously, thanks for bringing the MWI into the discussion. I personally don't like the MWI, but your example does a good job of illustrating its intepretive power.

Personally, I evolved from rather anti-MWI to quite in favor of it, for several reasons, the most important being:
- all current attempts at incorporating gravity (string theory, loop quantum gravity) seem to take the superposition principle very seriously - although I think that the jury is still out on this.
- symmetry principles of which the guiding importance in physics cannot be denied are respected throughout the entire theory, which is not the case for any other formulation of quantum theory (copenhagen, or Bohm).

Nevertheless, I'm a heretic in the MWI camp, in the sense that I think that the probability rule (Born rule) does NOT follow automatically from the unitary evolution ; I even recently submitted a paper concerning this
(see http://perso.wanadoo.fr/patrick.vanesch/articles/borneverett.pdf). I think the Born rule IS an extra postulate which describes the ontological/epistemological transition.

However, I don't know how seriously I have to take it - as I pointed out already in the past, every century or so, our paradigms change, so it would be pretentious to think that we now reached "the end" and have "the right" paradigm: 300 years from now, our vision will be totally different in any case.

But I think that MWI, even just as a formal game, has the possibility of enlightening the understanding of a lot of "quantum mysteries", of which EPR setups and delayed choice quantum erasers are examples.

Especially the locality issues in the EPR case are well illustrated: it is to my knowledge the only explanation which clearly puts forward both facts: the clear observation of correlations, and the impossibility of making FTL telephones using the phenomenon. It also helps resolve issues of "when do we apply the collapse".
So I think that in this context, MWI has its place just as Bohm's theory has its place, as _examples_ of what is often claimed is not possible :-)

cheers,
Patrick.

 

[El Hombre Invisible]

Ahem. I won't pretend that any of that didn't go over my head, though I'm trying to get that link opened right now. I just had a thought relating to a point I asked about earlier - that is, is there any reason why the photon emitted has to be twice the energy of the original electron or, to put it another way, does the speed of the positron have to be the same as the electron? Would I be right in saying they would have to be equal, as momentum must be conserved in pair creation? Having said that, if the speeds weren't equal, could the relativistic momentum of the photon make up the difference? Thanks. Sorry for interrupting. What is MWI? Mars War One?

 

[masudr]

The momentum has to be conserved in any interaction, and so the momentums of both the electron and positron have to be equal and opposite. MWI = Many worlds interpretation (but I'm guessing if you didn't know it already, me telling you wouldn't help too much (:, look it up on the web, in your local library etc).

 

[El Hombre Invisible]

Sounds far out. I'll dig around. I tried to understand Patrick's explanation and I am thinking that, in words an undergrad can understand, the point is that the information isn't being transmitted instantaneously because to compare the results of a change to one of the entangled pair with the other, somebody or something has to travel between the two (such as Alice radioing Bob or vice versa) and it is this medium by which the information crosses..? If not, I'll... try again in a few years. ;o)

Thanks to all for your help with the pair problem. I think it has kind of brought me round full circle, as although Feynman's approach seems to yield a satisfactory explanation for spontaneous pair creation and annihilation, it does seem to depend equally coincidentally on the amount of energy released (forwards or backwards in time). Ultimately neither interpretation seems free of what I believe are scientifically known as niggles.