Explain crossing without invoking QFT?

[MWBratton]

Explain "crossing" without invoking QFT?

Hi there

For someone learning particle physics for the first time (Griffiths' intro book, no knowledge of QFT yet): Why can you "cross" a reaction? Is there an intuitive answer or does one truly need understanding of scattering amplitudes, quantum fields and something called "the S-matrix?"

 

[Bill_K]

The best you can do is say "antiparticles are particles moving backwards in time." Which is wrong, of course, but without QFT that's the best you can do.

 

[MWBratton]

thanks

 

[humanino]

The best you can do is say "antiparticles are particles moving backwards in time." Which is wrong, of course, but without QFT that's the best you can do.

I am not sure why you say it is "wrong". Thinking of antiparticles in this manner is useful enough that it should be recommended for every student to ponder about it at least once. AFAIK, many students are still told about antiparticles as "holes in the sea of negative energy particles" from Dirac, which has interesting historical value, but is more complicated and much more limited technically (e.g. it does not work for bosons). Thinking of antiparticles as "time-parity reversed particles" immediately let's you understand why relativity implies the necessity of fields (in the sense that all electrons are indistinguishable, no matter how they were created). It is the heart of the CPT theorem. There are caveats, sure. A particle moving "backwards in time" should carry "negative energy" along its proper (backwards) time. But realizing this caveats also allows one to understand better the definition of "particles" and why particle number ambiguous globally in curved spacetimes.

 

[Bill_K]

I am not sure why you say it is "wrong". Thinking of antiparticles in this manner is useful enough that it should be recommended for every student to ponder about it at least once. AFAIK, many students are still told about antiparticles as "holes in the sea of negative energy particles" from Dirac, which has interesting historical value, but is more complicated and much more limited technically (e.g. it does not work for bosons). Thinking of antiparticles as "time-parity reversed particles" immediately let's you understand why relativity implies the necessity of fields (in the sense that all electrons are indistinguishable, no matter how they were created). It is the heart of the CPT theorem. There are caveats, sure. A particle moving "backwards in time" should carry "negative energy" along its proper (backwards) time. But realizing this caveats also allows one to understand better the definition of "particles" and why particle number ambiguous globally in curved spacetimes.

Here we go again.

 

[humanino]

Here we go again.

I still do not understand your point. I am merely trying to engage students' thoughts. For that purpose, the picture you suggested is not "wrong", it is appropriate. For instance, it was used by Feynman in his 1986 "Dirac Memorial Lectures" to explain "the reason for antiparticles". I do not like "arguments by authority" but one would think Feynman is a good reference for teaching perturbative quantum field theory "for someone learning particle physics for the first time".

 

[MWBratton]

I understand "antiparticles moving backward in time" as a crude way of putting what is really going on. Relativity of simultaneity says one cannot tell the order of two events which are somewhat close together: Something like "Feynman vertex (1) emitted W+ which was, a short time later, absorbed by Feynman vertex (2)." But, according to special relativity, there exists yet another Lorentz frame in which the chronology is reversed, and the W+ must become a W- to conserve charge, and W- is its antiparticle. But even understanding that, "crossing" still seems somewhat arbitrary

there's a feynman story along the lines of: he tried to find an explanation of the spin-statistics theorem to give to freshmen, and when he couldn't do it satisfactorily he concluded "in the body of scientific knowledge, spin-statistics must not be understood well enough, because I can't explain it to freshmen." but i guess it comes down to, in our case, either explain using the full story (QFT) or be content with particles moving backward in time, which IS the "freshmen" explanation, and there's not a better one

 

[DrDu]

"Particle" is not a very useful concept, here. It is maybe more appropriate to think in terms of "charges" in the sense that an anti-particle is only defined for particles carrying charge. The point is that properties of particles like mass are due to the self-energy of a charge coupling to some field. This coupling has to be symmetric with respect to charge conjugation, if not, the vacuum (= lowest energy state) would not be chargeless.