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1/N. Why antiparticles exist (a thread)
2/N The starting point is that quantum mechanics and special relativity are almost inconsistent with one another.
3/N. The problem starts with a problem embedded in the relativity of simultaneity: the fact that different observers can disagree on the ordering in time of events if these events are spacelike separated (ie too far apart for light to get from one to the other).
4/N. Not having everyone agree on the ordering of events in time is a problem if you are in the business of predicting the future given the past (as science is).
(These are called causality problems in the trade.)
(These are called causality problems in the trade.)
5/N. Einstein knew about this problem, but also knew he could get away with relativity without causality problems anyway because nothing can go faster than light.
This means people can disagree on ordering of spacelike events bcs they cannot influence one another in any case.
This means people can disagree on ordering of spacelike events bcs they cannot influence one another in any case.
6/N. But quantum mechanics messes up this nice arrangement because of the uncertainty relations.
If you know exactly where the two events are, then you know nothing about how fast things might be moving after these positions are measured.
If you know exactly where the two events are, then you know nothing about how fast things might be moving after these positions are measured.
7/N. In particular there is some nonzero probability that they might be moving faster than light. (In quantum electrodynamics this corresponds to correlators of random operators not commuting for fields separated by spacelike separations.)
8/N. So the causality problem is back:
How do you predict the future from the past given that (1) people can disagree on the ordering of events in time and (2) that quantum mechanics allows a loophole to the proscription against superluminal speeds?
How do you predict the future from the past given that (1) people can disagree on the ordering of events in time and (2) that quantum mechanics allows a loophole to the proscription against superluminal speeds?
9/N. Suppose A and B are spacelike separated and you think A is earlier than B and a particle carries charge Q and mass M from A to B.
How do I interpret that if I am moving relative to you and think B is earlier than A?
How do I interpret that if I am moving relative to you and think B is earlier than A?
10/N. The answer turns out to be spooky:
I have to be able to think something went from B to A carrying exactly charge -Q and mass M. And the quantum amplitude for this must be *exactly* the same as for the process you saw.
I have to be able to think something went from B to A carrying exactly charge -Q and mass M. And the quantum amplitude for this must be *exactly* the same as for the process you saw.
11/N. The particle that does that for me is the antiparticle of the one you saw (which looks to you like a particle going backward in time).
To work antiparticle properties must be related to those of their particle partners (eg opposite charge, equal mass etc): the CPT theorem.
To work antiparticle properties must be related to those of their particle partners (eg opposite charge, equal mass etc): the CPT theorem.
12/N. This always gives me chills to think about.
It is one of the most epic, and most under-appreciated, tales of modern physics.
It is one of the most epic, and most under-appreciated, tales of modern physics.
13/N.
Things are usually not taught this way in QFT textbooks, where the focus is on fields commuting at spacelike separated points. Partly we don't want students to be distracted by the chills. And also bcs it is so bizarre you want to show that the math is absolutely solid.
Things are usually not taught this way in QFT textbooks, where the focus is on fields commuting at spacelike separated points. Partly we don't want students to be distracted by the chills. And also bcs it is so bizarre you want to show that the math is absolutely solid.
14/N.
SFAIK Weinberg's QFT vol. I is the place this is done most explicitly. This particular magic is somewhat hidden in his book, so needs a bit of digging out to see (though was not hidden in his lectures).
SFAIK Weinberg's QFT vol. I is the place this is done most explicitly. This particular magic is somewhat hidden in his book, so needs a bit of digging out to see (though was not hidden in his lectures).
