Relativity implies antimatter?

[angus podgorny]

https://arxiv.org/pdf/hep-ph/0609174.pdf page 8.
2.1.2 Special Relativity Requires Antiparticles

This article describes a scenario in which atom A releases an electron which is absorbed by atom B.
A=> A+ and B => B-
However in a different inertial frame (F) it is possible due to Heisenberg's uncertainty principle that the electron could arrive before it started. In this frame the electron travels back in time (and may have negative mass?).
Because this is unacceptable it is concluded that in frame(F) an anti-electron / positron travels forward in time from B to A giving B=> B- and A => A+ as before.
But a positron has the same mass as an electron so in frame (F) atom A has gained mass whereas previously it had lost it. Can anyone explain this?

 

[Leo1233783]

nice explanation but I prefer the original :
Weinberg S. Gravitation and cosmology. Principles and applications of the general theory of relativity (Wiley, 1972)
§ 13 temporal order and antiparticules
You may find it on the web

Weinberg added in the notes : this section may be omitted in a first reading. Indeed, it is an interpretation.

 

[angus podgorny]

I also read Weinberg's version. However the question of the mass of the electron /positron adding or subtracting remains

 

[Leo1233783]

Consider that you are asking a chronology question and they answer by the positron time reversal trick

 

[angus podgorny]

My point is the time reversal trick allows the same change in charge during the process in each inertial frame but reverses the change in mass

 

[Leo1233783]

If you accept that the model of emission-absorption describes well the phenomenon in a non-relativistic context, it is just a matter of chronology. It is controversial. Furthermore, here, relativity is only the context for a QM explanation. Without QM and the way the problem is analyzed, relativity fails.

 

[angus podgorny]

"However in a different inertial frame (F) it is possible due to Heisenberg's uncertainty principle that the electron could arrive before it started ". I now think that this assertion is flawed and that is what leads to the mass paradox. I agree that relativity therefore does not imply antimatter.

 

[haael]

Relativity does imply antimatter, in a sense that any relativistic theory requires the existence of an anti-field for each field. However, the existence of anti-fields may be also postulated independently.

The example quoted by the OP is good if you disregard its physicality. It makes perfect sense from mathematical standpoint. The only missing bit is the discussion about annihilation and creation operators.

First, an atom "emits" an electron. We have one vertex with the annihilation operator of the atom in question, the creation operator of the positively charged ion and the creation operator of the electron. Second, we have the vortex of the atom "absorbing" the electron. We have the annihilation operator of the second atom, the creation operator of the negatively charged ion and the annihilation operator of the electron.

Now we can do a Lorentz transformation so that the order of emission and absorption is reversed. Here comes relativity and antimatter. We must replace the creation operator of the electron with the annihilation operator of a positron. Also, we have to replace the annihilation operator of the electron with the creation operator of the positron.

Now please remember that this is only maths. This is not a physical theory yet. Indeed, this process is happening off-shell, that means the mass can be negative. But remember, this is not a physical process that is happening in reality. This is only mathematical formalism.

Now you can use that formalism to build a theory of a scattering matrix, where all particles are on-shell, mass is always positive and the process is happening "for real", not only on paper.

The point of the argument that "relativity requires antimatter" is that lack of an absolute notion of simultaineity requires swapping creation and annihilation operators of fields and anti-fields. You have an arrow that must point into the future, but you can reverse its direction with Lorentz transform (or any transform that doesn't preserve simultaneity). In order for it to still point into the future, you must swap its beginning and end and in order to agree with all conservation laws you must take all its quantum numbers negative.

But remember, it's maths, not physics. Maybe it would be easier if physicists didn't reuse terms in the two contexts.

When a physicist talks about an "electron", he might think of two things:
- Mathematical tool, created by human, an abstract object, that does not exist in reality, more akin to a number, whose existence is postulated by axioms.
- Physical object, created by God, real thing our bodies are made from, that exist objectively and that fly around, created in Big Bang.

Now we may try to devise a physical theory of the "physical electron" using the mathematical theory of the "mathematical electron".

 

[Leo1233783]

normally, physicists collect facts and phenomena measures and then build theories to explain them. To be credible, a new theory must predict something and so works the sector. Anything not fitting this scheme leaves me skeptical. For me, this paragraph is just to impress the reader and make him feel that he cannot understand anything. I prefer the Weinberg version ( not scholar + warning ).