Why particle and antiparticle have the same mass?

[ndung200790]

Please teach me this:
Why particle and coresponding antiparticle have the same mass,because in the annihilation process the mass does not conserve.
Thank you very much in advance.

 

[DrDu]

That's a good question. In general they really don't have to have the same mass. E.g. in solid state physics, electrons and holes in a semiconductor do have quite different effective masses although they may anihilate each other.
However in relativistic quantum mechanics they have to be equal which is a consequence of Lorentz invariance which has as a consequence CPT symmetry (Symmetry under a combined change of charge, parity and time).

 

[haael]

Lorentz invariance which has as a consequence CPT symmetry

CPT symmetry is not the consequence of Lorentz invariance.

 

[xlines]

CPT symmetry is not the consequence of Lorentz invariance.

Lorentt invariance is assumed when deriving CPT theorem. You knew what is that the man is saying and nobody likes nitpicking :P

 

[JK423]

Antiparticles are predicted by quantum field theory to exist with the same mass as the corresponding particle.
The only thing i can tell you is that, if antiparticles did not have the same mass with their particles then many principles would be violated. One of them that i can think of is causality.

 

[inflector]

Why particle and coresponding antiparticle have the same mass,because in the annihilation process the mass does not conserve.

Mass does not conserve but energy does.

Mass does not conserve but momentum does.

Generally, two photons are created when an electron and positron annihilate. One of the signatures of this annihilation is the presence of two photons of 511 keV going in opposite directions starting at the point of annihilation. So the fact that the photons have equal energy and by E=mc² this total energy (1.024 MeV) corresponds with the mass of an electron multiplied by two, we can tell that the positron has the same mass as the electron.

As to there being some deeper reason? I don't think physics has the answer at the moment.

Until we can explain why the different particles have the different masses they do (i.e. why the electron has a mass of about 1/200th the muon and 1/1836th the proton, etc.), I don't think we'll have a firm enough grasp on the underlying mechanisms of mass to explain antiparticle mass.

 

[Parlyne]

CPT symmetry is not the consequence of Lorentz invariance.

You might want to check http://arxiv.org/abs/hep-ph/0201258 before claiming that. The entire point of this paper is that violations of CPT (at least in interacting theories) necessarily imply violations of Lorentz symmetry. In other words, if there is good Lorentz symmetry, there must also be good CPT symmetry. How is that not an equivalent statement?

 

[Drakkith]

Please teach me this:
Why particle and coresponding antiparticle have the same mass,because in the annihilation process the mass does not conserve.
Thank you very much in advance.

Hrmm, that's like asking why an electron has an electric charge of -1. It just does.

 

[ndung200790]

It seem that the CPT symmetry leads to all observable quantities have the same absolute values for particle and antiparticle.So CPT symmetry permits the "direct" annihilation process of only particle and coresponding antiparticle allowing by conservation laws.
Please teach me about that.Thank you very much

 

[Parlyne]

It seem that the CPT symmetry leads to all observable quantities have the same absolute values for particle and antiparticle.

Yes. In fact, the CPT principle is stronger than this. It says that if you invert all conserved charges (that is, change their sign, at least for the kind of charges that add), invert parity (that is, reverse the direction of each axis of space), and reverse the direction of time, you will get back the exact same laws of physics we already have, meaning that the rates and probabilities of any given processes are exactly the same as for their CPT counterpart processes.

So CPT symmetry permits the "direct" annihilation process of only particle and coresponding antiparticle allowing by conservation laws.
Please teach me about that.Thank you very much

No. In fact, the weak force allows annihilations between particles and antiparticles that don't even have the same electric charge. For instance, an up quark and a down antiquark can annihilate into a positron and a neutrino. There are rules governing what annihilations are and aren't allowed. (In essence, the net electric charge of the two particles must be an integer number of electron charges, there must be exactly one particle and exactly one antiparticle, and, if the net charge is 0, the two particles must be of the same species.)

 

[ndung200790]

So,in weak interaction.the gauge symmetry U(1) is violated?

 

[ndung200790]

Sorry,now I can understand!

 

[ndung200790]

Why electron and antimuyon can not annihilate,despite both of them are leptons and seem that the conservation laws would not be violated if the annihilation happened.

 

[ndung200790]

I have just known that process violate flavour number conserve law

 

[DrDu]

Yes, but favour is not exactly conserved as we know from neutrino oscillations. So it is possible in principle for an anti-myon and an electron to anihilate.

 

[Parlyne]

So,in weak interaction.the gauge symmetry U(1) is violated?

No. Electric charge will be conserved in these processes. This is not an annihilation to photons.

 

[Parlyne]

Yes, but favour is not exactly conserved as we know from neutrino oscillations. So it is possible in principle for an anti-myon and an electron to anihilate.

I think this should be possible at one loop. However, in addition to the standard loop factor suppression of
$$\sim \frac{1}{16\pi^2}$$
of the cross-section, there will be a suppression of the amplitude by something like
$$\frac{m_\nu^{\phantom{\nu}2}m_em_\mu}{m_W^{\phantom{W}4}},$$
which makes this sort of process quite unlikely, indeed.