Does somebody study complex energy particle ?

[Genady]

This question is inspired by another thread in this forum, but it would be OT there. So:

Does anybody have a valid reason to believe complex rest energy/mass particle can't exist ?

[MigL]

There may be cases where it is preferable to treat mass/energy as a complex value, just as there may be cases where it is preferable to treat mass/energy as negative ( Effective mass ? ), but no, I don't believe the concept of complex, or negative mass/energy has any physical meaning.

[joigus]

You would have a violation of unitarity, which isn't a good thing.

All relativistic state vectors for massive particles have a factor that in natural units looks like,

\[ e^{-imt} \]

Assuming,

\[ m=\textrm{Re}\left(m\right)+i\textrm{Im}\left(m\right) \]

You would get,

\[ e^{-imt}=e^{-i\textrm{Re}\left(m\right)t}e^{\textrm{Im}\left(m\right)t} \]

Now, suppose you have \( \textrm{Im}\left(m\right)>0 \) => runaway solution everywhere for growing t.

But if \( \textrm{Im}\left(m\right)<0 \) you have a vanishing solution everywhere for growing t.

Both violate unitarity, so you have a much bigger problem than with a negative mass. Negative masses are no good because of decay. Particles would spontaneously decay to lower levels, 'more negative'-mass states. But non-unitarity is a non-starter.

I'm sure there are more other arguments but, to me, that would be enough.

Edited May 19, 2022 by joigus
minor correction

[Genady]

1 hour ago, joigus said:

You would have a violation of unitarity, which isn't a good thing.

All relativistic state vectors for massive particles have a factor that in natural units looks like,

 

e−imt

 

Assuming,

 

m=Re(m)+iIm(m)

 

You would get,

 

e−imt=e−iRe(m)teIm(m)t

 

Now, suppose you have Im(m)>0 => runaway solution everywhere for growing t.

But if Im(m)<0

This issue can be solved by replacing the m with its norm in that factor.

(But I was not serious to start with.)

Edited May 19, 2022 by Genady

[joigus]

36 minutes ago, Genady said:

This issue can be solved by replacing the m by its norm in that factor.

OK. But with that what you're doing is inventing a fancy complex mass m=Re(m)+iIm(m) (a quite esoteric quantity) which is only there to give rise to the 'actual mass', which is its modulus (norm.)

You're quite right. You can always declare any positive real quantity as the norm of some other inconsequential complex variable. But Ockam's razor will cut it off.

 

[studiot]

What is all the fuss about ?

Mass is not an 'invariant, but sometimes depends upon the environment as well as the frame.

Stoles invented 'negative mass' early in the 19th century for the dynamics of soap bubbles rising through water.

[Genady]

1 hour ago, studiot said:

What is all the fuss about ?

Mass is not an 'invariant, but sometimes depends upon the environment as well as the frame.

Stoles invented 'negative mass' early in the 19th century for the dynamics of soap bubbles rising through water.

Of course, you're right.

The "fuss" here is about the rest mass of fundamental particles, specifically.

[studiot]

30 minutes ago, Genady said:

Of course, you're right.

The "fuss" here is about the rest mass of fundamental particles, specifically.

My apologies to Mr Stokes for my mispelling of his name.