Re: Positrons

Den 08.07.2025 21:57, skrev Stefan Ram:

"Paul.B.Andersen" <relativity@paulba.no> wrote:

Stefan Ram wrote:>>> E_1 = E_0 "Energy is conserved"

p_1 = p_0 "momentum is conserved"
m_1 < m_0 "mass is converted into energy"

Please explain why these three assumptions are not compatible with:
e⁺ + e⁻  →  γ + γ

    Well, "energy", "momentum", and "mass" are /vague terms/. One needs
   to specify the energy (momentum, mass) /of what/ one refers to.
    If one would try to correct the vagueness of "mass is converted into
   energy" by saying, "the mass of 'γ + γ' is smaller than the mass
   of 'e⁺ + e⁻'" (thereby saying "of what"), then this would be wrong.
 

m₀ = 2m, m₁ = 0

    Well, this is the same point: It's too vague because the system
   is not specified. The mass of what system is "m_0"?  The mass of
   what system is "m_1"? So, to quote Dirac, it's not even wrong!

The mass of the two leptons is 2m and the mass of the two
gamma photons is zero.
How can this be "to vague" and "not even wrong"?  :-D

    But, if I assume that m_0 is the mass of "e⁺ + e⁻", then it's
   wrong, because when they move in their COG system m_0 > 2m
   (assuming m to be the mass of an e⁺ or e⁻ in its COG system)
   if they are moving with a non-zero speed in the COG.

So mass isn't invariant?

    And m_1 surely is larger than 2*0 (two times the mass of
   a photon). For one illustration: The mass of a gluon is 0.
   Yet the kinetic energy of gluons make up for 37 percent of the
   /mass/ of a proton. You don't get this value of .37*m_p if you
   take the mass of each gluon in isolation and then sum them up.

So the mass of two photons isn't two times the mass of a photon?
--
Paul
https://paulba.no/