Re: Positrons

Den 08.07.2025 16:17, skrev Stefan Ram:

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

Den 08.07.2025 00:02, skrev Stefan Ram:

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

e⁺ + e⁻  →  γ + γ
Energy and momentum are preserved.
The energy equivalence of an electron and a positron is 0.511 MeV,
so the energy of each of the gamma particles is 0.511 MeV. (0.024 Å)
(Mass is converted to pure kinetic energy of photons)

Mass is /not/ changed in this process when the mass of the system
"γ + γ" is being compared with the mass of the system "e⁺ + e⁻".

Why would you consider γ + γ as a closed system?

    Well, I was talking about a "system", not a "closed system".
    Many people go with
 E^2 = (mc^2)^2 + (pc)^2
    and emphasize that energy and momentum are conserved in a process
   "-->", while mass can be converted into "pure kinetic energy".
    Now, let's call the values before a process (left of the arrow "-->")
   "0" and those after the process (right of the arror "-->") "1".
    Then, what the people say would be:
 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

    But these three assumptions are not compatible with
 E_0^2 = (m_0c^2)^2 + (p_0c)^2 and
E_1^2 = (m_1c^2)^2 + (p_1c)^2
    !

Let the mass of the leptons be m.
Let the speed of the leptons be equal v in opposite directions.
  γ = 1/√(1 − v²/c²)
For Each of the leptons we get: (E₀/2)² = (mc²)² + (γmvc)²
   E₀² = 4(mc²)² + 4(γmvc)²
The momentum for each of the gamma particles is p = E₀/2c
  E₁/2 = pc = E₀/2
  E₁² = E₀² = 4(mc²)² + 4(γmvc)²
  E₁ = E₀ "Energy is conserved"
           -------------------
Since both the leptons and the gamma particles are moving
with the same speed in opposite direction, the net momentum
is zero both before and after annihilation.
  p₁ = E₀/2c - E₀/2c = 0    p₀ = γmv - γmv = 0
p₁ = p₀ "momentum is conserved"
          ----------------------
  m₀ = 2m, m₁ = 0
   m₁ < m₀  "mass is converted into energy"
             ------------------------------
--
Paul
https://paulba.no/