How energy divided up in early Universe.

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Discussion Overview

The discussion revolves around the distribution of energy in the early Universe, specifically comparing the energy in the electron field to that in the photon field under conditions of high energy and temperature. The scope includes theoretical considerations of particle physics and cosmology.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that in the early Universe, where temperatures exceed the rest mass energies of particles, energy becomes thermalized and is distributed among various degrees of freedom.
  • It is suggested that photons, having two spin states, and electrons, along with their positrons, having four degrees of freedom, lead to electrons and positrons possessing twice the energy compared to photons when temperatures are sufficiently high.
  • Another participant introduces the factor of 7/8, noting that the energy density of a relativistic species of fermions is 7/8 that of a relativistic species of bosons, which adds complexity to the comparison of energy densities.
  • A later reply acknowledges the factor of 7/8 and expresses gratitude for the clarification, indicating a collaborative effort to refine understanding.

Areas of Agreement / Disagreement

Participants generally agree on the thermalization of energy and the comparative energy densities of electrons and photons, but the introduction of the 7/8 factor suggests some nuance that may not be fully resolved.

Contextual Notes

The discussion does not resolve the implications of the 7/8 factor in detail, nor does it clarify how the transition occurs as the Universe cools and the rest mass of the electron becomes significant.

Spinnor
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Say we are in the early Universe where energies are large compared with any rest mass in the standard model.

At this time how will the energy in the electron field compare with the energy in the photon field?

Thanks for any help!
 
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Spinnor said:
Say we are in the early Universe where energies are large compared with any rest mass in the standard model.

At this time how will the energy in the electron field compare with the energy in the photon field?

Thanks for any help!
Well, what happens in that sort of situation is that the entire system is thermalized: when you have temperatures far above the rest mass energies of various particles, then collisions will frequently produce particle/anti-particle pairs of them. So you end up with energy equally distributed throughout the various degrees of freedom of the system. Photons have two available spin states, and thus two degrees of freedom. Electrons have two available spin states plus anti-particles, so between the positrons and electrons you have four degrees of freedom. Thus the electrons and positrons will between them have twice the energy as the photons, as long as the temperature remains far above the rest mass of the electron.

As the universe cooled, however, the rest mass of the electron started to become important, as did the slight overabundance of electrons with respect to positrons.
 
There's also a factor of 7/8 that comes into play: Ignoring internal states, the energy density of a relativistic species of fermions will be 7/8 the energy density of a relativistic species of boson.
 
nicksauce said:
There's also a factor of 7/8 that comes into play: Ignoring internal states, the energy density of a relativistic species of fermions will be 7/8 the energy density of a relativistic species of boson.
Ah, yeah, I thought I was missing a factor somewhere, but couldn't find it quickly to make sure. Thanks.
 
Stuff every school child should know.

Thanks to the both of you!
 

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