Big Bang Temperature

[Steven Harris]

If temperature is a measure of the kinetic energy of atomic particles in matter, and at the instant of the big bang no elementary particles existed, how can the early universe be said to have huge or nearly infinite temperature?

[nicksauce]

Temperature isn't exclusively a measure of kinetic energy of atomic particles in matter; it's just what happens to be true for most simple systems. The proper definition of temperature is the rate at which energy changes with respect to entropy, i.e., T=\frac{\partial E}{\partial S}.

[marcus]

I didn't see Nick's reply! I was replying directly to the initial post.

If temperature is a measure of the kinetic energy of atomic particles in matter, and at the instant ...
Well light has temperature.

You have seen those oval blue and red maps of the CMB sky (cosmic microwave background). Those maps show the temperature of electromagnetic radiation seen looking in different directions. Temperature of (black-body) radiation is well-defined, so you don't need conventional matter particles like electrons and quarks to have temperature. You can have an empty metal box with a vacuum inside and the space in the box will still have a well-defined temp.

A far more serious problem in talking about the very early (you mentioned the "instant") is that the classical model model breaks down---it stops being applicable as you approach time zero. "singularity" = breakdown of the old unquantized model. The math starts to give meaningless answers and can no longer be trusted.

Need quantum cosmology models then.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+ 2005&FORMAT=www&SEQUENCE=citecount%28d%29