Re: temperature of radiation?

gagelman@xxxxxxxxxxxxxxxxx schrieb:
Something I have never understood is how it is possible to measure the
temperature of radiation, specifically the CMB. In my niave way of
thinking, temperature is a "property" of a material body that must be
measured with, say, a thermometer. Could someone please explain how
temperature is defined for non-material objects --- or explain to me
what is flawed with my naive view?

For a system of classical particles, temperature is the measure of
uncertainty of the velocity of each single particle seen as a
representative of a sample with Maxwellian or Gaussian or normal
distributed independent coordinate velocities.

Because of the classical relation between kinetic energy and velocity
E_kin = m/2 v^2
the mean and the variance of the expontial distributed kinetic energy
equals the variance of the velocity distribution. This is the formula
k T = mean(E_kin) = variance(E_kin)
for each degree of freedom, called equipartition principle in physics.

This principle carries over to single photons of frequncy omega with energy
E_kin=hbar omega.
The temperature of a collection of photons is the variance of
distibution over energy states or over frequency states. Because of the
unique properties of the exponential distribution, variance and mean are
equal again.

The thermometer principle rests on the entropy principle: Two systems in
contact maximize their common noise with the constraint of energy
conservation until the energy variance or temeperature is equal for each
small subsystem down to each particle and even their distinct degrees of
freedom. The result is the same variance or temperature of the energy
distibution after some time of contact in each single system after
separation.

Since all material bodies consist of electrical charges in in cyclic
motion, the temperature of such a body is coupled by the accelerated
charges in more or less chaotic motion to a field of photons with an
energy distribution of the same temperature.

--

Roland Franzius

.

Relevant Pages

  • Re: Temperature and radiation absorption
    ... why is the definition of temperature not just simply a constant ... Temperature is defined WRT an equilibrium distribution of ... > seems to me that if an electron absorbs a photon, ... > additionnal energy is acquired by the atom. ...
    (sci.physics)
  • Re: evidence for the existence of the ether
    ... > versus what is its temperature ... > Speed of transfer of a packet of thermal energy is not meaningful. ... within the conductor must be transported along the conductor. ... > finite speeds involved then that puts limits on some transient effects. ...
    (sci.physics.relativity)
  • Re: Cosmic acceleration rediscovered
    ... >> attempting to impugn all variants of tired light by picking another ... be from a different temperature. ... > of around 4.2GPc for tired light energy loss. ...
    (sci.astro)
  • Re: Thermo-dynamic philosophy for kids; was Re: Mail Server a long time ago
    ... This ties into the Einstein-Rosen paradox, ... But the stars reliably convert mass to energy, and in such a way that their ... heat up their environments without decreasing their own temperature. ...
    (comp.os.linux.misc)
  • Re: Solar Activity Reaches 1,000 Year Peak
    ... absorption characteristics of the clouds. ... Of much greater influence than CO2 has been the sulphate ... abot 1/2 degree reduction in temperature (though it did cut back ... And this from a university professor who has never taken money from the energy companies. ...
    (soc.retirement)