# A thermodynamic question

#### cyleung_2001

As temperature is emergent and is only describing the speed of molecules in a substance, is it meaningful to speak of temperature in an empty space? If not, can we say that the microwave background radiation is "heating" up the universe? As most of the universe is empty space

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#### CharlesP

cyleung_2001 said:
As temperature is emergent and is only describing the speed of molecules in a substance, is it meaningful to speak of temperature in an empty space? If not, can we say that the microwave background radiation is "heating" up the universe? As most of the universe is empty space
The microwave background radiation establishes a temperature for "deep space", the temperature that will be reached in time by a grain of sand located "far" from any other object. As the universe is expanding and the background is accelerating it will become cooler yet in a long time.

#### Crosson

As temperature is emergent and is only describing the speed of molecules in a substance
Temperature is not an imergent property (it can be defined for any system which can store energy in two or more different ways), and it is certainly much more general then the speeds of molecules in a substance (temperature can be defined for systems that do not have speed).

is it meaningful to speak of temperature in an empty space? If not, can we say that the microwave background radiation is "heating" up the universe?
No one talks about the temperature of empty space. It would be possible to define this mathematically, and work on formulas, but the results would be unmeasurable and uninteresting.

#### mathman

One "practical" definition of the temperature of empty space would be what a thermometer would read. Essentially it is the radiation background temperature, which is around 2.75 deg. K.

#### turbo

Gold Member
Interestingly, this question had been posed even in the 1800's, and there are quite some very accurate (better than OOM) calculations of that temperature, based on the energy contributions of all visible luminous matter.

#### Chronos

Gold Member
Welcome to PF, cyleung! It is pretty meaningless to talk about the the temperature of the vacuum. You must have some kind of thermometer, and no one has figured out how to make one without using matter. Until the photons crash into a hunk of matter, they are undetectable. But using 'thermometers' we can measure the photon density and energy per unit volume of empty space. And this works out to be the temperature equivalent of 2.725K, as measured by COBE and WMAP.

Indeed, as turbo noted, predictions of the temperature of space have been proposed since Stefan found, in 1879, that the radiation, F, emitted by a blackbody at temperature T is given by F=s x T^4, where s is the Stefan-Boltzmann’s constant - which was derived by Boltzmann in 1884. The earliest known estimate for the temperature of empty space was by Guillaume in 1896. Applying the SB formula to a crude estimate of the brightness of the night sky, he obtained a value of 5-6K. Eddington, in 1926, arrived at a similar result, 3.18K by similar means. But this method is fundamentally flawed. It only considers the effect due to stars in our own galaxy. Intergalactic space is millions of times more diffuse than a typical galaxy, hence the contribution of starlight to the CMB temperature in deep space is negligible. Here is a relevant article:
http://www.astro.ucla.edu/~wright/Eddington-T0.html
Note that in conducting the COBE and WMAP studies, the researchers subtracted out the contribution of our galaxy to obtain the actual CMB temperature.

The pre-CMB predictions of the temperature of space are sometimes cited by critics of big bang theory. But they do not hold water in the face of hard evidence. For example, in a static [steady state] universe, the background temperature would be constant at all times. But this notion was convincingly refuted in a paper by Varshalovich et al in 2000 when they measured the temperature of gasses in deep space billions of years ago. Here is a article on that:
http://www.eso.org/outreach/press-rel/pr-2000/pr-27-00.html [Broken]

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#### turbo

Gold Member
It may be helpful to point out that the energy received by an entity in "empty" space will be re-radiated at a LOWER energies (longer wavelengths). Before quantum physicists posited (and later demonstrated) the existence of a dynamical vacuum field, empty space was assumed by many to be truly empty. With a dynamical vacuum field, impinging EM transfers energy to the field and is re-emitted at lower and lower energies. The article that Chronos cited does not falsify Eddington's estimate of the temperature of space - the estimate was made at a time when "empty" space was assumed to be transparent to EM.

Taking into account the effects of extra-galactic sources does not significantly effect the results predicted by Eddington. Since energy flux falls off as a function of the square of the separation of emittor and sensor, galactic-scale separations make the energy contribution of a star in M31 VERY insignificant relative to a star in our own galaxy, to say nothing of a star in our local neighborhood.

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#### cyleung_2001

I see, so we are actually talking about the temperature of a body in space. But are there any other mechanisms besides EM waves that can have the same effect? And can we assign a temp to dark matter? As I know dark matter doesn't emit any radiation.

#### Chronos

Gold Member
turbo-1 said:
It may be helpful to point out that the energy received by an entity in "empty" space will be re-radiated at a LOWER energies (longer frequencies). Before quantum physicists posited (and later demonstrated) the existence of a dynamical vacuum field, empty space was assumed by many to be truly empty. With a dynamical vacuum field, impinging EM transfers energy to the field and is re-emitted at lower and lower energies.
That definitely qualifies as a minority opinion. It violates GR energy conservancy as well as observational evidence that empty space is virtually transparent to EM as far back as we can currently 'see' [~z=6].
turbo-1 said:
The article that Chronos cited does not falsify Eddington's estimate of the temperature of space - the estimate was made at a time when "empty" space was assumed to be transparent to EM.
The vast majority of physicists would say that article is a compelling refutation of Eddington's prediction on a number of grounds. But that does not rule out the possibility you have some new physics to pony up to the table.
turbo-1 said:
Taking into account the effects of extra-galactic sources does not significantly effect the results predicted by Eddington.
Agreed, but irrelevant. It says nothing about the 'true' background temperature of deep space. You are missing the point. I think you really should reread the article and further investigate how the WMAP team made corrections for local contributions to the CMB temperature.
turbo-1 said:
Since energy flux falls off as a function of the square of the separation of emittor and sensor, galactic-scale separations make the energy contribution of a star in M31 VERY insignificant relative to a star in our own galaxy, to say nothing of a star in our local neighborhood.
Also agreed, but irrelevant.

#### chronon

The CMBR is not a gas in thermal equilibrium. The radiation has not interacted with anything since it was emitted from the "last scattering surface". Just as the spectrum of radiation emitted from the surface of a star indicates the temperature of the surface of that star, so the CMBR gives us a temperature, although redshift means that the temperature found is much reduced from that of the last scattering surface when it was emitted.

#### Chronos

Gold Member
One more time, read the literature. The CMBR interacts with all matter it encounters along the way to our observational outpost. That was the whole point of the study I cited. I think the majority would agree you are not addressing the observational evidence. If you have an alternative explanation - show the math.

#### CharlesP

Chronos said:
One more time, read the literature. The CMBR interacts with all matter it encounters along the way to our observational outpost. That was the whole point of the study I cited. I think the majority would agree you are not addressing the observational evidence. If you have an alternative explanation - show the math.
I don't think that very many of the CMBR photons have interacted with anything on the way to our instruments. Else the nice maps and impressive science in the field would be meaningless. There are some absorption lines in some directions here and there but for the most part we see a black body curve.
Creationists have tried to make hay of some photon interaction that fools astronomers into finding the accepted age of the universe but they haven't gotten very far.

#### Chronos

Gold Member
Agreed, CharlesP. I misinterpreted chronon's post.

#### CharlesP

Question

Now for the tough question.
There was supposedly a dark age in the early universe, after the uncoupling of mater and radiation at age 10E5 years and before the appearance of the first stars. At this time the universe was filled with un-ionized gas which according to one source was opaque. If that is true then how could any of the CMBR reach us?

What was really going on?

"A thermodynamic question"

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