Thread: Temperature of Vacuum

Hi guys,

my question is:
What temperature does vacuum have? With "vacuum" I mean a volume - say, a cube with side length L - where there is, except for vacuum fluctuations, no particle or radiation, probability wave etc. (a very idealistic view).

I know that there is a statistical definition of "temperature" making it meaningless to ask for a definite value for systems without particles, but there is also a quantum statistical definition (or whatever one may call it) allowing for an attribution of a definite value (even be it infinity) of temperature to such systems.

Some variations of my question are conceivable, like allowing background radiation of the universe pervading the system.


Thanks for answers

Originally Posted by mastermind2007

Hi guys,

my question is:
What temperature does vacuum have? With "vacuum" I mean a volume - say, a cube with side length L - where there is, except for vacuum fluctuations, no particle or radiation, probability wave etc. (a very idealistic view).

I know that there is a statistical definition of "temperature" making it meaningless to ask for a definite value for systems without particles, but there is also a quantum statistical definition (or whatever one may call it) allowing for an attribution of a definite value (even be it infinity) of temperature to such systems.

Some variations of my question are conceivable, like allowing background radiation of the universe pervading the system.


Thanks for answers

Absolute zero, surely, on the basis of the absence of any extractable thermal energy. Or am I missing some subtlety? Though if the universal background echo of the Big Bang is allowed to be present then it is, er, whatever that is, I forget exactly, around 3K or something I think.

exchemist:
But what about quantum fluctuations? Even vacuum does have vacuum energy and fluctuations. This is why absolute zero can never be reached, not even with a presumed absence of any matter.

Originally Posted by exchemist

Originally Posted by mastermind2007

hi guys,

my question is:
What temperature does vacuum have? With "vacuum" i mean a volume - say, a cube with side length l - where there is, except for vacuum fluctuations, no particle or radiation, probability wave etc. (a very idealistic view).

I know that there is a statistical definition of "temperature" making it meaningless to ask for a definite value for systems without particles, but there is also a quantum statistical definition (or whatever one may call it) allowing for an attribution of a definite value (even be it infinity) of temperature to such systems.

Some variations of my question are conceivable, like allowing background radiation of the universe pervading the system.


Thanks for answers

absolute zero, surely, on the basis of the absence of any extractable thermal energy. Or am i missing some subtlety? Though if the universal background echo of the big bang is allowed to be present then it is, er, whatever that is, i forget exactly, around 3k or something i think.

2.7 k

Originally Posted by mastermind2007

exchemist:
But what about quantum fluctuations? Even vacuum does have vacuum energy and fluctuations. This is why absolute zero can never be reached, not even with a presumed absence of any matter.

I am open to be corrected by real physicists, but my understanding is absolute zero is the temperature at which no extractable thermal energy remains. The zero point energy of of vacuum fluctuations does not contribute to temperature as, by definition, it cannot be extracted.

By the same token, it is also my understanding that if you cool an atom to zero, the electrons will all be in their ground states, but they will still be movng, due to the fact that the lowest energy level of a particle confined by a potential is not at the minimum point of the potential (i.e. the lowest energy solution of the wave equation will not be at the minimum of the curve). This remaining energy is the zero point energy of the electrons and is again unextractable, so does not contribute to temperature.

As to why absolute zero cannot be reached, I think that is just because one has to approach it by extracting thermal energy and so one approaches it asymptotically, i.e. you can get as close as you like but can never actually get there.

See this Wiki entry for example:Absolute zero - Wikipedia, the free encyclopedia

But let's see if any proper physicists weigh in at this point........

Originally Posted by mastermind2007

What temperature does vacuum have?

None. However you can measure the temperature of an object IN that vacuum. Such a measurement would depend on energy in and out of the object (via EM radiation, gravitational tidal forces etc)

Hello,

vacuum fluctuations have no effect because these particles are virtual. Temperature is defined using system degrees of freedom but vacuum has no degrees of freedom therefore you can`t really define temperature through distribution functions. So you may say that temperature of vacuum is invalid term. I`m not sure if quantum statistics somehow helps here I don`t think it does.

Originally Posted by billvon

Originally Posted by mastermind2007

What temperature does vacuum have?

None. However you can measure the temperature of an object IN that vacuum. Such a measurement would depend on energy in and out of the object (via EM radiation, gravitational tidal forces etc)

This is interesting.

While I agree that, by the kinetic theory definition of temperature a vacuum has no temperature, due to having no matter in it with a Boltzmann energy distribution, I would have thought that by the broader thermodynamic definition, it does have a temperature of absolute zero.

If you were to introduce a body with a temperature >0K into this vacuum, it will radiate heat and its temperature will drop asymptotically towards absolute zero, will it not? So it seems to me that inasmuch as a temperature gradient is that which determines the direction of the spontaneous flow of heat, the vacuum does indeed behave as if it is at absolute zero.

What do you think?

give it a rest

Originally Posted by exchemist

Originally Posted by billvon

Originally Posted by mastermind2007

What temperature does vacuum have?

None. However you can measure the temperature of an object IN that vacuum. Such a measurement would depend on energy in and out of the object (via EM radiation, gravitational tidal forces etc)

This is interesting.

While I agree that, by the kinetic theory definition of temperature a vacuum has no temperature, due to having no matter in it with a Boltzmann energy distribution, I would have thought that by the broader thermodynamic definition, it does have a temperature of absolute zero.

If you were to introduce a body with a temperature >0K into this vacuum, it will radiate heat and its temperature will drop asymptotically towards absolute zero, will it not? So it seems to me that inasmuch as a temperature gradient is that which determines the direction of the spontaneous flow of heat, the vacuum does indeed behave as if it is at absolute zero.

What do you think?

This is, indeed, an interesting point. However, I think Gere is right with his statement about degrees of freedom. There is also temperature which is "in the spins" of particles. I might be wrong, but I think, due to the fact that, in absence of any magnetic field, the chance of spin-1/2-particles to be spin-up or spin-down is 50%, leads to a statistical distribution (also with magnetic field, but then it's different). The mean value should be zero, but it's not that the whole time 50% is spin-up and 50% spin-down. There are fluctuations which lead to values different than zero and a standard deviation. Now beta (= 1/kT) is related to these spin distributions and thus the temperature.

This means that a body consisting of fermions cannot reach absolute zero due to statistical fluctuations (if I am right; maybe I'm wrong). If, of course, temperature is defined as the mean value or by means of the partition function, then it might be that one can reach absolute zero. Ah...I forgot the exact definitions!

However, we were talking about vacuum. If you go by degrees of freedom, then you don't need an outside reference. If you don't have any degrees of freedom any more, then you probably can't define a temperature, as was said beforehand. Then there would remain the question if spacetime itself has any degrees of freedom, or not. If one could quantize spacetime and then apply some notions of quantum statistics, wouldn't that be possible?

Originally Posted by mastermind2007

Originally Posted by exchemist

Originally Posted by billvon

Originally Posted by mastermind2007

What temperature does vacuum have?

None. However you can measure the temperature of an object IN that vacuum. Such a measurement would depend on energy in and out of the object (via EM radiation, gravitational tidal forces etc)

While I agree that, by the kinetic theory definition of temperature a vacuum has no temperature, due to having no matter in it with a Boltzmann energy distribution, I would have thought that by the broader thermodynamic definition, it does have a temperature of absolute zero.

If you were to introduce a body with a temperature >0K into this vacuum, it will radiate heat and its temperature will drop asymptotically towards absolute zero, will it not? So it seems to me that inasmuch as a temperature gradient is that which determines the direction of the spontaneous flow of heat, the vacuum does indeed behave as if it is at absolute zero.

What do you think?

This is, indeed, an interesting point. However, I think Gere is right with his statement about degrees of freedom. There is also temperature which is "in the spins" of particles. I might be wrong, but I think, due to the fact that, in absence of any magnetic field, the chance of spin-1/2-particles to be spin-up or spin-down is 50%, leads to a statistical distribution (also with magnetic field, but then it's different). The mean value should be zero, but it's not that the whole time 50% is spin-up and 50% spin-down. There are fluctuations which lead to values different than zero and a standard deviation. Now beta (= 1/kT) is related to these spin distributions and thus the temperature.

This means that a body consisting of fermions cannot reach absolute zero due to statistical fluctuations (if I am right; maybe I'm wrong). If, of course, temperature is defined as the mean value or by means of the partition function, then it might be that one can reach absolute zero. Ah...I forgot the exact definitions!

However, we were talking about vacuum. If you go by degrees of freedom, then you don't need an outside reference. If you don't have any degrees of freedom any more, then you probably can't define a temperature, as was said beforehand. Then there would remain the question if spacetime itself has any degrees of freedom, or not. If one could quantize spacetime and then apply some notions of quantum statistics, wouldn't that be possible?

I don't think this is right. As I said before, the existence of residual zero-point energy does NOT prevent a system reaching absolute zero, because this energy is not available to be extracted.

Zero point energy can almost be defined as the thermal motion energy that is still there at absolute zero.