Exploring Temperature: Understanding Particle Vibration and Absolute Zero

[DLeuPel]

The understanding that I have of temperature is that it is defined as the vibration of particles. Now, does this mean that in a vacuum where there are no particles the temperature is the absolute 0 ?

 

[anorlunda]

You refer to the thermodynamic definition of temperature Thermodynamics deals with the study of large numbers of particles. But there are other definitions.

The Cosmic Microwave Background (CMB) also has a temperature (roughly 3 degrees K, -270 C, -452 F). It permeates the universe, even when there are no atoms around. Heat energy flows from warmer to colder. So if an object at absolute zero was set adrift in space, it would absorb energy from the CMB and warm up.

 

[Vanadium 50]

Now, does this mean that in a vacuum where there are no particles

How would you measure such a thing?

 

[sophiecentaur]

. It permeates the universe, even when there are no atoms around.

Is that true? Wasn't the CMB originated in the BB itself, where all the matter in the Universe was present when the radiation was formed? I think the 3K figure actually describes the temperature of a body that would be radiating with a spectrum of the CMB.
I think the OP is suffering from (as we all were) having been told half a story and half a definition, in his/her youth. Rather than 'vibrations of particles' there is a much better definition of temperature in most cases which is 'The average Kinetic Energy of particles'. It actually has Units.
There are a number of inconsistencies or confusions of how Temperature is manifest. The 'Temperature of the Sun's Corona is measured as several million K, which really doesn't fit in with the simple model of an 'atmosphere' around a body with surface temperature of 6000K.

 

[DLeuPel]

Is that true? Wasn't the CMB originated in the BB itself, where all the matter in the Universe was present when the radiation was formed? I think the 3K figure actually describes the temperature of a body that would be radiating with a spectrum of the CMB.
I think the OP is suffering from (as we all were) having been told half a story and half a definition, in his/her youth. Rather than 'vibrations of particles' there is a much better definition of temperature in most cases which is 'The average Kinetic Energy of particles'. It actually has Units.
There are a number of inconsistencies or confusions of how Temperature is manifest. The 'Temperature of the Sun's Corona is measured as several million K, which really doesn't fit in with the simple model of an 'atmosphere' around a body with surface temperature of 6000K.

So, how does the heat from the Sun propagate trough vacuum if there are no particles in the vacuum?

 

[jbriggs444]

So, how does the heat from the Sun propagate trough vacuum if there are no particles in the vacuum?

As light. That light has a distribution of frequencies [at least once you settle on a frame of reference to measure it from] and that distribution has a temperature which follows from the average kinetic energy per photon, $E=h \nu$

 

[anorlunda]

Is that true? Wasn't the CMB originated in the BB itself, where all the matter in the Universe was present when the radiation was formed? I think the 3K figure actually describes the temperature of a body that would be radiating with a spectrum of the CMB.

Yes it's true. So are all the other things in your paragraph true. There is no inconsistency among them.

But if you think the BB was at a point, that's wrong. We have Insughts articles on that.

Edit: BTW the CMB is just light like solar radiation is light.

 

[Paul Colby]

How would you measure such a thing?

I get stuck on "thing". In the absence of all particles and radiation (an impossibility AFAICT) is one left with more than one possible state? I think the usual assumption is vacuum is a unique state. This would seem to imply it has no temperature.

 

[anorlunda]

I get stuck on "thing". In the absence of all particles and radiation (an impossibility AFAICT) is one left with more than one possible state? I think the usual assumption is vacuum is a unique state. This would seem to imply it has no temperature.

But there is no such place. If there was, I guess temperature would be undefined.

I don't think vacuum as "a unique state" works. The word state must describe something, not nothing.

But please, lest us not descend into philosophy.

 

[sophiecentaur]

But if you think the BB was at a point, that's wrong.

Sorry - sloppy language there. But the 'stuff' was all around the same place at one time and there were definitely 'material sources' of the radiation that we see.

This would seem to imply it has no temperature.

No so much "no" but "indeterminate"?
I cross posted with @anorlunda there, I see.
Means means Σf_n/n and where n→0 ??

 

[stevendaryl]

Getting back to the original question: In thermodynamics, for every extensive quantity (something that is additive) there is a corresponding intensive quantity that can roughly be thought of as characterizing how willing a system is to give up or acquire more of the extensive quantity. Some examples:
Corresponding to the extensive quantity, "volume" there is a corresponding intensive quantity, "pressure". A gas at high pressure will tend to expand (increase its volume), and a gas at lower pressure will tend to contract. Internal energy and temperature are another example: A system at high temperature tends to lose energy to systems at a lower temperature.

Roughly speaking, systems with higher energy tend to have higher temperature, as well, but that's not always true.

Getting back to empty space. If the space is truly empty, devoid of matter or radiation, then it's temperature will be zero. It has no possibility of giving any energy to any other system. When they talk about the background temperature of space being 4 degrees Kelvin, they're talking about space that isn't completely empty. It has low-intensity radiation, so it has nonzero amount of energy per unit volume.

 

[DrStupid]

How would you measure such a thing?

Bring it in thermal equilibrium (not just steady state!) with a temperature reference.

 

[DLeuPel]

Getting back to the original question: In thermodynamics, for every extensive quantity (something that is additive) there is a corresponding intensive quantity that can roughly be thought of as characterizing how willing a system is to give up or acquire more of the extensive quantity. Some examples:
Corresponding to the extensive quantity, "volume" there is a corresponding intensive quantity, "pressure". A gas at high pressure will tend to expand (increase its volume), and a gas at lower pressure will tend to contract. Internal energy and temperature are another example: A system at high temperature tends to lose energy to systems at a lower temperature.

Roughly speaking, systems with higher energy tend to have higher temperature, as well, but that's not always true.

Getting back to empty space. If the space is truly empty, devoid of matter or radiation, then it's temperature will be zero. It has no possibility of giving any energy to any other system. When they talk about the background temperature of space being 4 degrees Kelvin, they're talking about space that isn't completely empty. It has low-intensity radiation, so it has nonzero amount of energy per unit volume.

And what is this low intensity radiation ?

 

[Vanadium 50]

Bring it in thermal equilibrium (not just steady state!) with a temperature reference.

And then it's not vacuum any more. (Or was this a joke...with your user name, I'm never quite sure)

 

[anorlunda]

And what is this low intensity radiation ?

The CMB. See post #2

 

[Paul Colby]

I don't think vacuum as "a unique state" works. The word state must describe something, not nothing.

In the current theory (The Standard Model), isn't vacuum that state in which every quantum field is in its vacuum state? Moving out of this state implies some quanta of these fields i.e. mater or radiation?

Of course gravitational waves have been observed, so one would need a region of space which is identically flat. That ain't happening just given all the hot matter banging around in stars and such. There should be a cosmic GW background but good luck detecting it.

 

[PeterDonis]

there are other definitions.

Can you give a definition that makes the temperature nonzero when there is no matter, radiation, or anything else present? See further comments below.

The Cosmic Microwave Background (CMB) also has a temperature (roughly 3 degrees K, -270 C, -452 F). It permeates the universe, even when there are no atoms around.

There aren't any atoms around, but that doesn't mean it's a vacuum by the definition the OP is (implicitly) using. The very presence of the CMB everywhere in the universe means the universe is not vacuum by that definition, because there is radiation present.

 

[PeterDonis]

Bring it in thermal equilibrium (not just steady state!) with a temperature reference.

A vacuum can't be brought into thermal equilibrium with anything, because it contains no matter, radiation, or anything else. So this won't work.

In fact, strictly speaking you can't make any measurements at all on a vacuum, because that would require interacting with it, and interacting with it makes it no longer a vacuum.

 

[PeterDonis]

I don't think vacuum as "a unique state" works.

It does if we restrict to inertial observers in flat spacetime. Any QFT in flat spacetime has a unique state that is a ground state--state of lowest energy--with respect to all inertial observers. This state is the vacuum state.

If we allow non-inertial observers, then the Unruh effect shows that these observers--at least, strictly speaking, if they have a constant proper acceleration--will see a different state as the vacuum state. So the notion of "vacuum state" is not unique in this sense.

Also, AFAIK there is not a unique vacuum state in a curved spacetime, even if we restrict to inertial observers.

 

[DrStupid]

And then it's not vacuum any more.

Is water not water anymore if you bring it in thermal equilibrium with a thermometer? If not, why should vacuum be turned into something else by the same procedure?

 

[DrStupid]

A vacuum can't be brought into thermal equilibrium with anything, because it contains no matter, radiation, or anything else.

Vaccum contains no radiation? Please provide a corresponding reference.

 

[Nugatory]

Vaccum contains no radiation? Please provide a corresponding reference.

It depends on how precise we're being when we use the word "vacuum". In casual use, "vacuum" is understand to mean "contains no matter" or "empty space" and interstellar space is an example of a vacuum even though electromagnetic radiation is present. More rigorously, vacuum is the ground state of all fields and there is neither matter not electromagnetic radiation present; this follows from the way that quantum field theories treat everything as a field, with no distinction between those fields that manifest themselves as matter

The casual definition is remarkably unhelpful when trying to understand what temperature is when working with systems that exchange energy by radiation, and this is the source of much of the confusion in this thread. The notion that temperature is the vibration of particles is even less helpful; it may be better to think of the vibration of particles as one of the many ways that a system can store energy, while temperature is a measure of how willing the system is to give up that energy - and @stevendaryl's post #11 above is worth another read.

 

[Klystron]

My working classification of vacuum "vacuum is a condition, not a thing" seems to contradict this dictionary definition

noun: condition; plural noun: conditions
1.the state of something, especially with regard to its appearance, quality, or working order.

 

[PeterDonis]

why should vacuum be turned into something else by the same procedure?

Because vacuum, unlike water or any other substance, cannot exchange heat with anything while still remaining vacuum.

 

[PeterDonis]

this dictionary definition

We're not talking about ordinary language here, we're talking about precise scientific terminology. The precise scientific definition of "vacuum" has already been given in this thread.

 

[PeterDonis]

Vaccum contains no radiation? Please provide a corresponding reference.

Check any QFT textbook for the precise definition of "vacuum".

 

[DrStupid]

In casual use, "vacuum" is understand to mean "contains no matter" or "empty space" and interstellar space is an example of a vacuum even though electromagnetic radiation is present. More rigorously, vacuum is the ground state of all fields and there is neither matter not electromagnetic radiation present; this follows from the way that quantum field theories treat everything as a field, with no distinction between those fields that manifest themselves as matter

Many thanks for this clarification. The "more rigorously" use of the term vacuum seem to be what Wikipedia refers to as QED vacuum whereas the OP refers to the subject of the Wikipedia main entry which refers to vacuum as "space devoid of matter".

The casual definition is remarkably unhelpful when trying to understand what temperature is when working with systems that exchange energy by radiation, and this is the source of much of the confusion in this thread. The notion that temperature is the vibration of particles is even less helpful;

As far as I can see the "notion that temperature is the vibration of particles" is the only source of confusion in this thread. Can you explain what the causual definition of vacuum contributes to the confusion?

 

[Mark Harder]

The precise thermodynamic definition of temperature is T = (∂U/∂S)_v,n,..., where U and S are internal energy and entropy, respectively. Subscripted variables are all independent variables upon which the internal energy depends, volume, no. of particles, etc. The equations of thermodynamics are differential equations, so it best handles changes in its critical variable values. In that spirit, suppose we create a volume of space devoid of matter/energy such as the CMB, perhaps separated from its environment by an adiabatic barrier that keeps out radiation. This volume contains no energy and no entropy (remember, it's only a hypothetical case, so S=0.). Now, remove all barriers between this 'perfect' vacuum and the rest of the universe, thus adding CMB, dark matter, vacuum energy, whatever to our volume. Clearly, internal energy increases. What about entropy? Does it increase? I would argue that it does, because the distribution of the CMB and any other mass/energy that may be present is not uniformly distributed. I base this on observations of the CMB across large volumes of space, which is not perfectly uniform. Also it would be a very peculiar situation if the volume should have photons of CMB moving with identical directions and exact wavelength; and any other candidate for constituent of this vacuum should be particulate as well. Since the energy is not uniformly distributed, the volume can exist in many states consistent with the energy in the volume we have carved out of space. Pick the usual symbol, W, for the number of ways this system's energy can be distributed.Since S=K Ln(W), the volume now contains entropy. We could also base the existence of nonzero entropy on the third law which specifies this fact, but I like the Boltzmann definition better for this purpose. What we have just described is the transition from a true vacuum containing no energy and no entropy to one that contains both. Therefore, T = (∂U/∂S)_v,n,... > 0 and the region of space has nonzero positive temperature.

 

[sophiecentaur]

Is water not water anymore if you bring it in thermal equilibrium with a thermometer? If not, why should vacuum be turned into something else by the same procedure?

I don't think that is any sort of valid argument. You could only draw that parallel if water and vacuum were the same sort of entity. There is a mathematical analogy here. The value Zero follows different rules from all other values. 1, 2 and even π behave the same but Zero is different.

 

[DrStupid]

I don't think that is any sort of valid argument.

It is valid for a classical vacuum. I just missed the point where the discussion drifted into quantum field theroy.

 

[PeterDonis]

It is valid for a classical vacuum.

No, it isn't. A classical vacuum can't be brought into thermal equilibrium with anything either; there has to be something present that can store heat, in which case it is no longer vacuum.

 

[DrStupid]

A classical vacuum can't be brought into thermal equilibrium with anything either; there has to be something present that can store heat, in which case it is no longer vacuum.

There can be radiation in a classical vaccuum. That's sufficient.

 

[PeterDonis]

There can be radiation in a classical vaccuum.

Please give a specific reference. My understanding of the term "vacuum" in classical physics is that it means nothing is present--no matter, no radiation, nothing.

 

[Paul Colby]

I certainly agree with what @PeterDonis said in #33. I would add the classical theory of EM in thermal equilibrium fails, badly. This failure was a key starting point of quantum theory (Planck and black body radiation).

 

[DrStupid]

Please give a specific reference.

https://en.wikipedia.org/wiki/Vacuum
https://en.wikipedia.org/wiki/Vacuum#Electromagnetism

All conditions given for the classical vacuum are still valid in presense of radiation.

With your restrictive understanding of vacuum there would not even be a speed of light in vaccum.