Quantum gas goes below absolute zero

[mijopaalmc]

Originally Posted by h.g.Whiz

Your looks are irrelavent.

My you're witty and bright.

Do you pity any boy who isn't you tonight?

/obscure reference

[fuelair]

Originally Posted by mijopaalmc

My you're witty and bright.

Do you pity any boy who isn't you tonight?

/obscure reference

In all fairness, slightly adapted stuff from West Side Story is hardly obscure!!!!!

[Farsight]

I have to say I'm beginning to dislike this paper. And the definition of temperature that allows for negative temperature. It sounds like Humpty-Dumpty physics: "When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean -- neither more nor less.". It sounds like a negative carpet. That's where you need 16m² of carpet for a square room, and claim that a carpet measuring -4m by -4m will do the job, because -4² = 16. If something burns you, it's hot. We say it's got a high temperature. So the idea that the thing that burnt you has negative temperature sounds contrived. What with over-unity and antigravity being dangled, I'm starting to form an opinion, and that opinion is negative. You know how Boltzmann has cropped up? Ever heard of Boltzmann brains? Woo!

[ctamblyn]

@Farsight: Negative temperatures are nothing new or controversial. There are papers regarding negative temperatures in spin systems going back to 1951.

The new thing about this paper, from what I understand, is that it demonstrates negative temperatures in motion degrees of freedom rather than spins.

[Dancing David]

Originally Posted by mijopaalmc

My you're witty and bright.

Do you pity any boy who isn't you tonight?

/obscure reference

How do you fire this gun Chino? By pulling this little trigger!

[edd]

Originally Posted by Farsight

I If something burns you, it's hot. We say it's got a high temperature.

That's everyday experience. Very low temperatures are hardly part of everyday experience, let alone negative temperatures.
Negative temperatures are a natural result of the thermodynamic definition of temperature though, and just because they're not quite as intuitive due to our lack of common experience with them doesn't mean they're invalid.

[Farsight]

Originally Posted by edd

...Negative temperatures are a natural result of the thermodynamic definition of temperature though...

Is that a thermodynamic definition of temperature, or a statistical mechanics definition of temperature? On page 2 of the arXiv paper you can read "according to the thermodynamic definition of temperature [8]" but reference 8 is K. Huang, Statistical mechanics (Wiley, New York, 1987), second edn. When I look up negative temperature on wiki and follow the link to thermodynamic beta, it says "In statistical mechanics, the thermodynamic beta (or occasionally perk) is the reciprocal of the thermodynamic temperature of a system.... Then when I look at definition of thermodynamic temperature I read this: "Equation 5 can be rearranged to get an alternative definition for temperature in terms of entropy and heat (to avoid logic loop, we should first define entropy through statistical mechanics)...". There seems to be some crossover here.

[edd]

Originally Posted by Farsight

Is that a thermodynamic definition of temperature, or a statistical mechanics definition of temperature?

Thermodynamic. It's the definition based on internal energy and entropy that's been mentioned upthread already. It doesn't require understanding of statistical mechanics, although it does help I think. Not that it really matters - after all, what's wrong with statistical mechanics?

[Perpetual Student]

Here is an interesting lecture by Leonard Susskind about negative temperature. It's from the final of his lecture series on statistical mechanics. The segment about negative temperature begins at 1:17 and is quite easy to understand: LINK

[Perpetual Student]

Originally Posted by Farsight

I have to say I'm beginning to dislike this paper. And the definition of temperature that allows for negative temperature. It sounds like Humpty-Dumpty physics: "When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean -- neither more nor less.". It sounds like a negative carpet. That's where you need 16m² of carpet for a square room, and claim that a carpet measuring -4m by -4m will do the job, because -4² = 16. If something burns you, it's hot. We say it's got a high temperature. So the idea that the thing that burnt you has negative temperature sounds contrived. What with over-unity and antigravity being dangled, I'm starting to form an opinion, and that opinion is negative. You know how Boltzmann has cropped up? Ever heard of Boltzmann brains? Woo!

Definitions exist is physics (like time and temperature) because they have utility in that they lead to productive theories. Productive theories are validated through experiment. They need not fit your intuition.

[mijopaalmc]

Originally Posted by Perpetual Student

Here is an interesting lecture by Leonard Susskind about negative temperature. It's from the final of his lecture series on statistical mechanics. The segment about negative temperature begins at 1:17 and is quite easy to understand: LINK

I think you've got the wrong lecture, the wrong timestamp, or both. At 1:17 in Lecture 10, Susskind is talking about comsological inflation.

[marplots]

Originally Posted by mijopaalmc

I think you've got the wrong lecture, the wrong timestamp, or both. At 1:17 in Lecture 10, Susskind is talking about comsological inflation.

Negative gravity, negative temperature, same difference really. Exotic physics animals you'll never see outside of a zoo.

[mijopaalmc]

Originally Posted by marplots

Negative gravity, negative temperature, same difference really. Exotic physics animals you'll never see outside of a zoo.

Not necessarily. There are are already metamaterials with negative indices of refraction.

[Perpetual Student]

Originally Posted by mijopaalmc

I think you've got the wrong lecture, the wrong timestamp, or both. At 1:17 in Lecture 10, Susskind is talking about comsological inflation.

You probably started at the beginning of the lecture. Inflation is discussed for about the first 20 minutes. A discussion of negative temperature begins at 72 minutes ( 1 hour, 17 minutes ). Or you may have stopped listening too soon. He gets there; try again.

[marplots]

Originally Posted by mijopaalmc

Not necessarily. There are are already metamaterials with negative indices of refraction.

Now that beats negative temperature hands down. Thanks.

[mijopaalmc]

Originally Posted by Perpetual Student

You probably started at the beginning of the lecture. Inflation is discussed for about the first 20 minutes. A discussion of negative temperature begins at 72 minutes ( 1 hour, 17 minutes ). Or you may have stopped listening too soon. He gets there; try again.

Yeah, I read 1:17 as 1 minute 17 seconds.

[Ziggurat]

Originally Posted by Farsight

I have to say I'm beginning to dislike this paper. And the definition of temperature that allows for negative temperature. It sounds like Humpty-Dumpty physics: "When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean -- neither more nor less.". It sounds like a negative carpet. That's where you need 16m² of carpet for a square room, and claim that a carpet measuring -4m by -4m will do the job, because -4² = 16. If something burns you, it's hot. We say it's got a high temperature. So the idea that the thing that burnt you has negative temperature sounds contrived. What with over-unity and antigravity being dangled, I'm starting to form an opinion, and that opinion is negative. You know how Boltzmann has cropped up? Ever heard of Boltzmann brains? Woo!

Statistical mechanics is probably a more fundamental way to define things than classical thermodynamics, though they end up with the exact same result. This is not actually surprising: temperature is defined the way it is because that definition ensures any two objects in thermal equilibrium with each other will be at the same temperature. If you try to use some other definition of temperature (such as using the ideal gas law or the equipartition theorem), the definition will fail: at best you will end up with systems whose temperature you cannot define even at equilibrium, and at worst you'll end up with systems in thermal contact at equilibirum with each other but not at the same temperature. And that rather defeats the entire purpose of defining temperature to begin with.

Negative temperatures are exotic, but they don't violate anything other than your sensibilities. But the universe doesn't care about our sensibilities.

[sol invictus]

Originally Posted by Farsight

Is that a thermodynamic definition of temperature, or a statistical mechanics definition of temperature?

If you understand the microscopic constituents of some macroscopic system, you can use their statistics to derive the laws of thermodynamics for that system. Alternatively, you can simply determine the laws empirically. Either way they're the same laws in terms of the same quantities.

The definition of temperature is the same in thermodynamics and statistical mechanics.

[fuelair]

Originally Posted by Dancing David

How do you fire this gun Chino? By pulling this little trigger!

Thanks Offisuh Krupke!!!

[Farsight]

Originally Posted by edd

Thermodynamic. It's the definition based on internal energy and entropy that's been mentioned upthread already.

That's what it said, but like I said statistical mechanics seemed to be creeping in repeatedly.

Originally Posted by edd

It doesn't require understanding of statistical mechanics, although it does help I think. Not that it really matters - after all, what's wrong with statistical mechanics?

Nothing per se. But there's two definitions of entropy, see wiki. And we no longer have a clear definition of "hotness".

Originally Posted by Perpetual Student

Definitions exist is physics (like time and temperature) because they have utility in that they lead to productive theories. Productive theories are validated through experiment. They need not fit your intuition.

This isn't intuition. This is ambiguity. See temperature on wiki where you can read this:

In thermodynamics, in a system of which the entropy is considered as an independent externally controlled variable, absolute, or thermodynamic, temperature is defined as the derivative of the internal energy with respect to the entropy...

The temperature of an ideal gas is proportional to the mean translational kinetic energy of its molecules.

The latter doesn't allow for a negative.

Originally Posted by Ziggurat

Statistical mechanics is probably a more fundamental way to define things than classical thermodynamics, though they end up with the exact same result. This is not actually surprising: temperature is defined the way it is because that definition ensures any two objects in thermal equilibrium with each other will be at the same temperature.

I'm not sure either of them are particularly fundamental in that we're dealing with emergent properties. Energy is fundamental in that it's the one thing you can neither create nor destroy, and I think it's fundamental to talk about entropy in terms of available energy. Quick mental picture: the universe consists of hills and valleys of energy density, and doing work reduces the height of the hills to fill the valleys, so you're left with a flat plateau of uniform energy density but no available energy.

Originally Posted by Ziggurat

If you try to use some other definition of temperature (such as using the ideal gas law or the equipartition theorem), the definition will fail: at best you will end up with systems whose temperature you cannot define even at equilibrium, and at worst you'll end up with systems in thermal contact at equilibirum with each other but not at the same temperature. And that rather defeats the entire purpose of defining temperature to begin with.

Imagine you have two containers of gas. In one the molecules move at various speeds, in the other they're all moving at the same speed. However the average kinetic energy of the gas molecules is the same for both containers. In the ideal gas law we start with PV = nRT, both pressure V and volume V is positive, as is number of moles n. The gas constant R relates the energy scale to the temperature scale, and it's a constant. So T is positive for both gases. When you look further down the page you see the statistical mechanics form PV = NkT where P is pressure and V is volume, N is number of particles, k is Boltzman's constant, and T is temperature. But then wiki says Boltzman's constant is the gas constant divided by the Avogadro constant, which is defined as "the number of constituent particles (usually atoms or molecules) in one mole". So again T is positive for both gases. There's no mention of entropy here. And yet introducing entropy, which is only a concept, and is essentially "sameness", ends up giving us a negative temperature for the second container? When both containers are hot? I'm missing something here. It's as if two measures have been combined into one.

Originally Posted by Ziggurat

Negative temperatures are exotic, but they don't violate anything other than your sensibilities. But the universe doesn't care about our sensibilities.

It doesn't care about our definitions either. I remain dissatisfied by this.

[edd]

We aren't talking ideal gases here, Farsight.

[ctamblyn]

Originally Posted by Farsight

In thermodynamics, in a system of which the entropy is considered as an independent externally controlled variable, absolute, or thermodynamic, temperature is defined as the derivative of the internal energy with respect to the entropy...

The temperature of an ideal gas is proportional to the mean translational kinetic energy of its molecules.

The latter doesn't allow for a negative.

No-one is saying the temperature of an ideal gas could be negative.

ETA: edd beat me to it

[BowlOfRed]

I liked when someone mentioned the relationship with lasers. Lasers require a Population_inversion^WP to work. If you can understand that, you can get a handle on this.

[Reality Check]

Originally Posted by Farsight

Nothing per se. But there's two definitions of entropy, see wiki. And we no longer have a clear definition of "hotness".

If you had bothered to read that article carefully you would seen that the 2 definitions only differ by Boltzmann's constant.

Quote:

Boltzmann showed that this definition of entropy was equivalent to the thermodynamic entropy to within a constant number which has since been known as Boltzmann's constant. In summary, the thermodynamic definition of entropy provides the experimental definition of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature.

And there remains a clear definition of "hotness". See temperature on wiki where you can read this:

Quote:

For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.[17]

As other posters have noted: Going to the specific case of an idealized gas which has nothing to do with the experiment is a bit dumb.
You may as well start talking about the temperature of a solid .

[Ziggurat]

Originally Posted by Farsight

The temperature of an ideal gas is proportional to the mean translational kinetic energy of its molecules.[/i]

The latter doesn't allow for a negative.

Well of course not. An ideal gas cannot have a negative temperature. Most systems cannot. Only some systems can. Again, all of this comes out naturally from actual statistical mechanics.

Quote:

Quick mental picture: the universe consists of hills and valleys of energy density, and doing work reduces the height of the hills to fill the valleys, so you're left with a flat plateau of uniform energy density but no available energy.

Small problem: your mental picture is demonstrably wrong. All you need to do to notice it's wrong is to note that heat capacities (whether it's by mass, by volume, by molar content, or whatever) are not all the same.

Quote:

Imagine you have two containers of gas. In one the molecules move at various speeds, in the other they're all moving at the same speed.

Your first gas might be at equilibrium. Your second gas is not. Defining temperature in non-equilibrium conditions is... tricky.

Quote:

However the average kinetic energy of the gas molecules is the same for both containers. In the ideal gas law we start with PV = nRT, both pressure V and volume V is positive, as is number of moles n. The gas constant R relates the energy scale to the temperature scale, and it's a constant. So T is positive for both gases.

Again, this is no surprise, and changes nothing about what I said or the reality of negative temperatures. Not every system can be at a negative temperature, because you need certain uncommon properties for that to happen. Ideal gasses cannot have negative temperatures, because they do not have those properties.

Quote:

There's no mention of entropy here.

So what? It's Wikipedia, not a physics textbook.

Quote:

And yet introducing entropy, which is only a concept

If you think energy is any less of a "concept" than entropy, you're kidding yourself.

Quote:

and is essentially "sameness"

No, it is most definitely not a measure of "sameness".

[Perpetual Student]

From Wikipedia:

Quote:

A definition of temperature can be based on the relationship:

T = dq_rev/dS

The relationship suggests that a positive temperature corresponds to the condition where entropy, S, increases as thermal energy, q_rev, is added to the system. This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and non-spin related electronic and nuclear modes. The reason for this is that there are an infinite number of these types of modes, and adding more heat to the system increases the number of modes that are energetically accessible, and thus increases the entropy.

As Susskind shows in his lecture, when S decreases as thermal energy is added to a system, we have negative temperature. The article includes three examples of negative temperature.