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Temperatures below absolute zero?

Scientific discovery and discussion
Mike4
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Temperatures below absolute zero?

#370261

Postby Mike4 » December 28th, 2020, 6:28 am

I woke up this morning to a 'popular science' programme on the radio (which had been on all night, doh!) discussing whether it was possible to have temperatures lower than absolute zero, 0 Kelvin.

Now obviously to me at least, and to the presenter team discussing it, the answer is 'no', as 0 Kelvin is when all the atoms have stopped moving. But their guest imminent scientist Cambridge Professor Wilkins said otherwise, sort of. He seemed to be describing an experiment with potassium which showed that as 0 Kelvin is approached, a sort of inversion can occur and the near stationary atoms 'flip' from a very cold state to a very hot state, thereby passing to the other side of 0 Kelvin but not passing through 0 Kelvin.

They went on to completely fail to explain properly other than than to say it is something to do with approaching 0 Kelvin requiring an infinite number of steps to actually get there. And as infinity is polarity conscious, i.e. infinity can be positive or negative, the potassium somehow skipped to being very hot thereby achieving a temperature on the far side of absolute zero, followed by much laughter and joking about it.

Now this makes no sense to me beyond seeing that quantum mechanics is involved here and nothing makes much sense where QM in involved. Do we have any physicists here that can perhaps translate what happened in that experiment into layman's language please?

The episode is here, FF to the last five or six minutes.
https://www.bbc.co.uk/sounds/play/w3cszv6t

Edit to make a proper sentence out of a jumble.

ursaminortaur
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Re: Temperatures below absolute zero?

#370416

Postby ursaminortaur » December 28th, 2020, 1:13 pm

Mike4 wrote:I woke up this morning to a 'popular science' programme on the radio (which had been on all night, doh!) discussing whether it was possible to have temperatures lower than absolute zero, 0 Kelvin.

Now obviously to me at least, and to the presenter team discussing it, the answer is 'no', as 0 Kelvin is when all the atoms have stopped moving. But their guest imminent scientist Cambridge Professor Wilkins said otherwise, sort of. He seemed to be describing an experiment with potassium which showed that as 0 Kelvin is approached, a sort of inversion can occur and the near stationary atoms 'flip' from a very cold state to a very hot state, thereby passing to the other side of 0 Kelvin but not passing through 0 Kelvin.

They went on to completely fail to explain properly other than than to say it is something to do with approaching 0 Kelvin requiring an infinite number of steps to actually get there. And as infinity is polarity conscious, i.e. infinity can be positive or negative, the potassium somehow skipped to being very hot thereby achieving a temperature on the far side of absolute zero, followed by much laughter and joking about it.

Now this makes no sense to me beyond seeing that quantum mechanics is involved here and nothing makes much sense where QM in involved. Do we have any physicists here that can perhaps translate what happened in that experiment into layman's language please?

The episode is here, FF to the last five or six minutes.
https://www.bbc.co.uk/sounds/play/w3cszv6t

Edit to make a proper sentence out of a jumble.


I'm not sure I really understand it myself but from this article it appears to be an artifact of the way absolute temperature is defined with respect to the Boltzmann distribution of particle energies.

https://www.sciencedaily.com/releases/2013/01/130104143516.htm

Yet, the individual molecules possess different kinetic energies – from very slow to very fast. Low-energy states are more likely than high-energy states, i.e. only a few particles move really fast. In physics, this distribution is called the Boltzmann distribution. Physicists working with Ulrich Schneider and Immanuel Bloch have now realised a gas in which this distribution is precisely inverted: many particles possess high energies and only a few have low energies. This inversion of the energy distribution means that the particles have assumed a negative absolute temperature.
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At first sight it may sound strange that a negative absolute temperature is hotter than a positive one. This is simply a consequence of the historic definition of absolute temperature, however; if it were defined differently, this apparent contradiction would not exist.

This inversion of the population of energy states is not possible in water or any other natural system as the system would need to absorb an infinite amount of energy – an impossible feat! However, if the particles possess an upper limit for their energy, such as the top of the hill in the potential energy landscape, the situation will be completely different. The researchers in Immanuel Bloch’s and Ulrich Schneider’s research group have now realised such a system of an atomic gas with an upper energy limit in their laboratory, following theoretical proposals by Allard Mosk and Achim Rosch.

In their experiment, the scientists first cool around a hundred thousand atoms in a vacuum chamber to a positive temperature of a few billionths of a Kelvin and capture them in optical traps made of laser beams. The surrounding ultrahigh vacuum guarantees that the atoms are perfectly thermally insulated from the environment. The laser beams create a so-called optical lattice, in which the atoms are arranged regularly at lattice sites. In this lattice, the atoms can still move from site to site via the tunnel effect, yet their kinetic energy has an upper limit and therefore possesses the required upper energy limit. Temperature, however, relates not only to kinetic energy, but to the total energy of the particles, which in this case includes interaction and potential energy. The system of the Munich and Garching researchers also sets a limit to both of these. The physicists then take the atoms to this upper boundary of the total energy – thus realising a negative temperature, at minus a few billionths of a kelvin.

ursaminortaur
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Re: Temperatures below absolute zero?

#370443

Postby ursaminortaur » December 28th, 2020, 2:05 pm

ursaminortaur wrote:
Mike4 wrote:I woke up this morning to a 'popular science' programme on the radio (which had been on all night, doh!) discussing whether it was possible to have temperatures lower than absolute zero, 0 Kelvin.

Now obviously to me at least, and to the presenter team discussing it, the answer is 'no', as 0 Kelvin is when all the atoms have stopped moving. But their guest imminent scientist Cambridge Professor Wilkins said otherwise, sort of. He seemed to be describing an experiment with potassium which showed that as 0 Kelvin is approached, a sort of inversion can occur and the near stationary atoms 'flip' from a very cold state to a very hot state, thereby passing to the other side of 0 Kelvin but not passing through 0 Kelvin.

They went on to completely fail to explain properly other than than to say it is something to do with approaching 0 Kelvin requiring an infinite number of steps to actually get there. And as infinity is polarity conscious, i.e. infinity can be positive or negative, the potassium somehow skipped to being very hot thereby achieving a temperature on the far side of absolute zero, followed by much laughter and joking about it.

Now this makes no sense to me beyond seeing that quantum mechanics is involved here and nothing makes much sense where QM in involved. Do we have any physicists here that can perhaps translate what happened in that experiment into layman's language please?

The episode is here, FF to the last five or six minutes.
https://www.bbc.co.uk/sounds/play/w3cszv6t

Edit to make a proper sentence out of a jumble.


I'm not sure I really understand it myself but from this article it appears to be an artifact of the way absolute temperature is defined with respect to the Boltzmann distribution of particle energies.

https://www.sciencedaily.com/releases/2013/01/130104143516.htm

Yet, the individual molecules possess different kinetic energies – from very slow to very fast. Low-energy states are more likely than high-energy states, i.e. only a few particles move really fast. In physics, this distribution is called the Boltzmann distribution. Physicists working with Ulrich Schneider and Immanuel Bloch have now realised a gas in which this distribution is precisely inverted: many particles possess high energies and only a few have low energies. This inversion of the energy distribution means that the particles have assumed a negative absolute temperature.
.
.
.
At first sight it may sound strange that a negative absolute temperature is hotter than a positive one. This is simply a consequence of the historic definition of absolute temperature, however; if it were defined differently, this apparent contradiction would not exist.

This inversion of the population of energy states is not possible in water or any other natural system as the system would need to absorb an infinite amount of energy – an impossible feat! However, if the particles possess an upper limit for their energy, such as the top of the hill in the potential energy landscape, the situation will be completely different. The researchers in Immanuel Bloch’s and Ulrich Schneider’s research group have now realised such a system of an atomic gas with an upper energy limit in their laboratory, following theoretical proposals by Allard Mosk and Achim Rosch.

In their experiment, the scientists first cool around a hundred thousand atoms in a vacuum chamber to a positive temperature of a few billionths of a Kelvin and capture them in optical traps made of laser beams. The surrounding ultrahigh vacuum guarantees that the atoms are perfectly thermally insulated from the environment. The laser beams create a so-called optical lattice, in which the atoms are arranged regularly at lattice sites. In this lattice, the atoms can still move from site to site via the tunnel effect, yet their kinetic energy has an upper limit and therefore possesses the required upper energy limit. Temperature, however, relates not only to kinetic energy, but to the total energy of the particles, which in this case includes interaction and potential energy. The system of the Munich and Garching researchers also sets a limit to both of these. The physicists then take the atoms to this upper boundary of the total energy – thus realising a negative temperature, at minus a few billionths of a kelvin.


This seems to give a fuller explanation in terms of changes in entropy

https://www.physicscentral.com/explore/action/negative-temperature.cfm

In statistical mechanics and thermodynamics, temperature is defined as follows:

1/temperature = change in entropy/change in energy

For our hypothetical system of 100 atoms with only two energy states, there is an upper and lower bound of energy, and the entropy of the system equals zero at these boundary limits. This definition of temperature can go from positive infinity to negative infinity. The temperature makes a discontinuous jump at the point where the entropy changes from an increasing value to a decreasing value.
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The temperature for all the atoms in their ground state is zero. This is like a bunch of balls sitting in a valley.

As energy is added to the system, some of the atoms go to the higher energy state, the entropy increases, and the temperature increases. This is like moving some balls out of the valley and onto the hill.

As more energy is added, more atoms go to a higher energy level. The temperature approaches positive infinity as the entropy nears its maximum, which occurs when half of the atoms exist in the upper state and half are in the lower state. In the hill/valley analogy, half of the balls would be in the valley and half would be on the hill.

Still adding more energy, just as you reach the state of half the atoms being in the upper state and half in the lower state and pass it, the entropy of the system decreases. This results in the temperature discontinuously jumping from positive infinity to negative infinity (right at the halfway mark). This transition resembles the jump from having just less than to just more than half the balls on the hill and half in the valley.

As the system reaches its maximum energy state, the atoms all are in their upper energy state, the entropy goes to zero, and the negative temperatures increase, approaching zero. This is like all the balls being very stable on the hill, and not being able to fall off the hill.

Mike4
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Re: Temperatures below absolute zero?

#370453

Postby Mike4 » December 28th, 2020, 2:22 pm

Thanks for your replies Ursa.

I had a horrible feeling entropy would crop up in the answer(s). It's a concept I struggle to grasp, so maybe I should start there and get a good understanding.

I have a similar problem with enthalpy, which has cropped up in another subject I am trying to grasp on another forum!

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Re: Temperatures below absolute zero?

#370543

Postby stewamax » December 28th, 2020, 5:01 pm

Sounds like a temperature version of tachyons - theoretical particles of imaginary* mass that only (theoretically) exist at speeds faster than that of light. But their existence is consistent with Maxwell's equations.

* - in the complex number sense of SQRT(-1)

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Re: Temperatures below absolute zero?

#370560

Postby ursaminortaur » December 28th, 2020, 5:48 pm

stewamax wrote:Sounds like a temperature version of tachyons - theoretical particles of imaginary* mass that only (theoretically) exist at speeds faster than that of light. But their existence is consistent with Maxwell's equations.

* - in the complex number sense of SQRT(-1)


Not quite as the experiment has produced a gas with these "negative temperatures" whereas no-one has found any tachyon particles which travel faster than light (and I think few expect them to be discovered anymore).

The concept of tachyons arose in a 1967 paper by Gerald Feinberg looking at quantum fields with imaginary mass and he believed such fields would produce particles which travelled faster than light. However subsequent investigation showed that exitations in those fields would still be restricted to light speed or less. One field with imaginary mass is thought to exist - the Higgs field.

https://en.wikipedia.org/wiki/Tachyonic_field

A tachyonic field, or simply tachyon, is a field with an imaginary mass. Although tachyonic particles (particles that move faster than light) are a purely hypothetical concept that violate a number of essential physical principles, at least one field with imaginary mass, the Higgs field, is believed to exist. In general, tachyonic fields play an important role in physics and are discussed in popular books. Under no circumstances do any excitations of tachyonic fields ever propagate faster than light—the presence or absence of a tachyonic (imaginary) mass has no effect on the maximum velocity of signals, and so unlike faster-than-light particles there is no violation of causality.

The term "tachyon" was coined by Gerald Feinberg in a 1967 paper that studied quantum fields with imaginary mass. Feinberg believed such fields permitted faster than light propagation, but it was soon realized that this was not the case. Instead, the imaginary mass creates an instability in the configuration: any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the Standard Model of particle physics.

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Re: Temperatures below absolute zero?

#370576

Postby AsleepInYorkshire » December 28th, 2020, 7:01 pm

I love to talk about this sort of stuff. But ... understanding it really is well above my brain cell :roll:

How can particles still exist at absolute zero? Surely if there's no temperature all the energy has gone and the mass too?

AiY

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Re: Temperatures below absolute zero?

#370830

Postby ursaminortaur » December 29th, 2020, 2:14 pm

AsleepInYorkshire wrote:I love to talk about this sort of stuff. But ... understanding it really is well above my brain cell :roll:

How can particles still exist at absolute zero? Surely if there's no temperature all the energy has gone and the mass too?

AiY



Firstly there are different forms of energy not just kinetic energy. So if you had a box of gas which somehow was cooled to absolute zero sitting on top of a table it would still have the potential energy due to gravitation which could be converted to kinetic energy if you removed the table.
Secondly quantum theory prohibits reaching absolute zero anyway. If particles could be cooled to absolute zero then they would have both fixed positions and zero momentum which would violate Heisenberg's uncertainty principle. This also leads to the idea of virtual particles popping in and out of existence meaning that the vacuum itself has a certain amount of energy. Thus as close as we could possibly get to absolute zero the basic building blocks of matter would still exist (and if they were strings they would vibrate). Virtual messenger particles photons, gluons etc would still be exchanged between them providing binding energy. Massive particles would still interact with the Higgs field etc

Note. I am not a physicist so this is just a layman's view of how things work gathered from reading popular science books - a more accurate description would involve delving into the mathematics of quantum field theory where, as I understand it, the very concept of a particle becomes somewhat slippery.

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Re: Temperatures below absolute zero?

#370831

Postby AsleepInYorkshire » December 29th, 2020, 2:22 pm

ursaminortaur wrote:
AsleepInYorkshire wrote:I love to talk about this sort of stuff. But ... understanding it really is well above my brain cell :roll:

How can particles still exist at absolute zero? Surely if there's no temperature all the energy has gone and the mass too?

AiY



Firstly there are different forms of energy not just kinetic energy. So if you had a box of gas which somehow was cooled to absolute zero sitting on top of a table it would still have the potential energy due to gravitation which could be converted to kinetic energy if you removed the table.
Secondly quantum theory prohibits reaching absolute zero anyway. If particles could be cooled to absolute zero then they would have both fixed positions and zero momentum which would violate Heisenberg's uncertainty principle. This also leads to the idea of virtual particles popping in and out of existence meaning that the vacuum itself has a certain amount of energy. Thus as close as we could possibly get to absolute zero the basic building blocks of matter would still exist (and if they were strings they would vibrate). Virtual messenger particles photons, gluons etc would still be exchanged between them providing binding energy. Massive particles would still interact with the Higgs field etc

Note. I am not a physicist so this is just a layman's view of how things work gathered from reading popular science books - a more accurate description would involve delving into the mathematics of quantum field theory where, as I understand it, the very concept of a particle becomes somewhat slippery.

Thank you. I hope we don't have to sit an exam on this sort of thing :ugeek:

I note you said you're not a physicist. You seem to do a very good impression of one though :)

Seriously though, thank you for the interesting information, gratefully appreciate the heads up

AiY

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Re: Temperatures below absolute zero?

#371061

Postby 9873210 » December 30th, 2020, 2:25 am

https://www.physicscentral.com/explore/action/negative-temperature.cfm wrote:It is important to note that the negative temperature region, with more of the atoms in the higher allowed energy state, is actually warmer than the positive temperature region. If this system were to be brought into contact with a system containing more atoms in a lower energy state (positive temperatures) heat would flow from the system with the negative temperatures to the system with the positive temperatures. So negative temperatures are warmer! And all this has to do with the how we define temperature.


The negative temperature is below absolute zero but it is not colder than absolute zero.

At this point the concept of warmth and the definition of temperature are somewhat disconnected. Among other things the second law of thermodynamics is going to have to be restated.


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