# How can “absolute zero” be proven?

#### wegs

##### Matter and Pixie Dust
Valued Senior Member
Recently, I watched a documentary on how certain species of birds can adapt to super cold temps way below zero degrees Fahrenheit, and the narrator touched on “absolute zero.” My understanding of “absolute zero” is that there would be no movement. No vibrations.

But, how could we ever test for absolute zero if an “observer” would cause some movement? Is absolute zero applicable in theory only? And does absolute zero really have anything to do with temperature, as we define it in every day life? Something can be “hot” or “lukewarm,” and we can measure temperatures but when we examine absolute zero, is it really more about lack of movement, than lack of heat?

I thought I somewhat understood absolute zero but I hadn’t ever considered that it could be anything more than guesswork if an observer is unable to truly test for it, since an observer would generate movement and in turn, heat. If there is no way to test absolute zero, what’s the point in theorizing it?

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Absolute zero doesnt result in lack of movement. Atoms don't stop moving. Heisenbergs Uncertainty Principle forbids this. What happens is the atoms get smeared out into a Bose Einstein Condensate.

Recently, I watched a documentary on how certain species of birds can adapt to super cold temps way below zero degrees Fahrenheit, and the narrator touched on “absolute zero.” My understanding of “absolute zero” is that there would be no movement. No vibrations.

But, how could we ever test for absolute zero if an “observer” would cause some movement? Is absolute zero applicable in theory only? And does absolute zero really have anything to do with temperature, as we see it in every day life? Something can be “hot” or “lukewarm,” and we can measure temperatures but when we examine absolute zero, is it really more about lack of movement, than lack of heat?

I thought I somewhat understood absolute zero but I hadn’t ever considered that it could be anything more than guesswork if an observer is unable to truly test for it, since an observer would generate movement and in turn, heat. If there is no way to test absolute zero, what’s the point in theorizing it?
No ,maybe it doesn't exist as what you might think of as a "physical reality".

But you could say the same of the number zero.

I think the term to describe them may be "a limit"-a number or state that you can approach to any degree of nearness that you like but not a complete approach.

I am not exactly sure what "temperature" is correctly described as ,but I think you are right that at least one of the ways is the amount of movement in the body you are assessing.

Not sure that you are right about an observer causing additional movement in the object being measured for temperature.

Any body has to radiate electromagnetic waves and so ,if none are detected then maybe it is at absolute zero?

(I think the Cosmic Background Radiation is very close to absolute zero)

Recently, I watched a documentary on how certain species of birds can adapt to super cold temps way below zero degrees Fahrenheit, and the narrator touched on “absolute zero.” My understanding of “absolute zero” is that there would be no movement. No vibrations.

But, how could we ever test for absolute zero if an “observer” would cause some movement? Is absolute zero applicable in theory only? And does absolute zero really have anything to do with temperature, as we define it in every day life? Something can be “hot” or “lukewarm,” and we can measure temperatures but when we examine absolute zero, is it really more about lack of movement, than lack of heat?

I thought I somewhat understood absolute zero but I hadn’t ever considered that it could be anything more than guesswork if an observer is unable to truly test for it, since an observer would generate movement and in turn, heat. If there is no way to test absolute zero, what’s the point in theorizing it?
It's the temperature at which no more heat can be extracted from a body. Laboratory experiments have cooled systems to very very close to absolute zero - to within a billionth of degree above it - but you are right that to achieve it exactly is by definition not possible: https://en.wikipedia.org/wiki/Absolute_zero

However it is far from guesswork, as it is predicted from the gas laws.

As DaveC426913 says, it is not generally true that no motion occurs at absolute zero, because so-called zero point energy remains in many systems (including vibrational systems) in their ground state. However this remaining energy cannot be extracted, as there is no state below the ground state.

The point of absolute zero is that it allows a natural temperature scale to be defined in which temperature is directly proportional to the thermal kinetic energy of the system. In statistical thermodynamics each degree of freedom (translation, rotation, vibration) contributes 1/2 kT to the total thermal kinetic energy, where T is the temperature above absolute zero (k is Boltzmann's constant).

So for a monatomic gas like helium or argon, the energy at a given temperature is 3/2 kT (1/2 kt each for translational motion along x, y and z axes). Whereas for a diatomic gas which can also rotate in 2 mutually perpedicular directions as well as translate, it is 5/2kT. (When it gets really hot, vibration can also kick in, which counts as 2 more dgrees of freedom, so it goes up to 7/2kT.) You can verify this by measuring the specific heat capacity of these gases.

An absolute temperature scale, i.e. one that starts from zero at absolute zero, turns out to be vital for any number of relationships in physical science.

Recently, I watched a documentary on how certain species of birds can adapt to super cold temps way below zero degrees Fahrenheit, and the narrator touched on “absolute zero.” My understanding of “absolute zero” is that there would be no movement. No vibrations.

But, how could we ever test for absolute zero if an “observer” would cause some movement? Is absolute zero applicable in theory only? And does absolute zero really have anything to do with temperature, as we define it in every day life? Something can be “hot” or “lukewarm,” and we can measure temperatures but when we examine absolute zero, is it really more about lack of movement, than lack of heat?

I thought I somewhat understood absolute zero but I hadn’t ever considered that it could be anything more than guesswork if an observer is unable to truly test for it, since an observer would generate movement and in turn, heat. If there is no way to test absolute zero, what’s the point in theorizing it?
We were taught at school (pre uni), that it was simply a matter of extrapolation, using the relationship above between thermal and kinetic energy.
Once the relationship is established you can plot the numbers anywhere on the line. Like distance and time,in a car at a certain velocity you can say where you will be one hour. Or at T=0.
We were told you can never actually get to T=0, i cannot remember the explanation which would have been heuristic.
For reference interstellar space is a few degrees above.
The huge magnets at the LHC are cooled to something close to absolute zero.

It's the temperature at which no more heat can be extracted from a body. Laboratory experiments have cooled systems to very very close to absolute zero - to within a billionth of degree above it - but you are right that to achieve it exactly is by definition not possible: https://en.wikipedia.org/wiki/Absolute_zero

However it is far from guesswork, as it is predicted from the gas laws.

As DaveC426913 says, it is not generally true that no motion occurs at absolute zero, because so-called zero point energy remains in many systems (including vibrational systems) in their ground state. However this remaining energy cannot be extracted, as there is no state below the ground state.

The point of absolute zero is that it allows a natural temperature scale to be defined in which temperature is directly proportional to the thermal kinetic energy of the system. In statistical thermodynamics each degree of freedom (translation, rotation, vibration) contributes 1/2 kT to the total thermal kinetic energy, where T is the temperature above absolute zero (k is Boltzmann's constant).

So for a monatomic gas like helium or argon, the energy at a given temperature is 3/2 kT (1/2 kt each for translational motion along x, y and z axes). Whereas for a diatomic gas which can also rotate in 2 mutually perpedicular directions as well as translate, it is 5/2kT. (When it gets really hot, vibration can also kick in, which counts as 2 more dgrees of freedom, so it goes up to 7/2kT.) You can verify this by measuring the specific heat capacity of these gases.

An absolute temperature scale, i.e. one that starts from zero at absolute zero, turns out to be vital for any number of relationships in physical science.
Thanks exchemist! I didn’t really think it was guesswork, but didn’t understand the “functionality” of using it to describe a state that can never be measured with certainty. But your explanation is helpful - the remaining energy can’t be extracted, there is no state below the ground state.

How does an observer investigate the ground state with accuracy? I’m under the impression that there can’t be any interference (I’m not sure if that’s the right word, here) from say, an observer, as we explore these states because of the energy interaction any outside observer would create.

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Thanks exchemist! I didn’t really think it was guesswork, but didn’t understand the “functionality” of using it to describe a state that can never be measured with certainty. But your explanation is helpful - the remaining energy can’t be extracted, there is no state below the ground state.

How does an observer investigate the ground state with accuracy? I’m under the impression that there can’t be any interference (I’m not sure if that’s the right word, here) from say, an observer, as we explore these states because of the energy interaction any outside observer would create.
You are evidently thinking of the "observer effect". That is not really a question to do with absolute zero, but can be in principle an issue with measurement of quantum states. However we generally we measure the properties of ensembles rather than single systems, e.g. a gas sample comprised of alot of atoms emitting light of a characteristic frequency, say, rather than single atoms. In that case, the observer effect is not really much of an issue.

The energy of the ground state can be deduced from what happens when an atom is excited from it to another state, or when it falls back to the ground state from an excited state. In my gas sample example, light can be emitted corresponding to a transition from an excited state to the ground state, which allows us to measure the energy gap between the two. There will be a narrow range of frequencies over which this light emitted, because the atoms are in motion, creating a Doppler effect, i.e. the atoms moving towards the detector will have their emission slightly blue-shifted, where ones receded will be slightly red-shifted. There is also an intrinsic uncertainty in energy for any given atom, arising from the Uncertainty Principle. But the emission will be centred on one frequency, which we can take to be the "real" size of the energy gap between the states. This can be compared with the continuum of emission you get when the atoms are completely ionised, so you can work out the energy of all the states by reference to the frequency at the onset of ionisation. The spin and orbital angular momentum of the states can be worked out on theoretical grounds (these are much easier to calculate than the energy). So for atoms, this kind of exercise in spectroscopy can tell you quite a lot. It is harder for molecules as there is much more going on. So the properties of the ground state of molecules is usually a semi-quantitative exercise involving estimation, based on calculations, consideration of the symmetry of the molecule and so on.

I think the observer effect is more important in certain physics experiments, like the double slit experiment, than it is in chemistry. You'll have to excuse me if I do not launch into the double slit experiment, as it is a hackneyed topic on the internet and I have rather lost interest in it. There may be others here who can go into the observer effect as it applies in that case.

But, how could we ever test for absolute zero if an “observer” would cause some movement?
It's not really a question of whether it exists - we know it does because we know what the limit is, which is zero kinetic energy in the particles of a gas (for example.) As a comparable example we know that the 'speed limit' in the universe is the speed of light, and barring some very radical new discovery, nothing can go faster than that. We don't know this because we have accelerated things to 99.999999% of the speed of light and been thwarted from going any faster - we know this because even when we accelerate something to a few percent of the speed of light we see the exact same effects that will keep us from reaching that speed.

We may never be able to reach either limit with anything material, but we know with great accuracy what the limit _is_.

It's not really a question of whether it exists - we know it does because we know what the limit is, which is zero kinetic energy in the particles of a gas (for example.) As a comparable example we know that the 'speed limit' in the universe is the speed of light, and barring some very radical new discovery, nothing can go faster than that. We don't know this because we have accelerated things to 99.999999% of the speed of light and been thwarted from going any faster - we know this because even when we accelerate something to a few percent of the speed of light we see the exact same effects that will keep us from reaching that speed.

We may never be able to reach either limit with anything material, but we know with great accuracy what the limit _is_.
The difference with C is that photons move through a vacuum at that speed and have been measured.
Massive particles are restricted to <C.
Absolute zero has never been reached on earth or measured in the universe.
If it was out there, say in one of the great voids, no particles say, how would that be measured?

The idea of absolute zero originally came from studies of gases.

For a fixed mass of gas, we find that the pressure of the gas (which we can measure with a pressure gauge) is inversely proportional to the volume, at a fixed temperature. So, for example, if we allow the gas to expand (volume increases), while keeping the temperature constant, the pressure will decrease.

So, we can write $$pV=\text{a constant}$$, where p is the pressure and V is the volume.

Experimenting further, we find that the particular constant in this equation, for a fixed mass of gas, varies with temperature. Or, another way to put it is that we can define temperature by relating it to the quantity $pV$ and the amount of gas. In the end, we end up with the ideal gas law: $$pV=NkT$$, where N is the number of molecules in the gas, k is a fundamental constant that makes the units on both sides of the equation right, and T is the absolute temperature.

We can test that this formula holds by taking a fixed volume of gas (e.g. in a container of known volume), adjusting the temperature and measuring both the temperature and pressure. Since the equation predicts p is proportional to T, a graph of the pressure vs temperature should give a straight line in this case (and it does, to a good approximation, for many familiar gases).

Even if we can't cool the gas indefinitely, we can still extrapolate our straight-line graph to the point where its pressure would be zero. We then find the "absolute zero" temperature, which turns out to correspond to -273.15 degrees Celcius.

Surprisingly, perhaps, when we do the experiment and extrapolate the absolute zero temperature for many different gases (e.g. try it for oxygen, nitrogen, carbon dioxide, etc.), we find that all of these gases extrapolate to the same "absolute zero" temperature. On this basis, even without knowing anything else, we can hypothesise that the "absolute zero" temperature we have found is the lowest possible temperature.

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How nice to have, for once, a proper science thread! Keep 'em coming, wegs

Absolute zero has never been reached on earth or measured in the universe.
If it was out there, say in one of the great voids, no particles say, how would that be measured?
But, theoretically wouldn't those voids be 2.7 kelvin, that is, the cosmic microwave background temperature?

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But, theoretically wouldn't those voids be 2.7 kelvin, that is, the cosmic microwave background temperature?
Since it's everywhere yes.

The difference with C is that photons move through a vacuum at that speed and have been measured.
Yep. But they're not material things. They are an odd superposition of waves and particles, and have no existence if they are "stopped." And we can only observe them by stopping them.

So we say nothing can accelerate to the speed of light even though we really haven't made a serious try to do so.

Absolute zero doesnt result in lack of movement. Atoms don't stop moving. Heisenbergs Uncertainty Principle forbids this. What happens is the atoms get smeared out into a Bose Einstein Condensate.
I thought that “all” atoms above absolute zero are (thought to be) moving. So, in turn, I thought that when atoms get as close to complete stillness as possible, that’s absolute zero.

How nice to have, for once, a proper science thread! Keep 'em coming, wegs
lol! I could google my questions of course, but this is more fun.

No ,maybe it doesn't exist as what you might think of as a "physical reality".

But you could say the same of the number zero.

I think the term to describe them may be "a limit"-a number or state that you can approach to any degree of nearness that you like but not a complete approach.

I am not exactly sure what "temperature" is correctly described as ,but I think you are right that at least one of the ways is the amount of movement in the body you are assessing.

Not sure that you are right about an observer causing additional movement in the object being measured for temperature.

Any body has to radiate electromagnetic waves and so ,if none are detected then maybe it is at absolute zero?

(I think the Cosmic Background Radiation is very close to absolute zero)
I think that any movement around something still would be detected though, right?

I think that any movement around something still would be detected though, right?
Do you mean "something still" or "still would be detected"?

Anyway,do you mean you could bounce a signal or two off whatever you thought was moving and then you could tell if it was moving either with respect to you or with respect the the region that you suspected might be at absolute zero?

I don't think there are any regions anywhere at absolute zero although I cannot say whether it is possible such a region could exist inside a black hole.

Apparently black holes are very, very, very cold ,unlike my own preconception of them as very dynamic and energetic regions

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I think that any movement around something still would be detected though, right?
Not really. There is residual energy in the ground state of many systems but you can't detect any motion directly. Take the vibration of a diatomic molecule like oxygen O=O. The double bond between the atoms is stretchy, so the atoms move apart and together as if connected by a spring. In a classical ball and spring model one would say the energy of vibration changes from kinetic (when the balls are in motion) to potential energy (of the spring) and then back again, over and over again. According to quantum theory there is some energy like this even in the ground state. But all this amounts to is an uncertainty about their position, relative to one another, at any given moment. They are kind of smeared out a bit. This is the wave aspect of wave-particle duality making itself felt. The atoms are not entirely particle-like, but fuzzy due to their wavelike behaviour. So in a way it is not really "motion", or not in a classical sense, just residual kinetic + potential energy that they have.