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I was reading this question, and I had this doubt, if we can ever reach absolute zero, how can we measure it?

I ask this because as far I know, any measurement could change (increase) the temperature.

EDIT

Reach absolute zero is a hypothesis. My doubt is, if hypothetically one day we can get to absolute zero, have a way to measure this temperature? Or similarly to quantum computer, can not prove that is really quantum, can not prove that is really in -273 Celsius, or 0 K.?

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I think that some details would depend on how absolute zero is defined, but in any case, it might be theoretically possible to observe that a system was at absolute zero, but the act of observing it would cause it to no longer be at absolute zero.

Let's try this with two different definitions.

For the first, we'll use a thermodynamic (macroscopic as opposed to microscopic) definition where the temperature is a function of the average kinetic energy of all molecules in a system, and temperature defines the direction of heat flow. Let's pretend that we do have a way of siphoning off all heat to a region of less than absolute zero (obviously not possible in reality, so we'll use a magic freeze-ray) and the result is a collection of molecules with zero kinetic energy.

Now the question is - it has zero kinetic energy relative to what? If we measure velocities of the molecules relative to each other, we can say they have zero kinetic energy. But what about relative to us, the observer? Or to the container that the molecules are in? Since the molecules that we are made of are not at absolute zero, then relative to us, there is still some temperature.

So we use our magic freeze ray on ourselves and the rest of the universe until there is no kinetic energy left at all. Now, we want to observe or measure that we are at absolute zero. We are going to need to come up with some way of measuring the momentum of another molecule relative to ourselves. The least intrusive way of doing this is with light, but even with light, we will introduce some change to the system that will cause it to no longer be at absolute zero.

Let's look at another definition (the one used by @Count Iblis). Here we say that a system in its lowest quantum mechanical energy state is at absolute zero. It's another way of saying that no more energy (of any kind) can be removed from the system. As he said, if you could put such a system in its lowest energy state, then you must have had some way of knowing the current state, and thus, would know it is at absolute zero. This is sort of like the freeze-ray argument from above. However, if we want to observe it at absolute zero (which I think is what you are asking), we need to interact with it in some way. Again light is the best option, but even light will impart some energy to the system, and knock it out of the ground state.

And so in summary, I think we can say that if it were possible to get a system to absolute zero, then you would be able to say it was at absolute zero, but you would not be able to say that it is at absolute zero - you would not be able to observe it without disturbing it.

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  • $\begingroup$ Thanks for the answer, this expression was very good "then you would be able to say it WAS at absolute zero, but you would not be able to say that it IS at absolute zero" $\endgroup$ – Only a Curious Mind May 29 '14 at 16:10
  • $\begingroup$ Do you know how to measure if it WAS at absolute zero? $\endgroup$ – Only a Curious Mind May 29 '14 at 16:30
  • $\begingroup$ Not with any real apparatus. What I do know is: if you were to find a way, it must work by changing something about the energy state of either the observer or the particle, and therefore, the system would no longer be at absolute zero. $\endgroup$ – thomij May 29 '14 at 16:34
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First let's consider the problem of reaching absolute zero. This cannot be done using thermodynamic means only (which means that the rules of the game are that you only have access to some of the macroscopic parameters of the system). This is easy to understand; there are only two ways you can cool an object: you can bring it into contact with something cooler (obviously, if you are going to create something colder than you have access to, this option isn't going to be availabe), or you can let it perform work. Now, if you let an object perform work, it's entropy will at best stay the same, while at absolute zero it is zero. So, you can't reach absolute zero this way either.

Now, we can still reach absolute zero by simply putting a system in its quantum mechanical ground state. This requires having full control of all the degrees of freedom of the system. But that control then also allows you to know that the system is in fact in the ground state. Take e.g. a quantum computer with all its qubits initialized to zero. You then have arbitrary control of all the degrees of freedom of that system. However, you can then also argue that the whole concept of temperature and thermodynamics doesn't really apply here. It's only useful when you only have an incomplete macroscopic description of a system; there are then a large number of microscopic states consistent with that macroscopic description, the statistical treatment of the latter then lead to the laws of thermodymamics.

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  • $\begingroup$ Three words: Bose Einstein Condensates $\endgroup$ – eqb May 29 '14 at 13:18
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    $\begingroup$ Reach absolute zero is a hypothesis. My doubt is, if hypothetically one day we can get to absolute zero, have a way to measure this temperature? Or similarly to quantum computer, can not prove that is really quantum, can not prove that is really in -273 Celsius, or 0 K.? $\endgroup$ – Only a Curious Mind May 29 '14 at 13:21
  • $\begingroup$ I edited my answer $\endgroup$ – Only a Curious Mind May 29 '14 at 13:25

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