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6strings10holes t1_jd5htjc wrote

Reply to comment by Dr-Luemmler in Can a single atom be determined to be in any particular phase of matter? by Zalack

You can't establish energy really, only changes or relative amounts to a reference frame.

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Dr-Luemmler t1_jd5io43 wrote

Thats my point. Ofc, in a labratory you need a reference to measure the velocity of a single atom. The reference frame obviously can be broken down to other atoms if you want, but that doesnt mean a single atom cant have kinetic energy by itself.

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florinandrei t1_jd6bwq6 wrote

It definitely does have a kinetic energy.

The only thing is - when you go from kinetic energy to temperature, you run into all sorts of trouble if you do it for single entities.

Temperature is an inherently collective measure. If it's single particles, stick to kinetic energy.

What is the "temperature" of this marble I'm throwing? ;) (not the temperature of the glass, but the "temperature" of the marble as a single particle with some kinetic energy)

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Dr-Luemmler t1_jd75stk wrote

Defining temperature by kinetic energy, you could calculate it for a single marble. If you want to use the advanced definition of temperature via entropy, sure lets do it:

$T = dE/dS $

So temperature is the change of internal energy when changing the entropy. In statistical thermodynamics, one can now define entropy by the number of availible states $\Omega$ with its degrees of freedom.

The degrees of freedom a single atom has are $3N-3$ = 0. That basically means, this atom only has the translation dofs and the electronic ones. Lets neglect the electronic ones (even though they might be important, as with then we might be able to measure the temperature) then the temperature of a single atom is solely defined by its kinetic energy.

Can we access it in labratory without using the interaction with other atoms? No! But in simulations we can. Or what kinds of problems do we have?

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Quantum_Quandry t1_jde90h1 wrote

A single atom most definitely cannot have kinetic energy all by itself. SR/GR makes it abundantly clear that you must have something to reference against to make a measurement, and the answer changes depending on which reference point you're using. This should be obvious to anyone who has driven a car. Let's say you have three cars, yourself going 50mph north, a second car ahead of you and to your left going 45mph north, and a third car going 50mph ahead of you headed south. You have to swerve left or right due to an obstacle ahead, which do you choose? Obviously you're going to swerve left, ignoring the velocity of your swerve itself, you're going to overtake the car on your left a a relative 5mph and if you go right you'd be moving 100mph relative. Or you could split the difference and drive directly into the obstacle which is going 50mph relative to you.

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