Absolute zero and non particle movement

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i have read in some articles that when 0 Kelvin is achieved then particle movement within the cooled substance ceases. but my doubt is that einstein said that all objects have constant movement. this means that if the particles really stop then they will kind of stop in time because it is longer moving through space time. this i believe is not possible but am not sure of a reason. i think it may have to do with the frame of reference but cannot find a direct solution. can someone tell me a way to solve this paradox.
 
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No Einstein did not say that. That is basically the "uncertainty priciple" due to Werner Heisenberg, not Einstein. Einstein isn't the only scientist to have deep thoughts! And you are correct that means it is impossible to reach absolute zero. I don't know what "paradox" you mean. I see no paradox here.
 
i thought that the paradox was in effect, if we thought that absolute zero is achievable. can anyone verify that 0 K is achievable or not?
 
It's not possible to reach absolute zero; classical thermodynamics prohibits it. (and quantum physics doesn't change this)

Classically, particles are not moving at absolute zero, and quantum physics did change that: due to the uncertainty principle, things do have some kinetic energy even at their lowest achievable energy state.

This has no effect on the concept or reality of absolute zero though, because it was not originally defined in terms of the motion of particles. Indeed, it was introduced by Clausius (IIRC) around 1850-ish, long before the 'atomic theory of matter' had been commonly accepted among physicists. Rather, the definition of 'absolute zero' came about through the much more general concept of entropy - as entropy is linear with absolute temperature (barring phase changes), you can extrapolate back to the temperature where S = 0, which is absolute zero.

So as long as classical thermodynamics holds, you will have an absolute zero regardless of whether or not the particles are actually motionless and regardless of whether matter is even composed of particles.