Do bosons follow Boltzmann statistics if imaged individually?

[Philip Koeck]

Assuming a system of bosons at high density and low temperature so that they obey Bose-Einstein statistics. If one had a high resolution, ultrafast tomographic imaging system that would allow to track every particle in this system and therefore make the particles distinguishable, what would happen to the equlibrium distribution for this system? Would the BE-distribution be replaced by a Boltzmann distribution as soon as the particles are imaged?

 

[PeterDonis]

If one had a high resolution, ultrafast tomographic imaging system that would allow to track every particle in this system and therefore make the particles distinguishable

It wouldn't. You would be making position measurements of particles at very short time intervals, yes; but you would not be able to deduce from this data which particles in the measurements at time $t$ corresponded to which particles in the measurements at time $t + \epsilon$. When physicists talk about being able to "track" particular particles in measurements (for example, in cloud chambers or bubble chambers), they are talking about cases where there are only a small number of particles that are sufficiently separated spatially to be tracked individually. The system you are talking about does not meet that requirement.

 

[Philip Koeck]

It wouldn't. You would be making position measurements of particles at very short time intervals, yes; but you would not be able to deduce from this data which particles in the measurements at time $t$ corresponded to which particles in the measurements at time $t + \epsilon$. When physicists talk about being able to "track" particular particles in measurements (for example, in cloud chambers or bubble chambers), they are talking about cases where there are only a small number of particles that are sufficiently separated spatially to be tracked individually. The system you are talking about does not meet that requirement.

I am talking about a thought experiment so I don't need to limit myself to what is technically feasible. If one had a sufficiently fast camera, would the act of observing the particles change their equilibrium distribution?

 

[PeterDonis]

I am talking about a thought experiment so I don't need to limit myself to what is technically feasible.

It's not a matter of technical feasibility. There are no states of a boson gas at high density and low temperature that correspond to "individual bosons following trackable trajectories". But there would need to be such states for measurements to allow you to track individual bosons.