What you need to know:
A fundamental equation of non-relativistic quantum mechanics is the equation:
1. p= h/L
Where h is Planck ` s constant, p is momentum, and L is wave length.
The equation is true for whatever size
of the object in question.
2. p=m v
Where m is the mass, and v is the velocity.
What you need to know about Bose-einstein condensate:
YouTube - Bose--Einstein Condensate
If you have a collection of identical particles, and each is very close to one another. Is the collection of particles a single object? Well, according to Bose, and eistein, if you cool the collection of particles down( according to the video), the collection have a single wave length, L. Thus, by 1, the collection has a single momentum, p. Thus, it seems we can call the collection a single object. On the other hand, it seems, perfectly fine to called each particle in the collection an object. So, in this view, each particle in the collection would have it own independent p, and L.
Suppose the temperature T* is the temperature necessary, and sufficient for the collection to be a single object. One can in principle made the temperature T very closer to T*, but not exactly T*. Is the collection of particles, an object?
A. John ` s solution is: The notion of a object is flaw. This is revealed in 1. Our association of a object is such that it is localized in space, but QM shows that locality is false, and 1 shows that.
B. Mary replies: Perhaps, what we mean by object is the precise temperature such that the collection have a single wave length, and as such a single momentum P, according to 1.
C. John replies: Perhaps, if we cool the individual particles down, each particles momentum p becomes smell, and by 1, each wave length L become large. Thus, each wave length for the particles would interfere with one another to produce a single wave length. By fourier analysis, any single wave can be a superposition of many different waves!
D. Mary replies: What if those particles in the collection is not identical?
E. Jack replies: Suppose the solution lies in the superposition principle!
F. Fourier replies: It is true that every wave is a superposition of many different waves. To be economy, any waves is a superposition of a set of independent basis waves.
G. John replies: If the collection of particles are actually many waves, then by Mir Fourier theory, their superposition actually made the collection one wave! The fact that the collection is made up of identical particles matter. As they cool, their wave length will increase by the same amount. Superposition of each would give them all a single identity. On the other hand, suppose, the particles are not identical. As we cool the collection, some of the individual waves will superpose into one pattern, and other particles would have a different pattern.
Is john`s answer satisfactory?