Mordred posted this simulation quite recently.

 

Can I ask whether this melding of objects  occurs whenever the separation between them becomes small enough?

 

In particular ,would we find this behaviour in Black Holes?

 

Finally, once this melding happens has there been created a no gravity zone (within).

 

The object created can presumably  re differentiate if the temperature rises. What are the forces that cause this re differentiation?

Edited December 17, 20178 yr by geordief

The condensation is not because of separation. It's because the atoms are all in the same state. When the temperature goes up, they are not in the same state anymore.

Gravity does not disappear. In fact, BECs have used gravity to show certain effects, and have been used to measure gravitational acceleration.

As a generality (and attempt at an  approximation) does the notion of tempero- spatial separation get  replaced by "closeness of states" in QM? 

 

Anything like that? Does "closeness of states " mean anything?

In QM states are generally described as wavefunctions. In the Bose condensate state these wavefunctions don't merge but become identical. You cannot distinquish different particle species from one another. Nor can you distinquish individual quantum numbers (that is the loss of information) as all quantum numbers are also wavefunctions. (spin) being one example.

In essence every particle will have identical De-Broglie wavelengths that are all identical to one another. 

The paper I linked in that thread has these details.

Edited December 17, 20178 yr by Mordred

4 hours ago, geordief said:

As a generality (and attempt at an  approximation) does the notion of tempero- spatial separation get  replaced by "closeness of states" in QM? 

 

Anything like that? Does "closeness of states " mean anything?

Closeness of states does have a meaning; it would be the energy difference of the states.

It would probably not refer to spatial proximity, because that loses meaning in QM in many situations. A "state" refers to the eigenstate of the system. Energy, angular momentum, spin — these have eigenstates, or "good" quantum numbers. Position in many cases is/does not.

 

edit: xpost with Mordred

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://massey.dur.ac.uk/resources/mlharris/Chapter2.pdf&ved=0ahUKEwiVt4vUw_HXAhUQyWMKHQ91DtMQFggkMAE&usg=AOvVaw1DHUh-BTAMS7yr-2lNfTFf

Here is the article its fairly low key on the mathematics which is why I chose it.