“Referring to “an atom” versus “another one” here is just begging the question on the identity of atoms. Why is a BEC containing N indistinguishable atoms not allowed to evolve into a BEC of N-1 indistinguishable atoms and an excited atom?”
I think Eliezer and possibly the physicists are using “identical” and “indistinguishable” differently to me. Identity and identical is typified by things like 4 = 4. Under some circumstances two different numbers can be indistinguishable, without being identical. If you had a function that squared numbers you couldn’t distinguish from the output between 3 and −3, however other functions would allow you to distinguish them.
If you apply any function to any 4, you always get the same answer. The BEC case seems to me to be like having a group of 4s and then applying a function to each and one 5 popping out and the rest staying 4s. Now the physics would be more like a matrix of fours and then a single function being applied to the matrix. But then the 4s are different at least according to the math, because they are in different positions in the matrix. They no longer have individual identity.
I’m rambling a bit. I’m not sure this is a fruitful line of discussion, I’ll just have to try and get used to what Eliezer means by identical and indistinguishable.
Scott Aaronson, is the spin of an electron a definite property?
“Referring to “an atom” versus “another one” here is just begging the question on the identity of atoms. Why is a BEC containing N indistinguishable atoms not allowed to evolve into a BEC of N-1 indistinguishable atoms and an excited atom?”
I think Eliezer and possibly the physicists are using “identical” and “indistinguishable” differently to me. Identity and identical is typified by things like 4 = 4. Under some circumstances two different numbers can be indistinguishable, without being identical. If you had a function that squared numbers you couldn’t distinguish from the output between 3 and −3, however other functions would allow you to distinguish them.
If you apply any function to any 4, you always get the same answer. The BEC case seems to me to be like having a group of 4s and then applying a function to each and one 5 popping out and the rest staying 4s. Now the physics would be more like a matrix of fours and then a single function being applied to the matrix. But then the 4s are different at least according to the math, because they are in different positions in the matrix. They no longer have individual identity.
I’m rambling a bit. I’m not sure this is a fruitful line of discussion, I’ll just have to try and get used to what Eliezer means by identical and indistinguishable.
Scott Aaronson, is the spin of an electron a definite property?