Actually that isn't right. The reason that Alice can't take out more than $500 is because that is all there is.
Then alice has a separate account and her funds are not entangled at all and has nothing to do with bob. Nor does alice's funds have anything to do with anyone else's funds in the bank.
And when we are talking about an entangled quantum system, if one part of a system assumes a particular state, the other part has only one other state to assume. Well, that may not be quite right. But if one part of a system assumes a given state that limits the number of states that the rest of the system can assume.
And now you unentangled the system above and inserted GOD or a computer system and are trying to dodge the bullet with a wave of the hands in your comment below.
For an earthly bank the thing that keeps track of the balance is the banks computer. Just how the universe keeps track of the balance is a pretty big question, but it manages it just fine.
In that statement the bank is doing the balancing is a computer (IE Artificial intelligence and program monitoring it) and therefore for the universe to do it you can only have GOD, we live in a computer simulation or some AI controls it.
There are real structural problems in trying to make accounting and book keeping process on the physical world without the use of intelligence and that is the problem you are stuck up against.
Obviously the analogy is far from perfect, but then most analogies don't fit extremely well. One of the big differences is that if we are talking about a bank and money, money comes in variable amounts, but the quantum world comes in discrete states.
Money only comes in discrete states too it's called the monetary unit for me its dollars and cents and I would find it difficult to pay for a fractional cent item without overpaying or underpaying. The analogy is actually therefore almost perfect.
The fact is we were even to show two ways we could entangle two people and money in a bank account both of which are quantum mechanic like. The problem you are having is the same as everyone has you can't think of another way to do it without invoking a GOD or needing intelligence in the process.
I am not trying to be argumentative here I know how hard this problem is I doubt there isn't a QM scientist alive who hasn't spent days and days thinking about the problem.
Finally I will let you in a little secret go back and read the work of Bell (
http://en.wikipedia.org/wiki/John_Stewart_Bell) and you will find what Bell did was show mathematically it is not possible to entangle via EPR and that's how he knew how to setup the so called Bell's test
The mathematics is not trivial and for the faint hearted but for those of mathematical persuasion it is apparently satisfying.
If you want to follow the proof yourself
http://philoscience.unibe.ch/documents/TexteHS10/bell1964epr.pdfSo I am sorry mathematics and physics are both against you at this point Bill.
By the way, I have started saying system when I talk about entanglement, because as you have pointed out it doesn't just work for particle pairs, it works for large systems of particles. If you say system that could be 2 particles, or it could be any number of particles that you can work with. If you have a better way of phrasing that I would be happy to start using it.
There is really no better description as yet mainly because it's all a bit new and I haven't seen an expression I like.
By the way you can also expand our bank example above to cover these expanded entanglement by alice and bob having a son chris who also shares the account (3 entangled now) etc etc.
