- #1
ghotra
- 53
- 0
I'm looking for some insight/clarification on the definition of a microstate.
Consider two coins. Here are the possible outcomes:
T T
T H
H T
H H
Now, I have assumed something: The coins are distinct.
A better description of each microstate is:
{ (coin 1, T), (coin 2, T) }
{ (coin 1, T), (coin 2, H) }
{ (coin 1, H), (coin 2, T) }
{ (coin 1, H), (coin 2, H) }
That is, the microstate isn't _just_ the face of the coin but it also includes _which_ coin had which face.
Now suppose the coins were identical. Then, we can't distinguish coin 1 from coin 2. So we might as well drop the label. The microstates are now:
{ (T, T) }
{ (T, H) }
{ (H, H) }
That is, the microstate is specified _only_ by the face of the coin.
Now, what about real life? When I toss two coins, what is the probability that I receive exactly 1 head? Everyone knows that the answer is 1/2 and not 1/3.
Why? Why is the answer 1/2 when the coins are clearly identical (in the sense that I am restricting my interest to the "face of the coin" and not "which face was on which coin")?
Please comment.
Consider two coins. Here are the possible outcomes:
T T
T H
H T
H H
Now, I have assumed something: The coins are distinct.
A better description of each microstate is:
{ (coin 1, T), (coin 2, T) }
{ (coin 1, T), (coin 2, H) }
{ (coin 1, H), (coin 2, T) }
{ (coin 1, H), (coin 2, H) }
That is, the microstate isn't _just_ the face of the coin but it also includes _which_ coin had which face.
Now suppose the coins were identical. Then, we can't distinguish coin 1 from coin 2. So we might as well drop the label. The microstates are now:
{ (T, T) }
{ (T, H) }
{ (H, H) }
That is, the microstate is specified _only_ by the face of the coin.
Now, what about real life? When I toss two coins, what is the probability that I receive exactly 1 head? Everyone knows that the answer is 1/2 and not 1/3.
Why? Why is the answer 1/2 when the coins are clearly identical (in the sense that I am restricting my interest to the "face of the coin" and not "which face was on which coin")?
Please comment.