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## Indistinguishable black holes?

How different can 2 black holes of equal charge and equal (and half-integer) spin be while being indistinguishable fermions?

A black hole has no hair. Thus generally just 3 allowed parametres:
electric charge
spin/angular momentum
rest mass.

Plus the exotic ones like magnetic monopole charge and colour, which are usually zero and white respectively.

Now, the electric charge of even a black hole is quantized to be normally an integer multiple of elementary charge (and if not then a multiple of one third thereof).

The angular momentum is required to be a multiple of one half Planck constant.

Whereas the rest mass of a black hole is a free, continuous variable.

Now, if 2 black holes have identical charges, and identical spins being half-integer - how different can their rest masses be in order to amount to indistinguishable fermions?

2. With Hawking radiation, how long would you expect two "identical" black holes to stay truly identical?
Similarly, if you have a collection of atoms made of the same unstable isotope, if they were truly identical, they'd all decay together at once, but they aren't truly identical. Their electron clouds might be indistinguishable, but their nuclei aren't. Likewise Hawking radiation is a detectable aspect of something that keeps these black holes distinguishable... what exactly that is will depend on what String Theory resolves into (i.e. we don't completely know yet).

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Originally Posted by antoniseb
With Hawking radiation, how long would you expect two "identical" black holes to stay truly identical?
Similarly, if you have a collection of atoms made of the same unstable isotope, if they were truly identical, they'd all decay together at once, but they aren't truly identical. Their electron clouds might be indistinguishable, but their nuclei aren't.
No. Excited atoms of the same state are truly identical - and decay at different times. Likewise, nuclei of same unstable isotope decay at different times, but they are just as truly identical as nuclei of same stable isotope. Compare the rotational states of diprotium molecule with ditritium molecule - andboth with, say, HD molecule.

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can you distinguish between 1kg and 2 kg? How about .1 and .2? .01 and .02?

If the masses are different at all,then they are distingushable. that is kinda the definition.

5. Order of Kilopi
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Originally Posted by antoniseb
Similarly, if you have a collection of atoms made of the same unstable isotope, if they were truly identical, they'd all decay together at once, but they aren't truly identical.
I'm not quite following this argument. If i have two identical dice, it still doesn't follow that they should land on the same number if i throw them. Likewise if i have two atoms that are truly identical (in exactly the same state), and both have access to say 10 states of which 1 is "decay" and each randomly chooses, independent of eachother, its next state then it doesn't necessarily follow that both should land in the same next state.

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