>
If a black hole is obeying thermodynamic laws, we can presume that a statistical description of all its fundamental, indivisible parts can be made.No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole.
> Here’s another way in which the analogy falls flat. Black hole entropy is given by the black hole area. Well, area is length squared, volume is length cubed. So what do we make of all those thermodynamic relations that include volume, like Boyle’s law? Is volume, which is length times area, really length times entropy? That would ruin the analogy. So we have to say that volume is not the counterpart of volume, which is surprising.
This paragraph makes no sense at all. No sense at all!
First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. Trying to apply it to black holes shows a completely lack of understanding of the subject.
In particular:
> Is volume, which is length times area, really length times entropy?
What? First the entropy of a black hole is not equal to the area, it's only proportional to the area, there are some constants. (I had to look up S = A * c^3 / 4Għ.) Second, you can't pick any three length [1] and multiply them and expect that the result that has the units of a volume can be used in any formula you want.
[1] For example, the height of the Eiffel tower, the atomic radio of an iron atom in the Eiffel tower and the width of the door of the elevator of the Eiffel tower. You can multiply them and get a volume, but this volume doesn't follow the Boyle's law when the atmospheric pressure changes in Paris.
No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole.
> Here’s another way in which the analogy falls flat. Black hole entropy is given by the black hole area. Well, area is length squared, volume is length cubed. So what do we make of all those thermodynamic relations that include volume, like Boyle’s law? Is volume, which is length times area, really length times entropy? That would ruin the analogy. So we have to say that volume is not the counterpart of volume, which is surprising.
This paragraph makes no sense at all. No sense at all!
First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. Trying to apply it to black holes shows a completely lack of understanding of the subject.
In particular:
> Is volume, which is length times area, really length times entropy?
What? First the entropy of a black hole is not equal to the area, it's only proportional to the area, there are some constants. (I had to look up S = A * c^3 / 4Għ.) Second, you can't pick any three length [1] and multiply them and expect that the result that has the units of a volume can be used in any formula you want.
[1] For example, the height of the Eiffel tower, the atomic radio of an iron atom in the Eiffel tower and the width of the door of the elevator of the Eiffel tower. You can multiply them and get a volume, but this volume doesn't follow the Boyle's law when the atmospheric pressure changes in Paris.