Natural Order and Science

[Alex K]

Alex, I have a few questions about blackholes and physics that I have been pondering and would be grateful if someone who actually knows about this stuff could help explain to a lay person like me.

If a blackhole does not contain an entry to another universe and isn't a wormhole, but is a closed system, then what happens to all the light that falls inside? Is there a limit to how many photons can fit into a finite part of spacetime?

You have - perhaps unwittingly - raised one of the central problems of current quantum gravity research, the "black hole information problem".

Black holes grow in size when you throw something in. It has been shown by Bekenstein and others that, as seen from the outside, the amount of stuff (actually: information) that can be contained in a volume of space is proportional to the surface of the volume before a black hole is formed. So from this perspective, there is nothing too strange going on, more stuff needs more volume. Even disproportionately more volume.

However, if you would jump right in into the black hole, you would disappear in something like a singularity in finite time, so an arbitrary amount of stuff appears to get concentrated there. What happens at that would-be-singularity is an unsolved question as long as we don't have a firm grasp on what the correct quantum theory of gravity looks like.

Normally, one would say "forget about the singularity, it's separate from the universe and has no effect", but Nature doesn't allow us to entirely forget about it: what is usually called the information paradox arises because black holes don't seem to live forever, but evaporate by radiating random noise called Hawking radiation. Once the black hole is entirely evaporated, there is no "inside" region of space anymore that is cut off causally, the singularity has also dissolved, and any information about what was thrown in seems to get entirely eradicated ---- UNLESS the Hawking radiation is not fully random but subtly carries information -- people are currently still wondering how this information transfer could possibly work, and Hawking and collaborators have just recently stirred the pot a bit with their "Firewall" hypothesis which I don't understand.

If you combine two neutron stars then you can form a blackhole because the gravity increases to the point whereby light cannot escape. How do we know that the singularity isn't actually just a really big neutron star? Or even formed from something even denser than a neutron star, say like a quark star?

I'm not sure I get your question. My answer from the hip would be "because it's not big enough to house a neutron star". There are limits on how small e.g. a neutron star can become before gravity overwhelms the degeneracy pressure exerted by the neutrons.

Continuing on from this, I understand with normal stars that there is gravitational pressure pulling stuff together and outward pressure maintaining a certain size. Nothing can go faster than the speed of light, but can there be enough outward pressure equal to the gravitational pull strong enough to stop light escaping?

In a normal star, the gravitational pressure is not yet as large as it will be later in the collapse. Since gravitational pull increases at shorter distances, the more the star collapses, the stronger the gravitational pull becomes like in a vicious circle.

It goes as follows - the radiation keeps the star stable, when that goes out, it collapses until the electrons say "hey, we're fermions, we like to have our separate spots. If you want us to move closer, give us energy or piss off". This at first works and the electron degeneracy pressure brakes the core collapse and you get a white dwarf. If the star is heavier the collapse continues until the neutrons say "hey we're fermions, same as above!", which stabilizes the core and it becomes a neutron star. If the star is even heavier, however, the gravity will at this point be so strong that it releases enough energy to squish the neutrons together - at this point the collapse goes on unhindered until there is a black hole. Whether you have a quark star phase in between doesn't change the principle.

Why is it that information can not be destroyed in quantum mechanics? Is this because information = energy?

Information is measured by entropy, which is a quantity which is related to energy, but not quite the same. Entropy is related
to the amount of energy transferred and the temperature.

Quantum mechanics posits that that the state of a system evolves as dictated by the Schrödinger Equation, and the SE has certain mathematical properties which contradict that. This is a bit technical - so if you start with a state in which you know the wave function (maybe because you prepared it), the SE equation allows you to tell the evolution of the wave function. Hawking radiation is a random thermal thing which cannot be described in this way, so quantum mechanics seems to break.

How much wood would a woodchuck chuck if the woodchuck chucked wood at near light speed?