September 23 2014     

Sometime, somewhere, in this world in which we live: a poem plus a sum-up on the black hole information paradox

by archywillhe

Sometime, somewhere, in this world in which we live
a massive astronomical object would collapse and explode
illuminating its galaxy in a way
so substantial, it can be observed
at some point in the future, by a civilization light years away

Sometime, somewhere, in this world in which we live
energy in the form of mass would accumulate in a tiny region
distorting the fabric of space-time in a way
so non-Euclidean, it forms a boundary
a horizon across which even for photons there is no escape

You may find cosmological events like these
rather mind-boggling, rather strange
it is hard to imagine that this is indeed reality
But perhaps what’s more mind-boggling, more strange
is the very fact that you exist
sometime, somewhere, in this world in which we live

And what makes this even more astounding
is that you are capable of forming mental constructs
and with reasoning, you can have a better understanding
of how things in this universe work
Every theory you have learnt or dervied
may break down gracefully in the search for truth
But that is alright, for at least you have tried
sometime, somewhere, in this world in which we live

● ● ●

On line 10, by no escape I do not mean that photons would be “entrapped” in the black hole for eternity, and information is forever lost upon entering the event horizon, which violates the conservation of information in the universe (this is actually known as the black hole information paradox).

A black hole is constantly evaporating and would eventually disappear. Now and then, pairs of virtual particles are produced in the vacuum near the event horizon due to a phenomenon known as quantum fluctuation that happens everywhere in this universe. In the usual case they will just annihilate each other and back to non-existence. But there are times when one of them falls into the black hole, while the other escapes as black body radiation known as Hawking radiation. When this happens, the particle that falls into the black hole would appear to have negative energy. The creation of the particle pair requires energy. If they manage to annihilate each other within Planck time, they stay “virtual” throughout their existence. If one of them becomes “real”, a nearby region with high energy potential would experience a decrease in energy. And thus a black hole shrinks over time and loses its energy (in the form of mass). The total lifespan of a black hole of M solar masses is calculated to be roughly 2 x 1067 M3 years, which is still pretty long.

However, according to the no-hair theorem, Hawking radiation appears to contain information that depends only on the mass, angular momentum, and charge of the black hole, unlike normal thermal radiation which contains information about the body. It is as if information about the particles that fall into balck hole is lost. This is how the black hole information paradox arises. Information conversation in the black hole scenario is currently an open question in the physics community. One famous solution is the holographic principle within the framework of string theory.

When general relativity (the theory that predicted the existence of black holes) meets quantum mechanics, we can see that there is something more about the fabric of space-time - something very fundamental about our universe - that we do not yet quite understand. And that’s what makes this universe such an interesting place to be in. There are always new things to be discovered and new ways of seeing the same thing. is handcrafted by Archy archywilhes Will He
vi3w_s0urce (Haskell on Hakyll)