Hawking radiation doesn't make sense to me, with respect to black holes getting smaller.
It would seem that any particle (or anti-particle) leaving the Schwartzchild radius would have a similar anti-particle (or particle) similarly entering the black hole as well. So, over time, I don't see how...
I think it's actually quite a perceptive question for someone who has only seen the pop science description of particle/antiparticle pairs. However it is a duplicate.
I really, really must get around to answering Noah's question so I can use it as a reference for this sort of duplicate.
@Jiminion No need to delete duplicates, you should be seeing a button to agree with the duplicate vote, though (which you should click if you agree it's a duplicate)
@Jiminion Well...it's kinda what you have to introduce when you want to rescue the idea of pairs of particles being generated at the event horizon and one falling in, and as with the "negative energy" solutions back in the day of the Dirac equation, it is an indication that something is wrong. In this case what is wrong is the idea that Hawking radiation actually has something to do with these pairs of particles.
It's a classic "garbage in, garbage out" situation - if you start with that botched analogy, you won't get any reliably correct statements out.
A correct and accurate description of the process behind Hawking radiation requires a deep knowledge of Quantum Field Theory (QFT). Therefore, an analogy given by Hawking himself will be used here, with its flaws pointed out. Within the ergosphere of the black hole, virtual pairs of particles and anti-particles are constantly present due to vacuum fluctuations. Typically, the pair would then annihilate before this could be of any consequence, by the particles becoming real. However, as one of these two particles will be closer to the hole than the other, it will experience a greater gravita…
I really don't think that invoking virtual pairs is at all necessary for Hawking radiation because it happens even without considering disconnected loops
I would delete the last paragraph. People will ask you what it means, and you'll be forced to admit you don't really know. Other than it's as good a description as I've read of the process.
The best you can do is just write the equations citing Hawking as the source. The derivation of the equations is too hard for the vast majority of (non-theoretical) physicists let alone A level students.
Let's take an example the potential difference (PD) across a resistor. if there's a current flowing, the power lost is equal to the current x PD. But in reality, the electrons inside the resistor are losing this potential energy right? If so, what is the relationship between the potential energy (or the quantised energy) of an electron inside the resistor and voltage drop?
It's a great shame, but quantum mechanics has as little to do with quantization as any other field of physics. The theory itself makes no reference to quantization; quantization merely arises from particular boundary conditions in certain particular problems.
@NoahP : keep seeking a correct and accurate description that 1) you can understand and that 2) makes sense. If you don't get one, you might want to check this out.
I'm trying to understand the 'big bang'. What I've gathered so far is that initially the sum of all distances in the universe was zero or the distance between any two points in the universe was zero? Is that an accurate description of the current thoughts on the big bang?
How does this look for part one of the answer? I'll complete it tomorrow as I'm off to bed now ...
To answer this we need to talk a bit about how particles are described in quantum field theory.
For every type of particle there is an associated quantum field. So for the electron there is an electron field, for the photon there is a photon field, and so on. These quantum fields occupy all of spacetime i.e. they exist everywhere in space and everywhere in time. It’s important to realise that a quantum field is a mathematical object not a physical one - more precisely it is an operator field - however it’s common to talk as if quantum fields are real objects and I’m going to commit this si…
@JohnRennie it looks correct to me. Perhaps " the vacuum state is the state for which the number operator returns zero" is not 100% accurate, because the number operator is not well defined for interacting theories. The vacuum state is defined as the state for which the Hamiltonian returns the minimum possible eigenvalue, that is, the state with the lowest energy
OK, thanks all. Next step is to explain how the presence of a horizon creates a net flux of particles. But that will have to wait for tomorrow as I have to be at work in 9 hours and 7 minutes.
@ACuriousMind Yes, but we only retroactively made "quantization" have that meaning later on. The original Latin root certain had nothing to do with "generalizing a commuting operator theory to a noncommuting one."
@Slereah The LSZ formalism needs the presence of a single vacuum sitting at zero energy. You can certainly do something, but you're not doing standard perturbation theory if you have more than one vacuum
@JohnRennie I remember hearing and reading "time is a coordinate, not a parameter" to which I would nod but, in fact, it took a relatively long time to come to appreciate all that that simple phrase means.
Hawking radiation doesn't make sense to me, with respect to black holes getting smaller.
It would seem that any particle (or anti-particle) leaving the Schwartzchild radius would have a similar anti-particle (or particle) similarly entering the black hole as well. So, over time, I don't see how...
