[paul cotter (OP)]

In hawking radiation, virtual particle pairs separate with positive mass/energy particles emanating into space and their partner particles falling into the black hole neutralising a fraction of the  black hole's mass/ energy . What is the nature of the "negative" particle? Also why should only one species of the particle pair fall into the black hole? I suspect there is not a simple explanation without going deep into quantum theory.

[Eternal Student]

Hi.

    Yes.   The concept of virtual particle pairs and one falling in while the other escapes is known to be a very crude and very simple way of presenting the idea to the general public.    It's basically just wrong and you'd be better off thinking of it as a nice story with pictures.    It leads to all sorts of questions like the ones you have asked -  why does only the anti-particle fall in and not the ordinary particle?   etc.    There's no good answers to this, except to say the thing never really was about virtual particle pairs anyway.   It was about some results from Quantum Field Theory on a background of curved spacetime

Rather than have me waffle on about stuff,   here's a choice of two videos with someone else saying stuff to explain it:

1.   PBS Spacetime on YouTube,   "Hawking radiation",  12 minutes.    Complicated.   The presenter seems to worry more about being accurate and saying technical stuff rather than making it accessible to the general public.

2.Science Asylum,  "How does Hawking radiation really work?",  available on YouTube,   13 minutes,   Much more light hearted presenter, quite accessible but with less technical content.

Best Wishes.

[Halc]

In hawking radiation, virtual particle pairs separate with positive mass/energy particles emanating into space and their partner particles falling into the black hole neutralising a fraction of the  black hole's mass/ energy.

As ES has said, this is a popular way of presenting a complex subject to the public, and a better description requires significant background in quantum field theory. In the vast majority of cases, both particles cross over the event horizon (EH). It is an observational effect, a special case of the Unruh effect, which can happen anywhere, such as at the event horizon that forms due to accelerated space expansion. But such a horizon forms with any acceleration.

What is the nature of the "negative" particle?

Apparently the pop description gives the infalling particle negative energy due to the negative gravitational potential.

Also why should only one species of the particle pair fall into the black hole?

The vast majority of the time both do. They're not different species. They're probably both virtual photons.

why does only the anti-particle fall in and not the ordinary particle?

There usually isn't an anti-particle. They're mostly just photons and gravitons, which don't have anti-counterparts. Only the very smallest black holes might produce something massive like electron/positron pairs, and each would have equal probability of being the one that escaped.

[Eternal Student]

Hi.

There usually isn't an anti-particle.

   Firstly, this is a dispute over something that is basically irrelevant anyway.   The model with virtual particles isn't a good model.   However,  I'm always willing to pass the time in discussion.     Overall, we're both in agreement, the underlying explanation requires QFT.
   1.   Virtual particles ALWAYS appear in particle and anti-particle pairs.   For some particles, like photons, the anti-particle just happens to be same as the ordinary particle - but there will always be a pair and it is conventional to call one the anti-particle.
   2.   Saying that the anti-particle goes into the black hole, while the ordinary particle escapes is part of the myth or story that helps to explain why the mass parameter of the black hole decreases (as if ordinary matter is being annihilated by the anti-particles) and energy in the form of radiation is emitted.   For example, this is exactly the language used in the PBS spacetime video linked to above,  between time 8:20 and 8:44.

Best Wishes.

[Halc]

   2.   Saying that the anti-particle goes into the black hole, while the ordinary particle escapes is part of the myth or story that helps to explain why the mass parameter of the black hole decreases (as if ordinary matter is being annihilated by the anti-particles) and energy in the form of radiation is emitted.   For example, this is exactly the language used in the PBS spacetime video linked to above,  between time 8:20 and 8:44.

Ouch. Bad form on their part.
If I drop an antimatter planet directly into a black hole, it will raise the mass of the black hole by the mass of the planet. They seem to be confusing negative mass with anti-mass. An antimatter planet still has positive mass (a thing not entirely obvious, but actually demonstrated recently).

This sort of demonstrates the lack of a conservation of antimatter: I can destroy matter by forming a black hole with it,  which eventually evaporates into mostly radiation, but any matter that results from that energy will be equally matter and antimatter. But it's like thermodynamics: much easier to achieve a neutral equilibrium than to drive the imbalance further apart. Eventually the whole universe will be a near balance between matter and antimatter, but mostly because there's negligible amounts of either.

[Eternal Student]

Hi.

If I drop an antimatter planet directly into a black hole, it will raise the mass of the black hole by the mass of the planet.

   Agreed.

They seem to be confusing negative mass with anti-mass.

   Also agreed.   It's just part of the quaint story that usually goes along with the virtual particle explanation for Hawking radiation.   If you say it fast enough, people don't stop to question if anti-matter would reduce the mass parameter of the black hole.
     In defence of PBS spacetime.... I think he mumbles something at the end about explaining why the anti-particles don't raise the mass of the black hole in a later video.

Best Wishes.

[paul cotter (OP)]

After watching those videos, courtesy of eternal student,  i'm somewhat annoyed that Stephen hawking would pull a stunt like that(actually it's not surprising, in his book "the universe in a nutshell" he talks about one infinite quantity being greater than another infinite quantity by a finite amount-mathematical nonsense). However in the proper explanation I have great difficulty with time going backwards-all evidence points to the arrow of time being one way. All that said i'm not a physicist.                                 PS I might have been a bit rash there, I certainly do not intend to attack the legacy of Stephen hawking. He obviously had a brilliant intellect and he struggled with obstacles that would have totally inactivated the average person and yet he shone through. I guess i'm just annoyed with books that are not rigorously accurate.

[Halc]

i'm somewhat annoyed that Stephen hawking would pull a stunt like that

Like what? It seems that PBS is making the mistake. Neither video is authored by Hawking. Hawking, in his book, did attempt to describe the situation to a more general audience, and probably drew on the virtual particle phrasing to accomplish that without delving into the QFT mathematics upon which the actual conclusion was drawn.

he talks about one infinite quantity being greater than another infinite quantity by a finite amount-mathematical nonsense

Not entirely nonsense. One can add 100 guests to Hilbert's hotel and arguably say it now has more guests, but it is probably a violation to equate the guest count to a 'quantity' since, being infinite, cannot be a number, and a 'quantity' usually is a reference to a number.

I didn't watch either video. I'm just responding to what is posted. Don't judge Hawking by a video made by somebody else, especially somebody who probably isn't fully familiar with the underlying theory. I'm certainly not.

Perhaps you can post where it was said that 'time goes backwards'. Was that from the book? I mean, the arrow of time can be ambiguous in the absence of change of entropy, and I don't consider time to be a thing that 'goes' in the first place.

[paul cotter (OP)]

Halc, you misunderstand me and I should have been more clear. I have never read "a brief history of time", I have read "the universe in a nutshell" and in the latter the virtual particle pair splitting apart with one going out to space while the other falls into the black hole is the specified mechanism This is what I find annoying and lacking rigour. Infinity+x= infinity because infinity is indeterminate. Many thanks to you and eternal student for the tedious attempt to educate me. In the video#1 which I found the best, the explanation of relativity cum quantum theory to describe the mechanism invokes the concept of time reversal. You didn't watch the video-I very rarely watch any videos, I would much prefer some text.   

[Eternal Student]

Hi.

i'm somewhat annoyed that Stephen hawking would pull a stunt like that

    It's not clear how much of this popularisation is Hawkings' fault.  After the easy version was made public, everyone (especially the media) was just bound to keep running with it, whether it was right didn't matter, it was understandable to the general public.
   

... video#1...invokes the concept of time reversal.

    That's a rushed and probably needless description of what an anti-particle might be.   Very roughly, an anti-particle is a time-reversed solution for its ordinary particle.   This is not vital to the general understanding of the issue at hand.   Either the presenter was showing off or else (and let's be fair it's probably the later reason) it links to some other videos he's made about anti-particles.
   
Best Wishes.

[paul cotter (OP)]

Halc, I never stayed at Hilbert's hotel, what's it like, a bit rough, bed bugs?(only joking, I know who David Hilbert was). I consider a statement that infinity+x to be greater than infinity undermines the basic consistency of mathematics. Thanks again for all your help, i'm hitting the sack.

[evan_au]

I consider a statement that infinity+x to be greater than infinity undermines the basic consistency of mathematics

Mathematicians prefer to speak of limits as quantities "approach infinity".

An example (without TeX):
- The limit of a=1/x²→∞ as as x→0
- The limit of b=(1+1/x²)→∞ as as x→0
- I have no problems with the statement that b > a for all real values of x
- b > a, even though a→∞ and b→∞ when x→0
- In common parlance, we might even dare to say: b > a, even though a and b "are" infinite when x=0

Dealing with infinities is hard, and requires more information than comparing finite numbers
- Limits are one way of providing the necessary additional information
- But provided the additional information is obtained and properly analyzed by someone who knows what they are doing, I don't have a problem comparing infinities.

After all, some fundamental mathematical operations depend on dealing with infinities, for example:
      - differentiation ultimately comes down to calculating a limit approaching 0/0
      - and integration ultimately comes down to calculating a limit approaching 0*∞
      - Newton got correct answers for differentiation & integration, but apparently he used a bit of hand-waving in his proof that this was a valid thing to do.

[paul cotter (OP)]

It must be apparent that I am neither a physicist nor mathematician. In calculus we regularly deal with the limits of some function as a variable APPROACHES either zero or infinity but when it reaches infinity we have an indeterminate form. We can take an arbitrarily large number either added to or subtracted from infinity and there is no change. If there were to be a change, then the original quantity would not have been infinite. Infinity is not a member of the reals and we cannot use the operations associated with reals. I am vaguely aware of the extension to the set of reals, as far as I remember it doesn't help a lot with indeterminate forms. This could drift into the philosophy of mathematics and alancalverd will not be impressed.

[Halc]

This is what I find annoying and lacking rigour. Infinity+x= infinity because infinity is indeterminate

Context would really help. You are using infinity in an equation there in a way reserved for numbers. I don't know how this got into a conversation about Hawking radiation. It is apparently related to a quote from a video or book, but I just don't know what was actually being said.

I consider a statement that infinity+x to be greater than infinity undermines the basic consistency of mathematics.

For example, 50 is less than 150, but since there are infinite integers less than both of those, and the 'basic consistency of mathematics' would be undermined if the one wasn't larger than the other, then one has no basis to declare 150 to be greater than 50 since neither has a larger number of integers that are less than them. There would be no change between 50 and 150. But there is change between them, despite the infinite list on either side, and despite the continued 1-1 bijunction of values on each list.

Again, as I said, I have no idea if this is relevant since I've zero context about how this fits into this discussion. That's actually the reply I'm seeking.

[paul cotter (OP)]

Yea, that went wildly off topic, my fault. At the moment I have no further questions on the original topic and many thanks again.

[Eternal Student]

Hi.

   It is drifting off topic but I don't suppose anyone minds too much.

1.    It's still science.
2.    It's Mathematics, which is probably better.
3.   You ( @paul cotter)  are the  OP   (OP =  Original Poster,   or  Original Post).  It seems polite not to hijack a post from the OP but seeing as that is you and you're OK with it, there's no problem.
- - - - - - - - -
    Anyway,   yes,  Scientists do take liberties with Mathematics quite often.

...in his book "the universe in a nutshell" he talks about one infinite quantity being greater than another infinite quantity by a finite amount-mathematical nonsense...

    I don't know exactly where that reference appeared or what was being discussed but I would lay "odds on" that Hawkings was talking about a re-normalisation problem.
    The inability to keep quantities down to finite values stopped the development of Quantum Field Theory  (QFT) for about 20 years and almost lead to it's complete abandonment.     (Reference:  https://en.wikipedia.org/wiki/Quantum_field_theory#Infinities_and_renormalization  )
    What was finally done leaves many mathematicians pounding the walls in disbelief.  However, it seems to work reasonably well and no-one is claiming that QFT is the ultimate truth, it's just an effective Quantum Field Theory.

Best Wishes.

[paul cotter (OP)]

Yes indeed I do enjoy any diversions that lead to improved understanding of any area of maths or science. The cancellation of infinities in quantum theory would be very hard for me to accept as rigorous maths. However I do understand that a theory which is not realistic in simple terms can be very useful if it explains observations and makes predictions that can be verified.