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Thread: question about Hawking radiation

  1. #1 question about Hawking radiation 
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    I'm a bit confused on how it is produced. All I can find is a mention of quantum effects. Is there a reaction inside of a black hole that produces this radiation? Is a type of nuclear reaction? Why is it released? Just because of the finite temperature?
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    It's do with time / energy uncertainty that creates pairs of virtual particles. If one is headed inwards to the black hole and the other outwards then the outwards moving one can escaped the event horizon. By this theory black holes can evaporate so to speak.
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    how does the uncertainty relate to black holes? I couldn't see anything about that.
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    Why would it not relate to black holes if it relates to everything else?
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    I mean from what I have read on it. Which was only one paper since I only have a phone atm and its a hassle. It didn't state anything about what you have said. All it talked about was not being able to use T or t. Having time an uncertainty. I did not fully comprehend it and will continue to reread it. Again what I am asking is a more indepth explanation on how the time energy uncertainty and how it creates this radiation.
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  6. #6  
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    Quote Originally Posted by Jilan View Post
    Why would it not relate to black holes if it relates to everything else?
    He's right, Jilan. However I think you misread what he was asking. I think he meant to ask how the "uncertainty principle" can be used to arrive at your assertion, i.e.
    It's do with time / energy uncertainty that creates pairs of virtual particles. If one is headed inwards to the black hole and the other outwards then the outwards moving one can escaped the event horizon. By this theory black holes can evaporate so to speak.
    I don't understand why you said this. Can you please explain why? Are you referring to this; Vacuum energy - Wikipedia, the free encyclopedia

    Note that page says about the time-energy uncertainty principle regarding vacuum energy
    One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe. They are expected to do this everywhere, throughout the Universe. Their behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify.
    If you're using the time-energy uncertainty principle as most physicists use it, i.e.
    The time-energy uncertainty principle states that you can "borrow" energy E, as long as you "pay it back" in a time ; the greater the violation, the briefer the period over which it can occur.
    Then you're using it wrong. Please turn to page 118 of your copy of Introduction to Quantum Mechanics - Second Ed. by David Griffiths and read the following
    It is often said that the uncertainty principle means energy is not strictly conserved in quantum mechanics - that you're allowed to "borrow" energy E, as long as you "pay it back" in a time ; the greater the violation, the briefer the period over which it can occur. Now, there are many legitimate readings of the energy-time uncertainty principle, but this is not one of them. Nowhere does quantum mechanics license violation of energy conservation, and certainly no such authorization entered into the derivation of Eq. (3.74). But the uncertainty relationship is extremely robust: it can be misused without leading to seriously incorrect results, and as a consequence physicists are in the habit of applying it rather carelessly.
    Let's keep in mind that is not an "uncertainty in time" by any means. Also there is no such thing as a "time operator" and as such "t" is not an eigenvalue of any such time operator.
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    Physicist, it's more that the energy is not defined at very short timescales, so it is uncertain. Particle anti-particles pairs are theorised to quickly annihilate each other, but at the event horizon of a black hole they can become separated with one falling inside the event horizon and one escaping (the radiation that gets out). You will appreciate that energy can be conserved in this situation as the negative gravitational energy of the infalling particle compensates for the increase required for the pair production. Here is a nice explanation.
    Black Holes - Hawking Radiation In Detail
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    Quote Originally Posted by Jilan
    Physicist, it's more that the energy is not defined at very short timescales, so it is uncertain.
    Where did you get that notion from? In any case that's not how uncertainty is defined.

    Quote Originally Posted by Jilan
    Particle anti-particles pairs are theorised to quickly annihilate each other, but at the event horizon of a black hole they can become separated with one falling inside the event horizon and one escaping (the radiation that gets out).
    That's correct. It's caused by tidal forces at the event horizon separating the virtual particle pairs thus turning the virtual particles into real particles.

    Don't you recall that thread where I explained all of this? It's at
    How come Light can not escape a Black hole

    Quote Originally Posted by Jilan
    You will appreciate that energy can be conserved in this situation as the negative gravitational energy of the infalling particle compensates for the increase required for the pair production. Here is a nice explanation.
    Black Holes - Hawking Radiation In Detail
    In that the author is talking garbage about the time-energy uncertainty principle. That's not how it works. Look in your QM text page 118 and Griffiths will explain all of this for you.

    In any case that's exactly what I explained all those months ago. Look in my thread and the thread you post here and you'll see this

    As soon as these particles come in to existence they would both experience drastically different gravitational forces due to the sharp gradient of tidal forces caused by being so close to the black hole. One particle will accelerate towards the black hole giving the other a chance to escape and radiate out in to space.
    Last edited by Physicist; 09-20-2014 at 02:53 PM.
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    Physicist, i've just been back and re-read that thread. It was a very good thread indeed! You appeared to come under some flak for saying that in a virtual pair one particle has positive energy and one particle has negative energy at the point of pair production. Do you still believe that to be the case?

    Here is a nice paper which discusses various aspects of the time/energy uncertainty relationship that you might enjoy.
    http://arxiv.org/pdf/quant-ph/0105049v3.pdf
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    Quote Originally Posted by Jilan
    Physicist, i've just been back and re-read that thread. It was a very good thread indeed!
    For my contribution to what was good about it, I thank you!

    Quote Originally Posted by Jilan
    You appeared to come under some flak for saying that in a virtual pair one particle has positive energy and one particle has negative energy at the point of pair production.
    Not by anybody knowledgeable in the subject and thus of any consequence.

    Quote Originally Posted by Jilan
    Do you still believe that to be the case?
    Sure. The textbooks haven't changed and I haven't learned quantum field theory yet to be able to prove that Hawking was wrong and since he appears to be quite correct I don't see a problem with it. Especially since it's accepted by the physics community.

    Quote Originally Posted by Jilan
    Here is a nice paper which discusses various aspects of the time/energy uncertainty relationship that you might enjoy.
    http://arxiv.org/pdf/quant-ph/0105049v3.pdf
    Perhaps someday but you know me! I'm already flooded with work and material I need to read already. I'll take a quick look at it today when time favors it. Thanks.
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    ok
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  12. #12  
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    I could hear the violins playing. Here's to the overworked and underappreciated.

    Hawking, I mean.
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