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Escape Velocity of virtual particles

  1. Apr 6, 2003 #1
    I know that the escape velocity for virtual particles being emitted from black holes is c2+ (in the black hole entropy formula, there is an escape velocity of c3). I also know that Hawking radiation and for that matter*(I don't mean matter in physics terms), any radiation being emitted from a black hole supposedly escapes the gravitational pull of the black hole. But how does this happen? Does this imply superluminal travel?
  2. jcsd
  3. Apr 7, 2003 #2
    the way i understand hawking radiation it is not radiation that is emitted by blackholes but the result of a pair of virtual particles being created near the black hole, ie outside the event horizon, with one of the particles entering the blackhole and the other flying off into space
  4. Apr 7, 2003 #3


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    It is only at the event horizon itself that the escape velocity is c. Get a little above the horizon and the escape velocity is some value less than c. And it is a little above the horizon that the Hawking radiation arises, so the escaping particle does not have to move faster than light.
  5. Apr 7, 2003 #4


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    Greetings MajinVegeta !

    To make it clearer, gravity is not really the
    point here. The point is a VERY strong field -
    it could be an electric field (for particles
    that have electric charge) too for example.
    If it is strong enough then it can "split"
    the virtual pairs of particles created as
    a result of zero-point-field quantum fluctuations.
    But, like I said, it has to be VERY strong.
    So, when it comes to a gravity field it is only
    strong enough near(OUTSIDE !) a BH's EH to be able
    to split the ZPF particles.

    Live long and prosper.
  6. Apr 12, 2003 #5
    What's a EH and a ZPF?
  7. Apr 12, 2003 #6
    Re: Re: Escape Velocity of virtual particles

    Why do virtual particles do behave like so?
    Can you give me an approximate escape velocity of a particle NEAR the event horizon?
  8. Apr 12, 2003 #7
    Virtual particles behave more-or-less like real particles, which would do the same thing.

    As for escape velocity near the black hole... hmmm. That's a GR question, and I'm not sure how to do it -- or even how to frame it coherently right now. The problem is that around the event horizon (drag's 'EH') which frame you measure the energy in is tremendously important.

    One thing to remember is that the whole virtual-particles thing is just kind of a heuristic approximation: it almost always vaguely works, but the actualy theory is a field theory, of interacting fields, not particles. The actual derivation of Hawking radiation comes from looking at the ground state of the field near the black hole from two different reference frames (moving relative to each other), not from invoking virtual particles at all.
  9. Apr 12, 2003 #8
    aren't interacting fields composed of particles?
  10. Apr 12, 2003 #9


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    Shorts for Event Horizon and Zero Point Field(which
    I wrote in the body of the message too :wink:).
    ZPF quantum fluctuations are the virtual particles
    that are momentarily created in a relativly (for
    you as an observer) "empty" part of space with no
    strong fields passing through it - not fluctuations
    that are directly due to a "real" energy source.

    Live long and prosper.
  11. Apr 12, 2003 #10


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    According to QM - yes. What happens is that due to
    the HUP the value of these fields (or virtual
    particles if you wish) also fluctuates, which means
    that it could "jump" high enough in some places
    to allow other virtual particles to be created

    Live long and prosper.
  12. Apr 12, 2003 #11
    I am unsure about what a ZPF is (this is, its definition, not what it stands for).
  13. Apr 12, 2003 #12
    "Ground state", "zero point energy", and "vacuum state/energy" are more common terms AFAIK. In a quantum system, the lowest energy state -- this is the unexcited state in quantum mecahnics, or the empty state (no particles) in a field theory -- actually has nonzero energy. This lowest state is the vacuum/ground/zero point state.
  14. Apr 12, 2003 #13
    Whats the difference between zero point fluctuations and zero point quantum fluctuations?

    are virtual particles, from the way I understand them, particles, although they themselves cannot be detected exactly, but are detected to their indirect (virtual=indirect) influence in space?
  15. Apr 13, 2003 #14
    >>Whats the difference between zero point fluctuations and zero point quantum fluctuations?

    Same thing.

    Technically, virtual particles actually arise when you consider the perturbation-series approximation to a quantum field interaction.

    They are sort of "temporary" or short-lived particles... kinda. Real particles the long-time or long-distance limits of virtual particles.
  16. Apr 13, 2003 #15
    so they're not real particles? (i'm getting a bit confused here...)
  17. Apr 13, 2003 #16


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    Not really, they're the result of mathematical
    abstractions. In QM you can't have any
    continuos interaction/field/whatever because
    everything is made of qauntums - individual

    Live long and prosper.
  18. Apr 13, 2003 #17
    What do you mean by mathematical abstractions? What is their relation to their surroundings?

    I'm getting a notion this has to do with dark matter?
  19. Apr 13, 2003 #18
    Don't worry, you're not the only one confused about this! :)

    Nothing to do with dark matter -- dark matter is just anything not currently undergoing nuclear fusion and glowing like the sun. You are dark matter, I am dark matter, the Earth is all dark matter...

    No, virtual particles are not real particles. Hmmm... okay, they arise in the context of quantum field theory; in QFT everything consists of interacting fields. However, symmetries and conservation laws make it so that non-interacting fields always are of a form that can be described by some number of particles. That's why the idea of a particle is so useful: on a large enough scale, we can ignore the field-like nature of what's going on and talk about discrete particles.

    Now, when you get to interacting fields -- take two particles and shoot them really close together for instance -- the picture of these discrete particles breaks down, and you have to look at the underlying fields. However, much of the time, it turns out you can approximate the field picture very closely and in a very intuitive (if you know some QFT) way by introducing virtual or 'temporary' particles. They appear like regular particles, but can have any mass, velocity, etc (they need not "be on their mass shell") and only exist for short periods of time/distance.
  20. Apr 14, 2003 #19
    why do they exist for short periods of time?

    Dark matter is involved in the brane theory. Dark matter accounts for the wierd velocity of stars for instance. Their calculated velocities don't correspond with their current velocity. Their velocity relative to their placement in their galaxy (in the outskirts of a galaxy, this is a common occurance) doesn't make sense. For example, a star in the outskirts of a galaxy wouldn't be traveling at c+, right? That sort of thing happens. That's when dark matter comes in. Oh dear..I have to go to bed, but I'm pretty sure you know what I'm talking about, damgo.

    BTW, I'm only 13, in pre-algebra so if my questions involve some seriously complex math, can you try and simpliyfy it for me or just tell me what I need to know or something?
  21. Apr 14, 2003 #20
    maybe since the singularity is a source of untapped energy,outside the event horizon or in it spacetimes interaction with energy is what makes particles or matter just like in the begining.the amount of energy in spacetime somehow converts this excess energy into particles.so next to the black hole spacetime is highly charged with energy from the gravity,so what if every now and then spacetime steals energy from the blackholes gravity and creates particles from it!then when the two virtual particles come into existence,the normal one is then attracted by the blackholes gravity and is pulled back,then the anti particle then leaves travelling at light speed because of it's repulsion to spacetime,like photons just pure anti energy repelling against the positive energy background of spacetime.and all thats leaving the blackhole is anti matter.
    Last edited: Apr 14, 2003
  22. Apr 14, 2003 #21
    The Heisenberg uncertainty principle allows for h>2mc2t=2mc(ct), where m is the mass of one of the virtual pair which escapes the event horizon, mc2 its rest energy, and ct=h/2mc the maximum distance of the pair production from the horizon.
  23. Apr 14, 2003 #22
    I'm trying to boil it down as much as possible, Majin, but it's just not a simple topic. It's impressive that you understand it at all if you're only 13. :)

    Simple answer 1) Virtual particals do not really exist. They are just a mathematical trick that gives a good approximation of what's really going on, which is a bunch of quantum fields.

    The more complicated answer -- which is why virtual particles are such a good approximation, and why all particles are to some degree 'virtual', and when we can use them -- probably has to wait a while. I barely understand it myself! :)

    Branes are part of string theory and not really connected with dark matter. You're right about galaxies velocities! That's the evidence for dark matter: galaxies aren't spinning at the right speed for the amount of matter we can see in them; so we conclude they must have more matter we can't see. This could be just planets, burnt-out stars, etc; but AFAIK recent evidence is that it's probably something more obscure.
  24. Apr 14, 2003 #23
    dark matter giving a system of mass more energy for faster orbits at greater distances from the center than should be,can be explained by a different means than using dark matter.gravity is produced by matter as a property of energy itself.since spacetime was charged by matter itself when the universe was created when a star collapsed into a blackhole both matter and spacetime have the same properties.so gravity attracts energy from spacetime like a super energy sucker.as gravity pulls energy toward it it curves spacetime because magnets do to iron dust.the curvature of spacetime is like how the lines of force interact between gravity and spacetime.so spacetime energy is being pulled in toward a mass at light or faster.thus spacetime energy is at a high rate of motion.gravity is not a attraction between two masses but a masses attraction to the flow of spacetime energy.on the earth you have the same gravity field as the whole earth,so when you jump up.as the earth suck energy toward it you are attracted to the flow to the earth and follow the current and are pulled back down.so at great distances away from a galaxies center that is spinning causing energy to move in a spiral motion.toward the center as it moves around in a circle.the motion of the spacetime energy caused by the ratating center is attracted by the stars around it and start moving around the center from the motion of the energy.so the dark matter effect is because the largewr the mass of a star versus the distance from the center will cause a mass to move a different speed based on motion of spacetime energy and the gravity field of the star,so all the stars at the outer rim are just super massive stars.
    Last edited: Apr 14, 2003
  25. Apr 16, 2003 #24
    Damgo, in Stephen Hawking's The Universe In A Nutshell, Hawking distinctly, coherently specifies dark matter, and further associates it with branes. Maybe you could look it up or something.

    Tell me if I have this right:
    the event horizon is the "brim" of a black hole (or a singularity). And the schwartzchihld radius is the radius where schwartzchild radiation is emitted from. The radius is apparently (by speculation) on the event horizon. If virtual particles are only emitted from the surrounding area of the EH, (not on it), then either the whole idea of the emission of radiation from inside a black hole is, in a word, enitrely incorrect, (which I highly doubt) or I've gotten mixed up. My solution to my confusion is assuming that the emission of radiation merely appears to be comming from the schwartzchild radius. Is the radiation, though, emitted in a pattern that goaded the scientist schwartzchild to come up with a radius assigned to the particular area where the radiation is emitted?
  26. Apr 16, 2003 #25
    Hmm... I don't have the book, and honestly I can't think of any real connection. There was a proposal that really huge 'cosmic strings' might make up some of the dark matter, but AFAIK this is generally considered a long shot. Maybe someone else can clue me in?

    OK -- The Schwarzchild radius is defined to be the radius of the event horizon for a simple (non-spinning, 'Schwarzchild') black hole. The idea is that a pair of virtual particles appear near the event horizon, one headed away from the black hole at high speed, one headed in. Normally, they would attract each other and annihilate; however, sometimes the gravitational field of the black hole will pull one in quickly enough that the other can escape.

    A similar sort of thing can happen with a really strong electric or magnetic field... this is believed to happen around some neutron stars.

    Hawking (not Schwarzchild) radiation is pure theory -- it's so small that it's impossible for us to actually observe it. Hawking came up with it in 1975; Schwarzchild did his stuff back in the 30s I think. He got the radius by discovering black holes could exist and solving for where the event horizon was.
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