didnt understand casimir effect well

Discussion in 'Physics & Math' started by rohIT, Nov 21, 2012.

  1. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    I do think the last statement is probably the most relevant one. What is the net energy of a virtual particle pair? If your answer is zero, then you are correct. Hopefully at the same time you also noted that 2 x 0.511Mev is not zero; whereas, 0.511Mev + -0.511Mev is. A particle (that is not virtual) has to strictly obey relativistic energy-momentum conditions (aka: on mass shell). A virtual particle doesn't have to and can theoretially travel faster than light, have negative mass (energy), or traverse backwards in time. Part of understanding negative energy is understanding energy. It's a human-invented accounting system (i.e. it's not a substance). We associate certain balances of energy with certain things (often because its useful to see energy conservation). Like any balance in an accounting system, there is the possibility of a negative balance. When a virtual particle pair has a net energy of zero it means that there has to be a negative balance to offset the positive one. Hopefully that makes a little more sense and you may find the links I provided Billy T. useful as well.
     
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  3. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    Thanks. Particle->antiparticle collision vs. positive energy particle->negative energy particle collision often seem to both use the word annihilation to describe the result and it appears to lead to misinterpretation.
     
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  5. OnlyMe Valued Senior Member

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    The luminiferous aether was conceived of as the medium through which light propagates, and thus through which all EM radiation propagates.

    What it seems you were or are suggesting is that photons propagate through photons. That photons act as the medium of propagation for photons... Or waves the medium for waves if you like.

    The luminiferous ether is a dead end subject. It is not consistent with what we have learned over the last 100+ years.

    There remain explorations of the possibility of some form of relativistic ether, but none that have been successful, as of yet.
     
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  7. OnlyMe Valued Senior Member

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    The first link reads like an over head for a lecture and does not contain sufficient information, to be a credible reference on its own.

    The second is from 1933, there has been a lot happening in particle physics since then. Even then it was presented as theoretical.

    The third Wiki reference begins with disclaimers that it needs to be reviewed by a physicist and some externally supported references.

    Billy T addressed the issue of positive and negative energy better than I.
     
  8. RealityCheck Banned Banned

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    Thanks for your response. Much appreciated. Running out of time for the day, so briefly...

    No, not really. I am observing that Billy T's statement refers to VIRTUAL entities of diverse wavelengths permeating space on an 'instantaneous' basis/process which is ubiquitous and can be occurring at unknown 'rates'. Ie, such in-situ oscillatory entities can be construed as underlying e-mag TYPE 'fluctuations' creating a VIRTUAL FIELD (not necessarily of 'photons' per se) which REAL photons may be propagating along/by as the PERSISTENT excitation in a field on TRANSIENT excitations which do not themselves propagate 'as' photons. That is the speculative 'connection' which my initial reading of Billy T's post on that aspect invoked regarding what is being speculated in the alternative section under 'luminiferous aether' etc.

    That was all. Just speculating how the VIRTUAL field' of wavelengths existing in all space may fair in logical/physical comparison with the luminiferous aether as a similar type of 'field' in the alternative section speculations.


    PS: If I log out unexpectedly please don't take it amiss if I do not return for a couple days. Thanks again for your responses. Cheers!
     
  9. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    See? I told you there was no way of fulfilling a subjective request without objectively clarifying what you wanted to see; however, I did note that you didn't like Dirac's paper because it is old so maybe something modern will help. Below is a BBC documentary for Hawking Radiation and explains virtual particle pairs in the process (roughly around 1:20). They refer to the particles having positive and negative mass which means the same thing as positive and negative energy.

    http://www.youtube.com/watch?v=S6srN4idq1E

    Enjoy.
     
  10. OnlyMe Valued Senior Member

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    Read carefully.., my only comment on the Dirac lecture was that it was not up to date. QM had only been around for around 10-15 years. Dirac and others laid the foundations. That is not the same as assuming that nothing of what we understand today has changed since then.

    In an earlier post I mentioned that there were two kinds of virtual particle disciplines being discussed in this thread. Something that could and has been obviously comfusing to many lay readers. The thread OP asks questions about the Casimir effect.

    Explanations of the Casimir effect center on zero-point-energy (ZPF of vacuum energy). If you approach the ZPF from QED they are virtual photons, which can be discussed in terms of wavelengths.., just as all other EM radiation can be. From SED they are treated as real photons, and may still be discussed in terms of wavelengths. Billy T did a good job of describing this (zero-point energy as wavelengths) in a nutshell. Any in depth descriptions or discussion would be completely beyond the discussions in this thread.

    There was a brief mention of Feynman diagrams and virtual particles earlier. The virtual particles in that case are not limited to photons, and they are not the same as the photons of the ZPF. They are unobserved virtual particles which link two sides of high energy particle interactions.

    The virtual photons (with a range of wavelengths), of the ZPF are there all of the time.., virtual or real, QED or SED.

    The Virtual photons in a Feynman diagram pop in an out of existence as transition states during particle anillation and pair production interactions. They don't really exist in time, or at least within any time frame that we can measure. Even many of the particles we can measure before and after the transitions, exist for very brief periods of time....., as in nanoseconds.

    There has been some experimental evidence supporting the existence of zero-point-energy, including experiments confirming the Casimir effect.

    The virtual particles involved in high energy particle transitions, and Feynman diagrams, remain entirely theoretical. This does not mean they are not "real", it just means they have not been observed.

    Now, in nothing I have read about zero-point-energy has there been a suggestion of positive and negative energy. There may be some instances in high energy particle physics where the idea of a negative energy, an energy deficit or "hole" is conceptually functional. However, in some respects it might be better for a lay oriented discussion, if the virtual paticles in these interactions were thought of in the same way we think of dark matter and dark energy.., as place holders, for things that fill the gaps, we have so far been unable to observe and measure in known processes.
     
  11. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    To Crunchy Cat:

    Before quoting from your second reference - the text where Dirac clearly states that the positions have POSITIVE ENERGY, NOT THE NEGATIVE ENERGY you assume I will briefly discuss Dirac´s infinite sea of negative energy states in which rare unoccupied states has the properties of a positron. There are also other mathematical (not real) models of positrons – for example an electron which in the future scatters backwards in time, appears to be a positron also. I.e. a reversal of BOTH charge and time in any and almost* all of physics equations preserves CPT invariance in the equations as CPT = (-C)P(-T); however, this does not mean the future is already pre-determined and has sent particles backwards in time to be our real physical (not just mathematical) positrons.

    The “holes” or unoccupied electron states of conductive (or semi-conductive) solids also behave as if they are positive charged electrons or “positions.” In general many equations of physic have two solutions (any quadratic equation does) but that does not imply that both these solutions are real.

    Dirac´s electron equations do have negative state solutions. Dirac did not believe that there was an infinite amount of negative energy in the universe in real electrons occupying almost all of these negative solution states. He merely noted that a positron could be considered to be a hole in the mathematical sea of infinite negative electron states that do satisfy his equations. He did not believe these solutions were real any more than the other physicists who noted that electrons traveling from future to the past were real positrons. Positrons are real particles, not mathematical solutions to equations. Or in Dirac´s own words of the 1933 Noble Lecture (link from your link 2):
    I.e. just like the self consistent mathematical theory which describes positrons as electrons traveling backwards in time are self consistent with the known physics, but only mathematically so.
    The text Immediately after the above quote, states that the anti-proton could also be described as a hole in an infinite sea of negative energy states, given by the mathematical solutions to their equations, with most all of these negative energy states occupied; except for a recent (in 1930) experiment done with the proton´s nuclear spin.

    Now that we know electrons have spin 1/2 a very serious problem exist with taking positrons as holes in Dirac´s negative sea exists. I.e. the Pauli exclusion principle allows two electrons in each available state, one spin UP and one spin DOWN. Thus some "half holes" would exist (only one electron occupying a possble state in the negative sea.) Then that positron would differ from other positrons in both charge and mass by a factor of two, but all electrons and all positrons have exactly the same charge and mass. So spin, which Dirac knew made his negative sea model nonsense for the anti-protons, also makes it nonsense for the positrons. Face it: positrons are real positive mass particles.

    * A Noble prize was given to two physicists who found in certain rare weak force interactions a very slight bias towards one parity, P, does exist, so CPT is not always preserved.
     
    Last edited by a moderator: Nov 23, 2012
  12. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    Yes it is enjoyable to watch, but the part about negative mass members of a vacuum polarization pair falling into the black hole is easily demonstrated to be nonsense and does not come from Hawkings.

    Hawking´s model of a black hole has a non-zero surface temperature at the event horizon from which PHOTONS, NOT CHARGED PARTICLES, escape. This temperature is quite low until the last stages of the black hole´s life, when the PHOTON radiation is more than "white hot."

    The pretty video is confused nonsense because if the mass were negative then the force of the black hole´s gravity on the negative mass is REPULSIVE, NOT ATTRACTIVE. I.e. any negative mass particle near a black hole would be blasted away from the black hole, and never fall into the black hole to reduce its mass.

    The escaping PHOTONS from the hot event horizon surface do carry away energy E, which means the mass remaining in black hole decreases by m = E/(C^2).

    Again, for the third time: NEGATIVE ENERGY and/or NEGATIVE MASS particles DO NOT EXIST.

    If negative mass existed and could be produced and were collected then there would be no need of rocket fuel. Positive masses fall into the stronger gravity regions (like near the Earth) but negative mass particles "fall" away from the strong field regions (away from the earth).
     
    Last edited by a moderator: Nov 23, 2012
  13. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    Sorry, but that is 100% incorrect. Below is Hawking's original paper that spawned the famous phrase "Hawking Radiation". This quote in particular (from page 3) is what demonstrates your assertion as being incorrect:

    "As the mass of the black hole decreased, the area of the event horizon would
    have to go down, thus violating the law that, classically, the area cannot decrease
    [-7, 12]. This violation must, presumably, be caused by a flux of negative energy
    across the event horizon which balances the positive energy flux emitted to
    infinity. One might picture this negative energy flux in the following way. Just
    outside the event horizon there will be virtual pairs of particles, one with negative
    energy and one with positive energy. The negative particle is in a region which
    is classically forbidden but it can tunnel through the event horizon to the region
    inside the black hole where the Killing vector which represents time translations
    is spacelike. In this region the particle can exist as a real particle with a timelike
    momentum vector even though its energy relative to infinity as measured by the
    time translation Killing vector is negative. The other particle of the pair, having
    a positive energy, can escape to infinity where it constitutes a part of the thermal
    emission described above."

    http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Hawking_CMP_1975.pdf

    That's not something I really have an issue with. I *think* Hawking radiation may be limited to electromagnetic and neutrino radiation... but I haven't confirmed that by any means.

    This isn't correct either. The negative energy particle would be attracted to the center of the black hole. The center of the black hole would be repulsed by the negative energy particle, but the center is rather stuck there so the negative energy particle has no issues slamming right into it and subtracting from it.

    Hot or cold the now-real particles of radiation do carry away energy.

    Dirac seemed to think they did. Hawking thinks they do. Experimental demonstrations of zero-net energy virtual particles work. Heck, we're even seeing hawking radiation in a lab (http://arxiv.org/abs/1009.4634). Maybe you are correct and negative energy/mass isn't real and the notion is just a fudge that happens to work out; however, if we're to follow the evidence then that doesn't by any means appear to be the case.

    I don't disagree that there may be lots of useful applications for negative energy, but the implication of your statement is that if it exists then it should be easy to create. I would be curious to know why you think that would be the case considering history doesn't support it.
     
    Last edited: Nov 23, 2012
  14. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    That looked accurate.
     
  15. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    I don't think I ever addressed the ZPF assertions that were made. There was no reason to. I did see Billy's assertion that the Casimir effect "is best understood by an EM wave model.". That is his opinion but I found no reason to address it. The Casimir effect prediction; however, did not center around ZPF and I saw no evidence that the opening poster was referencing it. The Casimir effect prediction centers around your run of the mill virtual particle pair foam that is predicted by QM. Specifically that the foam's energy density causes pressure outside the plates that is greater than between the plates. The fact that the prediction works out experimentally does support a real tanglible existence of virtual particle pairs (no matter how fleeting). If ZPF also explains the Casimir effect then that is ok.

    The big contention of course is the concept of negative energy. As I mentioned, we use energy as an accounting system not a substance. It's a negative balance that shows up in virtual particle pairs to ensure their net energy is in fact zero (see the link from Hawking's paper that I put out there for Billy). Whether that balance corresponds to an objective particle property hasn't been directly observed; however, indirect observation does support it. The Casimir effect demonstrations and hawking radiation reproduction present a good case for it.
     
  16. OnlyMe Valued Senior Member

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    The Casimir effect has been experimentally confirmed, but since when has Hawlking radiation been reproduced?

    From Wiki on Casimir effect,
    In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. ... When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force

    When addressed from SED the virtual photons are considered and treated as real... In neither QED or SED, in any of the papers I have read are they talking about virtual particle pairs, as constituent components of zero-point-energy. Heck, I just spent the last two weeks on a cruise reviewing exactly these sorts of papers.., dealing with the Casimir effect, inertia and to some extent gravitation. In all cases the ZPF were treated as virtual or real photons (QED and SED).

    Try Casimir forces, Milonni and Shih, 1992

    Very often our understanding of things changes between the time it was first predicted and when confirmed.

    As far as not mentioning ZPF assertions, the thread began as a question about the Casimir effect, which is best explained and understood today as addressed by QED and/or SED. The whole discussion involving particle pairs, negative energy and mass is a distraction to the OP. Which is OK so long as the digression is clear. It really has seemed rather jumbled up to me, hence my repeated mention that there are two conversations....
     
  17. Crunchy Cat F-in' *meow* baby!!! Valued Senior Member

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    Since september 2010:

    http://arxiv.org/abs/1009.4634

    This *might* have been done at an earlier date as well but I don't recall definitively.

    Yep, this all looks great.

    Quite correct.

    When rohIT was asking about the Casimir effect, he framed it in the context of virtual particles and linked it to Hawking radiation. I think that segment of the discussion was the most relevant while ZPF assertions were the distraction. As to QED and / or SED best explaining the Casimir effect, that is certainly an opinion shared by some.
     
  18. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    to Crunchy Cat:

    Thanks for this early Hawking (1975) link. It is near my bed time so I only skimmed the text and ignored the equations, which are difficult for me so will continue to do so. Here are some quotes from what I read, with my comments on them {some short ones inserted in these curved brackets}:

    From page 202: “These small black holes, being at a higher temperature, {than the CB radiation temperature, which is near zero K now} would radiate more than they absorbed {from the CB radiation}. They would therefore pre- sumably decrease in mass. As they got smaller, they would get hotter and so would radiate faster. As the temperature rose, it would exceed the rest mass of particles such as the electron and the muon and the black hole would begin to emit them also. …

    As the mass of the black hole decreased, the area of the event horizon would have to go down, thus violating the law that, classically, the area cannot decrease . This violation must, presumably, be caused by a flux of negative energy across the event horizon which balances the positive energy flux emitted to infinity.{By Black Body thermal radiation at least until very hot.} One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike …”


    From page 203: “Perhaps the strongest reason for believing that black holes can create and emit particles at a steady rate is that the predicted rate is just that of the thermal emission of a body with the temperature •/2rc.”

    From page 219: "The baryons or leptons that formed the original collapsing body cannot reappear because all their rest mass energy has been carried away by the thermal radiation. .."
    {Note here he does not say it can be "pictured as" but flat out states that the BH´s rest mass is removed by Black Body radiation. That, I think is his POV in all of his later writing on how the BH evaporates.}

    Now only my comments:

    From the first part of 202 quoted Hawking is clearly speaking of thermal radiation of photons, but then noting when the Black Hole temperature (typical themal energy) exceeds the rest mass of the lighter paricles they will be produced (not captured vacuum polarization pairs) and when still hotter many types of particle will be produced by the black hole.
    From the second part of 202 quoted, Hawking states that classically the BH can not shrink and that the negative particle can not exist in space, but when in the very strong gravity field of a BH, space becomes time like and conversely. I don´t understand this, but have read it recently too so think it is still the accepted view. Note that Hawking only states that one can imagine or “picture” the negative energy flux as being associated with negative energy flux of vacuum pair particles – does not claim that is what it is. In fact he clearly states the negative energy particle is “classically forbidden” at least near the BH (and makes no statement to indicate that this classically forbidden nature of negative energy particles is not true every where also.)

    From the sentence of page 203 quoted, he is stating that this negative energy POV is identical to the Black Body radiation POV. I was not aware that Hawking had given rise to the common view that BH´s loss mass by having only one member of a vacuum polarization pair escape (adding it rest mass energy to the observable universe so that much mass energy must be removed from the BH to preserves conservation of energy.

    In my quick skim, I found no indication that Hawking was asserting that the member of the pair had negative mass; however, I did not find any discussion of some other mechanism by which the mass of the BH would be decreased. I get the quick impression that the logic runs the other way. I.e. Hawking´s equations predict the mass of the not cold BH does decrease (assuming no real matter is falling in) so one way to picture how this happens is with time like particle, which can in the non-classical / relativity theory have negative mass and energy being captured OR the other way to view this being that black body thermal photons are taking Energy E away from the BH and its mass must decrease by E/(C^2).

    Thus, I will weaken by assertion that negative energy and mass psrticles cannot exist to recognize that theory does permit that under the extreme conditions where time and space are mixed or even reversed concepts. This is much like theory also permits magnetic monopoles to exist, but does not mandate that they or negative energy and mass do actually exist.

    I.e. negative mass and energy particle are one of two ways to “picture” what is happening, but not demonstrated to be real even for these extreme conditions of mixed space and time as their predictions are exactly the same as the Black Body only radiation POV, which Hawking clearly states is what is happening for BH to lose mass when it is not yet hot enough to be producing particles from intense thermal energy.

    I may, but don´t promiss to, read more again tomorrow when I get up.
     
    Last edited by a moderator: Nov 24, 2012
  19. OnlyMe Valued Senior Member

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    From the introduction paragraph, of your link above;
    Event horizons of astrophysical black holes and gravitational analogues have been predicted to excite the quantum vacuum and give rise to the emission of quanta, known as Hawking radiation. We experimentally create such a gravitational analogue using ultrashort laser pulse filaments and our measurements demonstrate a spontaneous emission of photons that confirms theoretical predictions.

    You do understand the word analogue, no? It means similar and in this case theoretically similar since no one has confirmed any of that which occurs at an event horizon.


    The OP,
    i guess casimir effect speaks of particle pairs formin n annihilating all the time at pico scales.
    what i did not understand is that how is energy conserved here?
    everytime particle pairs are produced, some energy is "borrowed". fine.
    but when they annihilate, shouldnt photons be emitted n energy increased?
    same thing in hawking radiation also where he speaks of hawking radiation.
    particle antiparticle pairs are produced, one of which enters the black hole n causes annihilation while the other adds to the mass of the universe.
    plz enlighten me

    Clearly, from the title of the thread and the OP, the question centered on confusion about the Casimir effect. That is apparent in the first sentence, since the Casimir effect is at least generally accepted today to emerge from the interaction of matter with zero-point-energy (composed of EM radiation — photons). Rather than from particle pair production and anillation.

    And yes pair production and Hawking radiation were mentioned.., however, that is where the confussion began, and the discussion splintered off into a whole different line of thought.

    I am not even sure rohIT is even still following the discussion, if so I am farly certain no clarification has been had.

    Billy T already gave a good and simple description of the currently accepted mechanism involved in the Casimir effect in post #4, which is consistent with both QED and SED, allowing that SED treats the photons of zero-point-energy as real, rather than virtual. I favor the SED approach, but then I am no expert.
     
  20. brucep Valued Senior Member

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    The experiment, you linked, uses an 'accessible model' where Hawking Radiation is predicted to occur. Great experiment. Awesome result.
    This is in the first paragraph of the paper: "In a simplified description of the process, vacuum fluctuation pairs close to the horizon are split so that the inner photon falls in and the outside photon escapes away from the blackhole. As the out going photon cannot return to the vacuum, it necessarily becomes a real entity, gaining energy at the expense of the blackhole. It was soon realized that the essential ingredient of Hawking radiation was not the astrophysical blackhole but rather the space-time curvature associated to the event horizon." Kip Thorne, Black Holes and Time Warps pg 441, says the distance separating the virtual pair, due to tidal accelerations, needs to be ~ 1/4 the circumference of the event horizon for the outside virtual to gain enough energy to become real [detectable] and escape.

    The fact they can create the environment on a table top is pretty cool.

    Simple derivation for the Hawking temperature

    T_Unruh = h*g_conv/4(pi)^2*k_Boltzmann*c [eq.1]

    In geometric units

    g_shell = g_conventional/c^2 = (M/r^2)(1-2M/r)^-1/2

    g_conv = (M*c^2/r^2)(1-2M/r)^-1/2 [eq.2]

    Substituting [eq.2] into [eq.1] and simplifying results in

    T_Unruh = [h*c*M/4(pi)^2*k_Boltz*r^2](1-2M/r)^-1/2

    To transform this result to Hawkings result you let r->2M [the event horizon] eliminating (1-2M/r)^-1/2 by factoring in (1-2M/r)^1/2 to cover the redshift expected for the remote observer at boundary condition.

    T_Hawking=[h*c*M/4(pi)^2*k_Boltz*(2M)^2](1-2M/r)^-1/2(1-2M/r)^1/2

    T_Hawking = h*c/16(pi)^2*k_Boltz*M
     
  21. RealityCheck Banned Banned

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    Hi brucep, everyone.

    Can anyone tell me what the process actually is that supposedly reduces the bh energy-mass internally.

    I ask this because I cannot find anywhere the explanation of how can the interior of a bh be affected by anything that happens to the escaped (now 'real') photon after it has left the vicinity.

    In other words, what precisely allegedly happens, in physical not abstract/logical terms, to the trapped/ingoing half of the erstwhile 'virtual' photon pair, such that it can reduce the bh energy to an extent equal to the escaped half?

    Any elucidation of that question will be much appreciated. Back later. Thanks.
     
  22. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    I mentioned in prior post that I did not know and had never seen a good answer to that question. I think it is almost as bad for the POV that what leaves the BH is black body radiation from the event horizon, but at least one can imagine that is a micro- cooling below the equilibrium temperature of that surface which makes it shrink. So then the energy is inside a smaller volume is hotter and thus some of the hotter energy re-heats the now smaller EH to even higher temperature than it had before that most recent thermal photon left. Do not take these words to imply there is some actual surface at the EH - there is not. It is just a mathematically defined surface.

    I don´t know if those skilled in the math of this very strange environment can "turn the crank" to show this is valid under mathematical analysis or not, but at least it sounds plausible to me. I can´t think of anyway the longer living than allowed by the uncertainty principle product for the duration of 0.511Mev member of the pair not "eaten" can make the BH loss mass and even more troubling is why it does not gain mass of 0.511/(C^2) for the one it eats?

    I do believe as your link indicates that which of the two 0.511Mev particles gets "eaten by the BH" is determined by chance of it being closer to the EH and thus in a stronger gravity field. It is ONLY the gravity gradient that makes a different gravity force of attraction on the two members of the pair. Why the "not eaten" member escapes is also a great mystery to me. It too is in a great gradient and should be eaten "micro-nano seconds" after the by-chance-closer one is.

    The only reason why one is eaten and the other is not that I can think of is that the BH is not exactly electrically neutral and it is the polarity of the electric field of the BH which selects which to eat. That however will tend to reduce the net charge on the BH but perhaps as the EV shrinks the inverse square law lets the electric field at the EH actually increase despite the reduction in net charge.

    I nearly sure these humanly understandable ideas (instead of mathematical analysis) are just comforting nonsense. Probably the most reasonable position to take is that, like the photon, this part of the things existing cannot be understood by humans, only accepted by us as the experiments when possible and theory tell us about their strange nature.

    No human can really understand how a single photon can go via different, widely separate paths, but that is easily demonstrated (I have done it) to be the truth about photons.
     
    Last edited by a moderator: Nov 24, 2012
  23. brucep Valued Senior Member

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    The virtual gains energy from the tidal force separating the pair. The tidal field is the g_field of the black hole. It extends from the center of the black hole to far away. If the virtual escapes it carries away energy from the black hole g field. There is no coordinate singularity associated with measurements of the local g_field but there is for real particles. Real particles will take the shortest path to r=0. According to QM a virtual can tunnel the event horizon. Based on HP uncertainty relationships. Measurements reckoned from remote coordinates do blow up at the event horizon.

    g_shell = (M/r^2)(1-2M/r)^-1/2 = y(M/r^2)

    The temperature derivation: Accounting for the redshift you get the remote Hawking Temperature [reckoned by the remote bkkpr far away]. In the proper frame of the free falling observer the temperature is ~0 K.
     
    Last edited: Nov 25, 2012

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