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    Observer Dependence Of Hawking Radiation Doubts Boltzmann Brains
    By Sascha Vongehr | January 10th 2013 10:00 PM | 15 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    That black holes radiate Hawking radiation is almost established knowledge although Hawking radiation has not been experimentally confirmed.  Hawking radiation, as of now, is founded on the consistency of the thermodynamics of, for example, black holes.  Hawking radiation being also found around string theory black holes for example adds confidence.  However, somebody who falls into a black hole does not see the Hawking radiation!  Could these kinds of quantum fluctuations differ from usual thermal radiation?  Or are they the same, but also usual thermal radiation should be seen as fundamentally quantum mechanical and observer dependent?

    Any black body radiates a radiation whose spectrum (a function showing how much intensity there is at any given wavelength) only depends on the body’s temperature T.  That spectrum is the so called black body spectrum, or thermal spectrum:

     

     

    However, there is a difference between thermal radiation of an oven and that of a black hole.  Hawking has been aware of it since 1977 when he and G. W. Gibbons published about this quantum radiation being observable from any event horizon, including cosmological horizons (that is roughly where the universe recedes with light velocity, due to its expansion, relative to an observer inside of it, so that nothing further away can ever be seen by that observer).

    Thermal radiation from a warm body “exists” more independently from the observer in the following sense:  If you move toward the body, the thermal radiation will become more energetic (blue shifted).  You “bump against the photons” in between you and the hot body, so in this sense, that light “is actually there*” in the space between the hot stove and the observer. (*This is not denying the “non-existence” of light - in fact, this whole observer dependence issue here is a further aspect supporting that "non-existence".)

     

    The radiation due to black holes and cosmological horizons however is due to Unruh temperature which accelerated observers are generally predicted to detect.  While an un-accelerated observer detects nothing, an accelerated observer is predicted to observe being in a thermal bath that has a temperature proportional to the acceleration she experiences.  Hawking radiation is this Unruh radiation that the observer sees when she is held at a constant distance over the black hole, firing her rocket motor all the time in order to not fall into the black hole.  The radiation is detected because the observer is accelerated against the gravitational acceleration of the black hole.

    What happens if any accelerated observer stops accelerating?  The Unruh radiation disappears!  What if the observer above the black hole switches her rocket motor off and stops hovering, now falling free?  Same thing: the Hawking radiation vanishes! (except for certain gray body factors - always nasty details)

    Consider observers hovering above a black hole and receiving Hawking radiation seemingly from the black hole, while other observers are in free fall somewhere in between the hovering observers and that black hole, and these falling observers however do not bump against the photons that the hovering observers think are “really there” in between them and the black hole.  Strange?

    Even weirder is the quantum radiation in an expanding universe:  In de Sitter space, which is what our universe will resemble after some further expansion, quantum radiation with a thermal spectrum will be seemingly coming from all directions, but it will be the same for all observers, even if they move relative to each other (as long as they move on geodesics).  The today visible cosmic background radiation is also having a thermal spectrum, namely one characteristic of a low temperature of 2.725 Kelvin, but you know whether you move inside of it or not, because it is more energetic (blue shifted) from the direction that you move into.  It is somewhat more “really there”; you running against it hurts a little more than letting it run after you.

    Is this an important difference?  Well, if Hawking radiation is thermal, we can use exponential functions valid for thermal radiation and calculate the probability of Boltzmann brains appearing as thermal fluctuations.  If this holds true, any kind of weird Boltzmann brain is possible, and since there is no difference between a Boltzmann brain and a usual brain, those weird situations that Boltzmann brains find themselves in are all possible; unlikely, but possible.  Even the weirdest most horrific “terrible states” would be possible.

    I suggest that we become less sure about the thermal nature and independent existence of Hawking type radiation – after all, there is no experimental verification yet!  I do not mean to say that Hawking radiation does “not exist”, however, we should carefully analyze the difference between these types of radiations; thermal radiation on one hand and the more observer dependent quantum radiation whose thermal spectrum depends much on assumptions stuck into the semi-classical derivation of the Hawking/Unruh radiation.

    The propagators of Hawking radiation [1] are interpreted as the probability that the event horizon emitted the detected fluctuation of energy E.  Calculating the probability P of a Boltzmann brain with energy E via the thus derived formula does not only assume a perfect P ~ exp[-E/(kBT)] dependence, to an accuracy that maybe unwarranted (e.g. exp[-1050]).  It also depends on neglecting to question the validity of certain approximations and limits like integrations to infinity during the derivation.  There are more troubling issues, one being the consistency of the description in the case of Boltzmann brains.

    The Boltzmann brain as a thermal fluctuation of gas atoms bumping together is little more than the time inverse of a brain exploding violently after we shot lasers on it – messy but conceivable.  Such a brain is not ever seemingly coming directly from an event horizon, and in fact one may argue such impossible:  With what velocity are we to expect a Boltzmann brain coming at us if its whole travel from the cosmological horizon (gazillions of light years) did only add up to a few milliseconds proper time (as experienced by the brain)**?  And since we need to detect it, how can we without at detection destroying it - what kind of weird detector is that to be - can it be distinguished from something that constructs the brain with the same probability?  I do not see that the case for observing Boltzmann brains being observers themselves, able to at least observe for a second, has been properly argued, nevertheless, there are articles in the peer reviewed literature that take these assumptions as if they are basically as given as experimentally observed black body radiation.

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    [1] G. W. Gibbons' and S. W. Hawking: “Cosmologicalevent horizons, thermodynamics, and particle creation.” PRD 15(10) (1977)

    [2] W. Unruh, Phys. Rev. D 14, 870 (1976)

    ** This is about the stability of the brain implying some reasonable size dx against its decaying on its boundary (dt ~ dx/c).  If it is supposed to be a whole freak world or laboratory, E goes up further.

    Comments

    And since we need to detect it, how can we without at detection destroying it - what kind of weird detector is that to be - can it be distinguished from something that constructs the brain with the same probability?
    Could you unravel that a bit please? Boltzmann brains do not have to arrive via a time-reversed explosion or decay process. If perfect, such a process would result in a time-reversed Boltzmann brain which would be hugely unstable (as you suggest); if less than perfect it would get to the un-exploding stage and then simply fall back into exploding, never having reached consciousness. That's the nature of the statistical ensemble, innit? However, Boltzmann brains can arrive via any prior state - there is no obvious reason for matter to have a preference for time-reversed explosions, indeed evolution of brains on Earth is only a brain-building fluctuation of a rather probable kind.  Boltzmann brains are just the ones that do not involve life on earth :) The question is - what are the statistics here? I would have thought that time-reversed explosions are a pretty small subset of all possible ways to build a brain by accident.  So most Boltzmann brains will run forwards in time and not be destroyed on contact with a detector. 

    vongehr
    Boltzmann brains can arrive via any prior state - there is no obvious reason for matter to have a preference for time-reversed explosions, indeed evolution of brains on Earth is only a brain-building fluctuation of a rather probable kind.
    Precisely - but the probability P for a brain of energy E (mass ~ few kg) that is without earth and solar system around it, is much higher in a thermal background of given temperature T, and nevertheless, they need some physical history (at least potential quantum histories that add up to the same probability), say as just the right photons and electrons and positrons comming along in a small region of space.
    I would have thought that time-reversed explosions are a pretty small subset of all possible ways to build a brain by accident.
    So how do you build a brain of mass ~  few kg inside de Sitter vacuum?
    Sorry, I meant to get back to you before now, but my internet connection gave up.

    My point was very simple though I went astray in the statistical argument - my bad. If you are going to argue from inverse destruction then you should use the most likely way a brain will decay in a cold vacuum. Arguably this is a gentle disintegration and any "explosion" is hardly comparable to firing lasers at it.
    vongehr
    OK - so a deep frozen brain starts at the cosmological horizon and travels to my detector, in front of which it gets just the right IR radiation to be turned on to think "I am just now typing this sentence on my keyboard" and then it dies.  What are the constraints on probability estimates that make me expect non-terrible states in my immediate future?  Is today's QM all that I need in order to show that I expect to send of this answer to your remark rather than being a turtle that steps into a unicorn's urine?
    Can QM give you the time-asymmetry that created a big-bang? Because, without a low entropy start, the population of Boltzmann brains in the statistical ensemble is going to be far greater than "universes".

    However, to test the hypothesis of a low entropy start you look at how consistent the records are. It seems to me that this gives you a Bayesian update - it is overwhelmingly more likely that the assumption of complete time-symmetry is wrong, that the universe is, after all, non-symmetric. And if so, then, even if it comes from a very low probability fluctuation, given that it did (WAP), that event may still be more likely than a Boltzmann brain.

    Which is where my lumbering thoughts took me before the previous post and I realized that I have not thought about this enough yet! :/

     

    Thor Russell
    I also find some things here very counter-intuitive and confusing. In the example where the observer in free-fall towards the black hole doesn't experience Hawking radiation, what if that is the time when the black hole evaporates (or becomes infinitesimally close to doing so)? Surely the resulting explosion/gamma rays are felt?
    I had also assumed that we could never detect Boltzmann brains (formed by the most random manner) even if they existed because they were so incredibly uncommon and short lived, and yes our detectors would be more likely to turn into one than find one that would have been there without them. Is there a simple reason why observing a B brain being an observer is important?

    Thor Russell
    vongehr
    observer in free-fall towards the black hole doesn't experience Hawking radiation, what if that is the time when the black hole evaporates (or becomes infinitesimally close to doing so)? Surely the resulting explosion/gamma rays are felt?
    I presume that this is about the difference between cosmological and black hole horizons.  There is no intrinsic curvature at a horizon due to mere acceleration in flat space, but there is curvature near a black hole.  Perhaps this is closely related to the gray body factors - I am no expert on that.  The problem is: why should we assume both spectra to be thermal to such a high degree as it is necessary to allow Boltzmann brains?
    detectors would be more likely to turn into one than find one that would have been there without them.
    You could imagine a detector cooled to T < T_horizon.  However, the fluctuation (brain) is supposed to leisurely appear from the horizon (E ~ few kg, thus quite slow)! That of course is much more likely (for a brain) if it happened to come together out of thermal radiation colliding in front of the detector (because otherwise, how would the brain stay stable for millions of years yet only remember a normal childhood and so on).
    Is there a simple reason why observing a B brain being an observer is important
    A B Brain can be in any (e.g. terrible) state*.  If it can, so can my future I.  The question is: Is the principle of plenitude as restricted by pure logic the same or is it more restricted than as restricted by current quantum theory?  It is a straight physics science question, because physics is about explaining all that is possible with its probabilities (how much can I expect that state S).

    *
    "If BBs were possible, crazy BBs would even outnumber the BBs that observe “normal” situations." - from the other post on BB = B brains.
    Halliday
    Sascha:

    You are quite correct to question the nature of Hawking, Unruh, and/or any other similarly derived radiation and/or temperature, etc.  They all depend upon meshing three (3) areas of physics that have yet to be properly/completely reconciled:  Quantum Mechanics/QFT/etc. (QM), General Relativity (GR), and Thermodynamics (a subset of Statistical Mechanics [SM]).

    It seems like practically everyone recognizes the lack of reconciliation between QM and GR.  However, there are similar issues with reconciling GR and SM.  (In fact, SM has yet to be reconciled even with Special Relativity, last time I checked, a few years ago, though there has been some progress.  [At least we do have candidate distributions for the relativistic equivalents for Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions.])

    Even QM and SM is a mismatch, even though we often see them blithely combined as if they belong together.

    David

    vongehr
    Yes, most surely, though some would say that QM/GR is the only question left, while others mean basically the same when they think that QM/SM is the only question left, or perhaps even just the causal logic of stories.
    Halliday
    Sascha:

    I'm puzzled at your apparent "need" to determine, experimentally, whether a Boltzmann Brain (BB) is an "observer", or not.

    Can you even, experimentally, determine whether I am an observer?

    True, we could perform an EPR type experiment, get back together and compare notes, but Hugh Everett, the 3rd, has already shown that by this "definition" even a simple automaton with memory is "equivalent" to an "observer".*

    David

    *  "As models for observers we can, if we wish, consider automatically functioning machines, possessing sensory apparatus and coupled to recording devices capable of registering past sensory data and machine configurations.  We can further suppose that the machine is so constructed that its present actions shall be determined not only by its present sensory data, but by the contents of its memory as well.  Such a machine will then be capable of performing a sequence of observations (measurements), and furthermore of deciding upon its future experiments on the basis of past results.  If we consider that current sensory data, as well as machine configuration, is immediately recorded in the memory, then the actions of the machine at a given instant can be regarded as a function of the memory contents only, and all relevant experience of the machine is contained in the memory.

    For such machines we are justified in using such phrases as 'the machine has perceived A' or 'the machine is aware of A' if the occurrence of A is represented in the memory, since the future behavior of the machine will be based upon the occurrence of A.  In fact, all of the customary language of subjective experience is quite applicable lo such machines, and forms the most natural and useful mode of expression when dealing with their behavior, as is well known to individuals who work with complex automata."

    vongehr
    I'm puzzled at your apparent "need" to determine, experimentally, whether a Boltzmann Brain (BB) is an "observer", or not.
    My desire to know whether there are such situations observed is no different and even the logical conclusion of what any physicist desires, namely to know what is physically possible.  Why do you want to work on theories that predict and thus constrain the possible?  Whether the BB is an observer - well I am not sure I asked that question rather than whether there are any BB in a unified theory.  I doubt it - call me religious and optimistic or hopeful.
    Can you even, experimentally, determine whether I am an observer?
    You are an observer, that does not need any experiment.  I define you as a me with different memory contents, and if I am an observer, so are you.
    Halliday
    Sascha:

    You stated:

    You are an observer, that does not need any experiment.  I define you as a me with different memory contents, and if I am an observer, so are you.

    This is an all too typical philosophy answer, and may be all too often acceptable to philosophers, but it is a decidedly poor scientific "answer".  In other word, it is not a truly scientific answer.  ;)

    David

    vongehr
    Science starts with good terminology or you will ask pseudo questions that have no answer.  Whether XYZ is an observer does need a definition of "observer" first of all, only then can we go out and measure.
    Halliday
    Sascha:

    It is quite true that "good" terminology and definitions are important.  However, it is also true that good science requires that terminology and definitions need to be subservient to the needs of the science:  In other words, we may, at any time, need to modify terminology and definitions to better serve the changes in scientific understanding garnered by increasing experimental observation.

    Simply defining a "thing" as some, potentially, "other thing" is not scientific.  That was what I was calling you on.  (Philosophers do it "all the time", it seems, but science cannot get away with such.)

    You are correct that there needs to be a good definition of "observer"—along with the characteristic of such—before one can, within some level of certainty, determine whether "XYZ" fits such.  Unfortunately, defining an "observer" to be something like yourself, as you did, doesn't quite "cut it", scientifically.

    Even worse, is to assume (or "define") that I am "as a [you] with different memory contents".  This diverges even further from a fully scientific approach.

    Now, one can usefully define an "observer" as the "models for observers" Hugh Everett, the 3rd, used.  However, even then you will not be able to unequivocally determine that I fit that model.  You will, however, be able to experimentally determine that I appear to fit that model, to the best measure of your experimental procedure(s), and I would tend to agree with that assessment.

    This latter approach, with its admissions of uncertainty, is far more fully scientific than your "defin[ing] [me] as a [you] with different memory contents, and if [you are] an observer, so [am I]."  (Emphasis added, of course.)  Especially when you claim that such "does not need any experiment."  (That was, arguably, the most scientifically damning part of your original statement.)

    I'm just trying to steer clear of unscientifically grounded "philosophy".  We are, after all, supposedly trying to talk about science.

    David

    P.S.  Even with what may, at least at first, appear to be "good terminology" anyone may still "ask pseudo questions that have no answer."

    While Mathematics and Philosophy begin from definitions and axioms/premises, and proceed to determine statements that are either "true" or "false" (or "indeterminable" [as in "no answer"]) therefrom (using logic alone); Science is a rather different "animal", since it must also determine whether the definitions and axioms/premises fit experimental observation!  (Furthermore, science has the ability to ask and attempt to answer even the "indeterminable"/"no answer" questions via experimental observation.)

    vongehr
    You will, however, be able to experimentally determine that I appear to fit that model, to the best measure of your experimental procedure(s),
    What more could possibly be achieved?
    Especially when you claim that such "does not need any experiment."  (That was, arguably, the most scientifically damning part of your original statement.)
    Experiment can tell you in what particular cosmos you happen to reside, but if it comes to the fundamental origin of all possible experimental outcomes in all universes, ... well think about it! You seem to confuse empirical science with science and seem to be unaware of the limitations of empirical science. Empirical science cannot be trusted as the ultimate foundation, because it can lead to quantum theory, which itself allows all kinds of freakbranches as far as we know, even those that would support classical physics! What you desire is a certain naive scientific doctrine, namely that you can stay inside empirical science and find out about distinctions that actually make no difference (word games gone wrong). There is no description that could possibly find out that you are not an "observer" in any meaningful way of "observer", and thus these are not empirical facts, but "apriori", given by our act of describing (~ language).