Friday, August 23, 2019

How do black holes destroy information and why is that a problem?

Today I want to pick up a question that many of you asked, which is how do black holes destroy information and why is that a problem?

I will not explain here what a black hole is or how we that know black holes exist, for this you can watch my earlier video. Let me instead get right to black hole information loss. To understand the problem, you first need to know the mathematics that we use for our theories in physics. These theories all have two ingredients.

First, there is something called the “state” of the system, that’s a complete description of whatever you want to make a prediction for. In a classical theory, that’s one which is not quantized, the state would be, for example, the positions and velocities of particles. To describe the state in a quantum theory, you would instead take the wave-functions.

The second ingredient to the current theories is a dynamical law, which is also often called an “evolution equation”. This has nothing to do with Darwinian evolution. Evolution here just means this is an equation which tells you how the state changes from one moment of time to the next. So, if I give you a state at any one time, you can use the evolution equation to compute the state at any other time.

The important thing is that all evolution equations that we know of are time-reversible. This means it never happens that two states that differ at an initial time will become identical states at a later time. If that was so, then at the later time, you wouldn’t know where you started from and that would not be reversible.

A confusion that I frequently encounter is that between time-reversibility and time-reversal invariance. These are not the same. Time reversible just means you can run a process backwards. Time reversal invariance on the other hand means, it will look the same if you run it backwards. In the following, I am talking about time-reversibility, not time-reversal invariance.

Now, all fundamental evolution equations in physics are time-reversible. But this time-reversibility is in many cases entirely theoretical because of entropy increase. If the entropy of a system increases, this means that it if you wanted to reverse the time-evolution you would have to arrange the initial state very, very precisely, more precisely than is humanly possible. Therefore, many processes which are time-reversible in principle are for all practical purposes irreversible.

Think of mixing dough. You’ll never be able to unmix it in practice. But if only you could arrange precisely enough the position of each single atom, you could very well unmix the dough. The same goes for burning a piece of paper. Irreversible in practice. But in principle, if you only knew precisely enough the details of the smoke and the ashes, you could reverse it.

The evolution equation of quantum mechanics is called the Schroedinger equation and it is just as time-reversible as the evolution equation of classical physics. Quantum mechanics, however, has an additional equation which describes the measurement process, and this equation is not time-reversible. The reason it’s not time-reversible is that you can have different states that, when measured, give you the same measurement outcome. So, if you only know the outcome of the measurement, you cannot tell what was the original state.

Let us come to black holes then. The defining property of a black hole is the horizon, which is a one-way surface. You can only get in, but never get out of a black hole. The horizon does not have substance, it’s really just the name for a location in space. Other than that it’s vacuum.

But quantum theory tells us that vacuum is not nothing. It is full of particle-antiparticle pairs that are constantly created and destroyed. And in general relativity, the notion of a particle itself depends on the observer, much like the passage of time does. For this reason, what looks like vacuum close by the horizon does not look like vacuum far away from the horizon. Which is just another way of saying that black holes emit radiation.

This effect was first derived by Stephen Hawking in the 1970s and the radiation is therefore called Hawking radiation. It’s really important to keep in mind that you get this result by using just the normal quantum theory of matter in the curved space-time of a black hole. You do not need a theory of quantum gravity to derive that black holes radiate.

For our purposes, the relevant property of the radiation is that it is completely thermal. It is entirely determined by the total mass, charge, and spin of the black hole. Besides that, it’s random.

Now, what happens when the black hole radiates is that it loses mass and shrinks. It shrinks until it’s entirely gone and the radiation is the only thing that is left. But if you only have the radiation, then all you know is the mass, change, and spin of the black hole. You have no idea what formed the black hole originally or what fell in later. Therefore, black hole evaporation is irreversible because many different initial states will result in the same final state. And this is before you have even made a measurement on the radiation.

Such an irreversible process does not fit together with any of the known evolution laws – and that’s the problem. If you combine gravity with quantum theory, it seems, you get a result that’s inconsistent with quantum theory.

As you have probably noticed, I didn’t say anything about information. That’s because really the reference to information in “black hole information loss” is entirely unnecessary and just causes confusion. The problem of black hole “information loss” really has nothing to do with just exactly what you mean by information. It’s just a term that loosely speaking says you can’t tell from the final state what was the exact initial state.

There have been many, many attempts to solve this problem. Literally thousands of papers have been written about this. I will tell you about the most promising solutions some other time, so stay tuned.


  1. Surprised no one has asked this before, but how come it's not an issue that measurement of a quantum state, which is part of a physical theory, is time-irreversible?

    1. Correct, probably if we understand the "collapse" of a wave function better there is no really any paradox. However, the believe is that BHs are quantum mechanical objects and hence everything interacting with them evolves unitary.

    2. BH is a macroscopic object, how could that be a quantum mechanical objects evolving unitary? it's not possible like in any measurement, where quantum objects interact with macroscopic objects, that's irreversible processes or that does not evolve unitary.

  2. Beautifully explained as per usual

    1. I thought that,and getting rid of the idea of information also helped to clarify the issue for me, at least. The basic problem is that the process is time-irreversible.

      However, Sabine, isn't the real problem with the idea of the collapse of the wave function - isn't that time irreversible - you don't really need a black hole to see irreversibility.

      Could it be that the universe simple is irreversible?

  3. I have just seen in google that the phrases "Jeder macht's wie er's versteht" and "cada maestrillo tiene su librillo" are both equivalent to "there is more than one way to skin a cat". But in the spanish phrase, instead of skinning a cat we talk about writting a book. In my case, I have written a book (which I have just called "Quantum") showing a quite different view on all this issue regarding black holes and the information lost.
    It is quite a coincidence that in my brief talk to Mr. t'Hooft, many months ago, I tried to tell him that: QM, by means of dynamical models, would not require unitary evolution (avoiding not only the measurement problem, but also) preventing us from getting lost in this paradox that relates black holes and information lost.

    1. Antonia, do you have any other publications on this topic, than this book? I would like to learn more about the formulation of natural laws by the means of dynamical models in general, it seems to me a "hot topic".

  4. Part of black hole mass could be dark matter. How will dark matter radiate from the black hole?

    1. Black holes might be compared to being the ultimate equalizer. Anything that goes into a black hole just defines the mass, angular momentum and charge of the black hole. So photons emitted as Hawking radiation could just as well come from dark matter. Think of a black hole as a sort of elementary particle, and in fact Arkani-Hamed wrote a paper recently about this. A high mass elementary particle can decay into lots of constituents, and what comes out is only determined by conservation of quantum numbers. For black holes that is mass, charge and angular momentum.

      Now there is what might be called quantum hair associated with black holes. This is holographic information of stuff that went into a black hole as seen from the outside. Of course it is hard to "see" because everything is so red shifted. However, this quantum hair contains all these quantum numbers of stuff that went into the black hole. Where does that go? If we consider quantum information as conserved then in an open world perspective it ends up in a different form. It may be in signatures of gravitons.

      If one set a black hole in the middle of a dark matter cloud so the cloud slowly falls into the black hole one could say the final state black hole is largely made of dark matter. The Hawking radiation that comes out though will largely be photons.

      This question does have some relevancy to the question on just what is dark matter. I think the light supersymmetric particle phenomenology of the neutralino is looking suspect. The MOND idea has some creeping interest, for the log potential suggests this is from some sort of "edge effect" from a boundary of one dimension lower. Maybe these pocket worlds "pop off" as complete manifolds and the boundary fields remain as this strange field we call DM. These may indeed enter black holes.

      With this so called crisis in physics everything is really far more interesting. We can think anew.

    2. Lawrence. Thanks for the detailed response. Since information is unobtainable inside the event horizon we do not know if DM and normal matter have the same outcome. However, if there is just a singularity at the center as is generally believed, then you must be correct and normal and dark matter would be "equalized" and my question of how DM is radiated is irrelevant.

      Dr Hosenfelder once suggested the idea that DM undergoes a phase change near concentrations of normal matter. That may better explain some of MOND theory's strengths. Would that even be germaine to a discussion of black holes? Would it mean DM would form "clouds" as you suggest and slow down DM entry into black holes?

      I do not know of any evidence for supersymmetric particles. This crisis in physics is fun.

    3. First off the singularity in a black hole is not really a point in the usual sense. For the non-rotating charged neutral Schwarzschild metric the singularity is an entire 3 dimensional spacelike region. To an observer this region is in their future development where the Weyl curvature diverges. For a Kerr metric for a rotating black hole, or the Reissnor-Nordstrom metric for a charged black hole, things get a bit odd. There are two event horizons determined as r_± = m ± √(m^2 - Q^2), where Q is the charge or angular momentum parameter. Clearly m > Q in general and for m = Q this is an extremal black hole and r_+ = r_-. The region between these two horizons for the extremal case is discontinuously projected into AdS_2×S^2. For the an observer falling into the nonextremal black hole the outer r_+ horizon provides no “bump,” and she proceeds onto r_-. This inner horizon is a Cauchy horizon with a pile up of null rays. This will have a “bump” and some call this a mass inflation singularity, that is a null region.

      Those null rays that pile up may however be red shifted so this bump is not too bad. Our intrepid observer would proceed into an inner region where things get really odd. In this region there is a ring singularity for the Kerr metric. Geodesics wind around the ring, largely in the plane of the ring, and a subset of these geodesics are closed timelike curves. This set exists in what is called the inner ergosphere. Now what is odd is that spacetime can be thought of as the time development or foliation of spatial 3-dim regions. However, if you have a spatial region with what is called Cauchy data on it and this evolves back onto itself there can be an ambiguity as to what constitutes Cauchy data. In effect there is no general system of diffeomorphisms for this spacetime. This inner spacetime shares features similar to the 4-manifolds of Donaldson, Freed and Uhlenbeck that are homeomorphic but not diffeomorphic. These are exotic 4-dim spaces. Donaldson won the Fields Medal and I think Karen Uhlenbeck won the Abel Prize last year. At any rate if you should find yourself here I think the words of Shakespeare's witches in Macbeth put it best, “Bubble Bauble Boil and Trouble.” Space and time are twisted up in ways that no longer make intuitive sense and any observer here has really entered the Twilight Zone.

      On to DM, an idea intrigues me that with eternal inflation the occurrence of a pocket region is a local collapse of the vacuum, or better put a tunneling from false vacuum to physical vacuum, that leads to reheating. The inflationary FLRW or de Sitter 4-dim spacetime becomes like Swiss cheese with pocket regions, and the boundary of these pocket regions have boundary states of some sort. Now, consider the prospect these Swiss cheese bubbles pinch off and become spatial manifolds detached from the inflationary spacetime. These boundary fields contain quantum numbers or degrees of freedom that are conserved, and one possibility is that gravity in 2-space plus 1-time, or BTZ relativity, will have this logarithmic potential for weak fields. It is a standard exercise to get students to compute this using Gauss' law. There may then be these edge states on pocket boundaries from the inflationary period persist in one dimension larger. This would have some MOND-like features. How this might connect with elementary particles or physics such as supersymmetry I have no idea.

    4. Lawrence Crowell: if a black hole can be completely characterized by its mass (not quantized?), spin, and electric charge (both quantized), how do these change as it emits Hawking radiation (and "evaporates")?

      I can imagine that the spin somehow ends up in the photons, but not the electric charge.

      Also, if a black hole has maximal spin, does it develop "over-max" spin as it evaporates?

    5. Mass, charge and angular momentum are not short ranged. The mass and angular momentum is associated with gravitation that is long range. The electric charge is long range with the Coulomb force law. Other forces such as the nuclear force are short ranged and have no long range influence. This is because the intermediate boson has mass and decays. In the case of the weak nuclear force the W and Z gauge bosons have mass. For classic nuclear force the mesons also have mass. Things get more subtle with the underlying QCD physics that underlie nuclear physics, but confinement and other things render it short ranged.

      There is quantum hair on black holes and while the quantum numbers for these short ranged forces is violated, I think quantum information is conserved. Much of physics is about transforming and combining degrees of freedom. I think these quantum numbers survive as quantum information entangled in spacetime.

      A black hole with net angular momentum emits photons with a preferred spin or helicity state. Black holes emit radiation in a way that prevent them from reaching an extremal state or beyond extremal where they would be naked signularities.

    6. @Lawrence
      This inner spacetime shares features similar to the 4-manifolds of Donaldson, Freed and Uhlenbeck that are homeomorphic but not diffeomorphic. These are exotic 4-dim spaces.
      That sounds interesting. I have read some literature on exotic 4-manifolds (unfortunately this is the topic I least understand) but I have never come across any connection between these manifolds and the interior of black holes. Are there any references you can give or can you further elaborate on what you mean by "shares features similar"?

    7. The Kerr/Reissnor-Nordstrom metric seems an apt enough description of Hades, from Bob’s Arnowitt-Deser-Misner perspective anyway. However FYI, our intrepid fallee to inner circle surrounding that renowned spot carries with her her own malleable-to-less-odd perspective for her fateful confrontation with well charged eternality that be there. Whence after-all frame-dragging’s drag? Except to perfectly balance to that spinning fiery maw (to too resolve puppy’s quandary as sure as dinosaurs are dead), as -- having spat out all else -- it takes its delicate cotton candy morsels swirled all around. Which it thusly makes only of certain small pieces folded altogether in certain large measure, albeit yet quite a bit smaller than Alice, which alas is a problem for her indeed, but surely not for the dragon -- nor for Bob for that matter.

  5. I had never heard the "information loss" problem described without needing a reference to "destroying information". So it is really all about violation of time-reversal.

    What if the time-reversibility of the evolution equation is the thing that is wrong? I've always found the entropy explanation as to why time moves in one direction to be unsatisfying. Perhaps we need a new evolution equation that is not time-reversible.

    1. “So it is really all about violation of time-reversal.”
      Yes, mentioning information only caused a lot of confusion. Thanks to Sabine for stating this so clearly.
      And whether or not the evolution is deterministic is also a separate issue.

    2. But time-reversibility entails complete determinism, right? The measurement postulate appears as a patch designed to inject indeterminism into a completely deterministic framework. Something important is missing.

    3. The converse “determinism entails time-reversibility” is for sure not true, see figure 9 and 10 here.
      The quantum version of a time-reversible, deterministic law is unitarity, see here.

      Information (Shannon entropy) is a relational aspect between two systems (sender and receiver or two QM systems, getting entangled and being measured, exchanging energy/momentum) and its definition needs a certain bit of uncertainty, i.e. probability and randomness. (*)

      There is deterministic randomness. e.g. the digits of pi are pseudo random. They are entirely deterministic, since they are computable, but normal - pick two of them and they are statistical independent.

      Why do I mention pseudo randomness? Well, it leaves the possibility open that our world behaves like QM including measurements that involve (pseudo) randomness, but at a deeper level it is deterministic.
      (here a bit more technical)

      (*) Also the notion of cause and effect would be pretty meaningless in an entirely deterministic universe. (Note that no agency in the sense of free-will is needed, but only a bit of randomness [pseudo randomness would be enough]).

    4. Reimond,

      Thanks for the links!

  6. Bee wrote:
    Quantum mechanics, however, has an additional equation which describes the measurement process, and this equation is not time-reversible. The reason it’s not time-reversible is that you can have different states that, when measured, give you the same measurement outcome. So, if you only know the outcome of the measurement, you cannot tell what was the original state.


    Now, what happens when the black hole radiates is that it loses mass and shrinks. It shrinks until it’s entirely gone and the radiation is the only thing that is left. But if you only have the radiation, then all you know is the mass, change, and spin of the black hole. You have no idea what formed the black hole originally or what fell in later.

    That suggests from simple AI-type logic that "falling into a black hole constitutes a quantum measurement process". Why is that wrong?

    1. The problem is to write down a theory for that.

    2. How do classical no-hair theorems work? Somehow as material passes the blackhole horizon, the blackhole sheds classical information.

    3. This is the Penrose Interpretation: large gravitational (spacetime) differences between superposed states collapse the system just like a measurement.

  7. "the reference to information in 'black hole information loss' is entirely unnecessary and just causes confusion. The problem of black hole 'information loss' really has nothing to do with just exactly what you mean by information. It’s just a term that loosely speaking says you can’t tell from the final state what was the exact initial state."

    "Information" (the term) carries no information.

    (Maybe some physicists should advocate banning the term "information" from physics entirely.)

  8. One of those central equations in physics is the von Neumann-Shannon-Khinchin formula for the entropy of a quantum system S = - tr(ρ logρ). This is as important as F = ma or E = mc^2. This is easy to compute for a system with density matrix diagonal entries ρ_n = 1/N, with N the number of states or equivalently N^2 the size of the matrix. The trace is essentially a summation and this gives

    S = -sum_n=1^N 1/N log(1/N) = sum_n=1^N 1/N log(N) = log(N).

    This is Boltzmann's result, where N is the size of the system.

    What occurs with Hawking radiation is the density matrix evolves ρ → ρ' so that tr(ρ'^2) < tr(ρ^2). This is not a unitary process, for if ρ' = U^†ρU then we would have ρ'^2 = U^†ρUU^†ρU, and since UU^† = 1 then tr(ρ'^2) = tr(ρ^2). So something is amiss. It also impacts quantum information for the entropy is under an expansion

    S = -tr(ρ logρ) = -tr(ρ[ρ - 1 - ½(ρ - 1)^2 + …]),

    and the evolution of entropy has the square of the density matrix. Remember that the diagonal elements of the density matrix are less than one, which means the logρ_n = - log(1/ρ_n), as seen above in the ρ_n = 1/N case above, and this means entropy does increase.

    Black holes have entropy S = kA/4ℓ_p^2, A = 16πm^2, k = Boltzmann constant and ℓ_p the Planck length, so if the black hole radiates quanta of radiation the black hole horizon area shrinks. The entropy of the black hole decreases. However, the Hawking radiation is uncorrelated and total entropy of the black hole plus radiation has increased. This means either information, entropy as a measure of information, has been destroyed or in some way scrambled so it is inaccessible. I choose the latter interpretation.

    We tend to treat black holes as closed systems, and we may be running into trouble. Further, the semiclassical approach assumes the metric adjusts with the emission of a quanta of radiation in a back reaction. Yet if we throw a pebble into a black hole there is some small amount of gravitational radiation emitted. If a black hole emits a quanta of Hawking radiation we should then expect gravitons to be emitted as well. These gravitons are entangled with the Hawking radiation. However, gravitons are extremely weakly interacting, and so we miss them. They are silent, should we say silent like the p in swimming. There are then BMS symmetries carried off to I^+. So then in principle quantum information is conserved, but we have a very difficult time knowing about it. If a tiny black hole were to enter its final evaporation near us it should make the LIGO and Virgo interferometers ring.

    It is not likely this will happen. There do not seem to be a lot of quantum black holes out there, and the idea of dark matter as tiny primordial black holes has suffered observational set backs. We may have to rely upon analogues. Some analogues involve light trapping materials or a reference beam that serves as a “flow of space” that can model curvature. Some data with such experiments have come forth indicating Hawking-like radiation. This Hawking analogue may then be entangled with diphotons, which act “like gravitons” and are a feature of Hanbury Brown-Twiss effect in quantum optics. For a solid state material there may also be some entanglement of phonons. We can think of a graviton as a color neural entanglement or bound state of two YM gauge bosons or gluons. Our analogue would then be photons or optical phonons in strange entangled states and entangled with the Hawking-like radiation.

    Completely uncorrelated quantum states are really rather the exception to the rule. Einstein realized this with his coefficients for the emission of photons. Hawking radiation should generally appears as black body photons that are completely uncorrelated, but it is entirely possible there are underlying correlations or entanglements with spacetime we are not considering theoretically, and would be virtually impossible to measure experimentally. We will have to rely on black hole analogues. We may then find Doug Adam's Deep Thought result of 42 persists.

    1. This "Hawking analogue" would follow all the equations of general relativity but would not be connected with gravity. There are soloton in nanoplasmonics called dark mode solitons that may serve. These are generated in the contact points between metal microparticle. We might find a fully relativity compliant "Hawking analogue" in the spaces between these microparticles.

    2. I did not mention this, but I and a coauthor have a paper in review that works with quantum hair. We have it tentatively accepted with some revisions needed by the reviewers. It is a pain, but I will get through it. Of course at the same time I have three dogs who the last two days have been really sick with some analogue of the flu.

      A Hawking particle emitted by a black hole forces a change in the metric. The back-reaction approach is a sort of fix done by hand. In greater generality this back reaction should be a dynamical response that produces gravitational radiation. The converse should also be the case; if you throw a pebble into a black hole there should be gravitational radiation produced in response. Of course the ultimate case of this occurs with the coalescence of black holes. Using the hyperbolic dynamics of the late Miryam Mirzakhani, that connects with the Ryu-Takayanagi formula, quantum hair on the event horizons of two black holes extremely close to merging are highly excited and this generates gravitational waves. A video simulation of black hole coalescence here ( ), video at top right, shows this in part with the region between spiking up. In some ways it is the converse of Hawking radiation, where one might think of a quantum black hole as quantum transitioning to two quantum black holes. This quantum hair should be correlated with gravitons, which may be found as BMS translations. The spacebased interferometer eLISA should be able to detect this.

      Analogues are useful in that they may illustrate some universality of this sort of physics. So we may in the future by various means be able to put together forms of data that give at least some confidence level in Hawking radiation, and maybe how information is conserved or then again maybe not. If we are fortunate to not have budget killing axes or other problems then by mid-century we might have some experimental understanding of these things.

  9. For clarification, what is the equation you refer to as "the measurement equation"?

    1. The measurement postulate. Wave-function collapse.

  10. Hi Sabine - little typo : "started form" should be "started from"

  11. Typo: "wouldn't know where you started form" form=from.
    Typo: "if you only know precisely enough" know=knew.

  12. Dr. Hossenfelder:

    It seems to me the issue is not in the randomness of the radiation; but in the irreversible nature of crossing the event horizon. In other words, the "information" is lost when that occurs, at least to those outside the event horizon, the particle that fell in an no longer be measured.

    But I seem to recall reading that those virtual particles are produced in pairs, and become "real" (and do not annihilate each other) because one crosses the event horizon and the other does not.

    Is that true? Because if that is the case, then all the information about the particle that fell in is represented by its anti-twin that did not; so no information has been "lost". Each particle of radiation is a record of what fell in.

    Is the result of matter meeting anti-matter irreversible? Can we in theory know everything about the two particles that annihilated each other?

  13. It seems to me that the quantum mechanism of superposition is incompatible and contradicts the “evolution equation”. Superposition introduces an uncertainty in the way a process evolves. When a process is in a state of superposition, that process cannot be constrained to follow a predictable path to a resolution.

    The situation where a particle must take every possible path between two points, but when you check which path it took, it appears that it only took one of them. But the particle has taken all those paths and the observe path is an illusion.

    1. This actually makes the most sense to me (in terms of this "problem").

  14. Why could different evolving beginning situations in principle (by co-incidence) not lead to exactlty the same outcome?

    1. Because that wouldn't be time-reversible and the dynamical laws we currently have are time-reversible.

    2. mmm... meaning that if we turn back the movie of time a little bit, we follow the accepted formula, meaning there is only one solultion for the situation a bit earlier, and so back and forth.

      But what if there are two possible formula's giving the same result, but if we reverse the time lead to a different beginning situation? We don't have that second formula, but I wonder whether it is in principle possible?

    3. If you postulate reversibility as a necessary condition, does that imply that if we accept 'splitting realty into multiverses' during quantum-processes, we should also accept the possibility of merging of different universes into a combined universe during quantum processes?

    4. Perhaps I misunderstand quantum mechanics, but wave function "collapse" is just the wave function changing shape and becoming very, very spiky. The reverse, the wave function (spiky) becoming very wavy happens all the time because of the Schrodinger equation, it tends to do that.

      So all you have to do in practice is "not observe" a previously observed particle (say an electron). Let it be...

      By the way, this also implies that we are in fact constantly living in a combined, merged universe.

  15. Sabine,
    While basic QM formalism "closes eyes" during measurement, is it really sufficient to conclude fundamental lack of time-reversibility?
    Let's look at idealization of measurement: Stern-Gerlach experiment. To reduce energy (by avoiding precession) spin tilts to parallel or anti-parallel alignment.
    But this is not the end of the picture, e.g. this transition releases some tiny energy: most likely as some EM radiation - the difficulty of time-reversal is exactly reversing this energy release or other accompanying effects.
    It is analogous to atom deexcitation - which can be reversed by just providing required energy in photon to be absorbed.

    Also I disagree with black holes being just a few numbers - they have also an unimaginable number of hidden microscopic degrees of freedom, which are practically noise - storing a lot of information.

  16. We are only interested in the art of living: which is a mind without measure. Being judgmental is measurement just as being prejudiced or biased is also measurement. Anyway, comming back to Physics and Mathematics, we can argue as follows:

    Looking at fractions differently, let us consider the fraction 1/1. Here, we are asking what is 1 with reference to 1? It is one and the same thing. Let the numerator be a thing, and let the denominator be the reference or the frame of reference. Now, what is 1 with reference to 2? 1 is halved, or 1 looks like it has grown smaller in magnitude when we enlarge the frame of reference or alter the frame of reference, which is the denominator. Its numerical definition changes. Suppose we decrease the frame of reference to ½, then we have 1/half; in which case, 1 looks like it has grown to twice its original magnitude. If I further decrease the frame of reference to (one fourth), then we have 1/ (one fourth); in this case, 1 will look like it has grown to 4 times its original magnitude. Let us call this process: “defining” the magnitude of a thing “1”. We keep on repeating this process until the frame of reference i.e., the denominator approaches 0. When this happens, the frame of reference, the denominator, becomes 0; but now what is “1”? “The undefined”, isn’t it? The frame of reference has vanished that is akin to removing the observer, and I can’t numerically define the thing “1” anymore; in other words, if the denominator is the observer, then obviously the numerator is the observed. This means that in the absence of the observer, the observed is undefined. There is no observer; there is no observed; there is only “one whole thing”, “the undefined”.
    Conversely, if I keep increasing the frame of reference, the denominator, the numerical definition of the thing “1” changes or decreases. When the frame of reference becomes infinitely large, then definition of the thing “1” becomes insignificant; it loses its individuality, its separateness. Consequently, there can be no comparison between the numerator and the denominator, between the insignificant and the frame of reference that means measurement stops. The thing “1” merges into infinity and becomes “one whole thing”. In contrast to the above case in the first paragraph, the observed, which is the numerator, has disappeared or has become insignificant; and, there is now only “on whole thing”, infinity, the denominator. Because measurement stops, there is no observer; and because, there is no observer, 1/(infinity) = 0.
    Comparison requires at least two things, and there can be no measurement without comparison. Measurement is when there is a separation as the observer and the observed. When the observer ceases to exist or when the observed disappears, either gradually or instantly, the ultimate result is “one whole thing” or “the undefined”; in such a case, isn’t 1/0=1/infinity? Zero may also mean the point where measurement stops, or the point where measurement breaks down.

    1. Gokul,

      I will not publish your other comments because they are as off-topic as this one. The topic here is black hole information loss. Please read the comment rules before commenting, thanks.

  17. Sabine,

    't Hooft claims to have solved the information paradox by applying QM's rules to the black hole. See for example this paper:

    The Quantum Black Hole as a Hydrogen Atom: Microstates Without Strings Attached

    From the abstract:

    "Three pieces of insight are obtained: One, we learn how the gravitational back reaction, whose dominant component can be calculated exactly, turns particles entering the hole, into particles leaving it, by exchanging the momentum- and position operators; two, we find out how this effect removes firewalls, both on the future and the past event horizon, and three, we discover that the presence of region II in the Penrose diagram forces a topological twist in the background metric, culminating in antipodal identification."

    What do you think?

    1. Nobody seems to have cited 't Hooft's paper, so either (a) nobody understood it or (b) nobody believed it or (c) nobody noticed it. I suspect (a).

    2. Peter Shor,

      It is puzzling for me that what 't Hooft publishes is almost completely ignored. It is unlikely that all those string theorists cannot understand his paper. And if the paper is wrong someone could have published a small rebuttal.

      I guess Sabine should understand it, or if not, she could ask 't Hooft to clarify it. I am sure he would be more than happy to help. If true, his papers would be highly significant.

    3. I don't see how you're justified in criticizing 't people for not understanding 't Hooft's paper. Do you understand it? For some of 't Hooft's recent papers (I haven't read looked at this one) it is very difficult to figure out what he is saying.

    4. I (a) noticed 't Hooft's papers (b) read them and (c) talked to him about it. There's nothing obviously wrong with his idea. However, as I have said many times before, it is pretty clear that this problem isn't solvable by requiring mathematical consistency alone, as we already know several consistent solutions. For this reason I am not terribly excited about it.

      As to people not understanding what he is saying, 't Hooft was one of the people on my mind when I wrote this recent blogpost.

  18. Hawking radiation and black hole evaporation have never been observed and are likely fiction.

    1. This statement does not resolve the inconsistency.

    2. It does. Once you understand why Hawking radiation is pseudoscience, you understand why the information paradox is a wild goose chase and a total waste of time. Sadly hardly anybody has actually read any of Hawking's papers, such as or or , so they don't know how dire they are.

    3. Black Holes are non return Valves.But the exemption is only for radiation.That is all we knew so for. Rest of the things explains by Scientists are only theories on assumptions Exactly what is happening inside the BH will be a permanent misery because of no ways of knowing that.
      V.Vijayaraghavan 8.25 am 25-8-2019

    4. John,

      I and everybody I know who has worked on the topic has read Hawking's original papers. They are in fact quite readable.

  19. I would add that particle pairs do not pop out of the "vacuum".
    Problem solved !

    If you consider Philip Thrift's comment on "information", then we have a complete non-problem.

    IMHO, of course

    1. You can't just throw out quantum field theory. It's an experimentally well-confirmed fact that virtual particles exist.

    2. Sabine,

      I remember a discussion here some time ago in which you were speculating that maybe HEP went wrong somewhere down the stack of theories.

      Isn't it at least possible that another theory would produce similar effects in calculations, but might behave differently in the extremely intense gravitational fields that would apply when a small black hole was expected to be generating Hawking radiation?

    3. You are falsely thinking that the gravitational field is strong near the horizon. It is not.

    4. Sabine

      I thought that the only chance of actually observing Hawking radiation would be to observe a micro-black hole, and that in that case the gravitational field would be strong at the horizon. I was aware that larger black holes have much weaker fields at their event horizon.

      I mean, my point is that like so many discussions in HEP, we are talking about a phenomenon that isn't likely to be observed - possibly ever.

  20. If there is information loss due to Hawking radiation, would that imply that there should be information loss in all physical processes due to the fact that in principle virtual black holes should make a contribution to any arbitrary process?

    1. Excellent point. Yes, that's a risk. In fact people have tried to find out just how large the effect is. (The brief answer is no one knows because we don't have a theory of quantum gravity.)

    2. Why should that be a risk? The Planck mass is so large that it seems quite plausible that the amount of information loss in any process we can observe experimentally would be tiny.

    3. Peter,

      Isn't the problem that unitarity is violated? And if unitarity is violated, then probabilities do not continue to add to one?

      Which just does not make any sense.

      Now, of course, there may well be some escape from this that no one has yet thought of. But that escape better go pretty deep conceptually to break the connection between unitarity and probabilities adding to one.

      Of course, the same problem occurs with the "collapse of the wave function." And, since the same problem occurs with both the measurement problem and with gravity, Penrose can suggest the two are related.

      I myself have no idea what the solution is, but I do think there is a big problem.

    4. PhysicistDave,

      Yes, unitarity is violated. But the reason is not that probabilities do not add to one, the reason is that the time-evolution is not reversible. A unitary transformation must have both properties.

    5. Sabine,

      Well, I suppose another way of saying it is that a pure state ends up as a mixed state. The problem is that this simply cannot happen from the Schrodinger equation alone.

      So, if there is "information loss," we necessarily go outside the normal framework of QM (or QFT).

      I do think it is a theorem that if unitarity is violated, then norms for some states are not preserved. But, I'll agree that this is probably a pointless way of putting it physically: if you go from a pure to a mixed state, the rules of QM are necessarily being broken and unitarity, etc. are all rather beside the point.

      Of course, I do not disagree with you that time reversibility is lost, unless there is a Planckian remnant that somehow supplies all the information needed to reconstruct the previous state when you run time backwards.

      And, of course, a Planckian remnant like that is a mess for other reasons.


    6. PhysicistDave,

      "I do think it is a theorem that if unitarity is violated, then norms for some states are not preserved."

      I very strongly doubt this. The measurement process is a non-unitary transformation that does preserve probability. The reason it's not unitary is that it's not a linear transformation. The reason black hole evaporation is not unitary is that it's not reversible. If it was merely the norm that wouldn't work, it would be easy enough to fix that.

    7. Sabine,

      You wrote:
      >"The measurement process is a non-unitary transformation that does preserve probability. The reason it's not unitary is that it's not a linear transformation."

      Well... I think the issue is that the measurement process changes a pure state into a mixed state: it therefore cannot be described by Schrodinger's equation.

      Similarly, the Hawking process, as usually understood, changes a pure state into a mixed state and therefore also cannot be described by Schrodinger's equation.

      Of course, as normally understood, the Hawking process is indeed not reversible. And neither is the measurement process.

      After all, Schrodinger's equation is what normally allows time reversibility. Abandon Schrodinger's equation -- as is the case for the normal measurement process and the normal understanding of Hawking radiation -- and, yes, you are going to lose time reversibility.

      So, I'll grant you that the breakdown of unitarity, while true, is a bit of a red herring. But it seems to me that the real problem is that when you go from a pure to a mixed state, which necessarily means you are giving up on Schrodinger's equation at that point, then, as a consequence, you lose time reversibility.

      I think each individual fact I have pointed out is pretty clearly true. How I'm stringing them together and my claim that going from a pure to a mixed state is the key issue (thereby implying that one has abandoned Schrodinger's equation), well, I don't see any error in reasoning, but it is surely debatable!

      Any errors you can point to in my reasoning? I certainly do not claim to understand either the measurement process or Hawking radiation, so I do not doubt I am missing something.


    8. Dave,

      It's not the measurement process that changes a pure state into a mixed state. It's integrating out part of the system that does. The difference between black holes and quantum measurement is that with black holes that integrating out is supposedly fundamental because the inside information is destroyed in the singularity.

      In any case, I am merely saying that the origin of the two problems (information loss/measurement) is entirely different.

    9. Sabine,

      You wrote:
      >"The difference between black holes and quantum measurement is that with black holes that integrating out is supposedly fundamental because the inside information is destroyed in the singularity."

      But, if the black hole eventually evaporates completely because of the Hawking radiation, then no mass is left to warp spacetime, you are just left with Minkowski spacetime, and therefore no singularity to destroy the information.

      Or, if a Planckian remnant is left that is stabilized by quantum effects, then presumably those quantum effects prevent a singularity.

      Indeed, my own memory, ever since the '70s, is that pretty much everyone has assumed that quantum effects prevent a singularity, one way or another.

      So, one way or another, no singularity to eat the information.

      Am I missing something? Or have I just restated the information-loss paradox in different terms?


    10. A measurement is a non-linear transformation that changes a pure, entangled state into one of its superposed pure, product states, e.g. in EPR |↑>|↓> + |↓>|↑> → |↑>|↓>. More exhaustive [ a|↑>|↓>⊗(...) + b|↓>|↑>⊗(....) ]⊗(.....) → |↑>|↓>⊗(...)’⊗(.....) with probability |a|² and where (...) is the state of let’s say Alice measurement device and (.....) is the rest of the universe, which again consists of myriads of products of tiny entangled states. The probability in the transition (...) → (...)’ reflects the information (Shannon entropy). (*)

      Further in EPR when Alice takes her result to Bob, they will see the non-local correlation. BTW everybody looking at Alice stored result e.g. scribbled on a sheet of paper will see the same result, because the storage is a macroscopic object, of course consisting of myriads of QM particles, but in a more or less stable configuration. That everybody sees the same result I would say contradicts Rovelli’s relational QM.

      In a double slit ∑(a_n + b_n) |n> → |n> with probability | a_n + b_n |² arriving at the n-th location the QM particles in the screen play the role of the measurement device i.e. |n>⊗(...). The non-locality here is that once the particle shows up at one location it will instantaneously not be at any other location, preserving the probability.

      Just to mention von Neumann’s density matrix. It comprises statistical and QM probabilities and further uses “squared” states |i>(i| (**). As elegant as it is, these are also the very disadvantages as Penrose points out here also referring to gravity. Thus, by just integrating out to get a mixed state (statistical probabilities) one might lose some important details.

      (*) The big question is: Is the measurement time-irreversible? Can the initial state of the measured particle be reconstructed from the state of the measurement devices and the rest of the universe?
      Did the initial condition at the very beginning of time determine what happens?
      Is QM randomness real randomness? Or maybe god plays dice, but also knows the random seed?
      (**) “(” is meant to be “<” - this is a blogger error that Lawrence already spotted. Maybe blogger also does not like the density matrix and von Neumann entropy ;-)

    11. The time evolution applied to quantum wave function (quantum state) is itself reversible, then the information bore by wave function is actually conserved under this condition. But, IMHO, we must not forget that wave function is just a mean to compute probabilities of random physical real events. At the very beginning quantum real processes are mainly random and then irreversible ruled by the uncertainty principle. Physical Uncertainty is physically linked to Physical Entropy and realization of a real random physical event provide information. The Compton wave length like the Planck length are the quantum physical limit of spatial resolution which is source of entropy in any interaction. For instance Planck length is the length in the famous Bekenstein BH entropy, based of the fact that Planck length is the quantum limit of spatial resolution of any physical process. More over, This quantum limit and associated irreversibility or loss of information lead to the gravitational field equation according to the physicist Erik Verlinde.

  21. Event horizon is just mathematical, not physical object. You can compute where it's located for Earth or Sun. It still has finite volume, even for such body.
    When Black Hole radiate, it would loose its mass. Why last seconds of this process have to be just radiate to the end? Maybe it stops when event horizon become smal, and there are finite and quite normal remanants of BH interior?

    1. Maybe.

      But there would be an awful lot of information tucked in to that little remnant!

      And what do the remnants look like? Are they essentially elementary particles with a finite number of quantum numbers? If so, where did the information go?

      Those are real questions, by the way, not rhetorical attacks on your suggestion.

      I and, I believe, many physicists take seriously this possibility. But it does raise as many questions as it solves.

      'Tis a puzzlement.

  22. How nature destroys information, and why that is not a problem:
    Take N vectors with the same dimension, sum them. From the resulting sum alone, you possibly can not know which vectors were involved in the operation. That is called information lost. Nature routinely destroys information by the simple fact of summing a set of vectors, or a set of scalars. What is problematic about information lost, you ask? Nothing. Why do physicists think it’s problematic? Because they have been told as students it’s problematic, but the problem doesn’t exist.

    1. The totality of information present in a physical state doesn't get destroyed. If nature did erase information and you could control that process, then you could lower the entropy of a closed system via a suitable Maxwell Demon method. You would be allowed to clear the memory of the Demon without having to pay any entropy cost.

  23. A link to a paper explaining why this is a non-problem. Paradox? Issue?

    At least, in this individuals perspective.

  24. Hi SABINE !!!

    I have a moment.,,,
    I hope your day is going well.

    - more important than that,
    _-_--wait a minute...

    There's Nothing more
    important than that.

    Read your be posts.

    Thank You.

    Love Your Work. To

  25. Is it possible for the cosmological constant to go to zero the black hole event horizon and inside black hole to be an anti-deSitter space ?

    1. No, because the cosmological constant is constant.

  26. Regarding singularities: we speak of energy scales that decrease as length scales increase (or vice-versa). We know the quantum-mechanical relationship between a length scale and an energy scale. We can state that a particle with a given rest energy can't be confined to a region of space whose diameter is significantly less than a certain value, found by a common relationship given by the uncertainty principle. Think in terms of an energy scale on the order of the energy equivalent of a black hole mass. As long as that energy scale is finite we have a finite length scale, implying that no singularity can exist in any black hole with finite mass. This seems too obvious. What have I missed or misinterpreted?

    1. Maybe I've left out too many steps. I am trying to apply a fundamental QM feature (Heisenberg relations) to a hypothetical compact mass within a black hole. I treat it like any other massive particle. What is the meaning of that finite length scale? You should think of that compact object as "smeared out" within a finite volume, so that, for all practical purposes, in terms of what can be known or measured, it makes no sense to speak of a singularity. It also makes no sense to think of any infinite distortions in spacetime-- QM at best gives you a tiny region of probabilities for the location of that hypothetical singularity, which remains hypothetical. How you would do GR in that environment is not at all clear to me.

    2. Rick,

      Naively, the potential energy becomes so negative when the gravitational radius gets small enough that it can overcome the kinetic energy. (Everyone -- note that I said "naively": I know there is not literally potential energy in GR. But if you work it out naively as I said, you get the right order of magnitude.)

      So... let's not be naive. Let's do it right. But then you need a quantum theory of gravity. And, we do not have one yet.

      I hope it's clear that I am not attacking what you said but just indicating that working out in detail what you suggest is harder than it sounds and no one yet knows how to do it. I think you're pointing at some of the right questions, but we do not knows how to get definitive answers to those questions.

      Sabine, can you perhaps make the point more clearly than my funbling attempt here?

    3. PhysicistDave, I appreciate your reply. Yes, I am making things overly simple and ignoring a lot that might be relevant, but my rationale is that even when we have that long-awaited and much anticipated Quantum Gravity, bedrock principles of QM will remain. So in the absence of that theory, I just wanted to try to make an argument from fundamental principles. In this case, I'm ignoring GR, thinking that no matter how distorted spacetime is, as long as we are not in the realm of infinite curvature, whatever that would actually mean, QM is still valid. And we can apply QM considerations to any mass, any object, even whatever might lurk in the heart of a blackhole. It could be a matter of dimension. An object with the size and mass of a star is not ordinarily a quantum object, but if you let it collapse until it forms an event horizon, and it shrinks down to the size of an elementary particle, why not regard it as a quantum object and treat it accordingly? But, I admit, that is probably naive. And certainly it would be much better to have Quantum Gravity-- and I hope that does not turn out to be pie in the sky!

    4. Rick,

      One of the reasons I replied to your comment is that a few weeks ago I scribbled down a trial calculation on a notepad to try to work out what you suggested.

      Great minds think alike.

      What I found out is that it is not obvious (at least to me) that the idea is absurd. But, I was not able to work it out quantitatively.

      I suspect Sabine has thought this out more carefully and either concluded that your and my idea is a non-starter (alas, that is my impression from random remarks among fellow physicists) or that the idea is in fact promising or, perhaps, that it is too hard to tackle at all.

      It should be possible, in principle, to do an analysis when the black hole (i.e., the central singularity) has not quite formed (after, perhaps, radiating away most of its masse as Hawking radiation) and naively apply QM and see what happens.

      A big part of the problem will be that you will be doing quantum field theory in heavily curved spacetime to analyze the quantum field's behavior in the almost-black hole. We know how to do this in principle... except for the "backreaction" problem (hence the name of Sabine's blog).

      There is an additional effect that I have never seen thought through carefully: in quantum electrodynamics, the uncertainty in the position of the electron causes the "self-energy" of the electron not to increase as fast as you would expect when you shrink the electron size towards zero.

      A similar effect should (I think) occur with black holes as they become sub-microscopic. As their size becomes comparable to the uncertainty in their position, this should "smear out" the Schwarzschild solution in such a way as to soften the singularity.

      The short response is "Yeah, that is the Planck-scale problem, which no one knows how to solve." However, i think some progress can be made on this via semiclassical methods in analogy with the QED case.

      I hasten to add that someone who has thought this through more carefully than I have may be able to say, "Yeah, but if you look at the renomalization-group running coupling constant (or the one-loop correction or whatever), you find it does not work at all like QED!"

      So, again, someone may know if my analogy here with the electron in QED is worth pursuing or is a non-starter.

      We're all blind men stumbling around in a cluttered room. The problem is figuring out what (partial, approximate) analysis may help move us forward while trying to find out what other people already know that will help us avoid dead ends.

      Of course, that is what scientific research is all about. I will say that I feel that there is less collegiality among physicists today than there was in the heyday of the mid-twentieth century: too often, in subjects such as the black-hole issues, there is more heat than light in discussions among physicists.

      Sabine is trying to turn down the heat and increase the light.

    5. By the way, I've given some thought to the kind of mathematical formalism that might work for Quantum Gravity. GR is a continuous tensor field theory. I can't see Quantum Gravity fitting into such a framework. So I'm thinking along the lines of a discrete field theory, whose elements are Hilbert spaces-- in fact, the same Hilbert space. Hilbert spaces are so beautifully adapted to QM, or the other way around. You make QM the bedrock. Remember, this is just formalism. This is just a sketch of a possible mathematical framework for a theory we don't have.

  27. Please define exactly "virtual particle".

    1. Read this interesting article to know more about the concept of "virtual particle":

    2. Thanks. Tis Strassler's article is familiar to me. When Sabine said virtual paricles exist, in fact, she said that fields exist. Still, we know that fields are mathematical tools, not observables (at least not direct).

      I would say: virtual particles don't exist. For example there can be real photons as boosting antipodals between particles charged with the same sign only and particles with opposite charges fall towards each other because of lack of boost.

      We can model physical phenomena as math in many creative ways so that calculations give the same result. I only hope that physical existence is seen to depend on measurable observables.

  28. I'm missing why black holes are different than other quantum phenomena. Suppose we boosted the LHC energy to where it could make little black holes that live for fractions of a second, how would that be different than what happens when we make a Top Quark or a Higgs?

    Is the mechanics of a black hole such that we could not possibly figure out what had happened in the reaction chamber? Or, perhaps oddly scrambled photons exiting the reaction that do not obey any symmetries would say "that must mean a black hole".

    1. Nick,

      The decay of top quarks, Higgses etc fits in the framework of quantum theory. It is reversible. Black hole evaporation, according to Hawking's calculation, is not. As I explained in my blogpost.

    2. So what would we see if we made a particle accelerator that could make tiny black holes that hawking-evaporate nigh instantly? I'm guessing its going to create high energy hawking radiation photons that carry away the energy from the short lived black hole in random directions with random polarization. Energy in must equal energy out, and momentum out must also balance. I predict there would be such randomness to the photons released that there would be no statistical correlation between them even after many events.

    3. No one knows what happens in the final decay.

  29. Another excellent blog post, Sabine, well done!

    I have some very basic questions, satisfactory answers to which I have been unable to find so far.

    "For our purposes, the relevant property of the radiation is that it is completely thermal. It is entirely determined by the total mass, charge, and spin of the black hole."

    Is the charge a black hole has quantized? If so, is it integer values of that of the electron?

    How does the thermal radiation from an evaporating charged black hole differ from one which has zero charge (cet. par.)?

    Ditto, spin vs zero spin.

    About "spin": is this the same sort of thing as the "spin of the electron", say? If so, is it quantized?

    Can a black hole have a non-zero hypercharge? If not, why is electromagnetism privileged over the weak and strong forces?

    1. Yes, the spin and charge are quantized. Black holes can have hypercharge in principle, but in reality it's expected to not matter.

  30. From a classical point of view, all the emissions of radiation coming out from particles going in, including jets convey the information. The jet convey the information of the BH spin. How a BH is so cold and has so much entropy at the same time? If you consider all the history of a particle from its creation until the moment it crosses the event horizon, the Unruh-Hawking radiation convey the information of its path history and more, neglecting other interactions. In this context, Unruh-Hawking radiation is similar to the radiation of an accelerating electric charge.

    1. A black hole jet does not come out of the black hole. (And consequently it does not contain any information about what's in the black hole.)

    2. Classically, the black hole cannot evaporate if there is a true horizon because there is no virtual particles and no randomness. The Hawking radiation wouldn't be made of virtual particles but it would be made of real photons. The BH wouldn't be a fuzz ball but a supersolid ball with an ultra low entropy. Spin, mass and charge seems a pretty low entropy to me. What I really think is that matter never forms a black hole but only tends toward it, but the redshift prevents us to observe any differences.

    3. The BH entropy may be proportional to its surface but its high value is due to the introduction of randomness...

      Alice is looking at Bob approaching the Event horizon. Alice sees Bob slowing down but neither Bob nor Alice will ever see him crossing the horizon. Bob sees the entire history of the external universe pass in a small fraction of a second and sees himself either evaporated or in a new Big Bang if the Big Bang is cyclic and there is no sufficient time for evaporation.

    4. Because my model breaks the Lorentz invariance... It works if you have a minimal length like the Planck length as a reference.

    5. The observer falling into a black hole does not see the entire future of the universe in a finite time, at least not before crossing the horizon. In the case of a Kerr metric for a rotating black hole there is something like that, but the in-falling observer witnesses events up to the time the black hole quantum evaporates. This may occur as the observer approaches the inner event horizon. I have not seen analysis on this done, but it could mean this inner horizon is a sort of singularity.

      The Planck length does not mean that spacetime is sliced and diced into discrete units. There were some LQG claims along these lines, but data on the arrival times of radiation from very distant burstars contradicts this idea. In effect different wavelengths of radiation arrive at the same time and so there is no dispersion of photons based on a Planck cut-off. The Planck length only means that a unit of quantum information or qubit can't be isolated into a volume smaller than the Planck volume. In the case of event horizons it means a qubit can't be isolated in an area smaller than a Planck area.

  31. I have never understood Hawking radiation. Virtual particles are so-called because they are not real. They represent terms in the perturbation expansion of a process in field theory. So how can a non-existent particle go over a horizon? Can someone explain this to me?


    1. drl,

      At large distances from the black hole, the Hawking radiation is plain old regular particles, not virtual particles -- real photons, real neutrinos, etc.

      The problems comes in discussing where these particles come from somewhere down near the apparent horizon. There is no consensus on this among us physicists. Sabine has posted on this issue in the past.

      Personally, my guess is that it comes from the infalling matter getting very close to the apparent horizon and changing the stresses on the vacuum in such a way as to change the zero-point oscillations of the vacuum into real particles. (I think the previous sentence is at least meaningful if not correct, although even that is debatable -- almost everything about Hawking radiation is debatable!)

      However, the exact point at which the old-vacuum oscillations become real particles is probably not definable.

      I think that Sabine may disagree with what I just wrote, and I am open to being shown that I am wrong.

      My reading of the literature is that the old explanation of a virtual pair, one partner of which falls into the black hole and the other of which flies out to infinity to become a real particle, is now losing favor among physicists.

      But, on this question also, perhaps I am just biased by reading only one side of the literature.

      The whole subject is a mess of arguments and counter-arguments, which, of course, is what makes it interesting. A non-physicist is unlikely to resolve the controversies, but non-physicists can indeed raise some interesting questions that show that physicists themselves do not agree as to what is happening.

    2. The problem is that a virtual pair is not real. They are bookkeeping terms in an expansion. It's like saying the sin 2x term in the Fourier expansion of some function has an independent existence. Actually it is worse than that. The real problem is that we misinterpret Feynman diagrams.


    3. Well, drl, there is no sharp distinction between virtual particles and real particles, as I point out in my replies to Phil and you below.

      "Real" particles that do not last forever or have not existed forever (and does anything last forever?) can be very slightly "off mass shell."

      In practice, of course, you can make a rough-and-ready distinction between real and virtual particles: virtual particles live such a brief time that there is no real hope of directly detecting them experimentally.

      But, in principle, there is not a rigid division.

      And, most importantly, "virtual" particles have very real, measurable effects. If something has real effects, isn't it real?

  32. How can one not come to the conclusion that physics communication - informing ("information" in the true sense of the word) the general scientific public about physics - is not in a crises?

    Example from above:
    "It's an experimentally well-confirmed fact that virtual particles exist."
    "Virtual particles are so-called because they are not real."

    But here [ ]

    "Virtual particles - not essentially virtual, though are particles - are the temporary particles forming all around us at all times in all of the universe , juggling their way in and out of existence throughout the entire universe and happen to explain every weird phenomena at the quantum scale."

    As (originally) a student of applied mathematician, I consider math as (sometimes useful) fiction, but the way physicists think sometimes baffles me.

    1. Phil,

      It's just different ways of using words, though I agree that this should be spelled out more clearly in textbooks than it is.

      "Virtual particles" are not real, in the sense that they cannot be detected in drift chambers (or, to take older technology, bubble chambers or cloud chambers) as finite tracks.

      On the other hand, virtual particles are real in the sense that they have real measurable effects.

      Since you come from applied math, I can tell you what is happening fairly simply in mathematical terms.

      You know that if you take the Fourier transform of a function whose support is a finite interval in the time domain, say Δt, then the spread in the frequency domain must be at least Δf ~ 1/Δt. I am ignoring numerical factors, but I note that this can actually be made precise if one carefully defines Δt and Δf.

      Now, in QM, frequency just is energy, up to a factor of Planck's constant. So, the smaller Δt is, the larger ΔE is. I.e., for a particle that exists for a very short time, the uncertainty in the energy is very large.

      Different language can be used to describe this: we can say that "energy is not conserved for a short time," or "the particle is off its mass shell," for example.

      But nothing is happening here beyond routine old-fashioned results in Fourier analysis, well-known to communication engineers.

      And, thus there is not really a rigid division between real and virtual particles. A particle that lives long enough to leave a track in a detector or that has a small ΔE compared to its mass, etc. is usually considered "real."

      If not, it is "virtual."

      Both are as real or unreal as anything in quantum mechanics. Or at least the "real" particles are really real (!) because they live long enough to be observed, and the virtual particles are not viewed as quite real because they do not live long enough to be observed (collapse of the wave function and all that).

      The idea that the distinction is that virtual particles only exist in some metaphorical sense as part of Feynman diagrams is wrong. After all, real particles can be a part of Feynman diagrams, too.

      The only things that are really mysterious here are the central mysteries of quantum mechanics: amplitude mechanics, the measurement problem, etc.

    2. This and the linked associated essays are highly recommended.


    3. Well, Neumaier is confused.

      If you work through the math of QFT (or even non-relativistic QM) it works as I said.

      Just to take one example, Neumaier makes fun of the so-called time-energy uncertainty principle. But, whatever you call it, a very short-lived particle does indeed have a wide spread in its observed mass / rest energy.

      This is in fact useful in high-energy elementary particle physics, the field in which I have my Ph.D.

      For example, when the ψ/J particle was discovered in the famous "November Revolution" of 1974 (I remember it well: I was taking QM from Dick Feynman himself at the time), the proof that the particle was long-lived was the narrowness of the peak in terms of energy. Small ΔE means long lifetime.

      This basic principle has been used ever since the discovery of the various hadronic "resonances" back in the 1950s.

      I will agree with him, however, that a lot of nonsense has been written about virtual particles and vacuum fluctuations. For a free bosonic field theory in Minkowski (uncurved) spacetime, vacuum fluctuations are just the zero-point motion of the ground states of the simple harmonic oscillators that represent the degrees of freedom of the field. No virtual particles needed.

    4. ''whatever you call it, a very short-lived particle does indeed have a wide spread in its observed mass / rest energy.'' This is called an unstable particle or resonance (with complex energies), not a virtual particle (with real off-shell energies). See
      for the precise nomenclature and how the various notion are differentiated.

  33. Surely the eventual heat death of the universe will require an evolution equation that takes a larger number of states to a smaller number of states?

  34. Pascal, I'm not sure if you read it, by Lawrence Crowell wrote a comment, above, that I think addresses much, if not all, of your concerns. It's timestamped "3:34 PM, August 23, 2019" (for me anyway).

  35. So, if I understand correctly, the central issue is that when you put the laws of quantum mechanics (the Schroedinger Equation) in the curved spacetime near a block hole's event horizon, you end up with a result that contradicts the laws you started with. However, do you actually need something as extreme as an event horizon to generate this contradiction, or will any gravitational field "break" quantum mechanics in a similar fashion?

    1. It's not the event horizon that causes the problem. The event horizon is merely where information becomes irretrievable for the outside observer. The problem is the singularity, which is what ultimately destroys the information/causes the irreversibility.

    2. So quantum mechanics and gravity together are still time-reversible as long as you don't introduce a singularity?

    3. Well, that depends on how you combine quantum mechanics and gravity. For this you need a theory of quantum gravity. Which we don't have.

    4. I guess I'm a little confused on this point, because in the video you talk say that Hawking radiation is derived by applying normal quantum theory in the curved space-time of a black hole, which makes it sound like you have already combined quantum mechanics and gravity. Are you saying that the resulting violation of time-reversibility is proof that this particular way of combining quantum mechanics and gravity is wrong (thus demonstrating the need for a proper theory of quantum gravity)?

  36. Could this be interpreted to say that Black Holes = Time
    (in the same way as entropy is called times arrow) ?

    1. If black holes indeed destroy information, then I think one could say so, yes.

  37. Then, presumably, some other process (that we don't know about) must occur when matter (or whatever) crosses the event horizon on its way in. This process must have the property that it ensures the overall system is time reversible. So, no information goes into the black hole. And nothing is lost when the black hole evaporates as it never had it in the first place. Now all we have to do is come up with this other process.


    New theory draws connections between Planckian metals and black holes

    Is Planckian dissipation a new connection between quantum mechanics, general relativity, the information paradox, hawking radiation and black holes. Bee will know.

  39. Bee what are the implications to QM if black holes destroy information?

  40. In the famous Parikh, Wilczek tunneling paper the authors make an interesting remark at the end:
    "The resulting corrected formula has physically reasonable limiting cases and, by virtue of nonthermality, suggests the possibility of information-carrying correlations in the radiation." Could that point to a solution to the information loss paradox?

  41. Passing the BH horizon is in theory a reversible process , if you do time rehearsal like any reversible process it's possible but in reality it's not possible precisely because of the loss of information. The time symmetry T: t=>-t is not valid precisely because the information (or entropy) is not conserved.

  42. ''quantum theory tells us that vacuum is not nothing. It is full of p
    article-antiparticle pairs that are constantly created and destroyed.''

    This is a myth frequently found in popular accounts; see

    That the statement is incorrect can be seen by looking at the vacuum state of the standard model. It does not have enough energy to create even a single particle-antiparticle pair.

    For quantum gravity we cannot tell at present what happens since we don't have a good theory for it, but at least in canonical quantum gravity it would be the same.

    1. Virtual particles are functions that appear in certain types of integrals. Of course the popular science accounts don't do justice to the math. The explanation that Hawking radiation is produced by tearing apart virtual particle pairs is okay to some extent because it's about the difference between two vacuum states. The problem with it is that it leaves people with the impression that (a) positive energy falls into the black hole, by which it of course cannot lose mass and (b) that the particles are localized nearby the horizon, which they are not.

    2. You end that article with ''If Hawking’s book taught me one thing, it’s that sticky visual metaphors that can be a curse as much as they can be a blessing.''
      Well said. What may be a blessing for a lay audience turns into a misleading curse for those who want to truly understand.

    3. The horizon is definitely important for Hawking radiation. A neutron star, which has exactly the same geometry as a black hole except that it doesn't have a horizon, doesn't produce Hawking radiation.

    4. When positive energy derived from the vacuum finds its way into the black hole, what transformative process converts that positive energy into a transmuting factor that causes the loss of mass of the black hole?

      What confuses our common perception of reality, when a positive quantity is added to another positive quantity, there is an increase in that quantity expected. But this expectation does not seem to apply to the addition of positive energy into a black hole.

      Is there any plain language explanation that can resolve this seeming contradiction?

    5. Peter,

      Hawking radiation is produced by the time-dependence of the background field. This happens in the vicinity of any collapsing distribution of matter, regardless of whether or not it eventually forms a black hole. It's just that the temperature of the radiation, which is tiny already, falls exponentially with the distance of the surface to the horizon. This should be obvious already because the Hawking radiation for black holes is in fact not produced when the horizon forms (because then we wouldn't be able to see it), but an epsilon *before* the horizon forms.

      The relevance of the horizon, as I said, is that it is where information becomes irretrievable for the outside observer. And, if there is a singularity inside, eventually gets entirely lost, leaving you with a mixed state.

    6. Axil,

      The energy that falls into the black hole is negative.

    7. Bee,

      You are very gracious to respond to my question.

      In thinking about your response, I hope that I am not going off the rails here.

      Negative energy confuses me.

      What also confuses me in coping with the details of negative energy and how I may see a way to resolve my confusion as follows: The negative energy virtual particle moving backward in time becomes a positive energy particle moving forward in time. But this change in its energy state based on the particle's characterization in time does not matter when it hits the singularity. Time no longer affects the particle near or at the singularity. The usual rules of space time no longer apply at the singularity. The time transformed virtual particle reverts to its negative energy origen when it interacts with the singularity since the only quantity that is defined at the singularity is energy.

    8. About the answer to Peter, can one then not simply regularize quantum gravity in some ad-hoc way and then get to a unitary description of Hawking radiation? Consider the analogy with Fermi theory of weak interaction. This theory is non renormalizabe, but just because the higher order corrections will depend on the way one chooses the regularize the theory doesn't mean that the higher order corrections are zero. If we pretend that the higher order terms don't exist, then that results in non-unitary results.

    9. Count,

      Well, yeah, you can do that and people have done that. There are many ways to enforce regularity conditions on the metric that remove the singularity and thereby "solve" the problem.

    10. Sabine wrote to Peter Shor:
      >Hawking radiation is produced by the time-dependence of the background field. This happens in the vicinity of any collapsing distribution of matter, regardless of whether or not it eventually forms a black hole. It's just that the temperature of the radiation, which is tiny already, falls exponentially with the distance of the surface to the horizon.

      Sabine, a couple years ago the same question occurred to me that Peter raised.

      It took me quite a lot of digging through the literature before I finally found a statement equivalent to what I quoted from you (I had figured out that the truth must be something similar to what you said, but I was very nervous that no one seemed to be pointing this out).

      I assume that all veterans in the field are aware of the facts you explained? But, believe me, they are surprisingly hard to dig out for the rest of us.

      I hope you will come back to this point in the future when you discuss black holes. I'm sure it's not just Peter and I who have had trouble grasping it.

      And, it raises additional points: e.g., why, for evaporating black holes, does the distance from the (apparent) horizon stay at the right distance to give the right Hawking temperature for a black hole of this mass? (No doubt I have phrased this incorrectly, but I hope you see the point.)

      All the best,


  43. I consider the information loss paradox and the singularity good indications of there not being black holes in the first place.

    Black holes are a theoretical artifact. They break all sorts of principles and axioms. For some reason the relativists decided that the speed of light in vacuum was an axiom, even though it is not a simple concept or a self-proving one. Stuff like causality is an axiom, and not the speed of light.

    1. Particle *ineraction* occurs at the "speed of light". This is why the speed of light is independent of the speed of the particles or an "observer".

      Interaction is a continuous process.

      In addition, there is really no cause and effect, *only* interaction between particles.

      IMO, as usual!

    2. "There is no cause and effect". What? Interaction is cause and effect, full stop. But you can call it interaction, if it pleases you. But all interaction following an arrow of time is plain and simple cause and effect.

      The whole point of axioms is that when we reduce our logic, at some point our deduction cannot go any further, and these simple lines have an axiomatic unbreakable nature. Our axioms can as such not be proven, but is the very foundation we use when building the rest of our logic. As such, axioms cannot be broken by the logic that rests upon them.

      Naturalism and empiricism gives us axioms of a single existence Universe with cause and effect. Black holes and multiverses is of a schizophrenic nature with breakable axioms. If the light speed postulate is in contradiction with cause and effect / interaction with an arrow of time, the very definition of axioms render the postulate non-logic.

      It is the very nature of Logic to rest upon a set of non-reducable axioms.

    3. One more thing, by "speed of light" i mean the the constant speed of light in vacuum defined as c, and its application across the entire Universe.

      When the application of c breaks with causality, causality by its axiomatic nature directly disproves this constant. Else we need a completely different set of axioms without causality / interaction with an arrow of time.

      Black holes render the philosophical question, do we have c or do we have causality? Only one of them are unbreakable by nature.

    4. Hi Olav,

      I agree with you about the arrow of time, of course, but I can't say this implies cause and effect.

      For example, the sun does not cause the earth to orbit around it. The two bodies orbit around a common 'center of mass'.

      Cause and effect is a useful idea when discussing terrestrial, and in particular, man-made collisions.

      Imo, etc
      : )

  44. If this statement about the radiation from a black hole is correct,

    "It is entirely determined by the total mass, charge, and spin of the black hole."

    then it is inevitable that information is lost. To preserve information, each black hole has to be unique somehow, defined or described by infinitely (?) more than just three numbers.

  45. it's an observer dependent question because space time and certainly time are not the same depending where you are inside or outside the BH horizon. for the outside observer time arrow is freeze by 2nd law of entropy, it's clear that information is lost by 2nd law but inside the BH it's hard to say since time metric coef change its sign, I would say that Entropy grows the same way and world goes toward simplification (less info) the same way on both side.

  46. Sabine Hossenfelder: I have questions. My understanding is that the black hole shrinks its event horizon by emitting radiation, due to some sort of quantum effect occurring near the horizon.

    1) So what is the smallest amount of mass it can lose by this quantum effect?

    2) And based on that, what is the smallest amount of radius that the event horizon can shrink?

    It seems that would be smaller for more massive black holes, so if there is no limit on the size of black holes, then there is no smallest distance in space.

    (Likewise, it should be a larger chunk of the radius for microscopic black holes.)

    But if space is quantized, then shouldn't either the radius of the event horizon have an upper limit, or the nature of radiation from a giant black hole have to undergo some sort of transition when it can no longer emit the smallest quanta of energy possible?

  47. Thinking about my reply makes me understand that this is a fun area to study.

    Blackhole evaporation maks me uncomfortable for many reasons.

    1. I do not understand how hawking radiation removes mass from the black hole. All I have heard is enegy conservation, but we know GR does not conserve energy. I'm sure the math is worked out somewhere but before I have seen it myself it makes me uncomfortable.

    2. Has anyone made an example of two states evolving to the same state? I guess it would require capturing all amplitude of a field inside the black hole. Is the state where this happens even a physical state? It seems to me that some amplitude will travel in other directions at the speed of light.

    3. Disconnected space. The inside of a black hole is infinitly far in the future. So while the outside of the black hole can evaporate in finite time, the inside can't be changed in finite time. So you would have a (disconnected?) region of space time. That region should have all information needed for reversebility. But how would you connect disconnected regions of space time? I guess it might work if our space time is a slice in a higher dimension space.

  48. Sabine,
    I thought that the modern view was that the information encoded in outgoing Hawking radiation is not "random", but "belongs" to the hole (microcausality). In that scenario, the shrinking hole doesn't //destroy// its contained information, it //evaporates// it.

    This is how things work with Hawking radiation in acoustic metrics. If the rules for HR in acoustic metrics are the same as the rules for other variants of HR, then Hawking radiation carries away data that originally "belonged" to the hole.

    You can also see this in the usual particle-pair description of Hawking radiation. Imagine that an electron and positron are created above the hole's horizon, and the electron escapes, and the positron is captured. The infalling positron carries information, and if that information is "random" it will make the information content of the hole go up, which is reckoned to be associated with an increase in the horizon surface area (holographic principle, etc). But what we actually //require// to happen is that when the radiation event has finished, the horizon radius and surface area has gone //down//.
    This only works if the information carried by the infalling positron is //not// random, and deletes a corresponding amount of information from the hole when it is captured. This is only possible if it meets an electron inside the hole that carries precisely the same information, and the two mutually erase.

    Since the information carried by the escaping electron E2 is a clone of the information carried by its infalling positron twin, which is in turn the mirror of the cancelled internal electron E1, the overall result is that an electron E1 disappears from inside the hole, and an identical electron E2, with the same information, appears outside the hole, and escapes.

    If the information encoded in E2 and E1 is identical, then in effect, the electron that escapes "is" the same electron that vanishes inside the horizon.


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