100 years ago, Einstein put forth his General Theory of Relativity, and 99 years ago, Karl Schwarzschild came up with the mathematical solution describing a black hole, a solution we now know is not only physically valid, but one that has many examples all across the Universe.

Yet when you consider quantum physics, the matter gets complicated: while you ought to be able to run the laws of physics the same forwards and backwards, a black hole seems to wind up in an irreversibly *different* state, in the end, from what you started with. That's the root of the black hole information paradox.

Image credit: Nature, via http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726.

So what's the solution? Sabine Hossenfelder has the scoop on all the latest research on the topic.

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From the point of view of the universe where the information comes from, the information never leaves.

"In quantum theory all processes can happen both forward and backward in time,"

Does this apply even to wave function collapse? I thought that was considered thermodynamically irreversible by definition.

@Michael Hutson #2: "Wavefunction collapse" is not part of formal quantum theory. It's an ad hoc description, part of the "Copenhagen interpretation" of how quantum systems map to classical (unique states) systems.

A quantum system evolves unitarily and reversibly according to the Schrodinger equation (if non-relativistic) or the Dirac and Klein-Gordon equations (if relativistic). The wavefunction does what it does based on the kinetic and potential terms in those equations, and always describes (when squared) a probability distribution of possible measurement results.

The ad hoc-ness comes in when one of us macroscopic humans asks "what happens when we make a measurement." According to Bohr, the wavefunction, now decoupled from actual quantum theory, makes a sudden, irreversible transition to a new form, which is a delta function at the particular value we measured. If we then stop measuring, that new wavefunction evolves unitarily and reversibly according to the appropriate equation (see above).

More modern views of quantum theory have worked very hard to get rid of this ad hoc assumption. One of the better (that is, in my view, more likely to be true :-) options is decoherence. "Measurement" is just human shorthand for an initially "isolated" quantum state interacting with the much more complex (10^20-something degrees of freedom) quantum environment of the measuring apparatus. With all those additional interactions, the wavefunction evolves (still unitarily and "reversibly" in principle!) to an approximation of a delta function (i.e., a "measurment"). But with that many degrees of freedom, we can't practically do the calculations and follow the whole complex wavefunction in detail. Instead, we have to average over (integrate out) the amplitude and phase data. That averaging process is equivalent to making the decoherence irreversible in practice.

This is quite analogous to the "irreversibility" of gas expansion in a thermodynamics problem. If you could really follow all of the positions and momenta of the particles in an ideal gas, then you could apply true, reversible Newtonian physics to them, and derive thermodynamics in a reversible way. But (even classically!) we _can't_ track all the individual motions of ~10^26 particles. Instead, we have to average over them to get macroscopic, and irreversible, quantities like pressure, temperature, entropy, etc.

So-called "wavefunction collapse" is philosophically the same, even if it's different in the computational details.

Michael H, you can figure on the collapse being similar to "count the votes". You don't know the answer of where something is (or who won the vote) without looking, but it is already decided when you looked as to what the answer is.

Collapsing the wavefunction==counting the votes.

@Wow #4: That argument assumes hidden variables. If you also assume locality, then your assertion is wrong. If you assume non-locality, no problem, but it seems counterintutive.

Not really. It assumes that the wavefunction is not a real thing, but a mathematical constrict.

@Sabine

Number 4 is false, and there doesn't have to be a firewall or a brick wall. At the black hole horizon direction becomes timelike. No structure remains intact because there is no path through space the pieces can use to maintain bonds with each other. Unless you mean an observer will not notice crossing the horizon because he's dead and not an observer any longer, then #4 is false.

Question: How do we know the mass-energy needed to create Hawking Radiation is coming from material on the singularity side of the EH? If the BH isn't evaporating, does that solve the problem?

Actually, I'm not saying ANYTHING about the wavefunction in that post #4 at all.

Solely and simply what "collapsing the wavefunction" is like. It's like counting votes. Where the particle IS (which can be calculated probabilistically with the wavefunction) is not a hidden variable. You really don't know. This is not like a sack of voting slips in that you wouldn't be able to tell even if you were omniescent what the quantum object's location is, whereas you could with the vote.

Not hidden. Just not known.

Unlike the votes, which SHOULD be hidden.

"Number 4 is false,"

Not entirely.

WE see something very different from the observer falling in.

The one falling in, from what I can deduce from the equations, doesn't notice an *event horizon*. At least until r=0, which is the problem of singularity, so may or may not exist in a real physical system which obeys the laws of reality, rather than the model of reality we have with our discovered laws of physics.

An extended observer able to magically hang about just above the event horizon we see out here would notice that there seemed to be noticeable time and space compression when trying to push their "foot" through the event horizon and then pull it back, but the bit still further out and doing the observing of the foot would not be able to *pass* the event horizon.

However, if they just dropped straight down and didn't try to pogo, they wouldn't notice anything odd when passing the event horizon ABOUT that event horizon.

So it depends on what "it" is in "will not notice it.".

"Question: How do we know the mass-energy needed to create Hawking Radiation is coming from material on the singularity side of the EH?"

In quantum mechanics, objects inherently have extent. Therefore a QM particle has to extend both into and out of a specifically defined event horizon.

Trying to solve that when there's a singularity with our "real world" space metric isn't possible, but other quantifiers do manage that and in the solution, the result should be a separation of pairs near the horizon depending on the axial radius of curvature of the space.

Which ALSO happens to be appropriate to the classical thermodynamical "entropy" associated with a blackbody whose temperature varies inversely with the radius of the black hole.

Oddly showing classical thermodynamics appears to be valid for even black holes.

AS LONG AS THEY EVAPORATE. Hence the theorem.

I didn't really answer the quote, did I?

If the stuff is posited as coming from inside the event horizon, then the relation with curvature is physically explicable.

It doesn't mean it IS coming from inside, though.

I suppose to treat it properly, you'd need to use quantum field theory, though. Making where "it" comes from moot due to the "it" in question being undefined in the field theory until energetically realisable. IOW *outside* the horizon, on our side of it.

@Wow #10 & #11

For the sake of argument, I'm admitting that particle production in the curved spacetime near a black hole is real and supported by well tested equations. It is the vague explanation of 'Conservation of Energy means the Black Hole evaporates' that I'm taking issue with.

How do we know the energy used to create the Hawking Radiation comes from the Black Hole? What if the energy used to create Hawking Radiation comes from the universe?

The idea of the universe absorbing and releasing energy comes from the red-shifting of light. As light travels across expanding spacetime, it red-shifts. The photon after crossing expanding spacetime has less energy than it did when it started. That energy isn't lost in heat, but rather it goes directly into the universe. What is to say the process can't work both ways? Being that not a single Black Hole has lost even an atom's worth of mass to Hawking Radiation yet while a massive amount of energy has been lost to red-shifting, I'd say the universe is way ahead on its energy budget.

What is to say the energy used to create Hawking Radiation isn't drawing directly from the universe, and the Black Hole never evaporates, and so there is no loss of information to create a paradox?

"How do we know the energy used to create the Hawking Radiation comes from the Black Hole? What if the energy used to create Hawking Radiation comes from the universe?"

Well, the black hole is in the universe too.

The theory is that the black hole is at a thermodynamic temperature and therefore radiates. If it radiates, it loses energy. If it loses energy, it loses mass. If it loses mass, it shrinks.

I don't really understand your alternative of "it comes from the universe".

"The idea of the universe absorbing and releasing energy comes from the red-shifting of light"

Redshifting isn't "the unvierse absorbing" energy.

Where the photon starts it is at a certain wavelength and the metric at that location is such that the wavelength is whatever size it is.

Further out, the metric is different, so matching the original locations metric to this other place will (if you're further away from a mass) mean the original wavelength is stretched when mapped here. Red shifted.

Alternative option of working this out is to look at the waving of the electric field you are looking at and, being in a deeper gravitational field, your observation sees a SLOWER frequency of change (due to time dilation of that location compared to your rest frame reference) therefore your electromagnetic field is a lower frequency or equally longer wavelength.

Denier, watch this:

https://www.youtube.com/watch?v=jlTVIMOix3I

Not long.

Observers in the universe will see time go slower and slower as something approaches the event horizon. This means that something falling into the black hole, will see the universe go faster and faster. Maybe the observer will see the black hole evaporating and the even horizon shrinking and never hit the event horizon and therefore never loose information?

If we are living in a Digital Universe then center of a BH would not be a singularity and would be a new state of matter instead. Then all information would be stored in the center, not on the Event Horizon.

In any case, if LHC someday can start creating micro BHs, as once feared, the problem may be solved finally :-)

You just gotta see this in expantion, its simple, the universe is suposed to be expanding in a continuos reference that we call time, expanding trough (-----------) unstopably so far we know. So asking myself the simple question, maybe you should too, can we go back in time? And the answer being Absolutly NO, makes me thinks we are exoanding into a bkack hole, so this expantion should last till all the matter finally gets to the next gathering point, and expans again, with te Posibility that it takes a similar path to wich is has took before.

@4&5: According to QM, a particle doesn't have an actual axis, until we try to measure it. So we get these weird correlations when we try to measure the particles axes by using different angles to probe against. If the axis of the spin was predetermined and independent of the way we tried to measure it, we could not get a violation of Bell's inequality. In other words we have can have no locality with QM because there is none to begin with, QM itself is based on a loophole to start with because we can't measure at the point of origin. So what information is lost … uh, we don’t know?

Frank, you need to prove your conclusion from your premise.

All you have is the claim and nothing about how it is consequentially linked.

I have never understood how Hawking radiation makes a black hole evaporate. The virtual particle pairs form near the EH, one is captured and the other escapes. Isn't that zero sum?

@Wow #14

I have no idea where you're going with this very basic description of classical gravity when Hawking Radiation is not a classical theory, Relativity stops working at the Horizon, and the central question over energy is not in any way addressed.

@Wow #13

The theory is that Black Holes have a thermodynamic temperature because of Hawking Radiation. It is not the other way around. Hawking Radiation was not a theorized to explain an observed thermodynamic temperature.

https://www.youtube.com/watch?v=3boy_tLWeqA

There appears to be no mechanism to pull mass out of a black hole. Conservation of Energy is well tested but it isn't magic. Even if Hawking Radiation didn't create an information paradox, you still have to explain how energy gets from here to there.

I think Hawking Radiation is probably real and in trying to reconcile how it works I've only got 2 ideas:

1 - The energy is coming from someplace else.

2 - The mass-energy of motion through space is stripped from the information bearing mass crossing the event horizon and the motion mass-energy component never enters the black hole. Hawking Radiation draws from the external mass-energy component so no information is being destroyed.

Option number 2 is harder to explain so I'm starting with option number 1.

"The virtual particle pairs form near the EH, one is captured and the other escapes. Isn’t that zero sum?"

The short answer is "No".

The long answer is a lot of maths and very long.

"I have no idea where you’re going with this very basic description of classical gravity"

Clearly you didn't watch any of it. It describes how curving space causes something that looks like classical gravity happens.

"The theory is that Black Holes have a thermodynamic temperature because of Hawking Radiation. It is not the other way around. "

It is not "the other way round". They are equally the case. Complementary. Read Hawkin's paper.

"There appears to be no mechanism to pull mass out of a black hole. "

There's no mechanism to pull it out of the universe.

"Option number 2 is harder to explain so I’m starting with option number 1."

Yeah, don't "start" with it and then just go "Well, I started with it, so I can stop there".

@Wow #25

Quantum Uncertainty supposedly has particle pairs popping out of everywhere, made from energy drawn from spacetime, then annihilating in under Plank time. That happens everywhere, not just when there is a nice big black hole nearby to borrow mass-energy from. That being said, you have a point.

Option 2 is actually the more likely, and it draws from the idea of frame dragging around a black hole.

Black Holes spin, but nothing in the interior of the Event Horizon can spin because a radial direction in that region is unphysical. The only direction that exists is towards the center. However there is observed frame dragging that indicates spin, and angular momentum must be conserved.

The idea is that because the interior of a black hole cannot spin, the spin momentum is being conserved by the torsion of spacetime outside the event horizon. Hawking Radiation draws from that so that each photo produced just lessens the amount of frame dragging.

In handling it that way, no information is lost. The amount of frame dragging could be measured before and after the Hawking Radiation photon was generated. As for the information of what made up the mass falling into the black hole, it is all safely conserved in a region near the center.

"Quantum Uncertainty supposedly has particle pairs popping out of everywhere"

Including a black hole? If not, why not?

"That happens everywhere, not just when there is a nice big black hole nearby to borrow mass-energy from"

So it DOES happen in a black hole.

So no need.

Now YOU need to explain why it appears around a black hole when there's no damn reason for it to happen there by your assertion?

"The idea is that because the interior of a black hole cannot spin"

Who said it couldn't?

"In handling it that way, no information is lost."

It isn't lost anyway. No need to make up "comes from the universe".

And I note that you've dropped the idea that redshifts are how the universe absorbs or gives off energy.

You need to go elsewhere and work out what it is you need to know to write down your idea.

At the moment, it's so unformed it doesn't actually mean anything.

I think you phycisists put too much into the notion of an event horizon. It simply doesn't exist. Only the collapsed mass exists.

How do you know either of those?

Insistence isn't enough.