### Black Hole Information

Hawking’s Greatest Mistake?

### Black Holes

• Black holes are regions of space where gravity is so strong that nothing can

escape, at least according to classical physics (the physics of large objects).

• They are believed to form from the

gravitational collapse of massive stars that burn out their nuclear fuel.

### Evolution of Stars

• Stars are held up by the pressure from heat generated by nuclear reactions.

• When low-mass stars like the sun burn out their fuel, they condense to white dwarfs (size of earth).

• Medium-mass stars end up as neutrons stars (tens of kilometers across).

• Very massive stars keep collapsing until light can no longer escape, forming black holes.

### Hawking’s Area Theorem

• In 1972 Stephen Hawking discovered how to define a black hole in terms of its surface, the event horizon, defined so that nothing could escape from inside.

• Then Hawking proved that under normal

circumstances, the area of the event horizon could not decrease.

• Black holes could only grow.

### St ephen Hawking

### Hawking Evaporation

• In 1974 Hawking found that quantum theory, how small objects behave, violates the

normal circumstances and allows black holes to shrink.

• Hawking radiation is emitted and causes black holes to evaporate away into a black hole explosion.

• Hawking evaporation is only important for tiny black holes unless you wait very, very long.

### Information Loss?

• Black hole radiation does not violate

energy conservation, since the energy in the black hole comes out in radiation.

• But Hawking proposed that it violates

information conservation, as it appeared that the information that fell into a black hole could not come back out.

### Quantum Information

• Quantum theory has the Heisenberg

Uncertainty Principle that there is a limit to how well one can know certain pairs of

quantities, such as position and momentum (mass times velocity).

• A pure quantum state gives the minimum uncertainty and maximum information

possible for a given system.

• A mixed quantum state has less information.

### Information Conservation

• In ordinary quantum theory, total information is conserved: Pure quantum states stay pure.

• Information may become spread out so that it is in practice inaccessible, and

then the loss of accessible information is called the increase of entropy.

• However, total information is conserved.

### Are Black Holes Different?

• It was believed that nothing can escape from black holes, so information that fell in would be totally lost.

• One might think the same about energy, but near a black hole, the energy of quantum

matter can be negative, and negative energy going in is equivalent to positive energy

coming out in black hole radiation.

• But negative information seems impossible.

### Breakdown of Predictability?

• In 1976 Hawking argued that the formation and evaporation of black holes leads to a fundamental loss of information from the universe, a breakdown of predictability, as pure quantum states turn into mixed states.

• One would not be able to predict the

maximum allowed quantum information.

### Is Black Hole Evaporation Predictable?

• In 1980 I noted Hawking’s argument used quantum theory for the black hole radiation but not for the black hole itself.

• We didn’t (and still don’t) know fully how to use quantum theory for a black hole.

• Therefore, his argument for information loss was not completely convincing.

• Black holes might not lose information.

### Early Debate on Information

• In the early 1980s, not many people paid attention to Hawking’s and my debate.

• General relativists mostly supported Hawking’s position that information could not escape from black holes.

• Particle physicists generally supported my position that black holes would

obey standard quantum theory and not lose information.

### 1993 Opinions about BH Info

• It’s lost: 25 votes; I thought 30% likely.

• It comes out with the Hawking radiation:

39 votes; I thought 35% likely.

• It remains accessible in a BH remnant:

7 votes; I thought 5% likely.

• Something else: 6 votes; I thought 30%

likely.

### It’s lost.

• This is the view that the information that falls into a black hole never comes out and

disappears from our universe if the black hole decays away.

• It would be like the decay of positronium into two photons (both spinning right or both

spinning left), a state of definite zero total

angular momentum, going into a mixed state of one photon of uncertain angular

momentum if one photon totally disappeared.

### It comes out with the Hawking radiation.

• This was (and still is) my main view that somehow the information comes back out while the black hole is shrinking.

• One would have to violate classical

general relativity, but one might suppose that quantum gravity could provide the right violation.

### It remains accessible in a black hole remnant.

• This is the view that black holes don’t completely decay away but retain the information in some small object that persists.

• Somehow the black hole would have to stop evaporating before it disappeared, which seems conceivable but unlikely.

### Something else occurs.

• Maybe the other possibilities envisaged do not cover what actually happens.

• Perhaps quantum theory is not the correct description.

• Or perhaps quantum theory should be reformulated not in terms of quantum states that evolve from before to after.

### Information in Black Hole Radiation

• In 1993 I showed that if the information does come out in the Hawking radiation, it would be initially so slow that one could never see it by the usual methods of analysis

(perturbation theory).

• The information could be very subtly encoded in correlations between all the radiation

emitted.

### Holographic Principle

• Gerard ‘t Hooft and Leonard Susskind formulated the holographic principle

1993-1995, that the information within a volume is encoded within its surface.

• Then any information that fell into a

black hole would remain encoded on its surface (the event horizon).

### Black Hole Information in String Theory

• String `theory’ is an incomplete set of ideas for a quantum theory of gravity and of all the rest of physics.

• It has made partial analyses of black holes using standard quantum theory.

• Andrew Strominger and Cumran Vafa showed how to account for information in black holes by string theory in 1996.

### Support for Holography

• The holographic principle is not yet

confirmed, but support came from Juan Maldacena’s AdS/CFT conjecture.

• This proposed that a theory of quantum gravity in asymptotically anti-de Sitter

spacetime is equivalent to a conformal field theory (CFT) without gravity on a surface a long way away, the boundary of AdS.

• Although this is not proved either, there is an enormous support for it in string theory.

### Black Hole Complementarity

• In 1993 Leonard Susskind came up with the idea that as seen from an

infalling observer, matter falling into a black hole carries information in with it.

• However, to an observer that stays

outside, it appears to stay outside and spread over the horizon.

### No Quantum Cloning

• In 1982 Dieks, Milonni and Hardies, and Wootters and Zurek proved one cannot make two copies of an unknown

arbitrary quantum state (though if one knows what is definite about it one can).

• Thus one should not be able to have one copy of information inside a black hole and one copy outside.

### Problem for Complementarity?

• If an arbitrary quantum state cannot be cloned, how can the information be both inside and on the black hole surface?

• Black hole complementarity argues that no observer can compare complete

measurements of both regions to falsify the complementary descriptions.

### Slightly Variant Viewpoint

• Quantum cloning forbids making copies of arbitrary information at differ places, but not at different times. (Think of the same information persisting in time.)

• Perhaps quantum uncertainty in the

spacetime geometry means one cannot say that inside and outside a black hole are different places rather than times.

### Causality

• In quantum field theory in classical

spacetime, disturbances cannot travel faster than c, the “speed of light.”

• But if spacetime is quantized (quantum gravity), there may be no definite c.

• String theory is often written as if there were a definite c but faster propagation.

### Information Transfer in Quantum Gravity

• If there is no precise limit to the speed of propagation of signals (information), then in principle information could come out from inside a black hole.

• Whether it actually does all come out is not yet really proved, but now the

weight of evidence suggests it is.

### Hawking’s Concession

• In 2004 Hawking, influenced by a key paper by Juan Maldacena and by his own

calculations, changed his mind and decided that information is not lost in black hole

formation and evaporation.

• At a conference in Dublin, he conceded a 1997 bet he and my other Ph.D. advisor Kip Thorne had made with John Preskill.

### My Reaction

• I regretted not having made a bet myself with Stephen Hawking.

• I thought perhaps I had never expected Hawking to change his mind.

• I also wondered whether it was my

moral objection to gambling as a tax on the stupid, but I realized this would not apply to a bet with Hawking.

### An Older Bet

• While preparing to lecture on black hole information in Barbados, I found a 1980 letter of mine, that I had bet Hawking!

• After a long search in my boxes piled to the ceiling, I found the bet.

• At a workshop hosted by the 9th richest billionaire in Texas, Hawking conceded.

### Hawking’s Greatest Mistake?

• In 1985, Hawking predicted that the arrow of time would reverse if the universe

recollapsed.

• I refuted this idea shortly afterward.

• Hawking later called this “my greatest mistake, at least in science.”

• However, his apparent mistake about

information loss in black holes has generated far more research and is truly much greater.

### Summary

• In ordinary quantum theory, information in the entire universe is conserved.

• Stephen Hawking originally suggested that black holes lose information.

• Now Hawking has changed his mind.

• Most think information is conserved.

• But this is not completely proved or understood. Maybe you can help!