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Black hole uproar is collision of quantum mechanics with information theory

Thumbnail for version as of 02:40, 8 September 2006
black hole/Alain r

Further to “The “no black holes” uproar a week later” (in which “Hawking now says there are no black holes” and New Scientist is calling the whole thing a “cosmological Wild West,” physicist Rob Sheldon kindly writes to say we should have a look at the New Scientist article again. It reads in part:

Trouble began brewing in the 1970s when Hawking mixed quantum mechanics into relativistic black hole theory and concluded that they should emit a tiny amount of radiation, which steals mass until the black hole evaporates. But that would erase all information regarding the matter that formed the black hole, violating quantum rules.

Sheldon notes,

Sentence #1 is Hawking radiation. Sentence #2 is Bekenstein-Hawking entropy, which Susskind and many others refer to as “information.”

So the Wild West in cosmology is raging because of the collision of QM with information theory. You could say the same thing about ID, the Wild West in evolution is occurring because of the collision of genetics and information theory.

He continues,

I downloaded the paper, and yes, Hawking is serious.

The problem Hawking is struggling with, which is recorded in Leonard Susskind’s The Black Hole War, is that Hawking got famous for suggesting that black holes can evaporate through a mechanism called “Hawking Radiation.”

There was a second Hawking paper too, suggesting that black hole entropy must stay constant–the Bekenstein-Hawking entropy. If it didn’t, then you could violate the 2nd law of thermodynamics by using a handy black hole to drop your entropy into, which would give you free energy, perpetual motion, the whole eternal works. Since that seems nonsensical, we must conserve Bekenstein-Hawking entropy.

Now we have a problem. Suppose we drop into a black hole, a hard disk with all of Hawking’s papers on it. The black hole gobbles it up, of course, and doesn’t even burp. Then a few bajillion years later, the black hole evaporates using Hawking radiation and sprays photons over the rest of the universe. What happened to that information that used to be in the Black Hole? Because when you lose information, entropy must increase, and if we’ve lost Hawking’s papers, then the Bekenstein entropy isn’t conserved.

Something is wrong with our two Hawking papers, they don’t agree with each other. Susskind’s book records that at first Hawking didn’t want the Bekenstein entropy to stay constant, but Leonard convinced him.

One of my colleagues here in Huntsville suggested that Hawking made a mistake in his black-hole evaporation paper (but Nature wouldn’t publish his result). Now Hawking is suggesting that we need to rework the entire Black Hole horizon thing to solve the problem. Evidently, the disk drive doesn’t actually fall into the black hole, it just looks that way. It’s reminiscent of GK Chesterton’s comments in “Orthodoxy” about skinning a cat.

If it be true (as it certainly is) that a man can feel exquisite happiness in skinning a cat, then the religious philosopher can only draw one of two deductions. He must either deny the existence of God, as all atheists do; or he must deny the present union between God and man, as all Christians do. The new theologians seem to think it a highly rationalistic solution to deny the cat.

My own opinion is that Hawking is feeling his own mortality, and wants to set the record straight before his legacy is forever tainted. He can’t solve the problem, but he doesn’t want to be accused of overlooking it either.

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