Saturday, June 23, 2007

The functional Schroedinger equation as applied to the Schwarzschild metric of spacetime

It's all quite simple, really, when you think about it. Quantum physics and general relativity are two aspects of the science of physics that lead to a paradoxical result when applied to information "lost" in a black hole. This is known as "the black hole information paradox" and is such because general relativity theory says if information crosses a black hole's event horizon it is lost forever into nonexistence, but quantum mechanics says information cannot be destroyed.

A team of physicists at Case Western Reserve University have come up with a possible solution to this paradox. I don't pretend to understand the complexities involved, and the article linked to on ars technica above does a superb job at explaining this for non-math types, but basically the new proposal is that, from the point of view of an asymptotic (distant) observer, an object or information approaching the event horizon of a black hole will never pass over it and hence, not be lost.

Wow. Kinda like the thought experiment from high school physics that concluded nothing ever really touches anything else when you bring two objects closer and closer by dividing the distance between them in half over and over again.

I also learned a new term that I'm going to have to use more often: dumbhole. I only fear the full implication of the word will be lost on its recipient.

A dumbhole is the sonic equivalent of a black hole, and is mentioned in the article because the physicists who are proposing this theory need a way to actually prove it, and in the absence of being able to create a black hole on earth, they can attempt to create a dumbhole, which is apparently much easier. All they really need to do is "create the beginning stages of collapse towards a dumbhole" to make their observations. Who knew?

The ars article caught my eye because I remembered a small story from the Feb 2007 15.02 issue of Wired in the parent article called "What We Don't Know" by John Hodgman, called "What happens to information in a black hole?" Actually, several of those small stories relate to this topic.


Xymyl said...

My big problem with Quantum anything is that label so many unknowns as knowns, often assigning them counterintuitive designations. Not that mainstream science never does this, but it has a history of doing it less.

And I don’t like the charming allegorical fluffiness of misleading statements such as, "If you cross the event horizon, you won't know anything has happened. You'll still get the morning paper; you just won't ever be able to tell anyone on the outside." What paperboy delivers papers to black holes? How many paper boys have been lost? I’m only an amateur scientist, but even I know that you can’t get the paper in a black hole. And even if you do, you’ll be compacted and frozen and/or used as fuel before you ever get a chance to read it. Plus, you couldn’t read it with your eyes even if you were fully functional in a black hole because all the light would be compressed. And the light that came with the paper would never reach your vision because it came later in the queue. This would also be the case for light and papers that came prior to you.

Many aspects of what we call black holes are hypothetical. Certainly, there is something there, and is sucks.

As for the paradox, I don’t really see one. And I’ll use something fluffy to explain: If you drop your keys - along with your keychain flash drive - off a boat in the deepest part of the Atlantic Ocean and it sinks to toward the bottom (28,231 feet) but at about 22,000 feet the pressure exerted by the water on the casing of the flash drive vs. the small amount of oxygen contained within, achieves a nearly perfect balance of buoyancy that will allow the flash drive and keys to slowly sink toward the bottom for all eternity, yet never quite reach.

In this case, information lost forever into non-existence is a “true” relativistic viewpoint. But relativity is a viewpoint science, where perspectives drive one closer to truth, and being seen from a perspective always leaves room for doubt as to accuracy. It is just as easy to say that from your perspective “my keys and flash drive are non-existent” as it is to say, “I will never find my keys”.

Now, if you wait until someone devises a method of deep sea key retrieval, it would be such a long time before you could actually get your keys back that they would be eroded to such a point that they were worthless, perhaps they were eaten by some sea creature during their eternal fall. Yes, you are experiencing a Schroedingeresque conundrum. This means, that from a quantum perspective the keys are capable of any state including non-existence until they are found.

Basically, the question comes down to this, will you ever get your keys back in your life time? And, if not, is there some reason to spend the billions of dollars it will take to retrieve them for the good of all mankind? If the answer to either of these two questions is “yes” then your priorities are all whacked.

Kevin said...

You are correct, Xymyl. The problem with theoretical physics is just that: it's theoretical. No one *really* knows how most of this stuff works, so assumptions have to be made, which introduces error.

I too, do not understand the idea that one could still get the morning paper after crossing a black hole's event horizon. As you said much more eloquently, you can't read something in a black hole when your eyes and the newspaper are crushed into a singularity, and besides, it's dark.

You hit the nail on the head exactly by stating that relativity is a viewpoint science, and that may be exactly why we'll never really know what happens when something crosses a black hole's event horizon. By this proposal's own terms, what an outside observer experiences is completely different than that of someone actually experiencing the event. Knowing what happens inside of a black hole would seem to require a trip there and a return to share data, which theoretically isn't possible.

In the meantime, I'll just replace my keys and buy a new keychain flash drive.