Ah, but as every teenager's mother knows, you can locally decrease entropy in an open system, so tidy that table up now!!!*
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On theory:
Time travel: About world lines crossing themselves. Do we need to ensure that world lines only refer to a microscopic (sub-atomic) particles, never a macroscopic thing like people, planets, etc? I mean, the second set are really collections of world lines.
In one sense it seems to me time travel is possible at a microscopic level, but not at a macroscopic level. No one can tell the 'age' of an individual electron or other subatomic particle, even unstable particles like neutrons. For collections of them, there emerges a sense of time, like 10^10 neutrons becomes ???—10^10 neutrons plus other bits after 8 seconds. Yet no neutron ever knows when it's supposed to decay, or how old it is.
This is like the second law of thermodynamics: entropy increases with time in a closed system. So, some say changing entropy gives a direction to time. I wonder if the second law of thermodynamics is really a 'law' at all. When you look at entropy as a measure of disorder, this inevitable increase of disorder turns out not to be so inevitable after all - it is simply the most likely outcome in large systems. Reduce the number of particles to a few, and ordered systems are much more likely to emerge spontaneously. Could you say time goes backwards when that happens?
Black holes: I think there's a problem with this elastic gridded space-time analogy - it's interpreted more literally than it was supposed to be, which makes some people think of tubes like wormholes. This analogy is sometimes used to create the concept of a u-bend wormhole, but I think that's wrong, it should be from a level above to a level below, because the analogy requires real gravity to a be mysterious force that causes the billiard balls to seek lower potentials on that rubber sheet... The proper analogy should be a vertical tube from an upper level to a lower level. The black hole drains the top level, the white hole empties into the bottom level. And only motion within the rubber sheet is allowed.
If you think about Stephen Hawking's evaporating black holes, then he's turned the black hole into its own white hole. But instead of familiar collections of objects coming out - like an astronaut - it's just a gas of sub-atomic particles, with maximum entropy. So you see, there's a difference between asking about time travel, black hole travel and entropy reversal at microscopic and macroscopic levels. Substitute an astronaut for an electron, and you'll get the wrong answer.
I think these problems are not easily solved so long as one fails to distinguish between the microscopic level and macroscopic level.
Spiff.
* The quickest way to do this is to throw the table away out of your bedroom - which is an open system**
** except when the door is locked after an argument about tidying up one's room.
Thanks for the black hole theory. You're the first person to respond to it.
