...Prove Their Worth...

"Problems worthy of attack
prove their worth
by hitting back." - Piet Hein

A kind of running diary and rambling pieces on my struggles with assorted books, classes, and other things, as they happen. You must be pretty bored to be reading this...

Friday, June 07, 2002

I found some interesting XXX material today. It's called Static Negative Energies Near a Domain Wall. I'm going to do a summary of a part of the paper, as I understand it right now, for future reference and laughs.


It's been known for a while that if you want relativity to allow 'closed timelike curves' (time-travel) or faster than light motion, the 'weak energy condition' must be violated. This just means that stuff like masses is positive. Quantum fields can violate this weak energy condition, while garden-variety classical fields can't. However, the stereotypical quantum field that has apparently been used in such calculations is what's called a 'free field', and those have to obey something called the 'averaged weak energy condition'. That means that you simply don't have negative masses on average. That is, if you've got one, it's damn temporary. So these aren't all that interesting, if you're interested in time travel.



Now, the most famous example of a thingie with negative energy is the 'Casimir problem'. That's that thing where you've got two metal plates real close to each other getting squeezed together by interesting quantum effects. I've written about it before (but not here). The interesting thing here is that that problem is 'static' - it can just sit pretty, with it's naugthy negative energy density. Which means that it violates the averaged weak energy condition.



What the paper in question does is look at a toy model, a '2+1' dimension (two space dimensions, one time) setup, with a 'domain wall' taking the place of a Casimir setup. And they show that close to this domain wall, you get negative energy densities. But wait! We ain't meetin' real furry creatures from Alpha Centauri any time soon. Because this 'toy system' does obey something called the 'averaged null energy condition', which is enough to rule out goodies like time-travel and faster than light transportation. Ya just can't win. But there's a small glimmer of hope, because the authors speculate that there's a chance the more complicated, but also more realistic 3+1 dimension model, can violate this other condition. Work on a paper exploring that is 'subject of our future work', the authors say. Should be an interesting read.

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