Spacetime Discrete? Continuous? Both?

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Spacetime Discrete? Continuous? Both?

#1  Postby twistor59 » Oct 22, 2010 6:58 am

Looks like an interesting paper. I didn't realise that in my day job I might actually be doing fundamental physics !

http://arxiv.org/abs/1010.4354

Abstract. There are competing schools of thought about the question of whether
spacetime is fundamentally either continuous or discrete. Here, we consider the
possibility that spacetime could be simultaneously continuous and discrete, in the same
mathematical way that information can be simultaneously continuous and discrete.
The equivalence of continuous and discrete information, which is of key importance in
signal processing, is established by Shannon sampling theory: of any bandlimited signal
it suffices to record discrete samples to be able to perfectly reconstruct it everywhere,
if the samples are taken at a rate of at least twice the bandlimit. It is known that
physical fields on generic curved spaces obey a sampling theorem if they possess an
ultraviolet cutoff. Most recently, methods of spectral geometry have been employed
to show that also the very shape of a curved space (i.e., of a Riemannian manifold)
can be discretely sampled and then reconstructed up to the cutoff scale. Here, we
develop these results further, and we here also consider the generalization to curved
spacetimes, i.e., to Lorentzian manifolds.

ETA + this paper
Last edited by twistor59 on Oct 22, 2010 7:25 am, edited 1 time in total.
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Re: Spacetime Discrete? Continuous? Both?

#2  Postby Mononoke » Oct 22, 2010 7:18 am

:coffee:

I'm starting to read this stuff. But how difficult is the information theory material. I know next to nothing about that subject
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Re: Spacetime Discrete? Continuous? Both?

#3  Postby twistor59 » Oct 22, 2010 7:27 am

Mononoke wrote::coffee:

I'm starting to read this stuff. But how difficult is the information theory material. I know next to nothing about that subject


You only need to accept equation (1) in the paper - it's the basis of your cellphone and, well, anything that has an analog to digital converter in it....
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Re: Spacetime Discrete? Continuous? Both?

#4  Postby hackenslash » Oct 22, 2010 8:05 am

This particular bit of information theory is actually quite simple. There's a really good paper on the relevant portions by Dan Lavry of Lavry Engineering, manufacturers of the best audio converters available to the audio profession.

Here it is in pdf format
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