Infinite complexity

[Ayatollah So]

@Xenocrates: Yeah, your last post makes sense for the implications of space being discrete. But why does space being continuous mean that thermodynamics doesn't hold?

I think he's getting it confused with energy being continuous. There's a famous proof that if energy levels were continuously variable, then black bodies above absolute zero temperature would give off infinite radiation (point 3 in link). So energy must be quantized. But I don't see why space must be.

 

[Xenocrates]

If space is continuous, there are an infinite number of ways that energy/mass can be arranged which violates classical thermodynamics, where entropy depends upon the number of ways that you can arrange the energy.


S=kbLn(W) http://physics.about.com/cs/thermodynamics/g/Entropy.htm

A big system has a higher entropy than a small one because there are more places in which the energy can exist. However if space is continuous even a small system will have an infinite entropy. That blows thermodynamics (in the school-book sense) apart.

It's a tougher question than immediately meets the eye!

 

[brennan]

Not really. The energy of a system depends upon the number of particles involved, not the amount of space, as long as the number of particles is finite so is the energy.

 

[El_Machinae]

I thought the background radiation was ubiquitous anyway?

 

[Ayatollah So]

I thought the background radiation was ubiquitous anyway?

But it's finite. It's only some teeny tiny fraction of a Watt per square meter. If classical electromagnetic theory were true, the radiant power emitted from any surface would be infinite, hence so would that received at any surface.

 

[Xenocrates]

Errm I'm talking about entropy (E N T R O P Y! Turn your hearing aid on Grandma!) not energy.

My wife will tell you that disorder is closer to my nature than energy!

 

[Sidhe]

Totally off topic but did you know if you drop a slab of concrete or whatever regardless of it's size it appears to break up into 3 and a number of small pieces over a long series of breakages. Thus breaking stuff appears to equate to pi I read that somewhere. Odd n'est pas? Could be bs though I don't believe everything I read.