SR at Small Scales

[Riogho]

I got a quick question.

 

In SR there are two postulates. That the laws of physics are the same in all reference frames, and that the speed of light is a constant.

 

So basically, there are two types of objects, those that go the speed of light, and those that move slower.

 

As you know, there is a length contraction for different reference frames. The Lorentz-Fitzgerald Contraction.

 

My question is this.

 

What about for objects of Planck Length.

 

That is, the smallest possible length there is.

 

If it was accelerating relative to me, SR tells me I would view it get smaller. But it is defined as the 'smallest possible length'. Obviously this is a breakdown of SR at the Planck Scale.

 

Possibly I am missing something, or something has been done to correct this. Help plz.

[Klaynos]

I think the uncertainty principle will deal with it... :s but not 100% sure... interesting question...

[Zephir]

...the uncertainty principle will deal with it.....

Yep, the quantum uncertainty is the direct consequence of Lorentz symmetry violation at low scales. You can consider the quantum chaos as a fluctuation of speed of light, which mediates the information about subject of observation.

[Riogho]

Okay, I've been looking into this myself, and it seems this question has been asked before.

 

And a theory has been presented that is called

 

"Double Special Relativity, or Deformed Special Relativity"

 

It seems to be pretty well accepted and make some real experimental predictions that we can actually prove it right or wrong....

 

 

http://en.wikipedia.org/wiki/Doubly-special_relativity

[NeonBlack]

Since relativity is a classical theory, you can not expect it to hold up at quantum scales.

I'll take some time to read the link. It sounds interesting. There was recently a question about "Is there a minimum wavelength" (you probably know about it though) which might give some insight.

[ajb]

Special and General relativity would presumably break down at that so of scale. Quantum gravity effects would become important.

 

So you question is good and is a big question in research right now.

 

Riogho is indeed correct, people do consider a version of special relativity with a fundamental minimum length called double special relativity.

[Severian]

The Planck length isn't the smallest possible length. It is just the length that gravity is conjectured to become strong. It is also conjectured that it becomes so strong that space breaks up on this scale, into a sort of foam, but since we don't have a quantum theory of gravity that is just speculation.