# B Planck Length and Lorentz Contraction

1. Oct 7, 2017

### Moayd Shagaf

I've heard that planck length is the smallest length ever! but if something that his length is equal to planck length and moving by speed dv which is infinitesimal change in speed or higher than that , then according to special relativity his length must be equal to L'=L \sqrt1-v^2/c^2
which is violate that planck length is the smallest length.
so I considered two soultions to this dilemma, first maybe I misunderstood and this is the smallest length possible when object at rest.
maybe when object get to planck length he can't ever move agian!
so what is the solutions?
and other thing since string length is equal to planck length? how they propagate in spacetime?

Last edited: Oct 7, 2017
2. Oct 8, 2017

3. Oct 8, 2017

### Moayd Shagaf

https://futurism.com/the-smallest-possible-length/

4. Oct 8, 2017

### phinds

I have put in a link in my original post that you should check out.

I did not read the article you pointed to but if in fact it says that the Plank length is the shortest possible physical length, then it is an unacceptable source because it is wrong.

5. Oct 8, 2017

### Staff: Mentor

This is not a valid source; it is presenting something which is speculation as though it were known fact. We will not know whether there is in fact a smallest possible length until we have a good theory of quantum gravity--at least that is our best current expectation.

Note also that even if it turns out that there is a smallest possible length in the correct theory of quantum gravity, that doesn't necessarily mean it will be the Planck length. That is also speculation at this point.

If in fact it turns out that a good quantum gravity theory says there is a smallest possible length (whether it turns out to be the Planck length or something else), that will mean that our current classical theories of relativity (special and general) will only be approximations, valid for length scales much larger than the smallest possible length.

6. Oct 8, 2017

### king vitamin

You have just (correctly) reasoned that special relativity and a "smallest possible length" are incompatible. Either one or the other is wrong. Right now, special relativity has more experimental evidence, but if the "smallest possible length" is small enough, it could be that special relativity is approximate and we will see violations of it with enough precision.

7. Oct 8, 2017

### phyzguy

Building a mathematical structure with a quantized spacetime which is consistent with relativity is one of the motivations behind Alain Connes theory of Non-Commutative Geometry. Connes has been successful, but it is a very different geometry than what you are probably thinking, so your objections are not valid. It involves the position variables being replaced by non-commuting operators. An example you might be familiar with is QM phase space, where the operators $\hat x$ and $\hat p_x$ do not commute, and the phase space volume is a constant (Planck's constant h) as seen by all observers.

8. Oct 8, 2017

Staff Emeritus
Phyzguy, those aren't really accessible at the I-level. And, given that the OP is IIRC a 13 or 14-year old, this really should be a B question.

9. Oct 8, 2017

### phyzguy

Sorry, I missed the I-level.