Planck Length and Lorentz Contraction

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Discussion Overview

The discussion revolves around the concept of Planck length and its implications in the context of special relativity. Participants explore the relationship between Planck length, motion, and the potential existence of a smallest possible length in physics, raising questions about the compatibility of these ideas.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants assert that Planck length is often misunderstood as the smallest possible length, suggesting that it may only apply when an object is at rest.
  • Others argue that if an object at Planck length were to move, it would lead to contradictions with special relativity, specifically regarding length contraction.
  • A participant proposes that if a smallest possible length exists, it could challenge the validity of special relativity at very small scales.
  • Some participants emphasize the speculative nature of claims about Planck length being the smallest physical length, noting that a definitive theory of quantum gravity is still lacking.
  • One participant introduces Alain Connes' theory of Non-Commutative Geometry as a mathematical framework that could reconcile quantized spacetime with relativity, although its accessibility is questioned.
  • There are concerns about the appropriateness of the discussion level for younger participants, suggesting that the complexity may exceed their current understanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of Planck length or its implications for special relativity. Multiple competing views remain regarding the interpretation of Planck length and its role in theoretical physics.

Contextual Notes

Some claims about Planck length and its implications depend on unresolved assumptions about the nature of spacetime and the validity of current physical theories at very small scales.

Moayd Shagaf
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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:
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Moayd Shagaf said:
https://futurism.com/the-smallest-possible-length/
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.
 
Moayd Shagaf said:
https://futurism.com/the-smallest-possible-length/

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.

Moayd Shagaf said:
according to special relativity

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.
 
Moayd Shagaf said:
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?

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.
 
Moayd Shagaf said:
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?

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.
 
Last edited by a moderator:
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.
 
Vanadium 50 said:
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.

Sorry, I missed the I-level.
 

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