The relativistic uncertainty principle

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Discussion Overview

The discussion centers around the concept of the relativistic uncertainty principle and its implications for quantum gravity. Participants explore whether the statements made in a specific textbook are applicable in the context of general relativity and the validity of these principles in a relativistic framework.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that the statement regarding the relativistic uncertainty principle could be a significant step towards understanding quantum gravity, while others question its validity.
  • A participant references a textbook by Landau, Lifshitz, and Pitaevskii, which presents a formula relating momentum and time uncertainty in relativistic quantum mechanics.
  • Another participant questions whether the principles discussed are valid in the context of general relativity.
  • One participant expresses skepticism, suggesting that the textbook only addresses special relativity and may not extend to general relativity.
  • A participant raises a technical concern regarding the formulation of the uncertainty principle, questioning the nature of the factors involved in the equations presented.
  • Another participant admits a lack of qualification to provide a definitive answer and suggests consulting the original textbook for further understanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the applicability of the relativistic uncertainty principle in general relativity and the interpretation of the equations presented.

Contextual Notes

Limitations include potential misunderstandings of the equations due to their formulation, the dependence on the context of special versus general relativity, and the unresolved nature of the implications for quantum gravity.

bayakiv
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TL;DR
Statement: the product (scalar product in the Minkowski metric or in the local metric of a pseudo-Riemannian manifold) of the uncertainties of the relativistic coordinate and the 4-momentum has the order of h.
Could this statement be the first step towards quantum gravity? Or is it trivial or not true at all?
 
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Textbook of Landau, Lifshiz and Pitaevskii on relativistic quantum mechanics says
[tex]\triangle p \triangle t \ \sim \frac{\hbar}{c}[/tex]
and for the rest frame of particle, e.g. electron
[tex]\triangle q \sim \frac{\hbar}{mc}[/tex]
in the introduction.
 
Is this true in general relativity?
 
I do not think so. The text deals only with special relativity.
 
The first formula on the left has two factors, one of which is a number and the other is a vector. What do we get on the right? Or is there 4-momentum uncertainty taken modulo?
 
I am sorry to say I am not qualified to tell it to you. I recommend you to read their book "Relativistic Quantum Theory" 1968 that is original in Russian, if available.
 
Last edited:

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