The relativistic uncertainty principle

In summary, the conversation discusses the equation \triangle p \triangle t \ \sim \frac{\hbar}{c} which is found in the textbook by Landau, Lifshiz, and Pitaevskii on relativistic quantum mechanics. It is asked if this equation is applicable to general relativity, to which it is clarified that it only applies to special relativity. The conversation then delves into the components of the equation and the uncertainty principle for 4-momentum. The speaker recommends reading the original Russian version of the book for further understanding.
  • #1
bayakiv
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TL;DR Summary
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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  • #2
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.
 
  • #3
Is this true in general relativity?
 
  • #4
I do not think so. The text deals only with special relativity.
 
  • #5
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?
 
  • #6
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.
 
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Related to The relativistic uncertainty principle

1. What is the relativistic uncertainty principle?

The relativistic uncertainty principle is a concept in physics that states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa. This principle is a fundamental aspect of quantum mechanics and is closely related to Heisenberg's uncertainty principle.

2. How does the relativistic uncertainty principle differ from Heisenberg's uncertainty principle?

While both principles deal with the limitations of simultaneously measuring certain properties of a particle, the relativistic uncertainty principle takes into account the effects of special relativity, such as the speed of light. This means that at high speeds, the uncertainty in position and momentum becomes even greater.

3. What is the mathematical equation for the relativistic uncertainty principle?

The relativistic uncertainty principle can be mathematically expressed as ΔxΔp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck constant.

4. How does the relativistic uncertainty principle impact our understanding of the physical world?

The relativistic uncertainty principle highlights the inherent uncertainty in the behavior of particles at the quantum level. It challenges our traditional understanding of cause and effect, and shows that the behavior of particles is inherently probabilistic rather than deterministic.

5. Can the relativistic uncertainty principle be violated?

No, the relativistic uncertainty principle is a fundamental aspect of quantum mechanics and has been extensively tested and confirmed through experiments. It is a crucial principle in our understanding of the physical world and cannot be violated.

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