Does the Heisenberg Uncertainty Principle Affect Relativity Calculations?

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Discussion Overview

The discussion revolves around the relationship between the Heisenberg Uncertainty Principle (HUP) and calculations in relativity, particularly focusing on how uncertainty in position and velocity may affect the ability to accurately determine events in different reference frames. The scope includes theoretical considerations and mathematical reasoning related to both quantum mechanics and relativity.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the HUP limits the ability to know the position and time of an event accurately in relativity calculations, particularly at small scales.
  • Another participant argues that position and time are not canonically conjugate variables, suggesting that they can be known with arbitrary precision according to the uncertainty principle.
  • A participant reflects on the setup of particle experiments, noting that the primary reference frame is often a sensor and the secondary frame is linked to a fast-moving particle, which may complicate the determination of position.
  • One participant clarifies that reference frames are mathematical constructs rather than physical entities, emphasizing their role in tracking physics rather than being "anchored" to physical objects.
  • A participant presents a mathematical derivation involving a non-relativistic particle and discusses how transformations affect uncertainty, suggesting that the uncertainty in position and velocity may increase after applying a boost.
  • Another participant acknowledges the simplification made by focusing on non-relativistic cases without detailing all terms involved.
  • A later reply questions whether satisfying the HUP in one frame implies a violation in another frame, but another participant asserts that the momentum expression used does not apply to relativistic particles.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the HUP in the context of relativity calculations, with no consensus reached regarding whether the uncertainty principle affects the accuracy of position and velocity measurements in different reference frames.

Contextual Notes

The discussion includes assumptions about the nature of reference frames and the application of the HUP, with some mathematical steps remaining unresolved or simplified. The implications of relativistic effects on uncertainty are also not fully explored.

Tegg Mentall
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Hi,

Just had a quick question... Relativity seems to require the position and time of an event in one reference frame and the difference in velocity with a second reference frame. Given this starting information you're suppose to be able to calculate the position and time of the same event as seen from the second reference frame... Does the Heisenberg Uncertainty Principle prevent you from accurately knowing all the starting information for small scales... Thanks.

Tegg
 
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Hi Tegg, welcome to PF!

Position and time are not canonically conjugate to each other so according to the uncertainty principle you can know both to arbitrary precision.
 
Thanks for replying... I guess I'm thinking that in particle experiments the primary reference frame is normally some sort of sensor equipment and the secondary frame is anchored to a fast moving particle. Then if you know the velocity of the secondary reference frame you have trouble figuring out the it's position... But maybe that's not the way experiments are set up...
 
Remember, reference frames are not physical entities, they are coordinate systems. They are mathematical tools for keeping track of physics, they are in no way "anchored" to anything.

So, let's say that you have a non-relativistic particle whose position you know to be x±∆x and whose velocity you know to be v±∆v such that (∆x)(m∆v) satisfies the HUP. Now, suppose further that you do a translation and a boost such that x'=0 and v'=0. Then in the primed reference frame the particle's position is 0±∆x and the particle's velocity is 0±∆v and (∆x)(m∆v) still satisfies the HUP.
 
Thanks again for replying... Sorry for the delay. Had to try and get my head around the math. Not sure if I did... For a relativistic particle with position x±∆x and velocity v±∆v such that (∆x)(m∆v) satisfies the HUP, after the translation and boost I seem to get:

∆x' = ∆x / sqrt(1- v^2/c^2)

∆v' = ∆v / (1 - v^2/c^2 - (v)∆v/c^2)

This seems to imply that ∆x'>∆x and ∆v'>∆v so that (∆x')(m∆v') > (∆x)(m∆v)...
 
Yes, I specified non-relativistic because I was too lazy to write out all of those terms.
 
Ok. Last question... Things being relative. If you set (∆x')(m∆v') so that it satisfies the HUP then doesn't (∆x)(m∆v) violate the HUP...
 
No. Remember, mv is not the momentum of a relativistic particle.
 
Thanks for your help.
 

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