The Debroglie Relation and SR?

Click For Summary

Discussion Overview

The discussion revolves around the physical significance of the expression (p.r - Et) in the context of special relativity (SR) and its relation to the de Broglie relation. Participants explore whether this expression, which is the Minkowski inner product of four-vectors, has any deeper implications in SR, particularly regarding action and angular momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the expression (p.r - Et) is Lorentz invariant and question its physical significance in SR.
  • Others argue that the wave function can be valid in both relativistic and non-relativistic contexts, depending on the chosen dispersion relation.
  • A participant suggests that the expression might relate to a different kind of relativistic action, seeking to understand its commonality in knowledge.
  • Some participants assert that the expression is merely a mathematical coincidence without physical significance, comparing it to wave functions in different theoretical frameworks.
  • There is a contention regarding the nature of the inner product, with some insisting it involves a 4-vector and a 4-covector, rather than two 4-vectors.
  • A later reply emphasizes the connection between action and the Lagrangian, discussing how action is invariant and fundamental in both classical and relativistic contexts.
  • Another participant expresses uncertainty about their understanding of the topic, indicating a lack of clarity on the implications of the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the physical significance of the expression (p.r - Et) and its implications in SR. There is no consensus on whether it holds any deeper meaning or is simply a mathematical artifact.

Contextual Notes

Some discussions involve assumptions about the definitions of vectors and covectors, as well as the nature of the Minkowski inner product, which may not be universally agreed upon. The exploration of action and its invariance also introduces complexities that remain unresolved.

  • #31
Jilang said:
I am curious as to how this might be applied to quantum tunnelling. Could it be interpreted that a particle spends only imaginary time inside the barrier?
No.
 
  • Like
Likes   Reactions: vanhees71
Physics news on Phys.org
  • #32
Why do you say not?
 
  • #33
Jilang said:
Why do you say not?

Well, it's not clear what it could possibly mean to spend an imaginary amount of time doing something.
 
  • #34
See "Interpreting attoclock measurements of tunnelling times" http://www.nature.com/nphys/journal/v11/n6/full/nphys3340.html

From the abstract: "We show that, in the hydrogen atom, optical tunneling is instantaneous."

Professor Anatoli Kheifets explains his results: (see http://phys.org/news/2015-05-physicists-quantum-tunneling-mystery.html#jCp)

"At that timescale the time an electron takes to quantum tunnel out of an atom was thought to be significant. But the mathematics says the time during tunneling is imaginary - a complex number - which we realized meant it must be an instantaneous process"
 
Last edited by a moderator:
  • Like
Likes   Reactions: Jilang
  • #35
stevendaryl said:
Well, it's not clear what it could possibly mean to spend an imaginary amount of time doing something.
Viewing it quite literally from the maths, time orthogonal to real time we experience?
 
  • #36
Jilang said:
Viewing it quite literally from the maths, time orthogonal to real time we experience?
"Time orthogonal to real time" is meaningless noise. Please do not further pursue this nonsense.
 
  • Like
Likes   Reactions: vanhees71

Similar threads

Wavelength = deBroglie Wavelength?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad De Broglie relation using four momentum in particle physics
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What specific momentum should be used in the matter wave?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Wave-particle duality and localization
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad The relativistic de Broglie equation
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Coord Transform in de Sitter Space: Phys Significance &Linearity?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate A question related to de Broglie wavelength and the Uncertainty Principle
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad De Broglie relation - new student
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How do angular displacement and rapidity relate in special relativity?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Resolving Tiny Structures: De-Broglie-Relation & Relativity
  • · Replies 2 ·
Replies
2
Views
955