Undergrad The Debroglie Relation and SR?

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The discussion centers on the significance of the expression (p.r - Et) in the context of special relativity (SR) and its relation to the concept of action. It highlights that this expression represents the Minkowski inner product of four-vectors and is Lorentz invariant, suggesting a deeper connection to the principles of both non-relativistic and relativistic quantum mechanics. Participants debate whether this mathematical relationship has physical significance, with some asserting that it is merely a coincidence while others suggest it relates to the fundamental invariant of action. The conversation also touches on the nature of the Lagrangian and its role in defining physical laws across different frameworks. Ultimately, the consensus leans towards recognizing action as a central invariant in both classical and quantum physics, linking various physical phenomena.
  • #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.
 
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  • #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"
 
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  • #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.
 
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