The discussion centers on the physical significance of the expression (p.r - Et) in the context of special relativity (SR) and its relation to the Minkowski inner product. Participants assert that while this expression is mathematically significant as it represents the inner product of a four-vector and a four-covector, it lacks direct physical significance. The conversation highlights the role of action in both non-relativistic and relativistic physics, emphasizing that the wave function can satisfy different wave equations based on the chosen dispersion relation, such as ##E=\frac{p^2}{2m}## for non-relativistic cases and ##E^2=p^2+m^2## for relativistic scenarios.
PREREQUISITESPhysicists, particularly those specializing in quantum mechanics and relativity, as well as students seeking to deepen their understanding of the relationship between action, wave functions, and the principles of special relativity.
No.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?
Jilang said:Why do you say not?
Viewing it quite literally from the maths, time orthogonal to real time we experience?stevendaryl said:Well, it's not clear what it could possibly mean to spend an imaginary amount of time doing something.
"Time orthogonal to real time" is meaningless noise. Please do not further pursue this nonsense.Jilang said:Viewing it quite literally from the maths, time orthogonal to real time we experience?