Question on shifting field gradients by an angle

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Discussion Overview

The discussion revolves around the implications of shifting field gradients by an angle in the context of energy representation in physics, particularly focusing on the relationship between energy, complex phases, and relativistic dynamics. Participants explore theoretical aspects, mathematical formulations, and interpretations of concepts such as the Dirac sea and negative energy solutions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that if energy can be expressed as E=Mφ, then φ can undergo a shift, leading to changes in energy represented by complex exponentials.
  • Others question the validity of a complex phase for energy, suggesting it seems odd and challenging its physical interpretation.
  • A participant references the Dirac equation, noting that negative energy solutions are common in quantum mechanics, which raises questions about the nature of complex shifts in energy.
  • Some argue that the Dirac sea concept is outdated, while others defend its relevance in understanding particle physics, particularly regarding negative energy solutions.
  • There is a discussion about the relativistic energy-momentum relation and whether it can be reconciled with the proposed shifts in energy expressions.
  • Participants express uncertainty about the implications of replacing constants like c with field variables in energy equations.
  • Some participants assert that the concept of virtual photons and negative energy in quantum field theory still holds relevance, while others challenge this view.
  • There is a proposal to evolve the discussion by questioning how to make E=Mφ relativistic, indicating a desire to reconcile the initial energy expression with relativistic principles.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of complex phases in energy or the relevance of the Dirac sea concept. Multiple competing views remain regarding the interpretation of negative energies and their implications in quantum field theory and relativistic dynamics.

Contextual Notes

Limitations include unresolved assumptions about the nature of complex energies, the applicability of classical versus relativistic frameworks, and the definitions of terms like "field" and "energy" in this context.

  • #31
Then let's not so hastily equalize the terms. Let us consider just E=M\phi. If it is Mc^2 then how do you make it relativistic? I saw your last answer and liked it, any others?
 
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  • #32
Goldstone1 said:
Then let's not so hastily equalize the terms. Let us consider just E=M\phi. If it is Mc^2 then how do you make it relativistic? I saw your last answer and liked it, any others?

No, I think that's all I can contribute so far.
 
  • #33
Polyrhythmic said:
No, I think that's all I can contribute so far.

Well thank you. I may have some more questions. These questions as you know are based on that paper I sent here, but was denied. The contributions of the posters will not be disregarded in the paper.
 
  • #34
Right I do have more questions:

In fact I do have one. Even though you are saying E=M\phi=Mc^2 is technically correct, we are to ignore any contribution to momentum, which seems like a strange and incorrect statement: In our normal notation, it would be:

E=M\Delta\phi(x)

since

\Delta \phi(x) =\phi(x) \rightarrow \phi*(x)

which through substitution, gives a more simplistic form

\Delta E=M\phi(\Lambda^{-1} x)

There is also now the question of what energy has been taken by the shift. If the change in the Hamiltonian of the system was purely gravitational and no other added energies, then the shift mathematically can be given as:

\phi(x) \rightarrow \phi*(x)=\phi(\Lambda^{-1} x)

where the inverse \Lambda^{-1} states that the field has definitely been shifted. If \phi is no longer arbitrary, we can state it is actually the gravitational field, then it's also an energy perturbation of the field as well:

\Delta E_g=M_g\phi(\Lambda^{-1} x)
 
Last edited:
  • #35
Goldstone1 said:
Even though you are saying E=M\phi=Mc^2 is technically correct, [...]

I didn't say that this was correct, I provided you with a modified version I could make sense of.
 
  • #36
You want me to start using the rest symbol M_0
 

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