Does Multi Path Integral Formulation Violate Special Relativity?

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Discussion Overview

The discussion centers on whether the multi-path integral formulation of quantum mechanics violates the principles of special relativity, particularly concerning the possibility of particles traveling faster than the speed of light (c). The scope includes theoretical implications and interpretations of mathematical constructs within quantum mechanics.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants question if the multi-path integral formulation allows for speeds greater than c and whether this constitutes a violation of special relativity.
  • One participant argues that particles with speeds greater than c are not physical entities but rather mathematical constructs introduced for convergence purposes.
  • Another participant clarifies that the discussion involves distinguishing between group speed and phase speed, suggesting that the context of "speed" needs to be defined.
  • A later reply asserts that while some paths in the formulation may correspond to speeds greater than c, this does not imply a violation of special relativity, as no information can be transmitted faster than c through these interpretations.
  • There is a contention regarding the reality of particles with speeds greater than c, with differing views on their significance in the context of the formulation.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of speeds greater than c within the multi-path integral formulation, with no consensus reached on whether these speeds have physical meaning or implications for special relativity.

Contextual Notes

The discussion highlights the complexity of interpreting mathematical constructs in quantum mechanics and their implications for established physical theories, with unresolved questions about the definitions and significance of various speeds.

cragar
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does the multi Path integral formulation violate special relativity ! do we get speeds faster than c.
 
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the particles with speed greater than 'c' are no physical particles they have no meaning at all, i think they are introduced just as a mathematical trick to make thing converge.
 
cragar said:
does the multi Path integral formulation violate special relativity ! do we get speeds faster than c.

What speed are you talking about? Group speed or phase speed?
 
feynmann said:
What speed are you talking about? Group speed or phase speed?
Neither. He's talking about path integrals, which add up the probability amplitudes associated with each classical path, and some of those paths correspond to speeds >c.

The answers to the questions in #1 are "no" and "yes". To "violate" SR you'd have to be able to send a message with a speed greater than c. You can't do it just by breaking a mathematical expression into pieces and interpreting some of the pieces as speeds >c.

zetafunction said:
the particles with speed greater than 'c' are no physical particles they have no meaning at all, i think they are introduced just as a mathematical trick to make thing converge.
They are no less and no more real than the ones with speed less than c, and this doesn't have anything to do with convergence.
 
i see
 

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