Why Does E=mc^2 Imply Creation of Particles?

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Discussion Overview

The discussion centers on the implications of Einstein's equation E=mc² in the context of particle creation, particularly within quantum field theory. Participants explore whether this equation inherently suggests the possibility of creating particle-antiparticle pairs or if this interpretation requires additional theoretical frameworks.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that references in quantum field theory often claim E=mc² implies particle creation, questioning the validity of this assertion.
  • Another participant argues that E=mc² alone does not demonstrate the possibility of particle creation, suggesting it only indicates that mass corresponds to energy, which might allow for particles if sufficient energy is available.
  • A different viewpoint suggests that initially, the focus was on extracting energy from mass rather than on particle creation, with later experiments revealing the dual nature of matter and energy conversion.
  • One participant critiques the statement regarding E=mc² implying creation as "sloppy," asserting that the full equation E²=p²c²+(mc²)² leads to the Dirac equation, which predicts antiparticles but does not directly address the creation or annihilation processes without field theory.
  • Concerns are raised about the clarity of the original statement in Peskin and Schroeder, suggesting potential context loss in their explanation.

Areas of Agreement / Disagreement

Participants express differing views on whether E=mc² directly implies particle creation, with no consensus reached on the interpretation of the equation in this context.

Contextual Notes

Participants highlight the need for field theory to fully understand particle creation and the limitations of relying solely on E=mc². There is also mention of the historical evolution of thought regarding energy and mass conversion.

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Many references of quantum field theory begin with an explanation of the necessity of a field theory as opposed to a single particle theory. Sometimes they use the argument that E=mc^2 implies particle creation.
For example, in Peskin "the Einstein relation E=mc^2 allows for the creation of particle-antiparticle pairs" (page 13).

How does Einstein's relation imply the possibility of creation of particles? Seems to me that you might as well say that the kinetic energy formula Ek=(1/2)mv^2 implies creation of particles.
 
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E=mc^2 (or, better, ##E^2=(mc^2)^2 + (pc)^2##) alone does not show that particle creation is possible. It just shows that mass has a corresponding energy, and indicates that it might be possible to get particles if you have that energy available.
 
I don't think that at first that was considered. Attention focussed on the possibility of obtaining energy from mass. (Energy from KE is a no-brainer)

Of course, experiments rapidly threw up the fact of matter/energy conversion both ways.
Then it becomes somewhat obvious with hindsight that E= etc. implies creation.
 
It's a really sloppy statement. E²=p²c²+(mc²)² is where you get Dirac equation from, but even that merely predicts existence of anti-particles. Not of creation/annihilation process. You can only get pair creation/annihilation once you consider field theory. The motivation for that has to come from experiment.

I'm not really sure why Peskin and Shroeder put it that way. I thought there might be some context loss, but no, that's all they say on the matter.
 

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