How do relativity and quantum mechanics contradict each other?

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Discussion Overview

The discussion centers on the contradictions between relativity and quantum mechanics, exploring the differences in predictions made by each theory and the challenges in reconciling them. It includes theoretical considerations and questions about specific equations and concepts within both frameworks.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that the Schrödinger equation is not Lorentz-invariant, leading to different predictions for observers in relative motion, which poses a problem for relativity.
  • Another participant highlights that quantum mechanics conserves particle number, while relativity allows for particle creation under certain energy conditions, suggesting a fundamental conflict.
  • Questions are raised about the Dirac equation and its ability to reconcile quantum mechanics and relativity, with some participants asserting it is fully relativistic but still lacking in addressing varying particle numbers.
  • There is a query regarding the claim that massive particles can reach the speed of light, with a response indicating that they cannot, but can approach it very closely.

Areas of Agreement / Disagreement

Participants express differing views on the compatibility of quantum mechanics and relativity, with no consensus on how to reconcile the two theories or the implications of specific equations like the Dirac equation.

Contextual Notes

Participants discuss the limitations of the Schrödinger and Dirac equations in the context of relativity, noting issues such as Lorentz invariance and the treatment of particle number, but do not resolve these complexities.

mrspeedybob
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I didn't think this question really belonged in either sub-section so I put it here. I hope that's OK. I've always heard that they contradict each other but I've never understood how. What predictions do they make differently?
 
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The biggest issue is that the Schrödinger equation (the fundamental equation of QM) is not lorentz-invariant. This means that the equations of QM are different for two observers moving at a relative velocity to one another---which is clearly unacceptable for relativity.

Additionally, QM always maintains a conserved particle number. From relativity we learn that E=\gamma mc^2, and thus whenever the energy of a system (e.g. a pair of photons) is greater than the rest mass energy of another particle-pair (e.g. electron-positron pair), we can expect some probability of particle creation.
 
some one told me yesterday that massive particles indeed can reach the speed of light, is this true?
 
snackster17 said:
some one told me yesterday that massive particles indeed can reach the speed of light, is this true?

99.99...% the speed of light and as many "9"'s you can afford, but never 100% the speed of light.

Now frankly, it does make sense that anything massive could never go as fast as something that is not.
 
Dr Lots-o'watts said:
What about the Dirac equation? What is it missing to reconcile the two?
http://en.wikipedia.org/wiki/Dirac_equation
I'm pretty sure the dirac equation is fully relativistic.

The Dirac equation is still missing other features... e.g. remember it only applies to spin-1/2 particles, and its still not a field theory---so again, it has issues with varying particle number.
 

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