Can we quantize Aristotelian Physics?

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SUMMARY

The discussion centers on the potential quantization of Aristotelian physics, which parallels Newtonian physics in its principles. The author contrasts Newton's second order differential equation, F=ma, with the first order differential equation p=mv in Aristotelian terms. The proposal involves utilizing the representation theory of the Galilei group, specifically excluding Galilean transformations, to construct Hilbert space operators. The author anticipates that this approach may yield fewer conserved quantities in the resulting quantum theory.

PREREQUISITES
  • Understanding of Aristotelian and Newtonian physics principles
  • Familiarity with differential equations, specifically first and second order
  • Knowledge of quantum mechanics and Hilbert space operators
  • Concepts of representation theory and Galilei group transformations
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  • Research the implications of quantizing classical theories in physics
  • Study the representation theory of the Galilei group in detail
  • Explore the differences between first order and second order differential equations
  • Investigate conserved quantities in quantum mechanics and their significance
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Physicists, particularly those interested in theoretical physics, quantum mechanics, and the historical context of classical physics theories.

lugita15
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Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an unbalanced force", we have "An object at rest stays at rest unless acted on by an unbalanced momentum." Newton's F=ma, which is a second order differential equation, becomes p=mv, which is a first order differential equation. Otherwise, we have business as usual.

My question is, can we quantize this theory? Instead of constructing Hilbert space operators using the representation theory of the full Galilei group, we just use the representation theory of the Galilei group excluding Galilean transformations, i.e. just consisting of spatial translations, spatial rotations, and time translations. What would such a quantum theory look like? I can tell right off the bat there will probably be fewer conserved quantities, but not much more.

Any help would be greatly appreciated.

Thank You in Advance.
 
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Aum, any thoughts on this?
 

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