Time Reversal Spin: Why Does it Require Flipping?

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SUMMARY

Time reversal in quantum mechanics necessitates the flipping of spin due to the fundamental properties of angular momentum. Orbital angular momentum, represented by the equation \(\vec{L} = \vec{r} \times \vec{p}\), inherently reverses sign when time is reversed, as momentum \(\vec{p}\) also reverses. Since spin is a form of angular momentum, it must also change sign to maintain consistency in the physical laws governing angular momentum. This relationship underscores the necessity of flipping spin during time reversal.

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  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum concepts
  • Knowledge of time reversal symmetry
  • Basic grasp of vector mathematics in physics
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  • Research the mathematical framework of time reversal in quantum mechanics
  • Study the implications of angular momentum conservation laws
  • Explore the relationship between spin and orbital angular momentum
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Students and professionals in physics, particularly those focused on quantum mechanics, angular momentum, and time reversal symmetry. This discussion is beneficial for anyone seeking to deepen their understanding of the interplay between spin and time reversal in quantum systems.

aaaa202
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Does anyone know why time reversal requires spin to be flipped? It seems like my book assumes that, but I have no idea why.
 
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aaaa202 said:
Does anyone know why time reversal requires spin to be flipped? It seems like my book assumes that, but I have no idea why.

Well, it's obvious that orbital angular momentum reverses sign under time reversal, because it's [itex]\vec{L} = \vec{r} \times \vec{p}[/itex], and momentum reverses sign. Since angular momentum can move from spin to orbital, I don't think it would be consistent to reverse one and not the other. But I don't know of a proof.
 
Spin is angular momentum in the rest frame. Angular momentum has to change sign under time reversal by definition.
 

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