Is a mobius strip spin 1/2 object?

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Discussion Overview

The discussion revolves around the concept of whether a Möbius strip can be considered a spin 1/2 object, drawing connections between classical and quantum properties of spin. It explores the nature of electron spin, the characteristics of the Möbius strip, and their potential relationships within the context of quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants question the derivation of electron spin 1/2 and its intrinsic nature in quantum theory, suggesting a connection to the properties of a Möbius strip.
  • Others argue that a Möbius strip is merely a twisted piece of paper and does not relate to quantum theory.
  • A participant points out that a Möbius strip is a non-orientable manifold and draws parallels between its orientation and the behavior of spinors, which require 4π rotations to return to their original state.
  • Another contribution mentions that the analogy of the Möbius strip is used pedagogically in discussions of spin, referencing its appearance in educational materials related to quantum mechanics.
  • One participant reflects on their high school physics experience, suggesting that classical theories were applied to understand electron spin, while expressing uncertainty about modern quantum mechanics and its implications for the concept of spin.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the Möbius strip and spin 1/2 objects, with some asserting a connection and others denying any relevance. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

There are limitations in the discussion regarding the definitions of spin and the assumptions about classical versus quantum interpretations. The relationship between classical angular momentum and quantum spin is not fully explored, leaving some mathematical and conceptual steps unresolved.

Sammywu
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Remember Phiysicist always say electron has a spin of 1/2; I can't remember how it was derived?

But I noticed a mobius strip exihibit interesting attribute. Can we consider a mobius strip a spin 1/2 object?
 
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Electron spin 1/2 is an intrinsic quantum theory property. A mobius strip is a twisted piece of paper - it has nothing to do with quantum teory.
 
Originally posted by mathman
Electron spin 1/2 is an intrinsic quantum theory property. A mobius strip is a twisted piece of paper - it has nothing to do with quantum teory.

Well, a mobius strip is a non-orientable manifold, not a "twisted piece of paper". The obvious "connection" between the orientation of a unit normal vector on a mobius strip and 2-spinors (the representations of angular momentum states) is that they both require rotations of [tex]4\pi[/tex] to regain their original orientation.

So, mobius strip normal orientation and spinor rotations aren't that different.

Shouldn't this discussion be in the Quantum Physics subforum?
 
Last edited:
As has been mentioned by many people before us, the entire spin-1/2 business falls out of relativistic Q.M.

The Mobius strip property is an analogy that is used in discussions of spin, at least pedagogically - I remember it being mentioned in undergraduate Q.M., as well as in the ever so delightful Principles of Magnetic Resonance by C.P. Slichter. It's intended to serve as a useful first step to understanding rotations.
 
I thought my high school Physics teacher already showed us the spin 1/2 of electrons by examining its angular momentum against its light absortion spectrum.

That's why I thought this could be put in here as all it involves is rotation and angular momentum.

What you told me now is that the electrons' spins are more likely a QM quantity not related to a classical anugular rotation. I am not familiar with the modern QM at all. But didn't this spin 1/2 come originally from applying classical theory to the spectrum?
 

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