If there was a region of space-time shaped like a Mobius Strip

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SUMMARY

The discussion centers on the implications of a hypothetical region of space-time shaped like a Möbius strip on particle spin. It concludes that spin, defined as an axial vector, would change coordinates when an observer alters their orientation, resulting in a potential reversal of spin for particles traveling along the strip. Furthermore, if such a structure existed, left-chiral particles could transform into right-chiral particles, contradicting the observed asymmetry in the universe. Therefore, under standard assumptions, the universe does not resemble a Möbius strip.

PREREQUISITES
  • Understanding of axial vectors and their properties
  • Familiarity with particle spin and chirality
  • Basic knowledge of topology, specifically Möbius strips
  • Concept of homogeneity in the universe
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  • Research the mathematical properties of axial vectors in quantum mechanics
  • Explore the concept of chirality in particle physics
  • Study the implications of topology in theoretical physics
  • Investigate the homogeneity of the universe and its effects on particle behavior
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The discussion is beneficial for physicists, particularly those specializing in quantum mechanics and theoretical physics, as well as students and researchers interested in the implications of topology on particle behavior.

Edward Solomo
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Would the spin of a particle be measured the same by any set of observers upon that strip?

Would an observer experience a reversal of spin if the particle traveled far enough along the strip?
 
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Edward Solomo said:
Would the spin of a particle be measured the same by any set of observers upon that strip?
Yes, if you correctly defined "the same". Spin is an axial vector. It will change coordinates when you roll upside down.

Would an observer experience a reversal of spin if the particle traveled far enough along the strip?
Yes, spin as an axial vector will change direction when you change the space orientation, which happens on the 3d equivalent of the Moebius strip.

If we lived on a Moebius strip, it would also mean that left-chiral particles can change into right-chiral. If we also assume that the Universe is homogenous, then there should be no assymetry between left-handed and right-handed particles, which is not the case. Thus, we don't live on a Moebius strip under most common assumptions.
 

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