Length contraction on quantum scale?

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SUMMARY

The discussion centers on the measurement of relativistic length contraction at the quantum scale, specifically regarding the Planck length, which is defined as 1.616 x 10-35 meters. It highlights the theoretical challenges in measuring length contraction due to the Planck length's indivisibility and its insignificance in current quantum theories of matter operating within Minkowski spacetime. The conversation emphasizes that while length contraction is not practically measurable at this scale, the failure of existing theories at the Planck scale remains an open question, necessitating a quantum theory of gravity for further understanding.

PREREQUISITES
  • Understanding of Planck length and its significance in quantum mechanics
  • Familiarity with Minkowski spacetime and special relativity
  • Knowledge of quantum theories of matter
  • Basic concepts of quantum gravity theories
NEXT STEPS
  • Research the implications of Planck length in quantum gravity theories
  • Study the differences between Minkowski spacetime and curved spacetime in general relativity
  • Explore current quantum theories of matter and their limitations at the Planck scale
  • Investigate experimental approaches to measuring phenomena at quantum scales
USEFUL FOR

The discussion is beneficial for physicists, quantum mechanics researchers, and anyone interested in the intersection of quantum theory and relativity, particularly in understanding the implications of length contraction at the Planck scale.

jbrussell93
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How can relativistic length contraction be measured at the quantum scale? Since a Planck length by definition cannot be divided, how can something that is 1 Planck length, traveling near the speed of light, contract with respect to an observer? In other words, how can an observer possibly measure the length of contraction?
 
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The Planck length is many orders of magnitude smaller than anything that can be measured, so there are no practical issues with length contraction. There is probably a theoretical issue, but it's only an issue in quantum gravity theories, where the Planck scale has a special significance. The current theories of elementary particles are just quantum theories of matter in Minkowski spacetime (i.e. the spacetime of special relativity), and the Planck length doesn't have any significance in Minkowski spacetime, so these theories don't predict that anything will be different at those scales. They are expected to fail at those scales (or sooner), but that's another story. The precise way in which they will fail is unknown. Only a quantum theory of gravity can explain that.
 

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