How are One-Dimensional Numbers Useful (Coupling Constants)

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SUMMARY

One-dimensional numbers, specifically dimensionless coupling constants, play a crucial role in quantum field theory by providing a standardized way to compare the strength of forces without ambiguity related to units. The discussion highlights that dimensionless numbers, such as the electric charge of the electron expressed as e²=1/137, allow for a clearer understanding of interactions in relativistic quantum theories. This approach eliminates confusion that arises from varying units, making it easier to assess the relative strength of forces in physics.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with dimensionless numbers and their significance
  • Knowledge of relativistic quantum theories
  • Basic grasp of electromagnetic interactions
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  • Research the role of coupling constants in quantum field theory
  • Explore the concept of natural units in physics
  • Study the implications of dimensionless numbers in force comparisons
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Physicists, students of quantum mechanics, and anyone interested in the foundational concepts of quantum field theory and the significance of dimensionless numbers in understanding physical interactions.

TheDemx27
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How would it make any sense to use dimensionless numbers to represent physical things?

From wikipedia:
The coupling constant arises naturally in a quantum field theory. A special role is played in relativistic quantum theories by coupling constants which are dimensionless, i.e., are pure numbers.

If you are comparing the strength of forces, and you are using these numbers to do so, I would have thought that these numbers would represent units of - well, force.

Clearly I must be missing something.

Thanks.
 
Physics news on Phys.org
The size of any constant with units is ambiguous. Is g=980 cm/sec^2 large or 0.0098 km/sec^2 small?
Expressed as a dimensionless number in 'natural' units, the electric charge of the electron is e^2=1/137 regardless of what units were used before it was made dimensionless, so the EM interaction is seen to be small.
 

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