How are One-Dimensional Numbers Useful (Coupling Constants)

In summary, the use of dimensionless numbers to represent physical quantities arises naturally in quantum field theory. In relativistic quantum theories, dimensionless coupling constants play a special role and are used to compare the strength of forces. This allows for a clearer understanding of the relative sizes of different forces, as seen in the example of the electron's electric charge being represented as e^2=1/137 regardless of the previous units used.
  • #1
TheDemx27
Gold Member
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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.
 
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  • #2
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.
 

1. What are one-dimensional numbers?

One-dimensional numbers, also known as coupling constants, are numerical values that describe the strength of the interaction between two particles or systems.

2. How are one-dimensional numbers used in science?

One-dimensional numbers are used in various scientific fields, such as physics, chemistry, and biology, to understand and predict the behavior of particles and systems. They are especially useful in the study of molecular structures and interactions.

3. What is the significance of coupling constants in quantum mechanics?

In quantum mechanics, coupling constants play a crucial role in determining the energy levels and behavior of quantum systems. They are used to describe the strength of the forces between particles, such as the electromagnetic force or the strong nuclear force.

4. How are one-dimensional numbers calculated?

One-dimensional numbers are calculated using experimental data or theoretical models. In quantum mechanics, they are often derived from the Schrödinger equation, which describes the wave function of a particle or system.

5. Can one-dimensional numbers be negative?

Yes, one-dimensional numbers can be negative. In some cases, a negative coupling constant indicates an attractive force between particles, while a positive value indicates a repulsive force.

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