The physical constants: relationship to mathematics?

In summary, the conversation discusses the possibility of physical constants appearing in mathematics papers that are not focused on physics. The speaker believes that this would be an amazing connection, as there is currently no known way to calculate dimensionless physical constants. While there are constants that are important in both pure mathematics and physics, they are not typically referred to as "physics constants" due to their more general use. The conversation also touches on the difference between quantities in mathematics and physical units, and how mathematics does not necessarily involve geometry.
  • #1
CuriousLearner
2
4
Do we have any examples of physical constants appearing in topics that are focused more on abstract mathematics? For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics? Could they do so if we modified their values by some sort of scalar multiple? I mean for classes of constants that may be related to a particular phenomenon such as mass ratios with respect to the electron of the fermions.
 
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  • #2
Do ##1, \frac{h}{ħ} \, , \, i ## or ##e## count? Or eigenvalues of matrices? If not, what makes you think randomly fixed numbers (due to the definition of units) could appear in math?
 
  • #3
CuriousLearner said:
For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics?
No, unless you count values like 2, pi or similar things.
Such a connection would be amazing, because currently there is no known way to calculate dimensionless physical constants - if the same numbers appear in mathematics somewhere it would indicate some connection between that part of mathematics and the physical constant.
 
  • #4
Certainly there are many constants ( e, π, Fibinachi numbers, the Golden Ratio, etc. ) that are important in purely mathematical issues and also important in physics. However, I don't think they would be called "physics constants" because their use is more general.
 
  • #5
Hey CuriousLearner.

The physical constants are (naturally) in terms of physical units and the relation is between constants that have physical significance - which often involve changes in quantities that have a visual characteristic (i.e. involve geometry in some capacity meaning it involves distance and angle).

Mathematics can be organized in a geometric way but it doesn't need to be.

Also - quantities in mathematics that are able to use arbitrary mappings are dimension-less (example - you can't say find e^x of a unit x since it will change the units).
 

Related to The physical constants: relationship to mathematics?

1. What are physical constants and how are they related to mathematics?

Physical constants are numerical quantities that are considered to be universally constant in nature, such as the speed of light or the gravitational constant. These constants are used in mathematical equations to describe and predict physical phenomena.

2. How are physical constants determined and verified?

Physical constants are determined through experiments and observations in the natural world. Scientists use precise measurements and mathematical calculations to determine the values of these constants. They are then continuously verified through further experiments and observations.

3. Are physical constants truly constant?

While physical constants are considered to be universally constant, there have been some discrepancies in their values over time. This could be due to limitations in measurement techniques or a lack of understanding of the natural world. However, constant efforts are being made to refine and improve the accuracy of these values.

4. How do physical constants impact scientific research and development?

Physical constants play a crucial role in scientific research and development. They provide a foundation for understanding and describing the laws of nature, allowing scientists to make accurate predictions and develop new technologies. Without physical constants, much of modern science and technology would not be possible.

5. Can physical constants change in the future?

While it is possible for physical constants to change in the future, it is highly unlikely. These constants have been observed and verified over many years and have remained constant within the limits of our current understanding. Any changes would require significant advancements in scientific knowledge and understanding of the natural world.

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