Why do particle masses apparently follow a power law?

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Discussion Overview

The discussion revolves around the observation of elementary particle masses and their potential relationship to a power law or exponential curve. Participants explore the implications of this observation, questioning the underlying reasons for the mass distribution among particles.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant notes that the masses of elementary particles seem to suggest an exponential curve, though nothing aligns perfectly, raising questions about underlying explanations.
  • Another participant inquires about the coordinates of the plot, seeking clarification on how the masses are represented.
  • A participant suggests plotting the particles by mass and assigning a "particle number" to visualize the mass distribution, indicating a perceived increase in mass differences at higher energy scales.
  • One participant challenges the notion of an "apparent power law," asserting that the observed increase in mass does not meet the definition of a power law.
  • A later reply rephrases the question, seeking an explanation for the rapid increase in particle masses and the appearance of exponential growth.
  • Another participant expresses skepticism, stating there is no real argument for a power law, but suggests that a deeper, undiscovered theory might explain the mass distribution.
  • One participant reflects on the discussion as a motivation to learn more about the Standard Model, acknowledging the complexity of the question and the need for further mathematical understanding.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the characterization of the mass distribution as a power law, with some asserting that it does not fit this definition. The discussion remains unresolved regarding the underlying reasons for the observed mass patterns.

Contextual Notes

Participants express uncertainty about the definitions and implications of mass distributions, and there are unresolved questions about the mathematical representation of particle masses.

Steve Davis
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Looking at the known masses of the elementary particles, they appear at first sight to be on some kind of exponential curve. It is certainly attractive for there to be such a simplicity - however, and interestingly ...nothing really lines up exactly. Is there any explanation for this or for the reason for an apparent power law underneath?

PS: Most curiously the biggest "bump" is that the strange quark mass is very close to the mass of the muon.
 
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What are the coordinates of the plot - mass vs. ?
 
For simplicity I was thinking a one-dimensional plot - just the masses. What I see is that (mostly!) the differences in mass between each known particle appears to dramatically increase as you go up the energy scale. To get this into a 2d plot I guess you could sort the particles by known mass then assign a "particle number" to each on x and do a plot on y to see what looks like a rather bumpy exponential curve (rather like the "graph of e"). Whichever, it seems hard to ignore the apparent power law that it suggests?
 
There is no "apparent power law". All you have said is that particles get big in a hurry - true, but that is not the definition of a power law.
 
Thanks for the answers! Let me rephrase the question: is there any explanation for why known particle masses seem to get big in a hurry? Why does it look like an exponential increase, and yet it isn't?
 
No, there is not.
A nice distribution on a logarithmic scale could be considered as "natural" in some way, as many things are distributed over many orders of magnitude, but this is not a real argument.

It might follow from a deeper, undiscovered theory.
 
Thanks to all. This problem has inspired me to learn more about the Standard Model. I'm sure that there has to be some explanation for the masses of fundamental particles, and there's a good reason why it isn't obvious as yet. It is however unlikely that I'll appreciate even the question fully until I know more about the math. A good outcome.
 

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