Why are free parameters bad for a theory?

  • #1
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It is often said that one of the drawbacks of the standard model is that it has many free parameters. My question is two-fold:
  1. What exactly is a free parameter? My understanding is that the free parameters of a model/theory are the ones that cannot be predicted by the theory and need to be measured and put in the theory 'by hand' so to speak. Are all constants of nature free parameters then? Also, can you give me an example of a non-free parameter in a theory?
  2. Why is it bad for a theory to have free parameters? Couldn't be that some quantities in nature such as the mass of the electron just 'happen' to have a certain value that cannot be predicted by a theory?
 
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  • #2
Orodruin
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1. You almost answered this yourself. A free parameter is a parameter in the model that cannot be predicted from the other parameters of the model and that a priori could take any of a number of values (often along a continuous spectrum).

2. It may not be ”bad” per se, but the more free parameters a model has, the less predictive it becomes. John von Neumann is often quoted to have said ”give me four parameters and I will fit you an elephant”. The sentiment bein that if you have enough free parameters, it becomes easier to fit almost any data.
 
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  • #3
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Also, can you give me an example of a non-free parameter in a theory?
Everything you can derive from other things. As an example, the mass of the electron or positron is a free parameter in the Standard Model, but their mass ratio has to be exactly 1. That 1 is not a free parameter because particles and antiparticles need to have the same mass in QFT. Often there is some ambiguity in what exactly you call the free parameter. You could e.g. say "the electron mass is a free parameter, the positron mass is derived" or call the positron mass a free parameter and the electron mass derived. Doesn't change the fact that there is one free parameter here.
 
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  • #4
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This begs the question do we have BSM theories that have only one free parameter in them?
I am assuming you have to have at least one free parameter.
What is the success if there is if such theories exist?
 
  • #5
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No. Reducing everything to a single parameter - or even the more modest goal of "fewer than the SM" - would be an amazing success. Generally BSM models come with extra parameters.
 

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