How are probabilistic equations of physics usually formulated?

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Discussion Overview

The discussion revolves around the formulation of probabilistic equations in physics, particularly in the context of quantum mechanics. Participants explore whether these equations are derived from established laws, developed from experimental data, or a combination of both approaches.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether probabilistic equations are derived from accepted laws or if they are formulated after conducting experiments, suggesting that both methods might be possible.
  • The same participant expresses a personal belief that derivation from established laws is more likely, citing the precision of the equations they have encountered.
  • Another participant challenges the notion that Schrödinger's approach was random, asserting that it was inspired by an analogy between quantum mechanics and classical mechanics, similar to the relationship between wave optics and geometrical optics.
  • A later reply appreciates the linked post that provides further details on Schrödinger's methodology, while also expressing frustration over the tendency of some individuals to fabricate answers rather than admit uncertainty.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the formulation of probabilistic equations, with differing views on Schrödinger's approach and the nature of deriving these equations from laws versus experimental data.

Contextual Notes

The discussion reflects varying interpretations of historical approaches in quantum mechanics and the complexities involved in understanding the derivation of probabilistic equations. There are unresolved assumptions regarding the methods used in formulating these equations.

Mingy Jongo
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Are they derived from accepted laws and then tested, or are experiments carried out first and then a function is searched for that matches the results (or possibly both, or neither)? For example, how would an equation that gives the probability of electron locations be thought of? My "gut feeling" is that the former would be done, as the equations I've seen seem too precise to be otherwise, but as I do not have much experience in this field, I thought it would be better to ask.
 
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Mingy Jongo said:
Are they derived from accepted laws and then tested, or are experiments carried out first and then a function is searched for that matches the results (or possibly both, or neither)? For example, how would an equation that gives the probability of electron locations be thought of? My "gut feeling" is that the former would be done, as the equations I've seen seem too precise to be otherwise, but as I do not have much experience in this field, I thought it would be better to ask.

I asked my QM professor this. He said Schrödinger just randomly decided to take the (well known) wave equation for string vibrations, etc. and modify it until it fit experimental data. Seems kind of sketchy to me... but hey, he has a Ph.D. :P
 
Last edited:
jtbell said:
No, Schrödinger did not proceed randomly, but was inspired by an analogy: quantum mechanics is to classical mechanics as wave optics is to geometrical (ray) optics. For some more details, see here:

https://www.physicsforums.com/showthread.php?p=418069#post418069

Nice post that you've linked to. I've always wondered why people feel compelled to make up answers instead of just saying "I don't know".
 

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