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In this post Matt Strassler talks about proportionalities and symmetry in the context of massless photons.

I asked this question

«x and y are not invariant, but the equation which relates them is invariant! » This sounds like the definition of a proportionality, ratios making up the equality of ratios vary but the rule of the proportionality stays same. What is the relationship?

Matt Strassler replied but I did not really understand the relationship between proportionalities and symmetry. I did not want to discuss the issue in comments. Can anybody explain this in more simple terms? Is symmetry more fundamental then proportionalities? What is their relation?

zeynel
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  • Proportionality is when the ratio doesn't depend on either value; symmetries in physics are when the rule relating the variables doesn't vary under certain ways of modifying your perception, even if those change the variables' measured values. – J.G. Jun 12 '22 at 19:05
  • @J.G. I don't understand. So in physics symmetry is related to perception? Can you give some examples? Also can you clarify Strassler's notation? – zeynel Jun 13 '22 at 14:25
  • This explains it better than I can in a comment, but the basic idea is this. If I describe the world in terms of a coordinate system (featuring coordinates such as $x$), you'll describe it in terms of another (featuring coordinates such as $x'$), e.g. because of our relative motion. But we'll still agree on e.g. the laws of motion, because they're equally true in both coordinate systems. However, that fact actually constrains the possible forms of these laws. – J.G. Jun 13 '22 at 14:30

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