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  Did nature or mathematical physicists invent the renormalization group?

+ 0 like - 2 dislike

Or in other words:

The renormalization group is a systematic theoretical framework and a set of elegant (and often effective) mathematical techniques to build effective field theories, valid at large scales, by smoothing out irrelevant fluctuations at smaller scales.

But does the renormalization group also describe something that nature does?

If you think the question doesn't make sense, please say so but also explain why.

asked Mar 7, 2018 in Chat by Giulio Prisco (190 points) [ no revision ]
recategorized Mar 7, 2018 by Arnold Neumaier
Most voted comments show all comments

Who has invented renormalizations? Physicists, mathematical physicists, mathematicians, but in no way the Nature. Our ways of nature perception, our commodities to describe this or that push us to advance this or that description. Our preferences, to be short.

I voted against this question as it's really a metaphysical question.

I  moved the question to chat because of its metaphysical nature.

One can suppose, perhaps, that Renormalization is successfully mimicking some aspect of Nature, but that leaves a question of whether renormalization is a complete and the only way to mimic nature successfully. Even if one thinks that renormalization is adequate mathematics, which it is, or even if one thinks that it is elegant (though to me there are too much complications for it to rise to that height), the aim of mathematical physics is always to create better systematic theoretical frameworks, more suited to the needs of physics, than we have now. We have to believe we can do better, that it is worthwhile to stand on the shoulders of those who did brilliant work, without anything other than respect for what they did. Otherwise we should go do something else, something we do believe is worthwhile.

@PeterMorgan - Of course every physical theory can and will be improved. At this moment I am interested in whether the current renormalization group theories do, as you say, mimic some aspect of Nature.

Most recent comments show all comments

@MathematicalPhysicist re "it's really a metaphysical question" - Perhaps, but than any really interesting question of the type "what is really out there" is a metaphysical question. If so, any interpretative physics discussion is really metaphysics.

@ArnoldNeumaier - Thanks for reminding me of the Chat option. I would have placed this thread here if I had thought of it.

Note to devs: Perhaps a box with the most recent chats could/should be featured in the front page?

1 Answer

+ 2 like - 0 dislike

Nature just is and happens.

Since the human culture is part of nature, whatever humans invent is in a sense invented by nature, if the latter term makes any sense. 

Humans discover (and do not invent) principles of Nature, including the renormalization group. Invented are only the particular forms the principles are represented symbolically. 

answered Mar 7, 2018 by Arnold Neumaier (15,787 points) [ no revision ]

The OP clearly distinguishes us humans and Nature, i.e., what we investigate in Physics. One should not say that Nature investigates Nature, because it does not make sense.

"Renormalization group" is not a "principle of Nature", but our own "technique" to deal with this or that problem. It has been conceived as such and as such it is.

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