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The concept underlying renormalization/invariance as we now understand it, is a fundamental and profoundly beautiful idea about the very nature of what it means
by ssivark 6y ago
The concept underlying renormalization/invariance as we now understand it, is a fundamental and profoundly beautiful idea about the very nature of what it means to make a model for a phenomenon. Essentially:
A theory is nothing but a way to turn (a finite number of) measurements into predictions.
The number of degrees of freedom in some putative model might be infinite, but all/most of them will be common between the observed context and the prediction context; it’s only the difference between those two that matters. And renormalization theory provides certain bookkeeping tools to track & ensure that, which then makes tractable the task of predicting.
- clickok 6y ago> A theory is nothing but a way to turn (a finite number of) measurements into predictions. That's a very nice way of putting it. Is there a particular book, lecture, or other resource you could recommend for this interpretation of theorizing?
- cloogshicer 6y agoI'd also love a recommendation here!
- ssivark 6y agoThat particular statement is something I made up once I finally understood what was going on; I’ve not seen any references which explain it quite that way. If there are any specific leading questions, I might try to unwrap that intuition here; otherwise it’s a little difficult and I’ll need to think harder to cook up a nice motivating example :-) That said, Simon Dedeo has a relatively accessible set of online lectures which explain the concepts behind renormalization and broader connections to ideas in computing and other fields, without needing as much heavy machinery as a typical theoretical physics treatment. I haven’t watched it, but in general I appreciate his pedagogy, so here’s the playlist: https://www.youtube.com/playlist?list=PLF0b3ThojznTzAA7bfLWh4RKzRrwNF4L0 https://www.youtube.com/playlist?list=PLF0b3ThojznTzAA7bfLWh...
- deleted 6y ago[deleted]