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I wonder if we’re in agreement? The key word is ‘numerical’. Maybe you’ve yet to see or do numerical analysis of both general relativity and quantum field the
by mungal 4y ago
I wonder if we’re in agreement?
The key word is ‘numerical’.
Maybe you’ve yet to see or do numerical analysis of both general relativity and quantum field theory but they are in fact both linear algebra.
Which as you point out is “fundamentally more accessible”.
- WhitneyLand 4y ago>Maybe you’ve yet to see or do numerical analysis of both >general relativity and quantum field theory I call you out. Don’t think you’ve done either one after reading your comments.
- hither_shores 4y agoNumerical relativity is not just or even mostly linear algebra. Even in the weak-field limit, where linearized GR is qualitatively correct, you still have to actually solve the resulting PDE.
- mhh__ 4y agoThey're both what now?
- mungal 4y agohttps://en.m.wikipedia.org/wiki/Tensor https://en.m.wikipedia.org/wiki/Tensor
- mhh__ 4y agoThat's very weak
- pfortuny 4y agoA tensor is a differential structure with pointwise linear properties. But the important thing is not the pointwise behavior but the differential nature of the “family of tensors in non-Euclidean space”.
- hither_shores 4y agoThis is too strong. There are important fields whose points are not tensors (e.g. spinor fields) and treating them like tensor fields risks introducing all sorts of subtle confusions.
- pfortuny 4y agoOf course you are right but I was just trying to explain to OP that certainly General Relativity is not just “linear algebra”.
- lkrubner 4y agoGeneral relativity is linear algebra? Has anyone called up Tullio Levi-Civita and told him that his services will no longer be necessary?
- mungal 4y agoI’ve seen this sort of reactionary response in mathematics and music as well. When talking to a musical educator complaining about struggling students just starting out I’ll say “I found it extremely helpful to paint the C major scale on my guitar when learning music theory.” And they respond “Well what about chromatic 12 pitch atonal music?! What would Anton Webern say?!”
- TheOtherHobbes 4y agoIn GR terms, Levi-Civita is more like "This is a major scale and you need to know it" than serialism. Some subjects are just plain hard and only accessible to smart persistent people. GR and QFT definitely qualify - but they seem to be warm up exercises compared to whatever Quantum Gravity will eventually become.
- wumpus 4y agoAs someone who has studied GR (at the grad school level) and music, no, that's a terrible analogy.
- sidlls 4y agoEh, no. The problem with your analogy is that the “not linear algebra” bits aren’t esoteric, rarely practiced or used edge cases: they’re the core of the mathematical model.
- rrss 4y agoNo, just because general relativity and quantum field theory use linear algebra does not mean they are linear algebra.
- pfortuny 4y agoI guess you are mistaking the “local linear nature” of tensors for differential geometry. GR is certainly not “linear algebra”.
- noslenwerdna 4y agoGeneral relativity is not linear algebra. Just glancing at the underlying equations, you can see they are non linear. [https://en.wikipedia.org/wiki/Einstein_tensor https://en.wikipedia.org/wiki/Einstein_tensor] The same is true for quantum field theory. I'm curious why you're so confident that they are "in fact both linear algebra"
- paulpauper 4y agothey involve matrices
- hither_shores 4y agoThey also involve addition, but that doesn't make them arithmetic. Knowing linear algebra gets you perhaps 10% of the way to having the math background for a first course in GR.
- oefrha 4y agoAs a physicist who used to work on unifying QFT and gravity, no, QFT is not accessible at all, to anyone. General relativity is kind of accessible to a non-physics student if they otherwise have a strong math background, which is like 0.001% of the population, optimistically.
- a9h74j 4y agoFun fact: When I was in a highly respected grad school in the 1980s (multiple Nobel Prize winners in the department), the QFT course was presented in such an obscure way, I stopped attending lectures, and I doubt anyone passed. The next year under "QFT" they taught Ashcroft -- i.e. a Solid State Physics course. That way requirements were met.
- oefrha 4y agoI took QFT in college and then grad school in two of the leading institutions in HEP. I can’t say the instruction was very enlightening in either place. Whichever path you take (not sure what you had in the 80s, I’m thinking of Peskin & Schroeder / Schwartz / Weinberg, maybe even supposedly easier textbooks like Nutshell) it’s just a very dense subject. Now, GR or at least the core of it is a lot easier as long as you’re mathematically prepared for differential geometry. Btw, I took particle physics from the Peskin in Peskin & Schroeder when I was an undergrad. Everyone in the class (like four of us by the third week?) was super duper lost by midterm.
- paulpauper 4y agoyeah like this for anything. String theory is easy if you're mathematically prepared by being a field's medalist
- oefrha 4y agoHaving attended many IAS talks, I don’t think string theory is easy for the likes of Ed Witten.
- 4y ago