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Noether's Theorem Revolutionized Physics
- adastra22 2y ago“Noether” nominative determinism strikes again in physics.
- twiceaday 2y agoTLDR: Do an experiment, then move 10 meters to the left (or rotate 90 degrees, or wait a few days) and do it again. The results don’t change, because the laws of physics don’t change. This realization alone is enough to produce conservation laws. Translational and rotational symmetries produce conservation of linear and angular momentum, and the time symmetry produces conservation of energy. Each symmetry you find leads to new physics. It's such an aha moment. PBS Space Time: https://www.youtube.com/watch?v=04ERSb06dOg https://www.youtube.com/watch?v=04ERSb06dOg
- gauge_field 2y agoAnother point to appreciate is how universal this principle of symmetry is. It is used in every branch of physics going from Classical Physics (Lagrangian Formulation) to quantum physics (with Feynman's Path Integral Formulation), from conservation of momentum to conservation of electric charge in (U(1) Symmetry) of fundamental particles. The fact that she was able to do this as a woman 100 years agos is also amazing.
- eru 2y agoIt also works backwards: for (most) conserved quantities, you can also find a symmetry. > Each symmetry you find leads to new physics. There's a few caveats and asterisks for that. Eg Noether's theorem only applies to continuous symmetries. Eg Noether's theorem has nothing to say about mirror symmetry or time reversal symmetry.
- immibis 2y agoSymmetries produce conservation laws if you accept and understand Lagrangian mechanics. That's a big asterisk IMO especially if you've never heard of Lagrangian mechanics and then you try to understand Noether's theorem. Doesn't getting from Newton to Lagrange already rely on the existence of conservation laws? Apparently if we take Lagrange as fundamental, then it works, and a variation of it works in quantum mechanics, so it does seem to be fundamental, but if you're trying to get from Newton's laws to Noether's theorem, you can't get from here to there without fully grasping Lagrange first.
- mckirk 2y agoI wonder what the conservation law is connected to the 'analysis invariance', i.e. the fact that no matter how well you've thought through everything beforehand, there will still be some recalcitrant pocket of the experiment that behaves confusingly. Maybe that's the 'conservation of surprise'.
- wholinator2 2y agoWell i have heard the term 'conservation of misery' quite a few times since starting my PhD
- ruuda 2y agoJohn Carlos Baez on that article: https://mathstodon.xyz/@johncarlosbaez/113964127171705485 https://mathstodon.xyz/@johncarlosbaez/113964127171705485
- ndsipa_pomu 2y agoI wonder if the cut off point of science popularisation is related to the point where maths becomes the most useful way to explain what's going on?
- jahnu 2y agoYeah I think that’s probably true and why I greatly admire efforts by people like Steven Strogatz and especially Sean Carroll who are leading the way from no-maths pop-sci to high school maths pop-sci where you know you don’t want to actually work with the maths but you can start to get an appreciation for the components of it and what the implications are.
- cubefox 2y agoOptimal would be something like 3blue1brown math animations, but for physics instead of pure mathematics.
- ndsipa_pomu 2y agoI'd definitely watch that.
- canjobear 2y agoThis is a booming genre. For example this one popped up in my recommendations yesterday https://www.youtube.com/watch?v=uVKMY-WTrVo https://www.youtube.com/watch?v=uVKMY-WTrVo
- mperham 2y agoSean Carroll’s Biggest Ideas in the Universe YouTube series is fantastic. Just enough math to be interesting but nothing requiring a math degree. https://youtu.be/HI09kat_GeI https://youtu.be/HI09kat_GeI
- MeteorMarc 2y agoObligatory: https://www.reddit.com/r/physicsmemes/comments/gtzprh/noethers_theorem/ https://www.reddit.com/r/physicsmemes/comments/gtzprh/noethe...
- bmacho 2y ago> In the fall of 1915, the foundations of physics began to crack. Einstein’s new theory of gravity seemed to imply that it should be possible to create and destroy energy, a result that threatened to upend two centuries of thinking in physics. Not just seem to imply, but they do imply[0]. Does that mean that we can build a machine that generates energy and negentropy forever (e.g. an artificial Sun), thus, we can outlive the heat-death of the rest of the Universe? Yes, absolutely. But there are other existential threats, like the collapse of false-vacuum. In the end, it is not known if we have limited or unlimited time here, but Noether's theorem doesn't answer that. [0] : https://www.google.com/search?q=general+relativity+and+conservation+of+energy https://www.google.com/search?q=general+relativity+and+conse...
- sigmoid10 2y agoThat's wrong, because the quoted part is wrong. Relativity doesn't say you can create or destroy energy. It only says that you can convert mass to energy (and vice-versa) - because in the end they are actually the same thing. And together, they are conserved. That means we still can't have perpetuum mobile stuff unfortunately.
- bmacho 2y agoThat was Einstein's 1905 paper about SR not his 1915 paper about gravity.
- talismanick 2y agoYou're talking about E=mc^2, which follows from special relativity. That was revealed in 1905; 1915 marked the advent of general relativity, where energy conservation no longer holds. The time translation invariance which gives rise to the conservation law is a special case of GR's broader energy-momentum conservation, namely the static one where gravity and such are disregarded altogether as in the Standard Model. This all ties back to the present crisis of foundations, as string theory and other approaches to reconciling GR with the Standard Model strain at the edges of what Noetherian tools can yield. (see: supersymmetry)
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- immmmmm 2y agoThe beauty and power of the Noether Theorem is what pushed me to theoretical physics. I consider it one of mankind’s greatest achievement.
- ElDji 2y ago"Like most Jewish academics in Germany, Emmy Noether was fired after the Nazis came to power in 1933. She left later that year for Bryn Mawr College in the U.S [...]" Compared to what's happening now, it's totally frightening.
- seanhunter 2y agoAlso, before that she worked for several years as an unpaid faculty member because she joined the faculty because David Hilbert recognised the importance of her work but there was some sort of Prussian regional bureaucrat who would have had to sign off on her getting a paid position or something and they and/or the university didn’t believe that a woman should teach at a university. So one of the giants of abstract algebra who made a key discovery in physics got screwed over for being a woman and then screwed over again for being Jewish.
- layer8 2y agoIncidentally, there was a report on Friday that German research institutions are seeing a substantial increase in applications from the US, presumably due to the US government cutting research funding.
- dist-epoch 2y agoWhat about information? We know that it is conserved, so what is the corresponding symmetry?
- thrance 2y agoTime symmetry I think? Any computation has to be reversible in theory?
- layer8 2y agoSee https://physics.stackexchange.com/a/75009 https://physics.stackexchange.com/a/75009.
- mikhailfranco 2y agoWe don't know that information is conserved. It is postulated by the linear unitary time-reversible Schrodinger/Dirac equation, and assumed by the Many Worlds Interpretation, but contradicted by the non-linear probabilistic time-irreversible Measurement Axiom of conventional QM. Some people (esp. Penrose) postulate that gravity can collapse the wavefunction, and hence destroy information (esp. Black Holes). The Black Hole Information Paradox is a hotly contested current topic.
- Isamu 2y agoI recommend the book Einstein’s Tutor” which came out last year. https://lee-phillips.org/noether/ https://lee-phillips.org/noether/ This is probably the best layman’s approach to Noether, her impact, and how she probably didn’t think much about the theorem later because she wasn’t interested in physics and abstract mathematics was her consuming passion.
- leephillips 2y agoI approve this message.
- jakobschwich 2y agoNot much meat in the article unfortunately. Far too short to contain anything substantial
- pfdietz 2y agoIt's sad she died when she did. Had it been a few years later penicillin would likely have saved her.
- btilly 2y agoHere is a cosmological issue from Noether's Theorem. An expanding universe shows time asymmetry, therefore it might not have conservation of energy. This looks like it actually happens. Photons going through empty space go through cosmological redshift, reducing their energy over time. The energy does not appear to go anywhere - it is just gone. I have no idea why this example is not more widely discussed.
- nyrikki 2y agoYou are confusing the map for the territory. Under our best current theory (map) General relativity, total energy might not be conserved globally, the divergence of the stress-energy-momentum tensor is zero, meaning that energy is conserved locally within a small region of spacetime. Physics is about producing models that make accurate predictions, it is a map, not the territory itself. The 'crisis in cosmology' e.g. Hubble tension is most likely a sign that current models of the universe are incomplete. Energy is conserved in static spacetimes and asymptotically flat spacetimes. The Friedmann-Robertson-Walker spacetimes that cosmology often uses are not static nor asymptotically flat. It is widely discussed, but all models are wrong, some are useful. Noether's theorm is a power tool to find useful models.
- mjburgess 2y ago> Physics is about producing models that make accurate predictions Very few models in physics ever make accurate predictions -- only in very limited experimental circumstances, mostly ones inaccessible at the time these models were developed. The ability to craft these experimental conditions, which enable accurate prediction, is predicted on the models actually describing reality. How else would one control the innumerable number of causes, and construct relevant devices, if these causes did not exist and the devices werent constructed to measure reality? No no, the hard sciences are not concerned about prediction at all. They are concerned about explanation -- it is engineers who worry about predictions, and they quickly find that vast areas of science -- esp. physics -- is nearly impossible to use for predictive accuracy.
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- PopePompus 2y agoI've never understood why Marie Curie is so celebrated in the popular press, but Noether is largely ignored. Noether's work is much more important, IMHO.
- GuB-42 2y agoNoether did maths, Marie Curie did physics, physics is more popular than maths. It is easy to see why, symmetries, conserved properties, boring, nuclear power, atomic bombs, deadly radiation, exciting. Einstein is a rare instance of a popular theoretical physicist. But all the mathematicians whose work led to the theories of relativity are largely unknown to the public.
- mikhailfranco 2y agoMarie Curie won 2 Nobel Prizes, for physics and chemistry. She was the first woman to win a Prize, and the first person to win two. She died of radiation exposure from her experiments. Can't really argue with that.
- jll29 2y agoIf you would like to know more about her: Her legacy https://www.mathgenealogy.org/id.php?id=6967 https://www.mathgenealogy.org/id.php?id=6967 About her https://en.wikipedia.org/wiki/Emmy_Noether https://en.wikipedia.org/wiki/Emmy_Noether Where she lived and studied https://thonyc.wordpress.com/2011/05/07/the-house-where-emmy-lived/ https://thonyc.wordpress.com/2011/05/07/the-house-where-emmy...
- bawana 2y agoThe article begins with claims of violation of conservation of energy but no examples. Then it posits that violations of energy conservation are explained by symmetries. What does that mean in English? Is there something else that changes in concert with changes of energy?
- MathMonkeyMan 2y agoNoether proved that for every symmetry of the action there is a conserved quantity. The action is an expression (a function of the coordinates) from which the equations of motion can be derived. Examples of symmetries of the action are time reversal, spatial translation, spatial rotation, and complex phase rotation. The corresponding conserved quantities are energy, linear momentum, angular momentum, and charge. In general relativity, symmetries that exist in the action for a flat spacetime are violated in curved spacetime. So, in curved spacetime, the corresponding quantities are not conserved. One example is energy. The reason has to do with the fact that integrating a tensor along a closed loop in curved spacetime might yield a nonzero result due to the curvature itself, rather than due to the dynamics of what is being integrated. I don't think that the article goes into any of this. The introduction about general relativity did seem like a curve ball, even if it's historically accurate.