at 51yrs of age, I’ve long since forgotten what it’s like to be in a classroom but only wish I’d had teachers with 1/5th the talent you possess in articulating and conveying your thoughts and ideas. You are a true gem, Professor. We all benefit greatly from your knowledge and expertise. God bless. Stay safe 😷 and best wishes...
I've heard about Noether's Theorem for years and knew it was about 'proving certain quantities are conserved as a consequence of specific symmetries', or whatever. Now I actually understand where this comes from. Eyes open! I've never seen how the math works out until now. Thank you Professor Greene.
With regards to Noether's theorem (1915), if we want to be more specific and inclusive, Emmy Noether was not the first person to discover the fundamental link between symmetries and conserved currents (energy, momentum, angular momentum, etc.). Many people in the physics community ignore this fact, but the intimate connection between symmetries and conservation laws was first noticed in classical mechanics by Jacobi in 1842. In his paper, Jacobi showed that for systems describable by a classical Lagrangian, invariance of the Lagrangian under translations implies that linear momentum is conserved, and invariance under rotations implies that angular momentum is conserved. Still later, Ignaz Robert Schütz (1897) derived the principle of conservation of energy from the invariance of the Lagrangian under time translations. Gustav Herglotz (1911) was the first to give a complete discussion of the constants of motion assiciated with the invariance of the Lagrangian under the group of inhomogeneous Lorentz transformations. Herglotz also showed that the Lorentz transformations correspond to hyperbolic motions in R3. What Noether did, was to put every case into the generalized and firm framework of a mathematical theorem.
I first came across Noether's theorem on a course I was doing about the Higgs Boson. Of course this famously breaks symmetry to achieve the required results!
Sir, i bid you please commence your videos on GR by first throwing a separate video on minkowski's spacetime exploring how it's an Euclidean continuum. I was really caught in dismay that sir finished his initial videos in this series without doing minkowski's spacetime. And thank u very much for doing these
This is a clear proof that when people say “university professors cant teach because they’re mostly there to research” is false. He is a great researcher AND a great professor.
So when x > x+lambda (translation) I is the momentum; and when there is rotation ... should be angular momentum; what transformation gives I= E (total energy) = constant ... ? It is been a long time since I learned about this theorem, and it was not very clear for me back then :-), guess the stile of teaching was more rigid or my mind too easily distracted. Very clever your way of explaining. Thank you.
Thanks again Prof. Greene. I got to watch this on Tues morning, as I am in Wales, UK. Not that it makes any difference really. This episode is a bit too "Mathy" for me I'm afraid. I still enjoy watching though, as always. Thanks, Best Wishes & stay safe. Paul C.
Yes there is! Actually there is a beautiful link between classical dynamics and quantum mechanics. Search poisson bracket formalism classical dynamics.
Can the differential equation be solved for any curve y = f(x)? That sliding path can be very complicated and the non-linear DE can become analytically unsolvable, no?
Is there a missing conservation law? Consider: Symmetry of position ⇔ Conservation of linear momentum Symmetry of orientation ⇔ Conservation of angular momentum Symmetry of time ⇔ Conservation of energy But there is one more: symmetry with respect to linear velocity, aka “inertial frames of reference”. What conservation law is the dual of this?
I was at a talk at UT Austin where this physicist said conversation of energy may not hold at the beginning of the universe because the symmetries that give us conservation of energy may not have held at the beginning of the universe. But she didn't explain what symmetries she was talking about.
In that rolling stone on a hill example, you used conservation of energy. Why don't you use the conservation of MOMENTUM on that same example? My common sense tells me: those can't possibly apply both. 1/2 mv2 is NOT mv ! Why don't I hear nobody stating that problem?!
Awk! For the sake of completeness you MIGHT have pointed out that all those high momentum chunks of exploding star had vectors that summed to zero BECAUSE THEY WERE SPHERICALLY SYMMETRICAL... (I think you meant to but just _forgot...)_
25:27 Not clear when you said d/dt of dx/dL was equal to d/dL of dx/dt. Would be true, if you treat x = x(L,t) where L = lambda & t are independent variables and d= partial derivative in both cases But you are using total derivative for t and a partial for Lambda. Yeah, I've seen physicists use this annoyingly unclear notation elsewhere, and as a mathematician it annoys me.
I have to study this video I'm not understanding all this mathematical terms because I don't use it I can't tell if you're studying P or E or C p=e=c=conservation If It is life finding conservation the gool coping conservation is the perpes.
As it is impossible for any “physical quantity” or system to not be subject to external influence; the principle of conservation can never apply to anything. Therefore this is one of several reasons why it is not a correct theory.
I quite addicted to watching these, it’s like learning German by listening to a newscast, with one better - the manipulation of symbols - so some visual input as well. I suppose I need to start at a beginning - whatever that means. The historical and sociological significances are so--??? Well for example,!today I tried to imagine what it would be like to be a female who liked mathematics in 1890’s, ....thanks for this!
You drank the junk of tea leaves leftover for science :) and here I give you the least we can, a subscription to your channel, a comment and a like on your video... Hope many can do... for science :)
Notoriety is fame in the negative sense, perhaps his fame would be better described as renown which carries a more positive connotation. Unless you truly intend to mean that he has a bad reputation.
It's absolutely astonishing how much innovation and science emerged from Germany from that golden period of less than a century. Noether is a prime another example of this creative thought.
@@coldblaze100 Even the Nobel Prizes are awarded to individuals and the country itself. Although it's interesting to note that the USA has the most Nobel Prizes by any one individual nation, with over 350 medals. But 95% of US Nobel Prize winners have either been born outside the US or their parents migrated to the US. Essentially, the USA has been importing its intellectual class and its creative output, especially since the end of WW2. Even today, almost 50% of the PhD candidates at US Universities are overseas students. This post war trend has slowed down recently because regions such as Europe and countries like China, Japan and Russia have been active in holding on to their talented young scientists and creative thinkers.
@@PetraKann heh I think he was strictly referring to the unfortunate 40 ish years between like 1935 and 1988. My numbers may be way off. I tend to be suddenly not so good with numbers in the field of history for some reason.
Yes. Consider an isosceles triangle cut out from a sheet of paper and label the vertices on one side 1-3 and 4-6 on the other. Pick one orientation at the starting position, and then rotate and flip the triangle so that it looks the same as the starting position. The labels allow you to see that one or more operations occurred, but the triangle is the same. Group Theory is the branch of mathematics which deals with symmetry; it's usually presented as a part of Abstract Algebra.
Thank you, professor Greene! Is there a link between this theorem and killing vectors? Or they independently say something similar? (Finally, I had a chance to watch the last q&a, wish your mom quick recovery!)
I always assumed it was "Nayter" (more like "Neuayter" lol but for ease) Oe in German sounds a bit like A to English speakers. Like "Groening" mostly rhymes with complaining. Not quite but close enough.
Potential energy is dual to kinetic energy, energy is inherently immanently dual. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought. Duality (energy) is being conserved -- the 5th law of thermodynamics Waves are dual to particles -- Quantum duality (photons are pure energy).
Symmetry is dual to anti-symmetry. Symmetric wave functions (Bosons) are dual to anti-symmetric wave functions (Fermions). Bosons are dual to fermions! Thesis is dual to anti-thesis -- the time independent or generalized Hegelian dialectic. Action is dual to reaction -- Sir Isaac Newton Energy is dual to mass -- Einstein Space is dual to time -- Einstein Certainty is dual to uncertainty -- Heisenberg Noumenal is dual to phenomenal -- Immanuel Kant
It is important to also mention the sexism of her era that prevented her from being as noted as she should have been. She also contributed to the studies of “rings” as well.
