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.
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...
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?
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?!
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'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.
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!
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!
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.
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.
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.
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.
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...)_
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.
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.
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.
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...
preach!
No! Do NOT preach! Make schools hire BETTER TEACHERS! For God's sake!
Again you made it look so easy. Thanks for another great explanation!
Sir please upload the DIRAC EQUATION too!🙏🏻
Greetings from Finland. THANKS for producing these videos!!
Drinking tea leaves for science 😅🖖
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
My brain can't handle your post both using an expressions like "Sir, I bid" and "caught in dismay" while also using "u" as you.
Thank you so much;great explanation for us amateur physicists not quite on the level of theoretical physics!
What's an amateur physicist? Is that like an amateur concert pianist or an amateur NFL coach? ;-)
professor it's quite surprising that you have not done maxwell's equations and dirac equation yet...please do them
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.
What software do you use to do these wonderful videos? Specifically, what do you use on you iPad and how do you split the screen in the video?
I was just wondering the same thing!!
i want to know this too. i like how it works and looks.
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, Brian!
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.
Thank you for a crystal clear explanation. Is there a Quantum Mechanical version of this theorem as well?
Yes there is! Actually there is a beautiful link between classical dynamics and quantum mechanics. Search poisson bracket formalism classical dynamics.
Is it so that the Poisson Bracket in Louisville's theorem gets converted to Commutator in Heisenberg's equation of motion?
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?
Thank you for nice lecture! Anyway, how about discrete symmetries? Can we say something similar to Noether's theorem about it?
Discrete symmetries leave us with things like crystallographic point groups.
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?
constancy of the speed of light?
Velocity is a function of momentum.
hello professor, you are treat to watch.
Emmy’s last name rhymes with Nurtah. (And the t is sounded as a t (not d). I wish I understood Noether’s Theorem as well as can I say her name.
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?!
But it will have angular momentum....! Am I right ?
you don't add milk to Earl Grey tea
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.
Gorgeous handwriting, then BAM - the ugliest zero you've ever seen.
I must say that Brian‘s handwriting is frickin beautiful
Yeah, I wish I could write M's as seriously as Brian.
@@ricardodelzealandia6290 MomentumtallicA 7:54
Heh I have the smallest handwriting on Earth and his just freaks me out.
@@BeckBeckGo I wish i had a small hand-writing. That way i'd not have to change my notebook every week.
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.
I was waiting for this One!
Dirac equation!?!? Please?
So you have chosen death 😇
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!
Thank you for this cool videos !!
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!
Shoutout Mr. Edmons
I really wish I understood this. It sounds almost like symmetry and conservation are the same thing.
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 :)
Professor can you explain mach's principle and its application in general relativity
"... that is a SERIOUS 'M' " rOFL
Can you describe how Noether's Theorem relates to gauge theory? I think it is important but don't understand how it works there
Thank you Dr. Greene as always!! Your notoriety is well deserved. You’re a rock star!!!
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.
What happened to equation no 24??
Best educator on the web!
This is fantastic. Professor, you make things so easy to understand, that one starts loving physics. Thank you!!!
1:29 subtitle no-there's theorem
thank you so much, thank you
*Rorri Maesu says useaMirroR*
Always pay Attention to comment 108 *BeCause*
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.
The 20th century was totally Germany's golden period... 🙄😜
@@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.
Could you please explain how The Conservation of Energy law is violated over time using the concept of symmetry?
prof greene, i am missing #24
@Bob Trenwith Yes that's true.
How is your mother now.
Happy mother's Day 🎉🎉
What happens when you take into considerations the second approximations?
What is the conserved quantity fur entangled particles?
In what situation/symmetry is entropy conserved?
This topic!
your handwriting is so dang beautiful xD
if more explanation , needed perhaps , better results can be provided .
Shouldn't this be equation #24?
Amazing, finally I got it :) THanks
Why did you choose I to be (dL/dxdot)(dx/dlambda)?
FORMIDABLE 👍👍👍👍
thankyou professor for beautiful videos..you are really amazing.😊😊
दाजु मनि छु है😁
thank YOU
Does the Big Bang at zero + time have continuous symmetry? Please remember
I am a CPA , so this question may be absurd.
Thanks
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.
Sam Harper thanks for your reply.
Thanks...
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.
Regarding symmetry, does “look the same” implies “is the same” after certain operation?
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.
Douglas Strother Thank you. I need to learn more about symmetry and Group Theory.
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...)_
Plz help me in finding the Noether symmetry equations for some particular spacetime
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.
Physicist on UA-cam with their knowledge is revolution in science.
each universes has huge turning around themeselves and at the same momentum stars and planet acting the same , and this live movment beautiful
No the tea drinking was not gross Sir, it was majestic...Professor!
I an so impressed by your ability to explain the Noether's Theorem in such simple terms. You are Brian green, so I am not surprised. 😘
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!)
This is incredible. Thank you for a wonderful lesson
I have learnt more here than my class .
The guy is a treasure !
Dr. Brian Greene,
you explain it perfectly!
Fantastic Explanation
Hope you are well prof Greene
great professor
Beautiful!
Wonderful!!
nice vid professor !!
Thanks! Awesome.
Thanks a lot !
Thank you,I too have trouble with pronouncing her name.may I make another suggestion,Leach lattice and the Monster/Moonshine.
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.
Recordar é viver!?!😀👍
What is time translation symmetry. How this symmetry in General relativity keeps the object attached to earth? When gravity is not a force
Curvature due to time dilation.
Are there any conserved quantities in the social or economic sphere?
No. All other sciences are subsets of physics.
14:51 both were perfect examples but when we do it we will not find them
How about an hdmi connector. Rotate by anything other than multiples of 360 degrees then it won't look the same. Any connector that is 'keyed'.
If angular momentum is conserved, how do cats spin around to land on all fours when they fall?
Lol by changing the moment of inertia
They rotate their bodies while maintaining zero angular momentum - sounds like a contradiction but it's not and is perfectly possible.
they rotate their tail one way and the rest of them the other way
brian is badass for real
rude
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.