Noether's Theorem and The Symmetries of Reality

[@orthochronicity6428]

It's also worth noting that she didn't really step in to tackle the energy problem that was dogging early general relativity: Klein asked her for her input after being prompted by a colleague. When he did, he was surprised to learn that she had already worked out most of the solution but had put it by the wayside for more important mathematics. When she did publish it, Einstein supposedly remarked that he had no idea that anyone could think about gravity in such a general way. In true mathematics fashion, her work was far more general than anything we deal with in physics. The universe was basically just a special case. It's hard to overstate just how amazing of a mathematician she was.

[@anandsuralkar2947]

😍

[@weatheranddarkness]

you mean hard to overstate?

[@orthochronicity6428]

@@weatheranddarkness Yes, that is what I meant. ...can't believe that mistake was there for a year without anyone else saying anything. Fixing it now.

[@capoeirastronaut]

I describe her as having contributed the single deepest insight in all of physics, during her one professional foray outside of mathematics. That helps capture it I think.

[@y8fpe]

> Einstein supposedly remarked that he had no idea that anyone could think about gravity in such a general way wow

[@alexanderf8451]

Favorite Noether story. Hilbert wanted her to teach a university class but they refused to hire a woman. So he hired her as a teaching assistant and never showed up to the class.

[@frankschneider6156]

Which is more than many scientists are today.

[@faiselbutt2944]

Humans do love their discrimination.

[@kaczan3]

@@faiselbutt2944 yeah, she wasnt sent to war to die. thats sexist

[@salvatronprime9882]

Yea but she got free drinks on ladies night, so everything evens out. hyuck hyuck hyuck

[@kaczan3]

Funny how you try to sweep men dying en masse under the carpet like it's nothing. But oh noes, someone said a bad thing about a woman.

[@fep_ptcp883]

I'm not lazy, i'm just following the universal principle of least action

[@marsel4812]

Yep.. so am i.. now i have a reason to make my physics teacher more understandable and tollerant with my laziness.. :T

[@HighMojo]

The problem with the Principle of Least Action is that it does not generate useful work. It is true in both Physics and humans.

[@NoActuallyGo-KCUF-Yourself]

The principle of least action is actually the principle of stationary action, which is not necessarily least.

[@michaelsommers2356]

There is a book about the principle of least action called _The Lazy Universe._

[@TheNamelessOne888]

You are one with the nature of the universe.

[@usmanadil4617]

The mathematics department at my university is called Noether Wing. I always wondered who that was. Now, I do. Thank you, PBS Space-time. Edit: I made this comment 3 years ago and forgot about it. It just popped in my notifications and boy am I surprised. I am a graduate now, and have studied Noether's theorem in Quantum Field Theory. Its absolutely beautiful and she's easily my most admired woman from the 20th century.

[@zumszum]

Usman Adil i think there was a dragon with this name in WoW :)

[@deustitties3589]

Doesn't that prove her contributions were recognized though? You have to pretty big to have a mathematics department in University to be named after you.

[@ArawnOfAnnwn]

Recognized in retrospect =/= recognized in her time. Don't forget that the video mentions she'd had difficulty landing a position.

[@zumszum]

If Einstein calles someone a genius that's a pretty big thing. :)

[@ArawnOfAnnwn]

Tbh, that shouldn't matter so much. She was a mathematician, not a physicist. But alas, math simply doesn't have as much pull with the general public as physics does. :|

[@kroyhevia]

"Einstein also called her a genius" greatest line for a resume ever

[@way2nasty533]

jay I looked into it, they said he’s a fraud but then they said just kidding. You needed to look deeper into it to see that part

[@brunolimaj7129]

He's a fraud dude

[@dabouras]

@@brunolimaj7129 ad he got the Nobel prize for what again? He deserved the Prize three times over.

[@noether9447]

@@dabouras many more times actually. He discovered SR, GR, Photoelectric effect, EPR paradox and many more things.

[@dirk-jantoot1167]

@@noether9447 SR, GR, Photoelectric effect and Brownian motion all deserve a nobel prize. That should be 4, not sure if EPR is on the level of the previous 4.

[@buxeessingh2571]

Emmy Noether is one of the greatest intellects of all time. She was just awe-inspiring.

[@GustavoValdiviesso]

If every scientist have at least one academic hero or heroine, mine has always been Emmy Noether. Not just her genius mind, but also the hardships and illness she had to face make her one tough person. She doesn't get nearly enough recognition, even among science outreach lecturers.

[@Aufenthalt]

Thanks for the enormous effort in trying to to bring very advanced subjects to the public without diluting them in oversimplification of. I cannot believe there are 14 people disliking this video.

[@grimwatcher]

You know you're smart when Einstein calls you a genius

[@thelemonddropskid5445]

In 2018, you know you're a necromancer when Einstein calls you a genius.

[@APAstronaut333]

That’s like extra salsa on an already very salsa-rich salsa

[@Butwhythoo]

He called Tesla a genius

[@firefly618]

You know the society you live in is unjust when Einstein calls you a genius, but all the academic institutions refuse to employ you because you have tits. Seriously.

[@DrWhom]

You know you are a crackpot when you think you are smarter than Einstein.

[@LMAccount1]

Cool, aNeother video

[@Algebrodadio]

I see what you did there.

[@User-jr7vf]

You got her name wrong. So failed joke haha

[@Danilego]

Failfish

[@amedicabg]

Diogenes TheDog Don’t tell me what to do mom. Meesa angery

[@marshacd]

Yess, butt ........

[@MrRolnicek]

It's pretty unfair. When there's a genius mathematician we don't hear a word from them. But as soon as they dip a single toe into physics, giving us even 1/10th the contribution they bring into maths, we get collectively fascinated.

[@helloyes2288]

What greater honor is there for a mathematician but to be remembered a physicist?

[@osmium6832]

That's at least partly related to the nature of mathematics. Math is more abstract and can take many generations before the information can be utilized in a practical manner. There were mathematical algorithms discovered centuries ago that were mere curiosities until the invention of computers, where they proved crucial in programming. Physics is more tangible and discoveries in it are easier to connect to and build upon the current pool of knowledge.

[@jzzy107]

What would physics be without Mathematics?

[@BenjaminCronce]

Unfair to the rest of us also. Imagine how much better off humanity would have been if they let a rare genius help further science.

[@101Mant]

MrRolnicek “Physics is to math what sex is to masturbation.” ― Richard Feynman

[@SophiaAstatine]

Noether's story is so sad. And her legacy is really great. Glad this episode is a thing.

[@tombombadillo1]

Lost my shit at the ending hahahah. Didn't expect my reading of the preface of LOTR in grade 9 would ever become relevant again.

[@ejejej9200]

Space time videos are a gift to the world. A huge thank you to everyone that make these videos possible.

[@Dascolino]

I actually hope reality is not based on HTML

[@gianpa]

omg I was obsessed with Brainfuck at one point in my life, I don't know why :|

[@frankschneider6156]

Which is still better then lolcode or ArnoldC.

[@glarynth]

It would explain the accelerating expansion...

[@ObjectsInMotion]

It's coded in Whitespace

[@Al-pb3fm]

Coded in maths

[@Stoic9]

Thank you... Its awesome any time I see recognition given to one of the many, many women who have made major contributions to science yet have been over looked by history....

[@cheaterman49]

Hahahahaha, etymology of Middle Earth languages as a prerequisite, awesome :D

[@domsjuk]

Finally something I do not need to rework for understanding what's going on here. :D

[@Hatchet2k4]

I come for the physics but stay for the hilarious wit at the end!

[@Arudis4x]

The Cheaterman 12:26 that has to be the single most politely awesome way for anyone to say "Get on my level, scrubs" that I have ever heard. Bravo

[@slashusr]

All this talk of dwarfs runes my day

[@TechNed]

I'm sure they chuck that in to check if we're still here!

[@BrendanBlake42]

I think I pulled my Landau-Lifshitz Pseudotensor once at the gym.

[@stephenfiore9960]

...Your “pulling” my leg, aren’t you..

[@ramirosilveira5326]

This has been on my mind since I took an introductory course to general relativity this year, now this video comes out and it even has Tolkien references. Perfection.

[@thatdude_93]

"Her work in abstract algebra redefined entire fields..." didn't you mean to say Rings? I'll see myself out

[@PinkIguanaRadio]

Hahaha! To be fair, this is only a physics channel.

[@frankschneider6156]

Didn't he cite Lord of the Rings at the end, where a group of people strolls along finite fields ?

[@pierreabbat6157]

Was Frodo the identity element? He had nine fingers after Frodo bit one off; there is a finite field of size 9 but not of size 10.

[@ninja250r2008]

U guys are freggin geeks smdh 😂😂

[@NoActuallyGo-KCUF-Yourself]

Nerds!

[@gregbrockway4452]

Thanks +Matt and +PBS Spacetime, another superb video! I confess that history is one of my least favorite subjects but learning about the unsung heroes of science is truly fascinating. Kudos to you and the team!

[@robharwood3538]

I too disliked history, based on what was taught in schools. I later became somewhat interested in it in order to understand some of the questions that plagued me about humanity. An example question: How was someone like Hitler able to get into power? (Surprising (for me, at the time) answer: He was voted in by the people (simplified answer, but essentially correct).) The history of science is definitely another one of those questions, especially: How did the Dark Ages happen, how did we get out of them, and how could we prevent a hypothetical future Dark Age from ever happening again? The main point: I eventually learned that my distaste for history was largely a byproduct of the way it was taught in the education system, and not because it is uninteresting in its own right. Of course, different areas of history will be interesting to different people, so that also plays a part in it. But I think understanding history is a necessity for understanding where we are, how we got here, and where we're likely to end up. And because of that necessity, there will always be some facet of history which each person would be able to enjoy, if only the education system hadn't bored them to death about the general topic of 'history' in the first place. Speaking of which, maybe we should study the history of our education systems, try to find out where they went wrong, and maybe figure out how we could fix them!

[@mysterymeat586]

Trump was voted in too. Creepy.

[@MetalicAtheist]

Gauge theories technically have nothing to do with quantum physics. Electrodynamics is an example of a gauge theory which is perfectly valid in the classical regime. It produces incorrect results when compared to nature (like the UV catastrophe) but fundamentally it is a valid mathematical construct without introducing quantum mechanics. Fermionic fields are the objects whose field equations host the symmetry in question. They are complex fields certainly, which may hint at the necessity for a quantum mechanical formalism, but on their own they are completely valid classical constructs. Quantizing (as in QFT) a gauge theory actually spoils Noether's theorem by introducing anomalies which violate the conservation laws non-trivially. This is best understood via Feynman's idea of "summing over histories." Not all the paths a quantum field can take are going to respect the symmetry which is true at the classical level. In more precise language, we might say "the path integral measure does not have the same symmetry as the action."

[@aclearlight]

Very profound point, thank you!

[@semmering1]

What an excellent KZbin channel this is..

[@ogliara6473]

Noether is such a personal hero of mine. What an absolutely wonderful inspiration.

[@Duncan_Idaho_Potato]

I already loved this channel but the cheeky hat tip to Tolkien's mythology (and etymologies!) has knocked me head over heels. You guys are the best!

[@jona5820]

Noether was one of the great ones.

[@Adityarm.08]

As a kid I used to dislike the fact that momentum/energy/angular-momentum all seem arbitrarily defined quantities in physics which somehow follow special rules. Loved this video - the underlying idea sure is beautiful.

[@Smitology]

I also like how it provides a broader definition for them. For example, the electromagnetic field has a momentum despite being massless. It's really hard to understand why if we has have a p=mv intuition, but it be derive it from the symmetry of Maxwell's equations over space translations, it becomes immediately clear where it comes from.

[@yazizme3852]

@@Smitology first lemme say, I know it's no man I respect, but look, tis the spirit I do adore and tis the spirit that birthed, so to speak, the truth that is the reason for which I so adore your chosen title.🤣 So good. Hear ye a round of smites for the house, 🕳️👻🔥 ⚡😁💥

[@Smitology]

@@yazizme3852 What?

[@yazizme3852]

@@Smitology was making an attempt to share some real joy amongst the more sincere responders with their own caliber of knowledge, and as is , in hindsight, perhaps a little out of place with voicing such a happy Spirit with a drastic peeling past the more , otherwise confined topic. So as interpreting your cut n dry , respond. One word , ? . I humbly retract my apparent, radical swerve off the main topic , on the one hand, .. But, it was not really really a change , radical or otherwise, if you didn't notice, "the likeness," then I can only hope this is a sufficient answer to your word posing a question

[@Smitology]

@@yazizme3852 You sound friendly but I hope you realise that both your comments are absolutely incoherent for me. Maybe gather your thoughts before you start writing the comment?

[@Psd863]

Thank you so much for this video! I've known about Noether's Theorem and the fact that symmetries and conservation laws are connected, but I've never felt the reason why they are linked explained to a satisfactory degree. Until now. The way it was presented here was most engaging, especially showing the cases where conservation breaks down and why, reconnecting back to symmetry and demonstrating the point. Very well done and a pleasure to watch!

[@Ikbeneengeit]

I'm so glad you did more on Noether's Theorem!! This is mind-blowing stuff.

[@soranuareane]

PLEASE get into tensor calculus, or at the very least tensor algebra. I've struggled with tensors for several years now and whatever insights I gain never stick. Thanks for the amazing episode!

[@jackozeehakkjuz]

If you want a soft introduction you can watch this playlist. kzbin.info/aero/PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c Now, if you really want to get into differential geometry, watch this other one kzbin.info/aero/PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic I hope you like them.

[@drumskateart]

i can vouch for the differential geometry class!! i was following it for a good few months earlier this year. It's a LOT of material though, so make sure to keep looking online for supplements. Although the class didnt make me amazing at tensor calc or algebra, it did demistify tensors a lot for me. Plus they use extensive Einstein notation in the class so if anything you'll at least get good at that.

[@shaunhumphreys6714]

tensor calculus is very hard. even einstein needed the help of a mathematician when writing up his General Relativity. Finding a good mathematics channel on youtube is the best option, as there isn't the time in physics videos to devote to explaining tensor and other calculus, only to give the equations in the videos.

[@Miles969]

ive heard physicists talk about conservation of information in relation to black holes. is that the same or a similar kind of conservation as you elaborated on in this video or something completely different? also, what does conservation of information mean?

[@User-jr7vf]

Sort of. Information is everything you know about a system. So the conservations he talks about in the video are information one has about the system, yes. But part of the total information, cause there can be more.

[@thstroyur]

Information = entropy, and entropy depends on "how random" your system is supposed to be. Now, if something gets swallowed by a hole, and later regurgitated as radiation, the entropy of the latter will be different than that of the former - which, according to our current models, means a "jump" in the evolution of the particles of that something as dictated by Schrödinger's eq. (technically, we say it's a non-unitary process). Now, very hand-wavingly, "non-unitary" can be read as "non-conservative" (WRT energy). So, all things considered, you can read "non-conservation of information" as "non-conservation of energy" - which is what is _thought_ to occur with GR, in general, but which I think is due merely to bad bookkeeping

[@electrikshock2950]

User Droid but where or what is it's symmetry

[@Bronze_Age_Sea_Person]

Just to add more information(no pun intended):Entropy is the amount of microstates of a system,the amount of randomness comes from that. It's just obvious,if you take a lottery with sixty "slots" and six or more numbers to fill them,how many would form patterns you would call ordered?And if you increase the amount of possible microstates,or slots,the amount of ramdom ones would increase way more than the ordered ones. That even explains why some physicists tell it's wrong to assume entropy is a measure of disorder,it's just that many of those microstates are disordered

[@anthonyscarfe4853]

The information of a system is the set of combined total values for the fundamental properties of the system. This should not change in a closed system. One such fundamental property is the mass-energy of the system, because mass and energy can swap values. The total mass-energy of the total universe, if you exclude the possibility for more universes, should be the same throughout time no matter how big the universe gets. That is not true if some of the value of mass-energy can be transferred to another fundamental property, for example charge, or to another universe.

[@shawnouellette1953]

PBS Space Time is honestly the best educational videos available.

[@willis936]

Yes! The standard model is something I want to know much more about and was hoping this channel would cover. I also love hearing the stories of the people who do this work. It was one of my favorite parts of Kip Thorne's book on black holes.

[@nikhil4kem]

Principle of least action- glad to know its not just me, being lazy, i mean economical, is an inbuilt quality of the universe!

[@rljpdx]

poorly said amid the cacophony of commas, however, it's meaning is brilliant and elegant... and true ;)

[@Sunberriyu]

As an undergrad I had this Lagrangian mechanics lecturer who seemed really obsessed with Emmy Noether but I think at the time I didn't really understand why. Now I think I get it ha ha

[@deadman746]

Thank you for pronouncing "Noether" correctly. I am amongst other things a mathematician, and for my money, she had the best mathematical mind of all time. Consider that she also put algebra on a firm theoretical foundation after it had been practiced for two millennia. To a zeroth approximation, it never happens that a mathematician is so at home in the utterly abstract and the utterly practical. There have been a very few exceptions. The clincher is that Noether once said that when proving X=Y, it is cheating simply to prove that neither XY is true. This cuts to the heart of what I call the ethics of mathematics, which is almost never addressed at all. If anyone at all before the 20th Century had those ethics, the work of Cantor, Turing, Church, and Gödel would not have been necessary. That does it for me. Doing this despite the attitudes against women is icing on the cake.

[@Sciolist]

I'll have to watch this many times to understand

[@thomasdam9916]

OneTwoThee I'd have to study physics to understand all this, but luckily I'll start doing that in September

[@RedLeader327]

I don’t get it at all, but it’s fascinating.

[@michaelraum3393]

Sciolist is your profile picture David Hilbert?

[@wvg.]

Thank you for giving this a normal title that accurately describes the content of the video instead of some all caps clickbait.

[@Master_Therion]

Noether Theorem: Light does not travel in the Ether.

[@adolfodef]

[Just to be pedantic] Technically speaking, "electromagnetic waves" do not "travel" through space at all. . A measured photon exists simultaneously at the begining (creation on the past) and at the end (absorption in the present) of its path through spacetime [it does not experience "time" at all, its whole "existence" is zero seconds relative to itself]. -> It always has to be this way, because otherwise it would mean it had interacted with stuff already in the past and it does not exist anymore to be detected. [This is also the reason why it can only move at the speed of causation [speed of light] on vaccuum (never slower nor faster)]. It would be more correct to say that a perturbation on spacetime itself always propagates unimpeded by anything but its own curvature (the difference in the contents of energy on any "patch of space" before and after it passes through being what it is called "a photon" is just an abstraction, not reality); until it "colapses" when interacting with matter/dark_matter. Then there is no need of a "medium" like aether.

[@SelcraigClimbs]

8-Bit Wizard the original post was a joke "no"ether's theorem. Get it? And the wave like behaviour of light propagates through the EM field.

[@childfs6865]

Oh, I get it... *NO* ether Theorem xD

[@jonasschwalb2787]

It's a lot more! That light doesn't travel through the ether is just one of it's countless implications. And it's not really a very relevant one, since it just follows from the fact that that general relativity doesn't require the idea of an ether, is consistent with Noether's Theorem, and is in every regard a better theory. It's special and interesting, because it is both very specific and has universal implications among the fundamental theoretical models, which is a strong indicator that it's fundamental. And, of course, the fact that we don't really know why this is the case makes it incredibly interesting for people who want to figure out a (or the) theory of everything.

[@jonasschwalb2787]

Argamis (SilverComet) Is a perturbation in spacetime affected by its curvature? Remember, you're looking at it from its own reference frame.

[@Catmomila]

My only doses of serotonin that my brain releases these days come when you end your episodes with space-time, thank you Matt. That joke with the Big Bang patreon supporter was gold, really.

[@Garen1]

Make a series explaining and breaking down Einstein’s field equation?! Teaching about the the different tensors.

[@jgostling]

You will probably find kzbin.info/www/bejne/nKC1gX53gL-Krpo interesting. Fair warning though, set aside a couple of hours to watch, perhaps some more for rewinds.

[@Garen1]

jgostling Thank u! I have actually watched that video. It be more fun if u have that information presented by PBEspacetime, with their awesome editing and style

[@The9gods]

Wow this is amazing timing for me! Last night I watched an MIT OpenCourseWare on quantum mechanics (#4) and he mentioned Noether and made me was to look into their work more. I wake up this morning and bam! Here you are! This is going to be a good day.

[@Hythloday71]

Leonard Susskind says there should be a minus 1th Law of Physics / thermodynamics: Conservation of Information. Is there an equivalent physical symmetry associated with this law ? If not why not ? How is it distinct from the other conservation laws ?

[@berserker8884]

Hythloday71 I am also super hungry to know this, after all the whole holographic principle is derived from this due to any part of the universe can be collapsed to a black hole, while if information is conserved, then it has to be on the surface of the black hole, hence the holographic principle. EXCITING!

[@berserker8884]

The Truth of the Matter watch the susskinds talk on the matter. This was the black hole war with hawking as Hawking asserted that not even information escapes the black hole but susskind and lads objected and developed the model where information is thermal energy basically as this layer at the even horizon of hot plasma with radiation and anything that goes in has its data on that surface layer basically, hence holographic (data on 2D about 3D world).

[@enterprisesoftwarearchitect]

YES! (and +1 for Susskind reference) The Continuous Symmetry in that case is the Quantum State's invariance with respect to unitary transformations. Meaning - if any system evolves without you trying to measure it (i.e. evolves according to the Schrodinger or Dirac equations that Matt has spoken about in previous videos), then certain mathematical quantities - the dot products of the state's eigenvectors - do not change. You see, the math description of quantum state of a system is a vector in a multi-dimensional space we imagine (called a Hilbert space) and other vectors in that space don't get 'mixed up' with each other. UNLESS you perform measurement on the system! Susskind's minus first law goes out-the-door as soon as you measure a system - it just randomly changes the Hilbert Space Vector ("Wave Function Collapse") - that's the thing that freaks everybody out in Quantum Mechanics.

[@frankschneider6156]

Believing is something you don't do in science.

[@drumskateart]

I can't seem to find much info on this without cracking open an information theory text (and I'm no expert), but it seems like information is conserved over quantum mechanical "unitary transformations" which is a rather technical term highly associated with the mathematical structure of Quantum Mechanics. This kind of transformation is similar to certain gauge theories Matt mentions, and are required by QM to make sure the spaces in which you're doing physics is well defined, should you want to go back and forth between them. These transformations also preserve the probabilities associated with quantum measurement though, and that might mean the two are correlated in some more technical way. I'm also aware of thermodynamic definitions of information that relate it to entropy, but as far as I know, this "conservation theorem" remains a hypothesis, and so we don't know what kind of continuous symmetries might need to be present for information to be conserved. Take what I say with a grain of salt though.

[@Spectacurl]

I know some physics and this videos always let me like "wow, that's cool, wow I didn't know that". Amazing channel, so well explained, so clear and simplified in a beautiful way.

[@gianpa]

Is it me getting dumber or these videos getting more and more complicated?

[@brendarua01]

or both!

[@gianpa]

now that was mean :(

[@brendarua01]

Awww Let's hug it out. Here kitty, kitty...

[@tonysales3687]

i am finding them easier - but conservation of intelligence requires that someone gets dumber ;-)

[@Mormielo]

Yep. Not sure what i was watching but it was really cool.

[@Alexander_Sannikov]

I think maths behind this theory is more beautiful than just words. Wish you had more formulas with examples.

[@timbeaton5045]

Nice to see that Emmy Noether is getting greater recognition at last.

[@mysterymeat586]

At least to those of us who are watching this video. At least it's something.

[@mysterymeat586]

Probably never. Most people don't share the things that interest you and I is the point I was making, in a roundabout way.

[@jonnnnniej]

@Justin batchelar you just focused a loooot on gender, and in a not so positive way. Maybe start by looking in the mirror? All I hear is fear

[@jonnnnniej]

@Justin batchelar I'm just worried about you, you seem so focused a negative narrative you created for yourself. I never focused on gender, I just reflected your own words

[@ManintheArmor]

I heard there was PBS Space Time and came here as fast as I could! Also, needs more symmetry.

[@michaelnovak9412]

Best episode in awhile. Keep up the good work that was awesome!!

[@Only1INDRAJIT]

That's the type of video I want you to upload more and more!

[@robertfletcher3421]

What a great ending. I knew there was some connection with Middle Earth.

[@teemusid]

I was expecting a great Enting.

[@edcoolidge]

Thanks again for breaking down and explaining physics far better that my college profs ever did. It was about a decade later before I found out who Noether even was, as they never bothered to mention her first name. I've had to learn about women in science myself, as schools were still indifferent to the matter back then.

[@lepthymo]

"Where does the energy from redshifted photons go?" Well, the redshift is there because there's more space as time goes on.. so tiem and space.. space-time? So that would imply a symmetry between space-time and energy? So, in a way, that would mean that space-time is energy, which is what we call dark energy, right? So I have to wonder, since there seems to be a movement towards more space-time and less energy in our universe, ultimately leading to the heat-death of the universe, wouldn't that imply a space-time/energy symmetry? "Something is continuously symmetric if it stays the same for any size-shift in a given coordinate" - So on a coordinate of time, the amount of space-energy would stay the same? More time is more space and less energy, but the amount of space-energy would stay the same. Or equivalently, on the coordinate of space the time-energy would stay the same. The more space you have, the more time exist/has passed and the less energy there is. So doesn't that mean that there's an equivalence there? That there is such a thing as space-time-energy? I mean it kinda makes sense. Energy exists as movement of force in space and time. Space exists as the relation between energy over time. Time exists as the interactions/movement of energy in space. So I guess my question is, is the amount of space-time-energy really continuous? Or is there some axis on which it changes, and if so what is that axis?

[@cngbuddah]

well noether's theorem actually directly applies to time and energy. If you move an object (or system) through time and it's energy remains the same then noether's theorem states the object (system) must be time-symmetrical. space symmetry does mean that the universe could be moved and momentum would be conserved. but the entire universe is constantly expanding therefore its changing along the axis of size in space so the amount of space is definitely different from one second to the next. although sir roger penrose has some ideas about the final state of the universe that would mean that space, time and energy are all conserved, i think, basically you should check out sir roger penrose if you are interested in theories about the end of the universe. Also if you are interested in more symmetry stuff look up c-p-t symmetry and "this particle breaks time symmetry" by veritasium

[@anandsuralkar2947]

Great

[@douglasstrother6584]

Noether's Theorem is discussed in Chapter 12 (2nd edition) "Introduction to the Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields" of Herbert Goldstein's "Classical Mechanics".

[@Valdagast]

Extreme Astronometry. I would listen to that band.

[@aragorn0006]

One og the best and clearest PBS space time vidoes. I've always been a little confused trying to grasp this subject, but now I think I got it :) Thanks. And thanks to Noether. :)

[@exoplanets]

*great video as always!*

[@nachannachle2706]

Beautiful! Easily one of the best episodes of PBS spacetime since inception. I can't wait to watch the symmetry series. :)

[@Kalumbatsch]

Oh no, please don't tell me the universe is written in Javascript. Urgh.

[@myname-pe2pe]

no it's HTML

[@fluffy_tail4365]

I mean, it continusly leaks usable energy thanks to entropy, it's clearly not the best code out there

[@BlameTaw]

Worse. It's HTML. And it's no wonder there's so much empty space, they probably didn't even write their CSS with cross-universe support.

[@recklessroges]

xkcd.com/224/

[@guppy100100]

I thought it runs on unity

[@luizbotelho1908]

The great Emil Noether solved the greatest philosophical problem of Physics : What are Laws of Physics ? . Now we have a mathematical formalism (Lagrangeans , the Variational principle of Maupertius on Physics and the Noether theorem ) to tell what Physical Laws are . They are just the conserved quantities of Noether Theorem applied to Physical Lagrangeans (KInetic energy minus Potential energy ) . The law of electrical charge conservation , the Law of Momentum conservation , The law of Energy conservation , etc...are all mathematical manifestation of the Physics being governed by the principle of least action. .

[@metacarpo10]

Hello! Im very courious about the principle of least action, where it comes from, the motifs and reasons for it and also how noethers theorem and conservation laws derive from it. I graduated at Physics but we didnt talked about it that much. Can you recommend a good book or source to learn those things?

[@C6438911]

I must admit.. like others I also read it as 'No Ether' theorem. :D I regularly watch pbs spacetime but most subjects covered I just don't understand. But still I find this channel most interesting and keep watching whenever there is a new video released.

[@thegentlemandj4629]

"Please do your assigned readings!" Proof that we've graduated into college level KZbin

[@Kevin_Street]

Wow, this video is amazing!!! I don't understand it too well yet, but I'm definitely going to watch it again! Probably a few times. Thank you so much for making it!

[@Bigandrewm]

"We only ask that you start with a passing familiarity with quantum physics and the etymological foundations of the languages of Middle Earth. Please do your assigned readings." LOL!!!

[@theespatier4456]

Damn... PBS Spacetime takes physics to another level compared to other YT channels.

[@culture-jamming-rhizome]

I thought so at first till I found Sky scholar, see the pattern, dissident science, ect... then I came to the conclusion we have much more testing and theory development to go. I feel pretty confident in saying that in the not so distant future most of the models of academia today will be viewed as pseudoscience.

[@slashusr]

Just imagine what the 21st Century would look like if half of the Earth's population had been treated to the education and offered the opportunities that the other half has enjoyed, lo, these many centuries. To quote the Chairman: "Women hold up half the sky"

[@deustitties3589]

Are you not tired of this constant baseless wishful thinking?

[@slashusr]

@ゴゴ Joji Joestar ゴゴ Yu are, of course, quite right--the number of those either unable to access or barred from access to a good early education and then advanced studies was (and still is) far greater than %50.

[@ipadair7345]

@@slashusr I also think that the educaion we get is ineffectial aswell as harming at worst. The education systems around the world require a massive overhaul, one focused on making a community for learning instead of an area to cram information and never think critically,

[@Aziraphale686]

Oh man, finally. The symmetries of the universe are the most beautiful part of physics, and it's a shame that more of the bigger science channels haven't covered the topic yet.

[@nmarbletoe8210]

kzbin.info/www/bejne/nnfCpnuciNSCfaM&lc=UgwjAO40GYtqBnZ2WH94AaABAg.9JzGMznmYJF9K1Du3E6zte&feature=em-comments ...

[@Neura1net]

Can we please get sn episide on the L-L-Peudotensor? Mindblowing episode.

[@MetehanDoyran]

I appreciate the effort you put in saying "effort" at 6:20.

[@AlanKey86]

I've heard of Flat Earth Theory but NO Earth Theory!? That's a just cra... ...oh. Noether's Theory. My bad.

[@TheReaverOfDarkness]

Nutter's Theorem.

[@johnnewall7208]

Nice ending. Despite the fact that at least 90% of this is over my head, I really enjoy these videos

[@charlesbeaudry3263]

Need more on Noether. What a rock star!

[@nipunkhare]

Please never terminate this channel.

[@redaabakhti768]

thanks a lot pleslase more in gauge symmetries

[@SupLuiKir]

CPT symmetry: charge conjunction, parity transformation, and time reversal. At first, these three were considered separate symmetries, but Parity was violated in the 1956 Wu experiment. They polarized a cobalt-60 nucleus between a coil of wire with current running through it and observing the direction it preferred to eject to. Then they repeated the observation, but used a coil coiled in the opposite direction. If parity conservation was universal, it should eject out the same side, but it instead it preferring the other direction. So then physicists fell back to CP symmetry, which is a combined symmetry where they both have to be violated simultaneously to actually be violated. And that happened in 1964 when it was discovered that kaons, while pairs can spontaneously and simultaneously transform in to the other's antiparticle, if the rate at which they switch is the same in both directions, they will never switch at all, which is an indirect CP violation. The direct version was proved in 1999. So now physicists fell back again to CPT symmetry, where all three have to be violated in order to violate CPT. So much of our current physics understanding depends on CPT that if CPT is ever provably violated, it'd cause one of the biggest scientific overhauls in physics history. I suspect that there might be a way to violate CPT symmetry by examining the similarities between the experiment that violated CP symmetry to the experiment that violated P symmetry to extrapolate an extra layer of dimensionality from the CP symmetry violation, applying it to a potential CPT symmetry violation experiment. There are quite a few predicted future technologies that aren't possible in a universe with CPT symmetry, so I think figuring out if it can be violated is pretty important.

[@XrollhaX]

Ok, have to watch it 15 times to make sense out of it... Happens quite frequently.

[@rameyzamora1018]

me, too Arnon. Feel like there's a bit of intelligence accruing due to sheer osmosis, but am always, always amazed at the complexity of Spacetime. Wonder why it's so addictive?

[@XrollhaX]

Tell me about it. Whenever I watch the Relativity videos I spot some new knowledge. Many times I'm like: "Daaaaaaamn now I know what u mean!" hahaha

[@Brianboy9494]

Matt, thank you for this video. This is a question I have had for a long time now and it is wonderful to see that independently from each other, physicists ask themselves the same questions - even several decades apart - and look for new answers to improve on one's understanding. I am currently studying mathematical physics in Hamburg, Germany. I am very much looking forward to discovering all of general relativity and quantum field theory next semester. Hopefully, we will also discuss this, because I want to see how the maths behind it all works out.

[@Uejji]

9:24 Her contibutions redefined entire fields, but did it have any effect on unique factorization domains?

[@mightyNosewings]

ayy

[@salvadorrossi8608]

I wonder know now where is the symetry that links matter with antimatter.

[@JackDespero]

When I was studying physics, many things felt "ad hoc", unnatural, taken out of the hat by a magician. Until I learnt about Noether's theorem, and then it all made more sense. Why are these quantities and not others conserved?? Ahh, because of the symmetries of the problem. And you can actually "see" why a symmetry gives you a certain conserved quantity, making it in turn more intuitive. Brilliant thing that theorem.

[@justinmiller7398]

Great video showing the symmetrical contribution that women and men can make to science!

[@deustitties3589]

Symmetrical?...

[@robertschlesinger1342]

Excellent video. Very interesting and worthwhile video.

[@Sooyush]

Emmy Noether 🙌🙌🙌

[@TheNeverposts]

yo... these videos are ACTUALLY GOOD

[@gerardopc1]

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.

[@Zdman2001]

I love this show so much. My favorite topics explained in such great ways. Sprinkle in some physics and nerd jokes to give it more flavor. It's the perfect recipe.

[@_BlackSpectrum]

When you say 'this' is worth another episode how much do you mean it?

[@frankschneider6156]

I'd guess exactly as much as somebody is willing to pay for it.

[@Algebrodadio]

Mathematically, a manifold (M) has "a continuous symmetry" if there is a Lie group (G) which acts on M by diffeomorphisms. In other words, each g in the Lie Group G is a smooth bijection g:M -> M and composition of functions is the group operation on G. Flat spacetime is symmetric under the action of the group of Lorentz transformations - which are the set of transformations between inertial frames. The conserved quantity for this action is "center of mass".

[@aidanclarke6106]

Grugknuckle - Please don't make KZbin videos 😋

[@thstroyur]

"The conserved quantity for this action is "center of mass" " ? Don't you mean "(relativistic) angular momentum"?

[@Dragrath1]

Glad to see Emmy Noether finally getting some attention here I hadn't even heard of her before my undergrad quantum mechanics class. It's a shame that discrimination like this has left such a mark on our society that many greats never received the recognition they deserved. I never could understand what some people have against smart females as unfortunately this kind of bias is still a thing. :(

[@deustitties3589]

Oh please, it's never that simple.' I've never even heard feminists talk about her, it's always Marie Currie, their number 1 go-to example of "women can be smart too". Even if Marie Currie is a muddied case, because I've read that her accomplishments can not be fully attributed to her, as her husband helped her a lot with the research. I reckon it has little to do with recognition and more to do with theoretical physics as the topic Noether researched has little affect on the public's imagination and is more intimate with those who are theoretical mathematicians or physicians by profession. What Einstein, Planck, Hubble proved had a profound effect on how we view the Universe and it is not that difficult to wrap your mind around bare essentials of what they've discovered. Noether's work on the other hand is hard to follow, even after watching this video I find it difficult to understand what exactly was discovered here. Besides, history is full of men who were not recognized for their contributions to scientific community as well (Currie's husband for example) and I'd say more so than women because of statistical deviations between gender when it comes to science.

[@toserveman9317]

How many mathematician males from one hundred years ago have you heard of? I bet she has a bigger entry in science encyclopedias /text books than most mathematician men up at her level who were smarter. Pro female bias is in everything. It is an instinct.

[@jamesjohnson2394]

I just don't understand this modern obsession with hating women who stand up for themselves. Why is it on the internet you praise a women and point out there is bigotry in the world immediately hundreds of men online go insane with rage and rant about "feminists taking over".

[@toserveman9317]

JJ, you are a simpleton and liar.

[@ArawnOfAnnwn]

@James Johnson Not that I agree with either of them (and I am happy to see her highlighted here), but to answer your doubt, it's basically anger. A little thing like this might not have pissed people off in isolation. However, by now plenty of people are so resentful of feminism that even the slightest allusion to it, such as by celebrating women in science, is spoiled by association. If the more controversial agendas of feminism didn't exist, then this little thing would simply be seen for what it is - a positive acknowledgement. But nowadays it's all seen as tied together by a common agenda and hence even the minor aspects are anathema.

[@peterb9481]

Amazing episode. Soo many deep concepts. Massive Emmy Noether fan. Her life and work is most interesting, inspiring and touching. Hmm - about the comments: I will do my assigned readings and watch LOTRs again 😊

[@Thats_A_Dummy_Name]

Which symmetry results in conservation of Information in Black Holes?

[@strategen9124]

Thats_A_Dummy_Name blackhole symmetry

[@sinephase]

lol

[@Rubbergnome]

It is not really known whether information is conserved when it "falls in". Many proposals lead to conservation due to preservation of "unitarity", making sure that every observer has some way of keeping track of stuff, in some sense. For instance the "complementarity" idea, or the fuzzball paradigm. Other ideas abruptly throw out unitarity, but they are very sad scenarios indeed.

[@erdemmemisyazici3950]

"If we think of all paths being taken by propagating waves, then those waves that take paths that differ only a little from the optimum path still interfere constructively. This is the principle of stationarity and is related to the principle of least action. All “nearby” paths interfere constructively, while paths that are farther away begin to interfere destructively. Therefore, the path of least time is also the path of stationary time and hence stationary optical path length and hence the path of maximum constructive interference. This is the actual path taken by the wave-and the light."

[@timsmith6675]

Great video and information! I believe more recognition of women and women scientists will only contribute to a better environment for the success of our species.

[@PerfectBlue7]

women are free from any boundary since 1920. they just have to work as hard as men for their nobel prize. and if they can't get one, we'll say it's because of the inexistant patriarchy

[@minhnguyenphanhoang4193]

Not really - some people still think that women are somewhat less intelligent than men and they should stay at home and cook meals. That's the stereotypes that need to be broken - so that a man can be a nurse and a woman can be a scientist when they want to. ^^

[@PerfectBlue7]

it's not a stereotype : they already have a choice. now for the capacity science tells a different story. but that kind of science must be buried. ;)

[@minhnguyenphanhoang4193]

I agree with you that that are choices they make, but because of the stereotypes about nurses and scientists discourage many from becoming what they really want to be - and that's not a good thing since we can miss excellent people due to these stereotypes. And the capacity, I don't understand what you mean, you mean capability ? Yes, they have smaller brain on average and there are significance differences - but the truth must be told that there's a almost none differences when look at the career path of a men and a woman , who has no child. And if you want to talk shit about woman on their scientific career path, please try to talk shit about Marie Curie. ^^ A remarkable woman. So my point here to sum-up - Yes, women and men are really different in many things and it's an undeniable fact. However, there are remarkable people in both genders - so these stereotype must not exist in order to make way for these remarkable people. ^^

[@esgaril]

Kindred's Kaiser I can't decide if you are a troll or really this blind and clueless. If it's the latter, you might want to talk to a few women around you about how free they feel to pursue science while carrying the burden of procreation. And if you dismiss their answer as whining about patriarchy, that's your first clue of what's still wrong with the society in general and you in particular.

[@enterprisesoftwarearchitect]

+1 for the most natural use of ending the video in the word "spacetime" in quite a while!

[@NewMessage]

I'm sure that if Scott Pruitt could railroad over the universe's conservation laws the way he does over America's, he would.

[@LordMichaelRahl]

Barbaric.

[@bakuya99]

don't you mean Ａｂｓｏｌｕｔｅｌｙ　ｂａｒｂａｒｉｃ

[@erodgenator]

Well yes but we would have to pay for it !

[@markanderson1088]

Can’t we keep politics out of this? Just enjoy the awesome science for a change!!!

[@lakshaymd]

Mark Anderson you can literally just ignore this comment ffs

[@Herb.]

Lord of the Rings, assigned reading?? PBS Space Time is the best of all time!

[@e1123581321345589144]

6:10 does this mean the universe is lazy?

[@Magnesius]

yep.

[@rajrocksadi]

Efficient

[@PredragKoncar]

It's optimal. In other words - yes sir, it's lazy.

[@alarafatlemon3219]

Yes sir it is

[@rocknestephenson2158]

e11235813213455891404

[@lindsayforbes7370]

So pleased I watched this one. Energy is not lost in cosmological redshift, nor is it gained through dark energy. Dark energy is the gravity of the cosmos and cosmological redshift is its gravitational redshift. Thanks for putting another piece of the jigsaw into my theory

[@gamereditor59ner22]

Quantum questions with weird but sort of well put answer.

[@suprith-science1441]

My class name is Emmy Noether so I wanted to know about that person and thanks PBS for this amazing video.