Quantum Invariance & The Origin of The Standard Model

[@Ender240sxS13]

Thank you PBS Space Time for fanning the flames of my curiosity enough to get this 28 year old mechanic back to school and pursuing a double major in physics and mechanical engineering. Having recently finished a 200 level differential equations class that I absolutely loved, I now understand the basics of what that equation is representing, there is still notation and terms there that I don't recognize, but I am so excited to continue delving into physics and mathematics and I am confident that one day I will, I have really found a love for, and understanding of, applied mathematics that I never thought I would I would achieve.

[@JohnSmith-cl3ez]

outstanding librepenseur! your 'applied experience' will be vital, much like Burt Rutan's etc. incidentally, what do you think of 'ionocraft rheometry'?

[@Ender240sxS13]

Not going to lie I had to some searching around to understand what you mean by 'ionocraft rheometry' and I'm still not entirely sure. I really don't know much of the field of ionocraft, the idea of using EHD forces to provide thrust for a craft in atmosphere seams impractical to me, mostly due to the energy needed to produce significant thrust and the mass involved with providing that much energy currently, much more work would need to be done in creating higher energy density power sources before such a device could be feasible. However this does parallel with a field that is dear to me and where I hope to work once I complete my under-grad and graduate studies and that is high energy electrodynamic thrusters for use in a vacuum. And I am unsure of how the field of rheometry applies to ionocraft so please let me know. My searches did turn up results referring to MR fluids (although this is mostly due to the rheometric study of such fluids and again isn't linked to ionocraft) which some auto-manufacturers have been using in shock absorbers for high performance vehicles for awhile, which I actually do have experience with in a racing setting but am not familiar with any of the engineering involved. However I don't think this is what you were getting at.

[@katphisH11]

Good luck! Wish you the best!

[@pbsspacetime]

Nice! Congrats on the new adventure. Now when they ask what kind of mechanic you are you can reply "quantum".

[@abhishekjoshi8413]

this made my day

[@RomanNumural9]

This video completely blew my mind. i love when the math comes together.

[@PheneticsCo]

Hehe yeah! Watching is so much better.. Vs failing it in school.

[@theflaggeddragon9472]

Thank you for including plenty of math in all its gory details. Another comment mentions their appreciation of your insistence not to "dumb it down" to poor analogies and really dive in to the mathematics. Even more of this in greater depth would be greatly appreciated, and thank you for these stunning videos!

[@dziban303]

I used to think of myself as pretty smart. Thanks for correcting that, Space Time.

[@Dragrath1]

The Dunning Kruger Effect in action one needs to know enough to understand how much they don't know. If it is any condolence realizing how little you truly understand is one of the first signs your truly learning so keep at it. :)

[@TheRealFlenuan]

No one is knowledgeable about all areas of knowledge, and no one starts out their life knowledgeable. "Smartness" isn't only innate; it's also a skill that must be developed. You're capable of becoming an expert in any field as long as you put in enough time and effort - _that_ is the challenging part.

[@enysuntra1347]

So you don't feel pretty anymore? That's tough!

[@LesCish]

Indeed. I once qualified for an "I Passed P-chem" bumper sticker. PBS Space Time is fascinating and new to me. I understand the words, but only barest of the principles involved.

[@kschuman1152]

This one left me in the dust also. But I do appreciate that Matt is presenting the material in a way that's not deceptively over-simplified!

[@lambda5949]

I came here from an undergrad lecture on the magnetic vector potential: I was curious about this new idea of "gauge fixing" that was employed and wanted to know more, so my teacher recommended this video. Zooming out from a mathematical trick in engineering into describing the entire Standard model I've been fascinated by since childhood but never thought I'd be able to understand will honestly be one of the most memorable experiences of my time studying physics. I can never thank you enough!

[@leobidussi5039]

I am a master student of theoretical physics and I am just preparing the qft exam. I never would have thought that they would do a video about local gauge simmetry. This is great! It has been very difficult for me to have an intuitive way of looking at it. During the qft course everybody get confused when they first hear about local phase shift invariance, it feels like an unnatural thing to demand. Than they explain Yang-Mills theory and the whole standard model business is explained in terms of local gauge groups. As a matter of fact, nowadays the entire world of theoretical physics speaks in terms of group theory and symmetries. Even when we think about particles, they are just different representations of some group. It is amazing to me that only a century ago a physicist would only know about differential equations and calculus, completely unaware of group theory, and suddenly a seemingly useless branch of mathematics (for the physics' sake, of course) became the top player among the tools that we have to understand the world.

[@thstroyur]

My biggest problem when I took a course on particles was understanding how the hell the group theory relates to experimental things - and I still mostly do. Thing is, you can mostly skip this stuff if you just want to pick out some gauge theory and work out cross sections or whatever and there you go, but you can't really do the other way around; there are three quarks/baryon with three color charges because reasons, weak hypercharge somehow is a thing, and all this adds up to the specifics of the SM which I really don't understand (which is not just the YM machinery)

[@leobidussi5039]

Hi Iago! I had the same doubts, but in fact the SM is built on experimental evidence, and from cross sections in particular. One of the first evidence of colour was the adronic cross section of electron-positron annihilation. At low energies you expect to produce just the down, up and strange quarks, but in fact the cross section seems to have 3 times more particles, later we understood that they are the down blue, brown green, down red etc. Then if you construct your theory to have local SU(3) simmetry, you expect to have 8 gauge bosons, the gluons, and this is exactly what you see in the partonic functions of the proton, but you can go the other way around. Even the electro-weak theory was just a model until we measured the coupling constants and the masses of the W and Z, and we saw that they are in perfect agreement with the theory, which is not at all an easy thing to achieve since the electro-weak theory has very strict constraints. We constructed the SM bit by bit from experimental evidence, and from the infinite universe of possible theories we picked the one that fits better the reality. The outstanding success of the SM is that every prediction that we make is confirmed by further experiments. It seems that from the simple symmetry group of the SM we get it all. If you want a more direct consequence of the simmetries to the cross sections, for every simmetry you have a Ward identity on the scattering amplitude. For example the Poincaré simmetry implies that the amplitude can be a function only of the invariant space-time interval so that the amplitude itself is invariant. The more simmetry you have, more strict is the condition on the amplitude.

[@thstroyur]

Leo Bidussi I think you misunderstood me: of course the SM is based off empirical evidence; what I'm saying is simply that, in my experience, textbooks (e.g. Griffiths, Halzen, Greiner, Peskin & Schroeder, Ryder) make a poor job of explaining the experimental stuff in terms of group theory - like defining what a 'charge' is, what is helicity and chirality (I only got they have to do with spin and gamma_5 in some sense), and so on; for instance, I have some idea why we need 3 quarks/baryon because of the parton model, but I have no idea why hadrons gotta be colorless, and other symmetry-related things. And don't ask me what 'flavor' is, I figure it has to do with the up/down, nonneutrino/neutrino labels, but I don't know how to ascribe the particles to SU(2)xU(1) unirreps based off their experimental data (even though I know the basic workings of QFT, cross sections, etc)

[@leobidussi5039]

I have to agree with you. I am studying from the Peskin Schroeder and there is very little room for experiments there. Without a course on elementary particle physics I would have had a tough time understanding why we should add colour or flavour to our model. If I can suggest you a textbook, you can check Bettini's "Introduction to elementary particle physics". To me it was great because it is very understandable and gives you an historical explanation of the development of experiments and theory. You see from experiments that a model of quarks without colour doesn't work, and you see how they gradually added more flavours of quarks based on the discoveries of new mesons and baryons etc. It has a really good intuitive explanation of the electro-weak model and the consequences of its spontaneous symmetry breaking, the Cabibbo mixing and the CKM matrix, as well as flavour oscillation. And all of this is construct from experiments. I hope I have been helpful.

[@thstroyur]

Leo Bidussi Well, I _did_ check out Bettini back then, and it didn't fare much better than the others in this department, but I will give it a revisit. Thing is, I'm not as interested in the experimental stuff per se as the theoretical description, so I think I'll be stuck with Weinberg's undigestable treatise or some other formal text when I have the time :( Still, thanks for the attention, and good luck with the Masters (I'm sure it will be better than mine >w> )

[@honghaohuang8766]

I really appreciate how this channel includes actual math. All other physics resources are either purely academic, or lack any mathematical content. I love how this channel is a happy medium and still does a fantastic job in explaining it!

[@yamansanghavi]

I am a physics graduate student. These videos help me a lot in grasping the physical content of the dry equations that I encounter everday.

[@danpenaliggon4055]

Second this

[@garfieldsam]

Thank you Matt and team for finding the amazingly elusive sweet spot of challenging your viewers with ever-more involved material while still making it accessible enough to fit in the incredibly limited format

[@corwin32]

The way Matt’s reflection on the floor is added makes him look like he’s standing on his tippy-toes the whole episode

[@DavidAspden]

This is perhaps the best video you have done in a while, you threw in a lot of Maths and bit the bullet. I think it works. Turning into a great playlist.

[@TactileTherapy]

This show has been instrumental over the past two years in helping me develop my series of novels. Thank you PBS Spacetime

[@TactileTherapy]

Yes, of course you can I'll be honored. Its called TACTILE THERAPY Volume One. It's a science fiction series about a woman with an inexplicable ability to warp the spacetime around her, trying to adapt to a society that is on the verge of collapse due to an impending asteroid collision. The asteroid is based off an actual asteroid called Apophis 99942 and in my series the government regrettably blows it up - something they really didnt wanna do. The book is on Amazon and you can search it up

[@wangtoriojackson4315]

Oh my god, same here. I've been using something like really tiny black holes and their Hawking radiation as sources for mana springs and mana in a high fantasy setting I'm worldbuilding for in preparation for an eventual narrative. PBS Space Time has been my main source of inspiration and knowledge for fine-tuning what started out as a very crude and cobbled-together rough idea.

[@SayyadinaHeresy]

Yay! I am going to check your novels out! This is awesome to meet people who have found PBS Spacetime's videos helpful in their stories. Same for me and my developing science fiction graphic novel. 😄

[@Denverian]

I was always curious about this... What's the point in using science facts to write science fiction novels?? Can't you just make up everything and claim that it is a sci-fi?

[@landreaeo]

Youn Gu you need inspiration. A person from 1700 couldn't imagine a sci fi novel like the ones we have

[@musicalfringe]

Thanks to Matt and SpaceTime for finally doing pop-sci right after all these years - dumping all the traditional bad analogies and "maths bad" nonsense that was kicking around 30 years ago - and also proving that such a rigorous approach has an audience! Fantastic!

[@shivsompura9497]

Honestly starting to take a class in quantum chemistry and realizing this channel can help me get a better intuition on the subject is actually amazing

[@LoyalZen0x]

I will start my second year in Theoretical Physics in September and this has to be one of the best (if not the best) video so far. Keep up the great work lately. You are truly inspiring a generation of scientists.

[@chrismous2169]

Your explanation about various deeply theoretical concepts of physics is amazing and extremely useful. You have a true skill in teaching and communicating knowledge of such difficult concepts. I am truly grateful that you are out there doing such a fabulous work. Greetings from an undergraduate student of physics from Greece.

[@Sleepy.Time.]

is it normal to have smoke coming out my ears? i think this video overloaded the hamster wheel...

[@pilfit]

You need to remember to oil it before watching one of these vids.

[@justadbeer]

You may have confused it for the Rick & Morty channel

[@ColdCutz]

kzbin.info/www/bejne/h5DIm5yoeZaaqa8

[@peterfaber9316]

Sleepy .Time Yeah, I can't follow everything either. I just try to get a big picture view from these videos.

[@Sleepy.Time.]

@Peter - yep, usually Matt does such a great job explaining things it is not hard to keep up but this time it went mostly over my head

[@Folse]

I used to understand these videos partly...I’m now lost before the intro on most of them lol

[@Mernom]

Watch the whole channel again then.

[@sausage4mash]

Me too, I'm working on my more Beer hypophysis to see if that helps

[@kukulroukul4698]

go to PBS Infinite Series then :) cool chicks/impossible language. Quote Tiafoe: ''It cant be that good! '' end quote

[@gregdesouza17]

This is realllyyy hard and abstract, don't bother yourself with that, I'm actually amazed that they tried to explain what they did and that they did it well, I wouldn't have the balls to try explaining this at this level in a video.

[@MakeMeThinkAgain]

I let it wash over me and hope that my brain will eventually make some kind of sense of it in the future.

[@Slattery777]

This show is so damn amazing Do it forever please

[@rayzhang3425]

Hey that would be awesome, but it's unfortunately not exactly an Infinite Series

[@carmangreenway]

@@rayzhang3425 Infinite Series turned out to be a finite series :(

[@ogginger]

I mean this in the best way- it's been a "second" since I've had to rewatch a STEM video. There's a difference between the material being "new", dense in content, and/or challenging and being ineffectively represented. Spacetime is with respect to it's current and past video's always representative of the first. I really appreciate you guys [and girls(?)] pushing the content and not being scared to publish challenging topics and on levels that go deeper than the conceptual and layman levels of understanding. Thank you!

[@robertstuckey6407]

Hey what's the difference between mathematicians and physicists? Mathematicians stop at Q.E.D

[@Rubbergnome]

Nice.

[@robinsuj]

They also only care if a thing exists and/or if it is unique. Not WHAT that damn thing is.

[@qzamboni]

Your average person is awoken by a fire in the hallway. They take one look at it, run to get the fire extinguisher, and put it out. A physicist is awoken by a fire in a hallway. They get the fire extinguisher, then spend several minutes calculating what trajectory they should aim it with to best put out the flames, before finally putting out the fire. A mathematician is awoken by a fire in a hallway. They spend a few moments looking around, spot the fire extinguisher, and say, 'Ah, a solution exists!' Then they go back to bed.

[@robertstuckey6407]

This has got to be my favorite mathematician joke of all time! the astronomer just sprays everywhere and makes a huge mess in the version i heard

[@blackmamba1261]

You get two points for nerd sniping a physicist and three points for nerd sniping a mathematician. Any other difference is trivial www.xkcd.com/356

[@WilliamDye-willdye]

This video went over my head, and that's what I love about PBS SpaceTime. Once again I'll have to watch it several times, and do some web research, but the payoff is genuine mental expansion. Worth it!

[@Alorand]

We will build the wall, and make Neutrinos pay for it! 12:55 Noooo! Damn it!

[@blackshard641]

No wall of lead? How will we ever keep Superman out, now?

[@davidhand9721]

It was only gonna keep 50% of them out anyway. Some of them, I assume, are good neutrinos, but 50%? You know, there are a lot of good quantum jokes waiting to be made here. There are plenty of every kind of joke, it seems, but quantum is relatively virgin territory. For example, schroedingers facts, which are simultaneously true and false until fox news has observed them polling favorably.

[@marmorealcandors]

No. Just put them in a box.

[@davidhand9721]

Leonard Marc Ramos and make sure their scatterings are kept in a different box.

[@alquinn8576]

the problem with a light-year thick wall is that neutrino that brings a light-year plus one foot ladder

[@s3cr3tpassword]

Even though i have taken all the classes for the topics covered and could follow the video pretty well, the nuances and the animations he brought out really helped shed a new light on my understanding of the equations. Im happy to be in a generation where such information is readily available for any level of people. Always love the videos that deviate from cosmology. Great Job.

[@polosolo638]

I swear Matt doesn't have ANY bad frames in these videos. Pause anywhere and he's smokin

[@bo_392]

am i getting dumber, or are these videos getting more advanced?

[@mrvocabulary6794]

Yes.

[@IemonIime]

This one was very advanced.

[@codedragon6237]

Same question here

[@a-blivvy-yus]

You already got your answer from iyoossaev. Yes.

[@phatpat63]

I love it. I love these deep dives that really start to get down to brass tacks. It's what makes what the folks here at Space Time are doing so unique and special. Best videos on KZbin.

[@Worldvisionary]

Did not understand most of the video, however that was expected as I do not know physics. I’m trying to self teach myself physics and helpfully in a month when I come back to this video I will be able to understand the whole thing 😊

[@alvinlam6975]

I like the fact that the videos are getting more technical. Well done and I hope the episodes can be prolonged for 3-4 minutes.

[@kebrus]

I usually only understand about half of each new video and only after following you for years, yet, I keep watching every new video. Its as if I actually like to feel ignorant o.O can anyone relate?

[@KoneSkirata]

Yes, but it started to bother me so I bought books on the subject that Matt and others recommended or that are popular and started reading my ass off. Now when I see a new PBS Spacetime video about quantum mechanics, I think "ohhh, you know this concept already! Time to further deepen my understanding on this stuff!" Moral of the story? Yay for PBS Spacetime!

[@BothHands1]

I often have to rewatch parts of episodes a few times to really grasp the concepts, but this one was a bit over my head from start to finish. I'm left scratching my head lol

[@kebrus]

I understood till the magnetic field inside the Schrodinger equation part, afterwards it was blank to me. And I only understood the phase stuff because that series of the void stuff they did a few months ago, but even that knowledge does sit anywhere, it's like I have all kinds of different pieces of knowledge in my head and no connection between them. @NoneSkirata what book, can you link those recommendations please?

[@steventeklinski9585]

Yep. Definitely feel like a knuckle dragging Neanderthal after these videos but I love them anyway

[@carl-henrikfelth3985]

I seems more like you like to learn stuff to me. Remember: confusion is the sound of ignorance leaving the mind.

[@RIchardBH3]

I love the in-depth videos when going down the quantum hole, and then come up for air to show how different points are to be used to make these connection; like this video.

[@mahditr5023]

I love how I dont understand anything after 30 seconds but I watch it till the end

[@jamesskiles9694]

Everytime I listen to this podcast when I'm tired it turns my brain to mush. I love it. Keep up the good work and thank you!!!

[@exoplanets]

Great video, as always !

[@markchadwick77]

Great video. Almost all physics videos are either simple with goofy analogies, or entirely mind-numbing equations. I like the PBS Space Time videos because they straddle vast middle ground. The combination of equations and animated diagrams is perfect for those of us want a better understanding of these concepts.

[@osmium6832]

They're a lot better nowadays but if you go back in the archives a few years, PBS Space Time used a lot of analogies with stuff like skateboarding unicorns and electrically charged monkeys to explain magnetic fields at relativistic speeds. It ironically made it much more complicated and hard to follow than if they just talked directly about the particles and electrons they were referring to. I guess the platform that is KZbin forces content creators to try the goofy option first to appeal to the masses before they find their groove.

[@MaraK_dialmformara]

Why does the weak force get more bosons than the others?

[@ChenfengBao]

The larger the gauge symmetry group, the more bosons a force has. So actually, the strong force has many more bosons (gluons) than the weak force, but we just don't bother to label them differently. The reason why we label weak force bosons differently but not strong force bosons has to do with the way they interact with the Higgs field. In particular, the weak force bosons gain different masses (W vs Z bosons), whereas the strong force bosons (gluons) don't interact with the Higgs and are all massless.

[@MaraK_dialmformara]

Chenfeng Bao Interesting. How many types of gluons do we know of, and why is Higgs field interaction/mass the distinguishing characteristic?

[@ChenfengBao]

+Mara K The number of gauge bosons is the same as the number of "generators" (or "dimensions") of the gauge symmetry group. In the case of SU(3), that's eight. So eight independent types of gluons. We don't label them differently, because in some sense, any one type of gluons is as good as any other type. Somewhat like electrons and positions, it doesn't matter what we call positive charge or negative charge, one is as good as the other. They're just labels. Weak force bosons' interaction with the Higgs makes things different, because this interaction breaks some symmetries, as a result, not any type of gauge boson is as good as any other, hence we need separate labels (W & Z). Mass is just the simplest example of their differences.

[@pedropasquini4311]

Mara K , by the way, if you want to know how many gauge bosons for a given SU(n) group you just need to calculate: n^2-1 (thus, n=2, we get 3, n=3 we get 8 and so on)

[@michaelgurnett3138]

Also, we label them differently (as opposed to just calling them all weak-force bosons or something) is because they also carry different electric charges (the W+[positive], W-[negative], and Z[neutral]) and do slightly different things. Whereas the different gluons are pretty much indistinguishable from each other (as far as I'm aware anyway).

[@MrOvipare]

YES YES YES! i was waiting for a video like this for years! This episode, with the previous episodes, really puts a context to the standard model. Thank you so much!

[@burtosis]

This video only existed as a probability amplitude to me until I observed it.

[@altareggo]

Only if the Copenhagen interpretation is true.

[@elijahgardi7501]

That was brilliantly done much respect for everyone that helped produce this master piece. It's a master piece because it's so simply explained but also very informative.

[@Nick-hk2ro]

I always loved to think of mathematics as our translation of the universe's language. We are bound to make errors in the translation process but can always smooth it out and correct ourselves as we work with the language more.

[@tushargopalka4905]

Amazing video...I just wanted to point out one fault which is at 8:40 i.e Noether's theorem is associated with every symmetry. No, it's not. It's only associated with global symmetry and fields being on-shell. However, a special case of local gauge transformation is global, and that is why we have a conserved charge..which is "magically"..the total electric charge.

[@cavalrycome]

10:58 "Mathematics truly seems to be the language in which the universe is written." Yes, but it's the language that all conceivable universes and laws are written in, whether real or not. For example, Newtonian gravity can be described mathematically, but it happens to be an inaccurate model of how gravity actually works in our universe. That the laws of nature submit to an elegant mathematical description says a great deal about the power of mathematics as a descriptive tool, and nothing about whether there is an intimate link between mathematics and one of the many things it can be used to describe (nature).

[@Freeroler]

"Yes, but it's the language that all conceivable universes and laws are written in, whether real or not." Well, in fact there's no particular reason why the Universe couldn't just be absolutely random. The fact that we can discover its laws is actually miraculous.

[@cavalrycome]

Our universe has quantum uncertainty, which leads to apparent randomness, so if randomness is disqualifying, then the laws of our universe are not all of the type that mathematics miraculously describes. But then, we could presumably only conclude that something is "absolutely random" along some dimension of measurement by doing statistics on it, which means that such a feature would have a mathematical description after all.

[@abhayshankar8762]

Newtonian mechanics were a grammatical mistake.

[@SernasHeptaDimesionalSpace]

Yes math works in the universe but if space is not realy flat? or what if light speed is not constant and multiplyes it self that we cant follow it as soon it reaches around 300000 K/S.

[@Theconnecteduniverse]

really amazing. i am an electronics engineer. But, space time made me a physicist with in one year. hats off to the kind of fundamental explanation .....

[@greenorange752]

3:10 This is nitpicking, but shouldn't the square of the magnitude of the wave function be called the probability density and not the probability distribution? Then again, these two terms seem to be often used interchangeably in literature.

[@greenorange752]

I see. I was under the impression that 'distribution' usually refers to the so-called cumulative distribution function. Thanks for the clarification!

[@guyedwards22]

This video inspired me to delve deep when you mentioned the other gauge fields! I read about how the gauge invariance of the color charge space under transformations in the SU(3) group gives the conservation of color charge in quantum chromodynamics, and I'd love to see a video on the mathematics of QCD

[@TheJackawock]

I don’t want to be too pedantic (but I will be, sorry) however SU(N) groups have a dimension of N but N^2-1 degrees of freedom. Hence they have N charges for particles in the fundamental representation but N^2-1 gauge fields. So the annotation needs correcting. :p Sorry not sorry... Love the series though.

[@Alorand]

TheJackawock I want to like your comment so that the Spacetime guys see it, but I have no way of knowing if what you so confidently stated is true or not. I guess I will assume that you are right.

[@Alorand]

+Oscar Thanks. I appreciate the explanation.

[@TheJackawock]

Yeah, that’s a really nice description of it Oscar. Well phrased. Putting a physics perspective aside, I was just being picky about maths nomenclature (dimension versus degrees of freedom). It makes a very big difference in acedmic circles but it’s likely that spacetime just tried to skip by it to get the point across. So what they wrote was technically wrong but I think only because they were trying to make it more understandable. For interest’s sake, as Oscar mentioned colourless (singlet) gluons; he’s right that we exclude these because of experiment. However that doesn’t stop us imagining a world with colourless gluons. This theory would be said to have U(3) symmetry, or U(N) more generally. The S simply means no colourless gauge bosons in this context. Trying to answer “why would we not want chargeless/colourless gluons in a theory?” is a fun quick question to think about. :P

[@TheJackawock]

My phone crashed and sent that like 10 times.

[@jgranahan]

Thank you for these videos! And for the feeling I occasionally get when hopping from one to the other (referenced within each video) and a semblance of ‘understanding quantum physics’ happens to this lay person with an art degree!!

[@campbellpaul]

Complete wizardry!

[@emceha]

I love this channel so much. I usually get lost around 1/3 of the video but I enjoy the rest even more

[@nastropc]

It looks so tantalising that one further abstraction with four degrees of freedom should elegantly have gravity fall out of equation, so what goes wrong when that is tried?

[@ChenfengBao]

You mean add a SU(4) gauge symmetry? When that was tried, it simply didn't correspond to anything we've observed in reality. A fundamental difference between gravity and other interactions is that gravity is the dynamics of spacetime itself, whereas other interactions just treat spacetime as a static background. So it's probably not that strange that a proper quantum theory of gravity should look very different.

[@thstroyur]

+Bao Yet gravity is still a gauge theory with group GL(4) - and so far I know nobody who tried to gauge SR via the generators of that instead of the tetrads ;)

[@truthisthenewhatespeech9572]

😳😳😳

[@The_Tauri]

One of the best explanations of Guage symmetry I've ever come across.

[@danielshults5243]

I try to take *something* away from each of these episodes, even if I don't fully understand them. In this episode, I think what I've learned is that the fundamental forces are described by the introduction of balances which preserve symmetries INTO the equations of quantum mechanics. Does that sound like a fair assessment?

[@Freeroler]

Sounds just about right.

[@photinodecay]

That's actually a decent paraphrasing of Noether's Law. This is a specific instance of that applied to symmetries under phase shifting. Local phase invariance is a broken symmetry that results in the effects of electromagnetic forces being applied to the particle.

[@brendanotoole5871]

Thanks for the great content. I feel very lucky to have access to this level of information at my finger tips. The whole of the PBS Digital Studios catalog contains some the very best educational content on KZbin.

[@bogdan_cx]

Great video

[@Freeroler]

Thank you so much, this is the simplest explanation of how do you get EM-field from the phase invariance that I've ever seen.

[@Salty_Nutella]

Something for last episode Matt! When you said the certain types of neutrinos cannot be candidates for dark matter, (& energy) can its density be calculated and compared to the cosmological constannt (and turn out unequal)?

[@Salty_Nutella]

In one episode, I learned that dark energy mysteriously increases to keep constant in an expanding universe. I just wondered if neutrinos won't just appear from nothing so that's another reason (right?)(unless dark matter and energy is an actual thing and don't appear from nothing 😯).

[@garethdean6382]

There's a few problems, the main one is that if you have neutrinos light enough they simply don't behave as 'solidly' as dark matter does. Regular neutrinos for example must move at nearly light speed all the time and so can't clump around galaxies like DM does.

[@rjblaskiewicz]

Holy cow. Been watching these in order. This...almost made sense to me. I am going to go back and rewatch the video; now that I know where it is going, it should make sense the second time through.

[@lordofentropy]

I am a simple man, I see quantum invariance, I click.

[@uncleweirdbeard86]

This is quickly becoming one of my favorite channels on KZbin. this is the kind of stuff that I wanted to learn in school before they decided that I wasn't normal and started putting me on medication that made me not normal #Ritalinbandwagon

[@nohbdy1122]

What does the imaginary component of the wave function really mean physically?

[@yakirey.2745]

I asked myself the same thing /: ... Confused me. If you find an answer would be great if you'll comment it here!

[@francispham6113]

Complex numbers provide the necessary degrees of freedom to mathematically describe the wave function. It's just makes math simpler, for example we can write sin(kx) as (exp[ikx]-exp[-ikx])/2i.

[@alvinoid12]

I want to know this too. Physicists, enlighten our plebeian minds!

[@thedeemon]

Same as the real component. Both of them contribute to amplitude (that gives us probability), and having them both allows to have some non-zero derivative even when the amplitude is constant, which means a plane wave can have energy and momentum. See kzbin.info/www/bejne/govMlmWHeJp9mMU

[@oktopussy9628]

thedeemon So is it like giving a function a futher parameter?

[@justinabsentia]

this is probably the best spacetime i've ever seen. and i've seen like, all of them. good job.

[@feynstein1004]

Hey is gravity a gauge field as well? Or is it not a field at all? I mean, can space-time be considered a field?

[@yakirey.2745]

Well, since the higgs bozon Isn't called a gauge bozon but a scalar bozon must say something about it not exactly being a gauge field... Since spacetime is something that doesn't only exist in a context of a particle, but all at itself, I'd guess it's not really a gauge field... Higgs bozon is described as a particle that exist all over in the universe, while the others are more on their own...

[@thedeemon]

In general relativity gravitational field contains a value of metric tensor at each point in space. So yes, it's a field. In some sense (not very strict) it is quite analogous to a gauge theory, with Levi-Civita connection playing the role of a gauge field. There is a covariant derivative too, it "corrects" a partial derivative by including effects of space-time geometry, instead of effects of local phase shifts as in U(1) of electromagnetism.

[@frankschneider6156]

Gravity has not been quantized and is not a Quantum Field Theory (yet) and not part of the Standard model, so no. That's one of the holy grails on the way to ToE. Do it and the Nobel prize is yours.

[@thstroyur]

GR _is_ a gauge theory, and the metric _is_ a field (even if not quantized); and no, the Levi-Civita connection does _not_ play the role of a gauge field (even though it's what defines what "curved" means in this context) because that role (oddly enough, IMO) is performed by the tetrad field, which is _not_ quite the same as "space-time". *phew*

[@coloradoing9172]

@@yakirey.2745 Wtf is a "bozon"?

[@danieleboccanfuso1723]

This is by far my favorite PBS spacetime video

[@xthe_moonx]

saying the universes language is math is backwards. it is what it is and we explain it with math.

[@yakirey.2745]

Totally agreed. 👌

[@frankschneider6156]

Yepp

[@firebladetenn6633]

yes indeed. The universe is not in fact, made of math. Math is simply the best way to explain it, has been developed to explain it, has symbols and specific orders of those symbols derived to better explain the universe. Almost like...a language.

[@jessrevill1852]

If you find the right answer, the math will (probably) work for it … but just because the math works doesn't necessarily mean you have the right answer. Being beautiful or elegant doesn't necessarily make it true.

[@mouzaalmualla3084]

But language is imperfect; it's just a means by which we describe our own emotions and opinions. The same goes with math, it is our means by which we describe the universe to the best of our abilities (with various limitations). In that sense, I think calling math the language of the universe is quite appropriate.

[@Locut0s]

Watching this high is fun. Watching this high while also understanding just enough the of actual physics to basically understand what he’s saying is AMAZING!

[@therealDannyVasquez]

1:45 Why's he stood on tiptoes?

[@anatolydyatlov963]

It's the deep need to appear higher than he normally is. Everyone is insecure in one way or another

[@truthisthenewhatespeech9572]

🤣🤣🤣🤣🤣🤣

[@truthisthenewhatespeech9572]

@@anatolydyatlov963 🤣🤣🤣🤣

[@Dealve]

Hearing him say spacetime at the end of every episode brings me great happiness.

[@krukerproductions]

Sounds like a synthesizer tutorial

[@sub-harmonik]

filter design/circuits/spectral processing also use a lot of complex sinusoids/signals in the math

[@FirstRisingSouI]

I've already gone through all my grad school course work, and I didn't know this. Mind blown.

[@Bassotronics]

E = MC Shrodinger

[@Dc-zu1ii]

Bassotronics www. gravitationlab.com. build the slow low-energy non-collider and stop using exterior solutions for things moving inside a gravitating mass (like molten orange juices in a ball of ice or Neil degrasse through the earth)

[@Bassotronics]

Dylan Childs I would be glad to build one! Just lend me $20,000,000 and I will pay it back through PayPal by the year 3069.

[@Dc-zu1ii]

That's a lot of money. These days you could probably build a Small Low-Energy Non-Collider on earth for less than Two-Million USD. That would be a really nice one, you could probably afford to make it out of luxury goods. Or you could spend more money than most people can imagine on a fancy gravity buoy made out of light. The National Science Foundation is willing to fork out enough to send a satellite around 10 AU Sol orbit to refine our measurement of G if you can build a spaceship that will complete the experiment... Richard Benish seems to believe you can do the same work from here on earth, or even just in low orbit. However it's done, I think, the results will be astounding to all physicists. Especially since it's been right under our noses the whole time. Wouldn't you like to know, Neil Degrasse would, in fact, oscillate if dropped through the center of the Earth? It is important to know before you try. It would be sad if he became an asymptote near the center and were trapped in the hottest part, think cave rescue plus plus because you wouldn't need just an SCBA you probably would need a rocket or some other flying machine in order to escape. half-fun everyone.

[@waynelast1685]

I appreciate the videos. You cover a lot of material in an advanced manner such that the only people really able to make sense of it are somewhat experts already. But the video you made is interesting and I will try to make sense of it over time.

[@ashbjorn]

Space Video + Epic Beard = Win!

[@sntk1]

If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electromagnetic waves of wavelength in the neighborhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow. ~Schrödinger

[@Salty_Nutella]

I'm starting my first year in Physics next month and I'm particularly interested in particle physics and cosmology. Any advice? (Oh and do leave a ❤️)

[@worf7271]

put a lot of effort into solving your homework problems, that's more important than going to the lectures

[@ephraxis]

ignore Worf, you should put effort into solving your problem sets AND attending lecture, at least provided the lecturer is decent. The absolute most important thing if you want a career in physics is to start research as early as possible and establish professional relationships so you can get really good letters of recommendation. You should try hard at everything but the letters are particularly paramount to success. It's convenient that you enjoy HEP & Cosmology since those two fields are hot right now. During your first year, try to figure out who in your dept. is actively doing research you enjoy and go talk to them so you know who you might want to be your adviser. Source: am a PhD student p.s. here are some hearts ❤️❤️❤️❤️

[@Salty_Nutella]

Thanks 🙏 love you all. Amd yeah, I've been reading textbooks (whether I understood them or not lol) and watching publicized lectures on physics and mathematics (from mit!) since 7th grade. Can't wait!

[@Salty_Nutella]

Adrian Thompson My uni has undergraduate research programs + scholarships so it will be a great start!

[@worf7271]

Adrian Thompson I didn't say that he shouldn't attend the lectures, I said that problem sets are more important. A lot of people underestimate the importance of hands-on practice and think that they can learn physics passively by listening to someone else.

[@4pharaoh]

Fantastic. You will never know how helpful this video was. Thank You.

[@NewMessage]

I thought this Gauge Theory stuff was gonna be about mathematicians with body piercings.

[@bimgo618]

This is my favourite channel on KZbin

[@gravijta936]

"Funzies"? Lol! Is that the scientific term?

[@LEVimmortal]

sounds just auzzie to me

[@thstroyur]

That would be "shits and giggles"

[@ASLUHLUHC3]

"Perhaps the greatest mystery here is not the nature of the quantum field, nor the connection between symmetry and the fundamental forces. Perhaps it's the fact that by pure exploration of mathematics, delving many layers of abstraction deeper than our capacity for intuition, we are led to true discoveries about physical reality. And following those mathematical labyrinths reveals physical theory with stunning predictive power, like the standard model of particle physics. Mathematics truly seems to be the language in which the universe is written. We should be amazed that we can learn that language, and through it, comprehend the underlying nature... of Space Time." Deep

[@gamereditor59ner22]

Quantum theory is fascinating and it brings possibilities to the table, as long as it is relevant.

[@tuele4302]

It will always be relevant. Old physical theories rarely die; they just have restricted applicability. Think Newtonian gravity.

[@sjzara]

Wonderful. This is the first detailed explanation of gauge symmetry that has made sense to me. Thank you!

[@youteubakount4449]

I find it fascinating that physicists think that "mathematics is the language of the universe", when this is the only language we bothered developping. It's similar to the idea that since we are capable of thinking about a god, our species would be special in some way. What would physics look like if the predominant mathematical dogma was finitism? The standard model is a projection of the laws of nature on the space of our mathematical theory. I would be extremely excited to see what physics looks like for an alien species that understands logic differently from us.

[@wiamleiss6175]

But there is no different logic, aliens may use different characters and notation in their mathematics but the underlying logical operations are the same. Mathematics is the language of the universe, we just have an arbitrary writing system to represent it

[@someone2973]

I agree with what Wiam Leiss said.

[@youteubakount4449]

Wiam Leiss But there are different logics. The fact that you can't think about them doesn't mean they don't exist. For example let's take a basic deduction rule that we use all the time: a proposition that isn't true is false. But if you use something like fuzzy logic, there is a degree of truth to the proposition, it isn't all black and white. Maybe there are 3 "states" and we are so limited we can only understand 2. There are so many ways we can see the world.

[@davidhand9721]

Goedels aside, math is not a language. We have language that describes math, but the map is not the territory. An alien (or person, or dolphin or whatever) might have an entirely different language for math in which the concept may look very different, but the concept itself has to be the same, or one of us is just wrong. Asking what physics would look like when projected onto a paradigm that isn't math is clearly answerable: it would look like gibberish. Eliminating math is eliminating logical structure. You can rephrase the math all you like for the aliens, but omitting it entirely renders theory totally meaningless.

[@RaT90909]

Its the old discussion of mathematics being either discovered or invented. I believe it is an invention, but that doesn't mean it doesn't work to predict certain aspects of reality and neither does it mean that mathematics can't also be invented by an alien civilzation. At the same time, mathematics isn't perfect, neither is physics. Humanity will never understand all the mysteries surrounding nature because those mysteries are in itself a construct of the human mind. We choose our own mysteries, and we go out to solve them, and mathematics has been a powerful tool in solving those mysteries that we chose to investigate. I imagine an alien civiliation would focus their research in something else that we are totally oblivious to and haven't even imagined, for instance maybe they will be experts in poetry. But can you reach space through poetry? Maybe the alien poetry is so powerful that they can, who knows.

[@remusgogu7545]

This is the first video after many, when I really got the gist of gauge symmetry and gauge forces. Thanks man! 🕺

[@jamesbrown4416]

its not coming home :(

[@ゾカリクゾ]

This is the most enlightening video about theoretical physics ever

[@it_was_my_cat]

England's coming home 😔😔😔

[@yaldabaoth2]

France are world champions. I don't see how Croatia stands a chance. England wouldn't have fared better, though.

[@youteubakount4449]

still waiting for my dad though

[@MrRockus]

To nothing

[@it_was_my_cat]

youteub akount oof

[@booboodadfool8015]

Viva la France.

[@comfyfloor7238]

insanely well explained wow

[@CloudsGirl7]

Jesus Christ, it's the BOURNE rule... ...I'm sorry, I had to.

[@frankschneider6156]

Ouch

[@xsk8rat]

Back in 19mumblemumble, i struggled to understand this stuff. You make it so easy! Thanks!

[@muskyelondragon]

The Standard Model works, but we know it's wrong and incomplete. That is a true statement. We believe General Relativity must be only an approximation and incomplete but cannot prove it. That is a true statement. We need a conceptual breakthrough. Don't know if I will live to see it.

[@yakirey.2745]

It wouldn't be wise to say it is wrong.. only incomplete. Newton laws are completely wrong in the way you define wrong, yet newton laws work very well when you are on Earth. They don't show the full picture, that's all. Doesn't make sense to call them wrong because of that.

[@muskyelondragon]

Thanks for the comment and I get your point but I'll expand a little. The Standard Model is clearly limited by our mathematics. It gives infinities right out of the gate and only works after "re-normalization", a dubious mathematical trick that is only considered legit precisely because it's the only way to get the Standard Model to work. Even with that it predicts mass-less neutrinos that don't exist or if they do have not been detected. The general consensus is that the base underlying reality is quantum in nature but is it? IDK maybe, maybe not. Does it have to be or is that just a reflection of our models? Gerard ’t Hooft has some interesting thoughts on this that are not without merit, he has a proven track record of intuition. Penrose is also doubtful that Quantum Mechanics is the final word on reality. He has been 15 years ahead of pretty much everyone for his entire career and most of his work not fully appreciated until years later. Stephen Wolfram clearly has thought very deeply on the nature of our mathematics and how it is limiting our paradigms. Is mathematics invented or discovered? Will AI allow a breakthrough since it is not limited by our brains physical structure? Einstein was the last great Classical physicist and GR is a classical theory, is it wrong? Not so far! What do you think about what Arkani-Hamed and his collaborators have been working on? What does it imply about the nature of reality? Is it shining a light on how our mathematics have shaped our theories and thinking or the other way around? Sorry I could talk about this all day.

[@frankschneider6156]

I tend to mostly agree with you initial post, but normalization is not as bad as it seens. Just because some values don't pop out automatically and this is solved by fitting is not that horrible. Yes, it's unsatisfying, but there are things worse than that. While t'Hooft is now probably greatest theoretical physicist alive, Penrose is an excellent mathematician, but not a physicist (although he meddles with it), so I wouldn't take him too seriously and Wolfram was a long, long time ago in a galaxy far away been a physics child prodigy that later turned sith lord , ehm I mean crackpot. He is roughly as sane as Kurtzweil, who also has absolutely no idea, what he is actually talking about.

[@fabienb449]

7:53 I find this discovery AMAZING

[@Algebrodadio]

U(1)xSU(2)xSU(3) ... wow. you could do a whole series of lectures just on the special unitary groups. Perhaps you could do just one episode on the representation theory of these and how that relates to QFT ?

[@VALERAFER1]

Wow! Excellent! The best explanation of such a complex topic I have seen or read so far. Congratulations!!

[@dominiccasts]

Videos like this make me wish I'd taken a lot more physics courses in university.

[@dominiccasts]

I took a fair number of math courses (mostly discrete math, mind you, but some calculus and linear algebra as well), so fewer regrets there.

[@yakirey.2745]

Same here. I learn Biology so I could live without so much math and physics, but would sure be great if I took more such courses. Personally I think math can help alot also though...

[@frankschneider6156]

Try Tipler "Modern physics" as refresher (as natural scientist most of it should be pretty familiar to you, it's all pretty basic stuff, nothing complicated) and one of the "Maths for scientist and engineers" books, of which there are several out there. Then move to more specialized literature, possibly starting with particle physics.

[@merinsan]

That was quite interesting. It's amazing how introducing imaginary concepts can lead to breakthroughs in understanding of actual concepts.

[@elsenorcostaricence]

I love this channel so much. thank you for another great episode!

[@jamieg2427]

Holy crap I wish I had discovered this channel a long time ago. The level of detail is fantastic!

[@micomrkaic]

Nicely done. Given the supreme elegance of the Standard Model, it is surprising that there is most likely stuff beyond it. Let’s hope the new stuff is even more elegant.

[@yakirey.2745]

Matt, Cmonnn start with String theory please!!!!!! There is infinite amount of stuff to talk about when you go into it, and it's just awesome af

[@bobanderson665]

Thanks for explaining gauge symmetries in a way that makes me feel I know a little more about them now. Now, why are they labelled U1 SU2 and SU3 ???

[@0jaza0]

I always find complex functions easier to understand if I imagine it in 3D space, with the y and z axes representing the real and imaginary part of the function. That way, you can actually understand the function as a whole, and local gauge invariance would only mean to rotate a point around the x axis, without changing its distance from it.

[@ahappyimago]

Know any videos that show this?

[@0jaza0]

​@@ahappyimago There are some videos by Eugene Khutoryansky in which he uses this kind of visualization, especially when talking about wavefunctions.