The Equation That Explains (Nearly) Everything!
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- Опубликовано: 18 окт 2022
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The Standard Model of particle physics is arguably the most successful theory in the history of physics. It predicts the results of experiments with a numerical precision unmatched by any other branch of science, and it does so almost unfailingly. The theory is encapsulated in a single equation known as the Standard Model Lagrangian. Today we’re going to explain to you how it works!
Want to Dive Deeper into the Standard Model Lagrangian? Check out:
• The Higgs Mechanism Ex...
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This is like when the teacher says: "OK, we've already covered all this. So it should be easy".
Yeah I barely got a few minutes in and realized I needed to rewatch some other videos first 😅
And this playlist is like all the homework you already did, but totally forgot: ruclips.net/p/PLsPUh22kYmNBgF_VMMLHFK0lbQGlVGk3v
*proceeds to explain the actual fecking universe*
@@ChristineB816 some? Try all... twice
And im still not 100%clear what's going on, true just like back in high school haha
@@pbsspacetimeAre you giving us homework?
The unpacked version of the Standard Model Lagrangian (density) shown at 14:00 in the video was the version I transcribed and posted in 1999 from the appendices in the book Diagrammatica by Nobel Laureate Martinus Veltman while procrastinating writing my dissertation. I'm glad folks are still getting good use out of it over 20 years out!
Thomas, thanks for taking the time to transcribe this out back in the day! I trust your dissertation was still fantastic, despite being an hour later than it would have been.
@@pbsspacetime Thanks for the shout-out and for the amazing content over the years! At this point, every question I get from my research students I just say "just watch the PBS Space Time video." Except for Majorana neutrinos and neutrinoless double beta decay. And intrinsic charm. I still have to explain those to them...please get on that soon so I can shorten my group meetings...
Seconded
I've written it down and it took me about 2-3 hours....
it is absolutely astonishing to me that I can read comments from actual physics professors in a youtube video, like any other comment, despite living on another continent!
If put to good use the internet can be a marvelous place.
I really like that fact that this episode and some of the other recent episodes are totally over my head. I studied math and engineering in college and most of the physics channels out there dumb down the science so much that they don't really say anything at all.
keep challenging the audience to become educated and keep up. keep setting the bar high. this content might be above many peoples head but I REALLY like that it challenges me to keep learning.
This channel is super well produced and I'm a huge fan. keep pushing us to understand at higher levels
It only feels over your head. The actual pure maths is over most, hence this.
h.c. especially feels like a very physicist hack-away, not formal logic, compute notation, better to just use descriptive word for mu and nu and usage constraints for example entirely in that case!! E.g. one h.c. cannot be equal the other h.c., otherwise you would just write / imply 2h.c.
Physists are practical... But then just put the entire equation in descriptive annotative words or leaf the maths pure and unobscured! Or use animated maths for each term. But especially not this h.c. notation.
This has a high level of 'entropy is chaos' simplification level, but for an equation notation standard. Entropy is the tendency of dispersal of energy with the constraint (!) absense of a energy barrier. Maybe formalise the constraints of your model too. It shows the weak points. E.g. the big bang clearly had an energy barrier breach of some sort. What was the barrier?
@@FriedPotatoFarmer 😂👌 They chose to fool the wrong people!
I love this physics stuff but I always fall asleep during it.
Yep. I fell asleep watching this episode too. Insomnia is a thing of the past with PBS.
I failed math 4 times, but I comprehend the concepts when explained in this manner. It's wonderful.
Still can't play darts without a calculator though.
I just want to say how unbelievably grateful I am for this channel. I've waited for something exactly like this for decades.
your passion excites my passion. we need educators. i have extreme ADHD. and i find these things incredibly hard to register but am really excited when gaining clarity. we do not have people like carl sagan anymore. i appreciate channels like this. this is perfect pacing. if we do not educate IDIOTS like me we willl have lost it in translation.
@@thatdudebro don't be so hard on yourself. The fact that you're into this clearly tells me you're not an idiot!
Yes! I wish this was around when I was in grad school - it would have saved me LOTS of angst at solving my homework like I'm casting magic 😭💀
You must be kicking yourself that you didn't set up RUclips.
I've waited for 13.7 billion years.
When I started watching PBS SpaceTime, I was just learning about quantum mechanics and relativity. 5 years and a chemistry degree later, I finally feel close to the frontier. It's been a pleasure taking this journey with you.
Same exact story here. Continuing with grad studies.
If you wanted to feel close to the frontier, you should've went down the physics route and got a PhD in theoretical physics...
This was the frontier 50 years ago
@@pyropulseIXXI No you don't. Only if you want to work with it.
i work in retail and enjoy watching pbs space time 🤷♂️ ... i understand like 10% of what he is talking about but i can make a general picture anyways
A grad student who’s studying particle physics worst nightmare is encountering the standard model Lagrangian. A few of my colleagues got their PhD in high energy theory, so if you ever want to scare them off that’s something you show them lol.
Normal people are scared of ghosts, while physicists are scared of ghosts particles in their equations.
Is there any benefit of taking the Lagrangian instead of the Hamiltonian?
Physics is the simplest of all scientific disciplines and is based on the highest number of "spherical cows".
Physicists can barely comment on the field of Chemistry which is at least an order of magnitude more complex, let alone Biology, physiology, psychology, economics etc or something that is totally unresolved such as consciousness and free will.
The Physics community doesn’t even have the courage and integrity to tackle the interpretation problems associated with Quantum Mechanics such as the measurement problem.
"Shut up and calculate" is simply not good enough.
It's probably why the field of Physics has been fundamentally spluttering along, near stagnant for almost 5 decades.
Physics has produced NO surprises in its field since about the mid 1970s. Many of the recent developments are due to theoretical predictions made many decades ago (eg Gravitational waves)
Physicists can’t hide behind spherical cows forever - the foul flatulence alone will plunge their clouded minds even deeper into the abyss. The self-referential putrid stench fuming out of the windows of Physics departments around the world is unbearable at the moment.
@@tayl9242 The lagrangian is manifestedly lorentz invariant, whereas the hamiltonian is not, which complicates things. In reality both approaches are used depending on the problem in both relativistic and non-relativistic quantum mechanics. lagrangians are also closer to the symmetries of the system and noether's theorem
Please no nuclear. UK🇬🇧 HM King George VI, the father of HM Queen Elizabeth, also died of nuclear dust attached to his lower rib.
Nuclear dust from 1945 August, two atom bomb dust blew from Japan🇯🇵 to China, killed more Chinese than Japanese, then blew to Spain🇪🇸 and the UK🇬🇧.
Please don't use nuclear in space. The Gods who maintain this Universe (aliens) are removing nuclear material from this planet Earth and hanging them on the outside of the metal wall of this Universe.
In 2019, 24 of the European Space Agency's Galileo satellites lost contact because these satellites provide services for nuclear power plants, nuclear facilities, nuclear military, and aliens shut down these satellites.
Global oil and gas prices and electricity prices jack up because nuclear power plants worldwide are nearly all broken and unable to generate electricity.
The nuclear matter is a true time-reversal machine and energy vampire. Because of the nuclear material, this Earth is so trash. Nuclear works by drawing energy from any being (human, animal, insect, soil, soul) attached to nuclear dust.
The Gods who maintain this Universe (aliens) made oil, gas, coal and minerals.
Please use these energies. Gods recycle the landfills, trash, plastics, waste, sewage, and the dead body of water creatures under the crust to make oil, gas, and minerals.
Gods use flying saucers to compress dead trees and plants under the soil to make coals. So Gods can bring better asteroid soil and better seeds to Earth to upgrade Earth. Most asteroids are worth hundreds of millions or billions or trillions.
guestbook.lingpai.org/d/30-move-the-himalayas-to-the-pacific-ocean-to-build-et-base-island
I understood literally nothing and was still fascinated. This is my favorite RUclips channel. ❤
I understood the parts about coffee.
@@DemPilafian me too! I understood that reference
Same for me, nurdgurl.
I understood some of the words and comprehended the words somewhat but over all, flat out nothing. Still fascinating
This is grave
Agree.
This video encapsulates why I didn’t go into physics. I’m absolutely passionate about the concepts of how and why things work, and the fact that humans know this equation is fascinating and I fully appreciate the importance of the mathematics.
But honestly, my eyes glaze over when I see that equation. I tried so hard to follow but I kept wanting to be brought back to physically what this indicates is actually going on.
Yea it is a highly abstract differential geometry problem so don't expect to make actual sense of this without lots of supporting resources.
I absolutely unequivocally agree. Once he passed over fermions & bosons, my eyes glazed over too.
I'm with you, brother.
Can you help me understand?
Sometimes they make the presentation so simplified that there is nothing meaningful left about the topic to be interested in. To appreciate quantum field theory as shown here, one should start with the classical theory of the electromagnetic field. This field is described through vector calculus, which is a fun topic if you don't have to do homework and exams on it. So you can learn some vector calculus, some E&M, then include relativity and you can see where the F_{mn} F^{mn} part comes from. There are probably whole videos that explain that sequence, but would need to have some intro university calculus beforehand.
Great that you kept the equation on sight at all times. Even better where exactly on that equation the explanation was at
This is one of, perhaps the best physics related channel on RUclips at the moment.
Sean Carroll’s Mindscape podcast is one of my favorites right now
@@odros Arvin Ash, science asylum, etc
@@odros Science Asylum, Fermilab, Sabine Hossenfelder
@@odros science clic, cool worlds
Scienceclic is also amazing.
What's funny about the search for the GUT is we often look for an elegant equation like e=mc^2 even if it's far more likely to be even more of a hog than the standard model.
Oh dear Matt… Look at him. Explaining everything with such confidence and conviction as if we understand even a single word of it. 😢😢😢
I actually do have a mug with the compact version of this equation, bought at the gift shop of the LHC, so it does fit on a mug ;).
Also, i have a masters in physics (admittedly, applied physics with an optics specialization) and until now I had no clue what the equation on my mug meant. But seeing the full version I'm happy I never had to work with that massive beast of an equation!
It's pretty bad when you don't even know what the notation means.
I have a black mug with the short version on it, and a mug with Picasso's "Violin and Guitar". Both of them were given together as a gag gift from a friend when we were in college. She and I had once had a drunken discussion at a cocktail party about how neither of them made the slightest bit of sense to us.
@@michaelsommers2356 Not really mate, physics is absolutely huge, people specialize, theorists work with the cool symbols, even then theorists in other fields wouldn't know unless they specifically studied it
The most astonishing bit of knowledge from this comment is learning the LHC has a gift shop. Lol
I have a mug with a photo of Rafa Nadal and still flub easy overheads
I always thought... How hard can it be?? Then I saw that equation and I was like... Never mind...
Just be glad you don't have to memorize THAT equation for an exam...
Is it hard or is it just the will to do it?
@@Nefville is humor hard... Or are you just not willing to be funny 🤣
And the key is most of this is not predicted but math, but retrodicted by experiment.
So, for me it is proof of a designer.
There is no way to stumble upon this set of interactions that make up U(1), SU(2), SU(3), etc. 🤯
These interactions are fixed in place by the consistent interaction of objects that have no reason to exist in the first place!
We still don't know what makes these objects exist. Nor what forces these interactions.
Only that this is what these things do!
"In the beginning, God created objects that follow the Lagrangian of the Standard Model"
Its not that hard, it just has a lot of parts and thingies you need to learn before to understand it. If you're studying physics you learn it eventually.
This is what makes PBS Space Time special: putting up multiple episodes so that then they can go to deeper topics that are otherwise not communicated to us nonexperts, but are still wicked awesome!
Not agreed upon. The problem with PBS is that they only present the mainstream approach. For examples, physics based on chronons and not on particles, is never discussed as a viable option. A chronon wave function is an event wave function. The probability of a chronon sums to 1 on an observer manifold. The idea resembles H.S. Snyder's spacetime from 1947 but has several differences. For example, the Lagrangian of the theory is not based on non-commutative geometry. It is based on non-geodesic alignment of events. The geometric formalism of the theory uses Reeb vectors to describe the non-geodesic alignment which results in forces with symmetries U(1), SU(2), SU(3) and SU(4). The first 3, use the Geroch function from the Geroch Splitting Theorem. It is a very different description of forces, unlike the use of Gauge fields in mainstream physics. One of the results is that not only mass generates gravity but also charge does, with weak anti-gravity by electrons and weak gravity by positrons and protons. This property, unfortunately, cannot be used in high voltage capacitors to generate an Inertial Dipole due to the anti-aligned induced dipoles in the dielectric layer. DC alone cannot make a spaceship. Both Amy Eskridge from Huntsville Alabama and the illustrator Mark McCandlish collaborated to build a craft. They are both not alive.
@@eytansuchard8640 yeah i think there's a reason this isn't presented in the "mainstream media". how they gonna get views of you need a master degree to understand the video lol
As a PhD student in robotics, your videos have provided such excellent insights into some of the math I use. Furthermore, your excellent presentation of the topics inspires me to push my own work further. Thank you for such phenomenal content!
I've watched every video on the channel for the past four years or so and this one has to be one of the most difficult to understand. I'm following, but I'm watching twice. I'll probably watch again 3 months from now and get more. You're doing a great job explaining and listing everything in a super detailed breakdown, it's just very complex.
It's expected, don't worry! :)
I was taken aback by the density of this episode. i at once knew i would not be able to appreciate the full gravity of it all, but i applauded having something as well made available for those who did need this talking to! i really appreciate the effort. this episode is something that makes me want to go back and try to piece it all together.
That's really the essence of this show. I find myself rewatching episodes time and again for the mental calisthenics. Do I retain it all? No. But a little more each time at least!
To be fair, the standard model can't appreciate the full gravity of the situation either.
@@hhaavvvvii Best comment
@@hhaavvvvii LMFAO
To be fair he explains that gravity isnt necessarily understood yet
I remember answering the annual survey for new video ideas, and suggesting a video about what exactly is a particle. It bothered me that most of the times we were talking about fermions, bosons, gluons, and I just tagged along, not really understanding the relations between stuff…
I was filled with joy when I began watching this, really! You listen to us! Thank you!
I'd love to hear more about those particles that can't be measured and infinities that make no sense that are eliminated by adding h.c.
Yes, Matt teased us with more beautiful weird Physics, now a full episode about it should be expected!
Some ghosts of the Lagrangian for you: en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost
@@thedeemon thanks, but it's still not clear to me if these ghosts have any physical meaning or are a pure mathematical tool to "fix" the lagrangian. In the wiki at a certain point virtual particles are referenced: are these ghosts conceptually a similar construct, meaning "just a way to make us understand more easily a more complex physical phenomenon" ?
Yes. the h.c. term appears twice at 11:54 but how is this term/operator applied?
@@marcrob100 the second time IIRC is for the Higgs Boson terms.
amazing episode. As a physics student I had to spend a lot of time studying the math of things like index operators and Lagrangians, but I never really understood *why* until I saw this episode.
Explaining the reason we do things should have been the first step... :)
the fact that nobody ever told you what you're studying for is worrying
This is your VERY BEST video yet. I have watched many others dance around this equation,
but you have absolutely nailed it. Words can not express our thanks.
I really enjoy how in depth you actually go on a lot of these topics, I honestly gave up on watching educational videos for awhile since they all usually stayed at really basic level but you don't shy away from getting complicated and showing the maths and I really enjoy that
I really appreciated this video even though I did not understand a lot of it, if I were being honest. I walk away with an appreciation of the power in math.
I understand the pieces, terms, and operations individually, but you have to do this for a living for years to fully grok it.
@@earthwormscrawl i think you'd need to do an entire career to understand this equation
@@LuisSierra42 Yeah, I have a Bachelor's in Electrical Engineering. When I was in college (PSU class of '82) I was comfortable with exam and homework problems involving Schrödinger's Equation every day. The math and physics rust has gotten pretty thick over the decades. Every once in a while I'll open my old college textbooks and re-study some subjects. I can come back up to speed reasonably fast, but then it fades again as I focus on the real world.
I'd suggest a rephrase: The DESCRIPTIVE power of math. Math is non-physical. Only when APPLIED does it gain "power" in the real world. What is most amazing is that the "real world" even cares about math at all. WHY is this so? Answer that, and you will get both the Fields medal and at least one Nobel.
Same ✨
Maybe this is yet to come, but I think it would be great to see a real life example of this equation in action. Meaning, pick a situation where someone would use this, show us how and where all the numbers come from to plug into the equation for the example situation, and then explain what the "results" of solving the equation mean in terms of the given situation.
That is impossible in a RUclips unless you have 8 hours to spare to even begin to see this thing in action. Even then, it wouldn't be computed to completion
I mean, I guess they could create a super simple made up example, such as a 'toy' model, but then that defeats the purpose if not seeing it "in real life example."
@@pyropulseIXXI To be fair I think it may be possible in a couple of videos. If you only consider the quantum electrodynamics part of the Lagrangian (which is the easiest to deal with) you can explain how to compute the Cross section of some interaction without getting into too much mathematical details. Of course the whole detailed and precise computation needs time and a lot of pregressed knowledge.
Someone at CERN who wrote this code for it to validate particle paths. Operational validity of measurements. Maybe.
I agree with you. This would be so great!
I just fear that such a video would be much longer than the longest version of Lord of the Rings!
A long long .... night with lots of pizza and coffee ...
@@pyropulseIXXI
It's not impossible. I have seen videos of people solve the equations for atoms, their orbitals and electron spins as well as their spectra, fine structures and hyperfine structures in a video. If it takes too long, make it a series.
People did it in real life, so you can do it too.
How many people checked the PBS store for the coffee mug with the full formula written on it?
Just in time for Christmas
Now, this will be the one I'm finally giving up trying to understanding PBS Space Time. You guys go ahead.
I'll want to support PBS Space Time by purchasing a coffee cup with the entire Lagrangian equation on it.
don't worry. . . like a strong morning brew, ideas are already percolating
I love math in the videos, it should be done more often.....
yes there is definitely a lack of math in these videos....
Agree
If only Space Time had a sister show about maths presented by somebody with excellent hair...
I also love math more than animation.
Could PBS please add some "Einsteins spooky action" Merch?
Check out physics explained if you haven't already the math is not skipped. I assume PBS has a reason they don't include the math accessibility might be it but I'm guessing so take it with a pinch of salt
I want that mug with the full detail Lagrangian. I knew you were leading us somewhere all this spacetime and it was super cool to see "the standard model" finally laid out. Thanks Matt and @PBS Space Time!
I have always wanted someone to walk me through this at a high level. This was absolutely brilliant. Thank you Spacetime 🙏🏽
This is why the gravitational path integral is so exciting; it extends our notions of action and configuration space to all of spacetime.
Thanks for talking to us like we're intelligent beings who can take the math -- while still dumbing it down for those of us who struggle to understand this new language.
Matt, thanks for another super video. This is science communication at its very best. You take incredibly complex topics and explain them in a way that is accessible whilst not talking down to those of us without a formal background in the subject. Chapeau sir, long may it continue!
This semester I'm taking multi variable calculus, and it's amazing learning something new in class and realize how the math is used. I just had a class on Lagrangians, and now I'm more curious about the universe than ever before
Great episode! I have always wanted to understand this equation and nobody has explained it as well as you did.
Another great video thanks to everyone involved for your time, effort and work.
This channel is the best thing to watch / listen to before I go to sleep.
You've done a monumental work that will help many future generations understand science better and will help with scientific literacy.
Thank you.
Such an important episode. I can't imagine another way to break down such an incredibly important insight and still being concise.
Truly great content! I think most people find it challenging to grasp how infinitely numerous pathways for a particle add up mathematically. It would be very helpful for viewers if you cover that a little bit in the future episodes.
this was a great conceptual breakdown of the math involved in the standard model lagrangian, thank you. I honestly have wanted this video for so long. I have a request: Can you make a playlist that includes all of these "working up to this topic" videos you mentioned, as well as this video (and subsequent ones on the topic as well). Having them together would be super useful in going back and making sure I understand it well.
Here it is: ruclips.net/p/PLsPUh22kYmNBgF_VMMLHFK0lbQGlVGk3v
@@AS-kf1ol thank you!
Very important, the work you do. Spreading this info without dumbing it down to much.
Perfect videos.
Now that's great! This morning, while looking at my cup of coffee bought at CERN, I was precisely thinking that I would like to have a much more detailed explanation of what each part of this Lagrangian meant.
So your video is very timely (for me)!
Thanks a lot !
More to the point, this channel now officially defines a "Tour de Force" in the particle physics context. All the pieces, years of pieces, come together. (With thanks to the clarifications in these comments!) Few channels dare to undertake such a journey, much less see it through to the end.
I'm now looking forward to the episode on the ToE. Even if Matt has to create it just to get the content out there!
The instant you said "subatomic", i noped out :D
Exactly what I was telling my friends the other day. Thanks for backing me up!
From my understanding the first h.c. was a typo/error in the equation due to the hermitian conjugate already is included in the previous term. This has later been addressed on the products in the gift shop at CERN and only the last h.c. is being used. The typo have resulted in that the first h.c. stands for hot coffee. So that in order for the universe to work you need the standard model and hot coffee.
I wish I could go back in time and see what it felt like to realize our universe is run on probability waves.
I only really just found that out in 2008 in my quantum physics class lol
It wasn’t that far back in time for me at all lol
We need an episode like this, explaining the full E=mc^2 equation as well :)
To me this video was a total win.
I'm not a maths/physics/scientific graduate at all yet over the last year or so of watching this channel and working through the various episodes the theories in video was completely understandable to a gumby like me.
And that is cool. Thanks
It is truly incredible that anyone ever managed to figure this out and that it actually can be figured out at all.
i'm so happy this channel exists. thank you Matt + team!
All this math reminds me of the (now discontinued) PBS infinite series, and I saw their collab with PBS spacetime (on both channels). If only they covered category theory...
Proper highlight of my day when I see you post, always so well presented and thoroughly enjoyable to watch.
The prof does that. I investigate singularities for 45 years and listening to him frees my mind all over again, everytime. Thank you Prof!
I think we need to look at low energy warp modes. Its what we seem to see here on Hilos Ufo racetrack.
Absolutely loved this one! Fantastic job, Matt and team!
O'Dowd has a perfect voice for this
my favorite PBS Spacetime videos are the ones I have to watch 20+ times over the course of a few years to fully comprehend. this will be one of those
I love this and want to dig a lot deeper. Thank you so much. Will have to listen to this a good few times first
Thank you for covering this extesive topic so reasonably. Few notes: from 10:03 onwards the photon field is missing an index (which is then corrected in the summary at 10:37). When talking about fermion-higgs interaction the Y in the upper part is lowercase while the one in the bottom is uppercase. And finally, which is the only slightly misleading statement I noticed: you say, that the D\phi^ 2 term describes "how it [the Higgs] interacts with massive bosons of the Weak force". But this is the term where the bosons acquire their mass, right? They are massless before that.
I wish I could hear Alex Trebek saying "Lagrangian" a few dozen times.
I've been into all things spacey for over 30 years, but your channel 99% of the time has me perplexed, amazed and gobsmacked at how little i know about the real mathematical side of astronomy/astrophysics/cosmology/quantum mechanics/entanglement and a tonne of other stuff. Could you please dumb it down to masters degree level, thanx in advance. Joking to one side, excellent vids, keep em coming.
Can you PLEASE make merch of that coffee mug with the full equation in it? I NEED it in my life!
The arrow of time points forward in time because of the wave function collapse. Because causality has a speed limit every point in space sees itself as the closest to the present moment. When we look out into the universe, we see the past which is made of particles. When we try to look at smaller and smaller sizes and distances, we are actually looking closer and closer to the present moment. The wave property of particles appears when we start looking into the future of that particle. It is a probability wave because the future is probabilistic. Wave function collapse happens when we bring a particle into the present/past.
Cool idea
This is one of those episodes that are nigh incomprehensible, which is not a bad thing. It just goes to show that being precise and accurate in quantum physics demands a staggering amount of data and know how. Would have been interesting to see how the equation is actually used with some numbers. Could be a future episode?
This. Definitely.
Still trying to understand the "indices" part -- not sure I'm gathering it entirely in how it's written.
I come from a programming background, so I'm seeing it as functions and variables. A Part 2 might be a great thing for those who are scared of the "h.c" for example.
Very good comment
@@awesomedata8973 The indices can be thought of as denoting the components of a vector or a matrix. Then two indices appear together they are summed over (called Einstein summation convention). For example V_a*V^a = -(V_tt)^2+(V_xx)^2+(V_yy)^2+(V_zz)^2 which is just a number, it's almost like the dot product though the sign of the time component is different because the rules for multiplying 4-vectors is different (because of special relativity, known as Lorentz invariance). Then for a matrix M_ab*M^ab we sum over all the different combinations of a and b (effectively matrix multiplication, though once again modified to preserve Lorentz invariance).
This is just one small step in understanding the equations, to really get a grasp of this one would have to watch some lectures and even better try and put these equations into practice. I hope that at least my explanation helps in some small way :)
The indices do work like array indices. If you have A^mu (called a raised index), that's like having a column vector A[mu] where mu runs over the size of the column. If you have A_mu, that's like having a row vector with mu running over it's length. They may feel like the same thing but you'd need to learn a bit about tangent spaces to understand why the distinction matters. Having A^munu means you have a matrix (a column or column vectors). There's also something implicit going on called Einstein summation. If you see an index repeated on the top and bottom of a tensor expression, you sum over that index - i.e you take true ith term of each, multiply them and then sum those products. This is also called contraction. Hope this helps!
Drawing on both the previous posts, the indices literally are that of a matrix. If you can imagine finding the value at [2,4] in a 5x6 matrix, you know how the indices work (what the indices cover is all implicit, it has to be defined elsewhere, but in General Relatively it's usually x, y, z, t). The fun comes from indices in the upper and lower sections of an equation. All the upper ones come together and all the lower ones come together, and then any indices that appear in both the upper and lower are summed together into one massive set of equations.
Keep up these amazing and high level topics I am really enjoying pushing the boundaries of my ability to comprehend the math and overall processes underlying what we know of the universe
Matt (and rest of the wonderful pbs spacetime team) please include more math in videos, and just put a timestamp on screen for people who dont want the math so they alone can skip ahead
Absolutely not. It's imperative for any viewer to be able to immerse themselves in the narrative flow. Too much math will kill this outright.
The whole point of this channel is to make is accessible to the general public, to serve as a gateway. There plenty of other channels who don't mind getting into the math behind it, there are plenty who present the whole concepts in a hand-wavy manner. This channel works because it balances both perfectly.
@@alfonsstekebrugge8049 okay then, include the math at the very end in a 5 minute segment
@@afterallitsme And we need to introduce the math to the general public because it's beautiful!!
@@mastershooter64 I would have no issue with a math segment tacked on after Matt effectively ends with some well thought out sentence that places odd emphasis on the word we all recognize as the finishing touch of an episode of this wonderful show we call Spacetime.
This video series is very thorough -- what was omitted during the episodes will be covered on the final exam (where the details are left to the viewer as an exercise) ... [ from one who has 'been there, done that' in graduate school ;) ]
I always wanted to study physics at Uni bit for different t reasons I went for a medica career. I’m 45 and I’d really like to take classes but seems hard to make it work with my job.
The level of complexity and details to explain physics of this channel is astonishing and I find it incredibly helpful to support my studying.
I’m literally addicted to this
Thank you for so fearlessly presenting the math of physics, now and over the years.
I cant believe we (humans) are this smart... to come up with something like this, my respects to all of you who understand this and for PBS for showing and explaining this and all its dependencies.
You guys should create playlists for each major topic you cover so you can start from a base level and work your way up to the full concept in chunks. Love these videos but sometimes it gets to a point and I get completely lost…😅
Woah. Gonna need to watch this one a few times. I'm very, very glad you published it though. I have wanted to see a video like this.
A few questions I thought of:
- Am I making spurious connections, or do the h.c. terms needed to exorcise the "ghosts" have something to do with supersymmetry? (Guessing I'm probably wrong)
- Why is so much of the (compressed) equation taken up by the Higgs mechanism? (Is that even an answerable "why" question?)
The definition I like using for Bosons is that all of their energy is in space (Kinetic).
And Fermions share their energy between space (Kinetic) and time (Potential/Mass).
I'm sorry but it's not true: boson do have potential energy; and the whole thing of space and time is deeply wrong
@@gabrielepatane3627 You're probably just not smart enough to get it yet ;)
I managed to understand the notation up to about halfway through the terms describing how the fermions interact with the bosons. Then I got a tad lost for a bit. Still, I'm surprised my Linear Algebra and self-taught Multivariate Calculus re-awakened to let me follow along for real this time around!
Nobody has ever explained the Standard Model equation in such a concise manner to a complete layman. I'm sure due to how short the video is there are some inaccuracies or possibly even errors. But still, I'm pretty sure Matt more or less knows what he's talking about when he's explaining each portion of the equation. That's already pretty damn valuable and has the potential to get people seriously interested in particle physics.
@@hyperduality2838 Yoda is my favorite Nobel Prize in Physics laureate. The Force was with him when he attended the ceremony.
Dr.O'dowd, you've been my favorite teacher ever since I subscribed over a year ago, even if I am definitely failing this class 😅
Amazing explanation. Very clear and straight forward. Congrats!
Whoa, even by spacetime standards this should come with a Boss Level warning!
Oh great, I've been waiting for a long(ish) super complex video to fall asleep to, and this one will do me in for weeks!
Totally serious BTW. Falling asleep to PBS Spacetime is how I got from knowing absolutely nothing about any type of physics to having serious, informative debates with actual particle physicists, astrophysicists etc. and actually getting recognition as someone who understands physics on a deep intuitive level.
Thanks. Now I want a coffee mug with the Standard Model Lagrangian in its full glory, wrapped around the entire mug in tiny font.
No point if you don't understand it in its entirety.
That was amazing. I always wanted a simple breakdown of equation
I know this is Dunning-Kruger at work but I can't shake the feeling of crystal spheres
Awesome can't wait to watch this. I'd love to see the entire standard model.
I spent years watching your videos, finally giving me the feeling that I got an idea what you're talking about.. and then you come with this >.
BOOM!! Now I'm ready to start hammering out that Fusion Reactor that I'd always penciled-in - very 'lightly' - at the bottom of my weekly 'TO=DO" list. Thanks Soooo Much PBSST!
I hated differential equations class. I don't think I'll ever be a physicist. But I still think it's interesting when explained to me, as long as I don't have to actually understand it.
lol same, i like watching these videos, but hate being in math class.
@Madame d'Badger you just had bad teachers...
@Madame d'Badger I think most people never actually understand math, they just get used to it. My method for solving problems was essentially a giant IF/Then tree for walking through each step for each type of problem. I have no clue what the steps are actually doing, but if you just write the magic symbols in the correct order then you pass the class.
I love this channel. I usually lose the plot about 30 seconds in, but I still watch it.
I appreciate the relentless lack of spoon feeding. I had to rewind and pause so many time to digest each chunk, but was very enlightening
When the unpacked Lagrangian popped up on screen in its little fine print my first thought was of an article I read ten or so years ago about how A.I., Machine Learning, Neural Networks, and Genetic Algorithms were increasing in power and complexity to the point where the researchers would feed them some data set looking for patterns (I think the example at the time had something to do with DNA) and get results out that they "couldn't understand." The "Couldn't Understand" bit was the click bait headline short hand for "The program produced a long long list of specific patterns and groups of patterns. It was able to generalize portions of the data, but even those generalizations were complex to the point where they were either meaningless outside of the very narrow context of that specific data set, or simply resulted in such a long equation that it would be impractical, if not impossible, to attempt a solution without using a computer." (I'm paraphrasing from an old memory, but that's the gist of it.)
When I look at that Lagrangian I see an amazing description of the underlying mechanism of reality, but I have no intuition about what it represents. I trust that we've run the numbers enough to be certain of the accuracy of the equation of the standard model. I just feel like I would need to actually achieve a doctorate in quantum physics if I ever wanted to really grok it.
Is this what was used to calculate how the muon was SUPPOSED to interact at fermi lab?
So when are the Standard Model Langrangian coffee cups going to be available in the PBS SpaceTime shop?
I'm on the 10th (hc) coffee and still recovering from the geek... anyway, it was a very pleasant shock. Glad you did this!!! Keep on!
Thank you so much for breaking it down for us!!
It's nice to see a Space Time episode with lots of confusing equations again, it's been a while. Honestly, I don't feel like I'm really learning something difficult unless I get horribly lost and confused at least once. This show taught me how to understand four dimensional physics back in the early days of the chanel
@@hyperduality2838 Um... okay...
Imagine if aliens tried to decipher all those random symbols and what that equation meant
It would probably look more similar to a language they know than most of the world's literature, trying to figure out subtext and slang would be much more difficult
If they do, then we can ask them what we're missing.
Exactly why it's a better idea to send them "1/137" instead
Math is the universal language of the universe. It does not matter if the organism producing the equation is an alien or an alien to the other infinite aliens, it will still be the same functionality wise.
I am a software developer by profession and objectively developing code, or an app you can use on your phone requires a certain level of IQ, just putting it out there (also I have done masters just in case someone says something otherwise). Having said that, I wouldn't last two minutes if I had gone to do a masters or even undergrad pursuing a physics degree. I am simply not built for it. BUT I understood in my highschool or undergrad year 1 the true meaning of the integrals and having integrals bound in all 3 axes. They calculated the area under the curve using infinitesimally small slices and that too even in 3D. At that point I understood that whoever laid the foundations (I think Euler, one of the greatest mathematicians of all time) was thinking in ways normal humans do not. Integrals would be an extension of the Pythagorean representation of 3 squares where you can visually measure the sides of the 3 squares. And this Lagrangian equation(s) would be an extension of many such equations level by level. And none of them require language or scripts. They are purely functional, and whoever realizes that should be humbled.
I know exactly how they will feel. 🤣🤣🤣
so what i get out of this is:
there is at least 1 unaccounted for extra spacial dimension (the "h.c." terms 'cancel out' not 'resolve' complex numbers from the equation) needed to make the standard model truly work
Thanks for doing this! I am a huge fan and have been for years. I appreciate you getting into the math a bit.... It is always a bit annoying when channels stay away for ratings...
If you haven't already, will you do a video on isospin and hypercharge? I hear about them a lot but don't really understand what they describe or why they're useful concepts.
They have a video about it. Look for “pbs hyper charge”