Special Relativity | Lecture 9

[@qwadratix]

What an incredibly elegant way of combining Maxwell, Euler-Lagrange mechanics and the concept of symmetries. He has a real talent for fitting things together into clear patterns.

[@MN-sc9qs]

He's a modern Archimedes. Fantastically amazing.

[@lionjudah98]

P6lppppppppppppppp

[@lionjudah98]

Pppppppppppp0pppppp000

[@lionjudah98]

00pppppppp6p6pppppppppppppppppppppppppppppppppp0pppppppppppp6ppp6

[@abysspanda]

As usual, brilliant Mr. Susskind, hats off to you, Stanford, MIT, and all the other universities that are generous enough to provide the open course wares.

[@KipIngram]

AMEN! I've probably extracted more than the equivalent of a four-year physics degree from Stanford and MIT over the last decade or so. I hope I don't find a bill in the mailbox one of these days! :-) I've paid UT Austin for three degrees and that's really all I can afford. These days I'm too busy paying for degrees for my daughters to afford any more of my own.

[@JWY]

It does help to watch this being done. Thank you professor Susskind.

[@fdaalderop5057]

There is an sign error in both equations with the time derivative. curl(E) = - d B/dt (sign has to do with Lenz law), and curl(B) = + dE/dt.

[@grahamashtonuk2554]

This is Leonardo. There's always a bloody sign error. It's to be expected. It wouldn't be him if there wasn't. Still a class performance though !!!!!

[@Sachin21cool]

There is a consistency with the F tensor he has defined and the sign error in his equations. The equations chance and the space components of his covariant F also have the opposite signs. Just a wiki search would do.

[@fsaldan1]

These two sign errors have been going on for a few lectures. Annoying but no big deal.

[@rojojaeroldchyle5611]

@@Sachin21cool uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

[@NazriB]

Lies again? MILF Division

[@xxthunderbird46xx]

Thank you for sharing Stanford!

[@KipIngram]

I have a suggestion for this course. I've also watched Dr. Susskind's general relativity course, where he gives a WONDERFUL overview of tensors during the first few lectures. That's the REAL, full story of upstairs and downstairs indices and such. I understand that he didn't want to open that can of worms in this course, when such a simple shortcut as "change signs of the time component" gets the job done. But it seems to me that at least MENTIONING that there was more to it - maybe just five minutes sketching out the general nature of it - would be good. Anyway, I don't know exactly what that would entail, but I think it would enhance the material.

[@joelcurtis562]

No matter what you're teaching, there's always more lurking in the background. It's tough to decide what background to give and what to leave for later. I think the choice not to delve into co vs contravariant indices for an SR course was a good one. Maybe a little bit about why you need both to make invariant quantities would have been appropriate, to take a bit of the mystery out of it. Beyond that, it's something students can look into for themselves I think.

[@AT-27182]

@@joelcurtis562 , I agree that at this stage the expedient means of reducing co/contra to just a minus sign on the time is good pedagogy. Prof. Susskind does not deceive us into thinking this is the end of the story: He tells us (several times in the course) that there is more to it then this and that if we go further then there is something more to learn. But if someone is not going further, then this is good enough (and good enough is a stated goal in this lecture series) and if someone is going further then this is a gentle introduction to something that will be covered and re-covered later on. A teacher could easily go into great depth on the subject of tensors and their manipulations at this point, but with only 20 hours of lectures, tensors could become a very large detour and the course would no longer be about SR and an introduction to Classical Fields. Prof. Susskind had to make a pedagogical decision and I both appreciate and admire his choice of using the skillful pedagogical means that he did.

[@abhirambhat2502]

So true .. I had to pause the lectures and learn about tensors and come back .. I'm glad to know that lenny himself is gonna explain a little in the GR course..

[@23s83]

This video is the definition of a perfect lecture

[@adityatripathi2725]

katai jeher, maza agya sirji. Thanks Stanford

[@PetraAxolotl]

At about 32:56, wrong sign for both Del x B on the left side and j on the right side. He realized the sign error for j at 1:29:47, but not for Del x B.

[@PetraAxolotl]

At about 1:01:00, he omitted the other (mu, nu) combinations which are different to (x, y) or (y, x). It does not matter because the purpose was to take derivatives. But it could be confusing if the student is not paying enough attention. It was addressed by a question at 1:08:30.

[@bikashthapa7316]

these lectures are so helpful to me

[@JudgeRhadamanthys]

A very fitting T-shirt!

[@abhijithrambo]

This comment needs more upvotes!

[@leNOIRfae]

Very intriguing. More please!

[@kamrannasir3871]

I wish if I had those notes ...

[@ares12265]

In fact, we are considering a multi-Lagrangian form, or, if we continue then we are talking about multi-action, but what does the principle of localization from one part to the other do to us, or, but what does the principle of locality from one action to the other action in multi-action do to us? In the light of the exact mathematical condition of the shell of the atom that led Einstein, pliz.

[@ares12265]

Found the answer in the fifth lecture of the same course. Which is called "Particles and fields". And the answer is that the older Lagrange is the connecting link.

[@Hack3r91]

1:29:30 is wrong: the wrong sign is in front of the derivative of E as respect to time, not in front of j. The student who "looked it up" got it wrong.

[@daccoa]

Alessandro Porcelli you're technically right. But if you take the divergence of J (which you need to do to prove charge conservation) it doesn't matter if the sign is in front of the j or in front of the dE/dt, because you'll end up with the right answer either way. Nobody really pays attention to signs when teaching the concepts of Physics. However, sometimes it leads to confusion, which is always fun to watch.

[@Hack3r91]

Anthony D Indeed, but that's just because the divergence of a curl is always zero. I can very much empathize with the signs debacle, that's a nightmare always ready to generate panic XD A professor I had would always say "[...] times (-1)^n" as a joke when he wasn't sure about the signs.

[@tehyonglip9203]

Alessandro Porcelli actually there is one more mistake, the curl of E should be minus the rate of change of B

[@gouranggehlot4896]

Neither it is circular nor it is a guess ,one just have to change the basic assumptions which are that action is minimised ,invariance and charge conservation then Maxwell equation are derived since they are derived from those principle it is possible to go other way around , it's not guessing the lagrangian it's finding the lagrangian that nature follows there are 100's of other lagrangians which under these assumptions will give different equation of motion but it so happens that nature follows this now in general practice we see equation of motion first so we have to find the correct one and that is used to derive those equations.

[@gouranggehlot4896]

It's like there a lot of faucets at the bottom of a lake and each faucet can allow water of different colours (the faucet are marked with the same colour) now if we can find out directly which faucet is open and what colour mark it has, we know what will be the colour of the lake but if the lake is already filled upto the top then we may have to dive into lake to find the correct faucet but that doesn't change the fact that cause this particular faucet was open say red, the water was red and not cause the water was red ,this faucet opened but what we can say is that since the water is red the red faucet must be opened.

[@patriciaheil6811]

I have a question. does it seem to anybody else that his equations all tend to have the form (kinetic minus potential) energy with a velocity term on the right?

[@jeffreylanz719]

If it were the case that E and B formed a symmetry (assume monopoles were prevalent like elections), then given the way that Susskind treats the invariant (E^2 - B^2)/2 as like Kinetic - Potential, would this also force a symmetric relationship between energies in this alternate universe?

[@zphuo]

@3:00, Bianchi identity. @32:00, Lagrangian for Maxwell's equations. @1:19:00, why J*(∂s/∂x)dx = - (∂J/∂x)s dx? Shouldn't it be J*(∂s/∂x)dx = d(Js) - (∂J/∂x)s dx??

[@洪瑜隆]

Boundary condition is fixed and so the d(Js) should be zero.

[@petergreen5337]

❤thank you very much

[@xxMafia101]

I WANT HIS SHIRT.

[@stupidpdj]

Why does he put minus sign on the derivative of the electric field in Ampere's law while on the right hand side? Everywhere I've looked has a positive sign. He ran into the same thing I did at the end of the lecture deriving continuity. I think it has to be del-dot-E = -del-dot-j, not +.

[@kamrannasir3871]

Oh, thank you so much !

[@aaronrashid2075]

Relativity is awesome

[@KipIngram]

1:32:00 - Right; this is creepily circular. Ultimately this is just another guess. We know we want Maxwell's equations, and we figure out what Lagrangian to write down to get them. That doesn't PROVE Maxwell's equations. It just proves that it is possible to get Maxwell's equations from an action principle.

[@gouranggehlot4896]

Neither it is circular nor it is a guess ,one just have to change the basic assumptions which are that action is minimised ,invariance and charge conservation then Maxwell equation are derived since they are derived from those principle it is possible to go other way around , it's not guessing the lagrangian it's finding the lagrangian that nature follows there are 100's of other lagrangians which under these assumptions will give different equation of motion but it so happens that nature follows this now in general practice we see equation of motion first so we have to find the correct one and that is used to derive those equations.

[@gouranggehlot4896]

It's like there a lot of faucets at the bottom of a lake and each faucet can allow water of different colours (the faucet are marked with the same colour) now if we can find out directly which faucet is open and what colour mark it has, we know what will be the colour of the lake but if the lake is already filled upto the top then we may have to dive into lake to find the correct faucet but that doesn't change the fact that cause this particular faucet was open say red, the water was red and not cause the water was red ,this faucet opened but what we can say is that since the water is red the red faucet must be opened.

[@KurohiNeko]

I actually had very similar opinions too with the the Lagrangian method as a whole. Ultimately, I think Physics is about a mathematical expression for post-experimental result ideas. And Leonard has a loose style of showing ideas but I think he does it so we can focus on the ideas themselves instead of how we got here.

[@KipIngram]

@@KurohiNeko Yes, I quite enjoy Dr. Susskind's "style." I've watched an awful lot of his lectures - I've probably picked up most of a physics degree just from his battery of materials.

[@goutammanna9207]

While deriving Lorentz Force Equation (in a previous video), he took the ACTION as invariant. That's ok with me. But here, while deriving the Maxwell's Equation, he took the LAGRANGIAN as invariant (doing this he put the ACTION out of the track of invariance). Is it justified?? Because in the Least Action Principle we choose the path with minimum ACTION (but here different observer will not agree to it ).

[@TadThurston]

The Lagrangian has units of energy, which is a scalar, so it sounds all right to me, but I'm not a specialist.

[@goutammanna9207]

@@TadThurston If you are in Einstein's relativity, Energy is not a scalar. Energy is the 0'th component of the momentum 4-vector (Just like time is not a scalar, it is the 0'th component of the space-time 4-vector). Here, we are not looking for the usual direction and magnitude to define a vector (like the Newtonian mechanics). So, anything that comes with a dimension of energy, can't be a scalar. By the way, I'm not a specialist too. I might be wrong.

[@tiagogarrao4908]

In the previous video he was integrating along dt, which is not an invariant interval. In this case, he is integrating along d4x which is invariant. As such, if the integrand function (lagrangian) is invariant, the integral (action) will also be invariant

[@runeinglev2782]

One important point to this lecture is to realize that Susskind is assuming "linear polarized" EM waves.

[@deanvillegas]

excellent

[@JWY]

At 1:27:07 - lol, it's not gonna work! j must be curl B minus partial E with time. Your going to get 2 E not 0. I think I'm learning this stuff professor Susskind - thank you. Oh, he used some clever math instead, but the error is made visible.

[@qbtc]

He always does integration by parts wrong. Correct form is ∫udv = uv - ∫vdu. He always neglects the uv part and uses ∫udv = -∫vdu. In the case of ∫JdS for the change in the action in the lecture, it is equal to JS - ∫SdJ. What you get is ∫JdS = JS - SJ which is 0. That means adding J times the vector field A to the Lagrangian keeps it gauge invariant.

[@netrapture]

His rule is not wrong. It is a rule of thumb. The JS term is evaluated at the limits of the integration which in this case is infinity, and as he went at lengths to explain, J is assumed to be zero at infinity so the JS term is zero. Integration by parts where part of the term evaluated at the integration bounds (at infinity) is assumed to be zero (making the entire term zero) happens so frequently in physics that the rule he gives, namely switching the differentiation and changing the sign is the rule in practice in physics.

[@DerMacDuff]

Too bad that not all the notes are available -.-

[@tehyonglip9203]

the real problem is dE/dt , it should be minus dE/dt, and the curl of E should also be minus dB/dt, of course, all partial derivative

[@nothingeverhappens8781]

So I am doing this youtube experiment where I go on the home page and click on a video that I find interesting.. Then I click on "next video" 10 times and see where the youtube algorithm takes me. I somehow landed on this video.. Why?

[@sandc411]

wait! i wanna ask questions...!!!

[@69erthx1138]

When I get done watching, think I'll go play some "Bianchi Kong."

[@KipIngram]

1:33:15 - I understand what's going on here. There is a "craving" in the audience for a PROOF. A presentation that produces an "AH HAH!!! YES! It HAD to be that way - no other way it could be, OBVIOUSLY." Unfortunately, it seems the closer we get to the true foundations of physics the less we get to have that. I suppose it makes sense - there are fewer "more foundational principles" to use to justify conclusions. Eventually you have to settle for just "agreeing with experiment."

[@joelcurtis562]

I find this very interesting as well. As Einstein said: "What I want to know is whether God had any choice in how he made the universe." I think a lot of people - myself included - come to physics hoping for some hint of a 'why' to it all, a satisfying explanation such as you get at the end of a well-written mystery novel. But I have concluded (tentatively) that physics cannot give that. It can only give ways of thinking about/predicting/post-dicting patterns in experimental data sets. Which is valuable in and of itself, but not as satisfying to our cravings for ultimate explanations. If I recall correctly, Roger Penrose expressed misgivings about the ultimate nature of the Lagrangian-Hamiltonian approach for just this reason: there are rules for narrowing down the form of the equations, but the whole scheme seems rather arbitrary from a physical point of view.

[@KipIngram]

@@joelcurtis562 Yes, Joel - precisely. Meanwhile a lot of mainstream physicists are happy with the "shut up and calculate" mindset, and I guess I get that - they have a job to do, and they want to get it done. Fair enough. Maybe a lot of this stuff is more philosophy than it is science, but I still can't help my curiosity. I spend altogether more of my time than I probably should creeping around the internet and KZbin trying to "knock on" those foundations. But I guess everyone has to have a hobby, right? :-)

[@Pranav_Bhamidipati]

@@joelcurtis562 You are absolutely right and that's why I think it does make sense to be a physicist and believe in the gods since we only study what came to be and the question "why it came to be" has no satifactory way of being determined with absolute confidence. Some people take the axioms of physics or "the standard model" (as it stands today) as granted. But, at the same time, you could believe, without any logical consequence, that the rules of the universe came to be because a god/ a pantheon of gods made them that way. This is similar to the "Let there be light" moment that Genesis refers to. In a similar fashion, we know that the rules of the standard model came to be at the time of the big bang. The question will always be "Why these rules?" and you can always choose to believe an answer of your own choice. It's pretty much a philosophical area of thought.

[@joelcurtis562]

@@Pranav_Bhamidipati I really could not disagree with you more. When we don't know the explanation of something, that is not a license to just make up any old explanation and believe in it. The only statement ignorance permits us to make is that we are ignorant. If the police don't have enough evidence to say who committed a murder, that's not a reason to shrug their shoulders and say "Well, it must have been a ghost! Or you can just believe whatever you want to believe about who or what caused this person to die." No, all the police can say is "We simply don't know who committed the crime." Similarly, we don't know the 'ultimate reasons' behind the universe. My hunch is we will never know. But that doesn't mean we are justified in believing in a deity. All it means is we don't know.

[@Pranav_Bhamidipati]

@@joelcurtis562 There is no "why" to anything, really. Literally, every goddamn thing that has ever happened can be just thought of as the evolution of the universe according to the rules of the standard model (at least according to the evidence we have until now). Now, if you are a student of physics, you know that no scenario is fully described just by the evolution laws, but also by a set of initial conditions. Now, you can only go so much far back asking why these initial conditions came to be. There does exist a singularity before which, our evolution laws break down and we definitely don't know if something even existed before it. Now, I'll tell you something you won't enjoy listening to. You're adamant that there is an Ultimate reason to the universe. You don't want to believe that the initial conditions were just that - INITIAL conditions - things that don't logically follow any pre-existing conditions. You want to stick to the belief that "there is an ultimate reason, but it just so happens that we will never know it." I'll tell you something. This is not physics. This is philosophy. And there are no rules in philosophy. If you want to believe that there is an ungraspable reason to all this, fine, be with it. But, also understand that your stance will neither be proved nor disproved. So just accept that people can believe what they believe and still have no consequences on anything. So peace out, and stop telling people that their beliefs are wrong. P.S.: If you haven't understood what I am saying, go study mathematics and then come back and tell me if you like the structure of rigorous mathematics. It's basically built on arbitrarily defined axioms: initial conditions that don't logically follow from any pre-existing conditions. There is no "why" to it. There is just the what and the how. Terrence Tao's Real Analysis I is a good place to start if you are seriously considering this.

[@DrDress]

22:35. Noooo! A magnetic field is blue!

[@danielmaclean4718]

I'm glad I'm not the only one

[@grahamashtonuk2554]

The electric field is green for God sake !!!????

[@lordofutub]

Only thing I didn't like is the speed at which he blew through some of these things

[@LouisXIV92]

I wish I understood this.

[@hasanshirazi9535]

@19:03 He says B instead of Beta.

[@РодионЧаускин]

Thomas Barbara Smith Brenda Hall Cynthia

[@BladeRunerUnit99S]

aweeeeee \o/

[@markyounger1240]

While susskind is great at math, he has difficulty explaining anything in a qualitative way.

[@Delfigamer1]

Physics itself is quantitative. Trying to explain it qualitatively would inevitably distort the ideas and take away their predictive power. While this may be fine for general audience, this particular course is aimed at people who want to get a more exact understanding of the modern physics, so professor Susskind tries to avoid such distortions whenever possible, invoking visual intuition only when he's sure it will not lead the students to wrong conclusions.

[@fsaldan1]

IMHO Professor Susskind explains the qualitative side of the theory better than anyone I have ever seen. On the other hand he is a bit sloppy with the math, which I actually like because it keeps the focus on the logic and the qualitative side. Sometimes signs are wrong, but that does not really matter.