Lecture 2 | String Theory and M-Theory
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- เผยแพร่เมื่อ 16 พ.ค. 2024
- (September 27, 2010) Professor Leonard Susskind discusses how the forces that act upon strings can affect the quantum mechanics. He also reviews many of the theories of relativity that contributed to string theory today.
String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding of gravity, cosmology, and particle physics. In this course we will develop the basic theoretical and mathematical ideas, including the string-theoretic origin of gravity, the theory of extra dimensions of space, the connection between strings and black holes, the "landscape" of string theory, and the holographic principle.
This course was originally presented in Stanford's Continuing Studies program.
Stanford University:
www.stanford.edu/
Stanford Continuing Studies Program:
csp.stanford.edu/
Stanford University Channel on TH-cam:
/ stanford
Lecture 1: 1.6M views
Lecture 2: 200k views
And that's String Theory
Thank you Professor Susskind!
I love how I can smoke weed and watch lectures. Thanks Stanford.
Yeah good luck with your grades
Marry it if you love it.
*Sees your comment as I’m hitting gravity bong
A, said that 10 years ago. lol. B, maybe he's watching these because he's NOT IN SCHOOL. Lol Think Benny, think.
@Benny Marshall
@@ChronicSkooma When you are a bit older maybe you will understand a little more about rhetoric Ghostpants.
i'm a chemical engineer and this lecture is so interesting for me in spite of my profession
Congratulations to Stanford that share this knowledge whit all of us, and of course congratulations to Professor Leonard Susskind for being a master in this field
it is a continuous form of education, the people in the room are not students in stanford, they are ordinary middle aged people, who want to study theoretical physics
I enjoy the difference in the amount of views in the first video of this series and the second video. Looks like a lot of people just said "screw it"
It sorted the amateurs out ;)
Gustav Lejeune Dirichlet was a German mathematician of Belgian descent. He studied and formulated the basic existence result for the Dirichlet problem, which is to find harmonic functions with given boundary values.
My dawg Lenny smashin that cookie at the beginning of lecture
something about eating cookies while explaining string theory cracks me up
Thank you Stanford for the free lectures, it's almost like I'm attending your university in real life. Haha.
❤Thank you very much Professor and class
Even ETH /Zürich in Switzerland not so easy String- theory , for sure you make Physics is simple (Reductionism) .
That is like Richard Feynman.
Thank you again Mr. Prof. Susskind
Yah, but at ETH, Profs do not tend to reiterate material from last week which you can familiarize yourself with. Always seems to have been double the speed I see here. And you will have to solve tough excercises ;-)
That's _Dr_ Mr Prof Susskind to you
@zcapwb1 there are two steps. Firstly, there is a P_z squared term out front. the physical explanation for that one is easy, it's just the huge z-momentum which you generated by doing the boost. In doing mechanics you drop that term because it plays no dynamical role - that's because it remains constant (the centre of mass of the system just keeps chugging along in the z-direction with the velocity you gave it, and doesn't affect the motion of the system in the two perpendicular directions). TBC
I woke up in the middle of the night and this was playing. I was like "why is Mike Ehrmantraut teaching string theory over here?" and then realized that I was not watching Breaking Bad.
Just woke up to this playing in the background...
The comprehension was the only wish of this powerfull reality. But this powerfull reality has needed for a 'free choose ', or "libero arbitrio ", to realizze the only wish it has.
So we are the only wish about this reality.
And when we comprehend that we automaticly became the realizaction of the only wish of this powerfull reality.
M-theory, comprehend, do you comprehend ?
@@b4byf4c3455451n I have a PhD in math (albeit combinatorial design theory and algorithms) and I have no understanding of M-theory. All explanations have been well above my head, I think.
@@vorpal22 have u heard nothing about E.Schrödinger ?
He was a math.cian like you.
And he saies: the reality is made by a cople of opposties thinks.
i , the imaginary number it is still an equazion. The first one.
In fact there are two solution.
That's means nothing was written.
And it's everythink possibile .
So we have to make a choise...
We're here only for that:
We HAVE TO MADE our choise
@@b4byf4c3455451n I'm not trying to be mean, but your post doesn't make a lot of sense. Is English not your first language?
Thankyou Sir!
1:47:15. String theory is saying photons are not particles flying around randomly. They are the wave in an ocean of particles. The complexity of that wave is amplified and attenuated by the relative state of the particle it traverses.
Awesome way to end the class!!!
34:48 For what it's worth, "catgut" is usually goat or sheep intestines, NEVER cat intestines. Just wanted to mention this to prevent any feline fans from getting totally discouraged with physics. Schrödinger did enough damage on that front already. 😎
Also, since I'm writing this comment on Father's Day, a quote from Schrödinger's daughter:
"I think my father just really didn't like cats." 😳
I appreciate the anecdote, thank you
Catgut comes from kitgut which means fiddle string
In the other Susskind "Topics in String Theory" lectures there is another interesting discussion about what is fundamental. It seems nothing is truly fundamental when conceived of as a fixed non-transmutable element of spacetime, but there are classes of similarity or duality-related objects in M-theory. This strange ontology in modern physics reminds me of the relational viewpoints adopted by Rovelli and others, in which elemental things are not physical, but only the relations between things are physical, because only relations have any consequence. Has anyone ever critically examined this sort of relational ontology and figured out if it makes any empirical difference over and above a more absolute ontology of real objects?
You should get familiar with the works of the Y. S. Vladimirov, e. g. "Relational theory of space time and interactions".
Light Cone: E^2 - P^2 hyperbolic, linked with circular an parabola, which are all "conic sections"
Thanks a lot Sir!
Does not any system look like a collection of harmonic oscillators if you expand it as a Fourier series? Where do specific properties of the spring come into the equation?
@zcapwb1 He did not really explain why motion along the boost axis can be neglected; he just said it is a fact in ST. I pict up from a question that it probably has something to do with holography ... Hope he will come to it later.
Good to finally have time to continue watching Lenny-Lectures. I just LOVE it :-)))
He should get a sponsorship from Starbuck's...
Cause he is teaching something that is evidently wrong? imo of course
@@fartreview1739 What is the evidence that it's wrong?
@@angusmitchell7033 hes just mad that he cant understand what the professor says, he deems it as just being wrong so he can satisfy himself
@@fartreview1739 tutututttuuttttutttuttutuufu
14:37 :D
man i wish i was taught physics by this guy
It's fascinating in a way that he speak in between like let's do only x not y then he is like ohh no let's do y too why not ..no wonder he given so much to the theory just pushing day by day
Oh, I think it means the dx/dt ? Could someone please confirm.
@aliienslayer1 in most of my classes, they use both blackboard and whiteboards
A good lecturer who decomplexifies string theory.
Thanks sir
man, 11 minutes in facing stupid points about particulars about his superficial examples, (atmospheric pressure in a metaphor) I automatically love this guy.
I Really Like The Video From Your Professor Leonard Susskind discusses how the forces that act upon strings can affect the quantum mechanics
Such a shame these series have such a small number of views!
Inf accel and applying neumann is kludgy
@zcapwb1 Secondly, P_z appears again in the denominator of the other two terms, which represents time dilation (the bigger P_z is, the more slowly the rest of the interesting dynamics seem to happen). Now he says it's huge but non-infinite: The contention is that we can consider the limit where P_z is large enough that higher order terms become negligible (i.e. much greater than P_x, P_y), but not so large that dynamics in the two perpendicular directions also becomes negligible.
Infinitely massive string with a volume of 0 => Stringularity?
Doesn't the total energy add up to infinity at 1:33:30 ?
If each term represents a quantum harmonic oscillator with frequency n, the total energy is the sum of all those harmonics. Does the series converge since it's a Fourier series expansion of X(sigma) ? Not sure I understand. Don't you still end up with infinite energy if you sum an infinite number of quantum harmonic oscillators with frequency "n" in their ground state ??. Seems to me like an Infinite number of particles?.. each with energy n*hbar
Thanks.
At the end, re the oscillator combos, I don't see why there aren't 14 combos
a at top level, two
b at top level, two more
ab top, two more
total now is 6
Repeat for the bottom
So now 12
The a top and b bottom, makes 13,
reverse them, 14.
@laspitarte Yes, I agree.
At 1:30, did he just put a WHOLE COOKIE in his mouth and continue talking..? :P
Fine ok Dirichlet was GERMAN ok guys!So he did one mistake!
This lectures arent about nationality of some scientists but about giving simplistic and clear concepts for understanding the nature!
+David Aghamalyan Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren, a town on the left bank of the Rhine which at the time was part of the First French Empire, reverting to Prussia after the Congress of Vienna in 1815. (From Wikipedia) So French by birth, German (Prussian) by education.
No, no, no. In Europe, every country has what is called Lex Sanguini, the law of blood. It states that no matter where you're born, you have the nationality of your parents. You can be born in Zimbambwe, if your parents are German, you are German and can apply for German citizenship. That is why nationality of some historical personas are highly disputable. I know that in the US there is Lex Soli - the law of soil, you have the nationality of the country you are born to, but in Europe, there is and has been Lex Sanguini for centuries. Keep it in mind.
Neumann was Hungarian but eh never mind.
Actually it was not John von Neumann (who was Hungarian indeed), but rather Carl Neumann, who was German.
Thankyou.
Does the "high p_z" physics become limited to the xy-plane because of space contraction in z-direction?
Pengochan No
no, its actually related to the holographic principal IIRC, which in some way implies that any relativistic system can be described as a non-relativistic system with the dimension of near-c motion dropped out.
1:32:14 This mess is why Lenny gets grad students to make PowerPoints when he gives talks outside the classroom. Heh.
Inside the mind of a sage
Just impose some known boundary conditions and see the results.
24:48 what is a particle
Mathematical tools (Derivative, Integral, Fourier, ) ; What is a particle 25:00; Is string a particle 33:00; Light Cone frame rehearsal 45:00; Endpoint of the String 1:16:00; Neuman condition at the endpoint 1:20:00; Quantum Mechanics of Strings 1:21:00; Energy Levels 1:37:00
studying string theory during quarantine ;)
@digital111x Sorry, but your wrong. Von Neumann was hungarian-american, he's talking about Carl Neumann
Good remark!
"It's been a minute...." that about sums it up
Also, Neumann was a Hungarian-American mathematician. NOT German.
As other comment stated. Here he mean Carl Neumann (not the "The Mathematician").
guy is just eating while giving a lecture lmfao
When you've helped create string theory .. You get cookes ;)
yes
All about X sub n to the power of t. Reminds me of how you make a square bubble.
Well... after part 3 I'll buy a book about this topic. Any title?
Dirichlet was German, see
Johann Peter Gustav Lejeune Dirichlet on Wikipedia.
Awesome lectures!
Actually Dirichlet was a German mathematician.
If you mean in high school, its because high school is meant o teach you how to be a janitor, or a construction worker. You're lucky if you learn calculus in high school these days. Basically if you want to learn this stuff, you need to learn it on your own, or go to graduate school in most cases.
He uses an approximation to see that the projection of the string onto the plane perpendicular to the boost behaves non relativistically. Also he says that the resulting formulas are exact. Can someone explain this?
He is using a simple and approximate derivation to show the general method.
I read it to mean that a full, rigorous analysis uses no approximations but results in precisely the same conclusions.
In other words, the approximations cancel.
It's not an approximation, it's exact. Reason being, any longitudinal oscillations are *completely determined* by the oscillations in the plane, and are therefore redundant, that is they don't constitute independent degrees of freedom. See 39:15 and 42:00. This is connected in some deep way to the holographic principle.
Dirichlet wasn't French, he was a German mathematician!
However, his family is of French Belgian origin (full surname: Lejeune Dirichlet < le Jeune de Richelette). He was also born in the French Empire since in 1805 German-speaking Düren was under Napoleonic control, although it's now in Germany.
@@likethemagician too soon
Funny how Part 1 of this series has 300K+ views and this a meagre 50K.
@ihateregistrations ... i'm not the only one?! *gasps....and puffs...and watches*
How and why is it that the first lecture has 2 million views and the rest don't even touch 500K ? (
In the exercise he gives at the end, is the next one 10?
[EDIT: I think I see my confusion now. See bottom of comment.]
Also, I think I’m confused what the excitations are, but I think that is because I need to better understand what a quantum mechanical simple harmonic oscillator is like.
So, for a harmonic oscillator with a particular frequency, are the different amounts of excitation just different levels of what the amplitude could be?
And so, the number of excitations of the string at each energy level is just, the number of, err,
ok, so, each of the oscillators has a frequency,
Ah wait, I’m confused again.
What is the difference between having 2 of the first level for a particular oscillator, and having 1 of the second level one for that oscillator?
Yeah, I guess I really need to understand a simple quantum harmonic oscillator’s energy levels better in order to really get this.
EDIT: ok, so I think the solution is “those aren’t different things, and he didn’t treat them as different things. I just got confused between, the different harmonic oscillators, and the different energy levels of each.”
Specifically, I was thinking each of the oscillators had, rather than just a particular energy level, a count of how many of each energy level it had. Kinda like I was thinking of each of the oscillators as if it was like how I should have been thinking of the entire collection of oscillators.
I think part of my confusion was because I got mixed up with having to treat the x and y separately.
Ok, so, the next energy level, 3, could have,
1) the 3rd x oscillator with amplitude 1,
2) the 3rd y oscillator with amplitude 1
3) the 2nd x oscillator with amplitude 1, and the 1st x oscillator with amplitude 1
4) the 2nd x oscillator with amplitude 1, and the 1st y oscillator with amplitude 1
5) the 2nd y oscillator with amplitude 1, and the 1st x oscillator with amplitude 1
6) the 2nd y oscillator with amplitude 2[EDIT2: amplitude 1 rather, whoops. Thanks maurits houmes for the correction], and the 1st y oscillator with amplitude 1
7) the 1st x oscillator with amplitude 3
8) the 1st y oscillator with amplitude 3
9) the 1st x oscillator with amplitude 2, and the 1st y oscillator with amplitude 1
10) the 1st y oscillator with amplitude 2, and the 1st x oscillator with amplitude 1
Ok.
That seems to make sense.
Does it work out conveniently to have the coefficients of the cosines be vectors instead of having a different term for each dimension?
For the Exercise he gave I count 12 for the 3 quanta excitation. Guessing you probably missed the excitation of the 3 oscillator of both x and y.
@@mauritshoumes744 Wouldn't that have total energy 6 though? 3 from each oscillator with frequency 3?
@@drdca8263 The states exist sperately for open strings. meaning there is a state with frequency 3 oscillating in the x-direction and an other state with frequency 3 oscillating in the y-direction. Both those states would have 3 units of energy each.
@@mauritshoumes744 Oh, I misunderstood, I had thought you meant, the state with both.
In that case, those 2 are the ones I listed as options 1 and 2. by "the nth x oscillator" I meant "the x oscillator with frequency n" (respectively for y)
@drdca I have redone the counting and arived at 10 aswell not sure where but i guess i counted stuff double. On an other note i assume the 6th option you give should be: the 2nd y oscillator with amplitude 1, and the 1st y oscillator with amplitude 1. Not "the 2nd y oscillator with amplitude *2*, and the 1st y oscillator with amplitude 1"
32:00 Difference betweeen mass & particle
when your phone goes off in a lecture about string theory...
Did anyone get what he was doing when he "got rid" of Pz from his equation? I'm not sure I quite understood it.
View the previous lecture
Are you looking at intergrating 4 with 10007999..
Nambu-goto? Nambu-goto?How to quantise I don't know. Polyakov!
No. Polyakov did not invent the method.
When you find the Euler-Lagrange equations (E-L) for the Polyakov action you will have found the energy-momentum tensor equal to zero.
In the Polyakov action there's the metric (call it A) *defined on* the 2d string (bosonic) worldsheet, and the product of the gradients of a smooth function (call it B) that *embeds* the worldsheet into a D-dimensional background spacetime with metric g. The metric g is used to lower the upper index of one of the two gradients - then the summation convention used.
When the metric A is *conformally equivalent* to the pullback of g by B (B*g), i.e., when A is equal to the product of B*g and a positive diffeomorphism (say k), and you substitute this into E-L you get an identity and the Nambu-Goto action. Viz., A=kB*g is the solution of E-L.
Next, when you use the Polyakov action *naively* in a Feynman-type functional integral (the term "path integral" should be reserved for use on the day that it's proved to be physics), as is done in traditional quantum field theory, the energy-momentum tensor of the functional integral is *not* traceless - the energy-momentum tensor of the Polyakov action is traceless - a condition that did not survive the attempt to quantize. This is called the conformal/Weyl/trace - anomaly.
Next, in order to quantize correctly whatever the Polyakov action represents requires an *unprecedented amount* of deep mathematical artillery - in order to renormalize the originally ill-fated Feynman-type functional integral. Renormalize means subtract out the undesireable features and redefine what you have leftover.
...and then we have (1/2pi) * (pi/2), which gives us a pi downstairs-wait, no no no, it is pi that cancels out so we have 1/4...
Fun to watch :-)
Dirichlet was not French, but German. See Dirichlet on Wikipedia.
“Sometimes I let 3=2” is my second favorite line ever
Umm, he does. Well, trig(3 * 2π) = trig(2* 2π). He said 2π meaning closed string, and π meaning open string.
31:32, 42:07, 51:13, 53:06, 58:40, 1:08:07, 1:19:30, 1:27:53, 1:47:42
Is our reality fundamentally linear?
How? In what context?
It's whatever you want it to be Andy.
14:35 Smiley! :D
d that you mean is a lowercase delta
and the t that you mean is the sigma
who is Michael?
Dk how I got here. Fell asleep and woke up to this
I want some coffee now :)
what uni- level is this?
Well string theory is usually taught at postgrad level but a first year should be able to follow this.
@@bennymarshall1320 thanks haha, yes i got it 2 years ago, im done now :p
"INTELLIGENCE."
12:00
What does the dot above the X mean?
Yeah I was wondering that
(denotes it's a vector ???)
It means dx/dt the time derivative of x
@@djamckechan Thanks for the reply, I worked it all out 7 years ago :D
5:30
Is that correct because in binary 1 plus 1 doesnt equal 2. And we know that particles will respond and react differently dependant on if it's being observed or not?
Right.
Actually Catgut comes from cattle gut. Has nothing to do with cats.
Why is there a guy in every lecture who debates points way beyond his understanding?
it's good. it means they want to learn. I would much rather students who ask arrogant questions that I can correct than students who don't ask anything at all. it fosters discussion as well. I know why this was upvoted but it's really a bad take.
@@felicityc I'm sure you relish the opportunity to correct your students Felicity ;)
29:30 ... The electron does have a squiggle of energy states right by itself though a difference of the energy of the wee little photon
Mire ha mi y tengo halgo ke exponer ha sobre de Hoyente al momento lo de inputar gustisia tanbien despues de muerte
@szjozsi
Because we learn English in general school and we only have Blackboards in our schools. So most people say all boards in classrooms are called blackboards. Do you use blackboards in America or are all boards white. In the simpsons they have blackboards :)
@Ihateregistrations1 Get out of my head.
I'm taking notes and everything. I swear I learn better high.
Not a regular class. It's a continuing ed class for adults.
He always eating cookies :p
karlwashere123 and Michael asking his questions
Professor Susskind,
For your Information, Lecture 1 is giving a message that it is privet, and I can't watch it,
Regards
Alonso
how the hell did i go from bumping 21 Savage and Chief Keef to this?! lmaaao bruhhh
I think that it's only one person who manages all those accounts. And was hired to spam "positive comments" on some videos. Look at their profiles they are very similar and they have been commenting like that on various videos from Stanford, Google and others.
A wave matter. Or pattern dependant on if it's being observed
14:33 - smiley face :D
no need for the confirmation... :)