Classical Mechanics | Lecture 2
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- Опубликовано: 30 сен 2024
- (October 3, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on some of the incorrect laws of motion that were first proposed by Aristotle. While they are invalid they provide some insight into how modern physics has developed to the state it is at today.
This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes.
Stanford University
www.stanford.edu/
Stanford Continuing Studies
http:/continuingstudies.stanford.edu/
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I've often reflected on the fact that p stands for "pomentum" and B for the "bagnetic field" sounds like a physicist had a cold some time.
@MrComrade wow, new information 👍
He's a yankee! More precisely a nu yoker. Lol.
The quality of this video may be bad, but its still great content from a good campus. Im glad you put it online regardless of the sound quality. Stanford does its part in giving everyone in the world informative, yet enjoyable, ways to enhance capeabilities to unterstand and form the world. Please accept a humble "thank you very much".
Aristotle's laws of motion; Aristotle's law is irreversible 13:00; Newton's law 17:00; momentum 31:00; phase space 33:00; Newton Oscillator is reversible 37:30; Conservation laws 52:00; Newton's 3 laws 55:00; Conservation of momentum 1:02:00; Energy conservation 1:07:00; Harmonic Oscillator 1:33:30
thank you mate
He takes a break from the lesson and what seems to be the Schrödinger equation suddenly appears on the board... What the hell happened during the break?!
These lectures are put on the internet for the public, but are not normal class hours from Stanford. it.s a programme some universities do, called further education if I am not wrong.
The people participating to these lectures aren.t just students, if any at all, they come from all walks of life and professions, therefore when you see other wild equations appearing on the board after a break it means they might have discussed something with the professor, or he just got bored and started doing other physics stuff..
The equation was both there and not there until you looked at it.
Take a few more breaks and maybe we get the TOE?
@@jcnotnot8120 Lol
@@vaishnav_mallya ha ha
53:53 *Different orbits of different radii corresponds to different tentacles*
I love the guy who added the subtitles lmao
Here's something odd: In the book The Theoretical Minimum, which is based on these lectures and follows them very closely, Susskind makes the opposite point: he shows that Aristotle's law *is* reversible (p. 62)! It seems a much more clear argument than the argument presented in this lecture that they are not. In this lecture, he seems to be mixing in the issue of sensitivity to initial conditions with this question of reversibility, in a way that I found very confusing. Anyway, to quote his own book:
"The conclusion is clear: If Aristotle’s equations of motion are deterministic into the future, they are also deterministic into the past. The problem with Aristotle’s equations is not that they are inconsistent; they are just the wrong equations."
I think what's written in the book is the right way.
here he aslo says that aristotles law is reversible, if you had infinite precision when you mesure stuff, but you dont so they are nit reversible in that sense.
he also assumed an interpretation of aristotles logic 4:21 4:53
. plus hes just giving historical progression. obviously there is an evolution on paridigm of force sparked by aristotle for following mathematicians. it was A lecture. not his book. the recording of this was.the only bad one. quality wise. the mit course is also dope.
Isn't the claim about the sign of acceleration being independent of time also wrong? If I watch a film of an accelerating car in reverse, I'll see it slow down.
I also stumbled across this point. If you look at the exponential function, you can of course trace the course of the equation back into the past. The reasoning seems to be that at a finite precision, all trajectories run into an endpoint below the discrimination threshold and are therefore indistinguishable. The reasoning seems flawed to me, as it could be applied to alls systems that evolve into a fixed endpoint. The argumentation book seems to me to be the correct one here.
The portion where Prof.Susskind mentions that Aristotle's law are not reversible didn't seem very satisfying. Indeed the Aristotelian 'force' is actually momentum(=mv) of the particle. In a closed system, if we know the momentum as well as the initial position of the particle, doesn't the Aristotelian law actually become generally reversible? I guess this is infact the very basis of Lagrangian and Hamiltonian formulations.
Momentum is conserved over time.Taking that as a postulate, if Aristotlean force is just momentum, how will it allow us to predict past and future of the particle's motion? It won't. At least not in both past and future directions. So Susskind is right.
Aristotle's force is something you can apply to an object to set it in motion. In that sense, it is a force and not momentum...
He takes a lunch break and suddenly a wild Schrodinger Equation appears. What did I miss?
a lot
Quick throw a Pokeball at it
@@ironmantis25 hahaha
we are living in such a strange world nowadays that this guys sneezing and coughing that often freaked me out
Same man! You should cover your ears XD
all the sounds of the person(s) setting next to the microphone are annoying
If Tywin Lannister tought physics...
Thanks for putting subtitles, made it easier to follow along.
46:02 , back when coughing was a normal thing
There is a very misleading error in the subtitles at 19:12. The correct sentence is: The laws of physics are that there exist inertial frames.
+Dávid Kertész Same in minute 28:49 where he says "they don't satisfy..." and the subtitle says that "they both satisfy..."
Professor Suskind is the first to know the shape of string in string theory.
He is a BOSS . They dont call him a rebel of physics just like that . He proved Hawking wrong once
53:35 Annotations: "Different orbits of different radii correspond to different tentacles." Physics is full of beautiful surprises.
Dammit, you beat me to the tentacles bit.
"..correspond to different energies". Just imagine an electron revolving around the nucleus on discrete Energy states--that energy is what is meant here.
I heard it as "testicles".
عظيم الشكر للعالم الجليل على هذه المحاضرة الاكثر من رائعة
"T" representing kinetic energy comes from "travail méchanique" (mechanical work)
He is the first person I have come across who says that Newton's first law is really just a special case of Newton's second law (set a = 0), so Newton's first law is essentially redundant.
KeysToMaths1 Set F = 0, not a! a = dv/dt, which is what you want to be 0.
This is actually not uncommon - in the sense you can find books "deriving" first law from second law
Hilarious scene in the last few seconds of the lecture and a great lecture as always in general, thank you stanford and professor leonard susskind for this!!!1
There's a subtitle/caption error at 02:15 where the caption says "He thought that velocity was a natural consequence, of course" when Susskind is actually saying "He thought that velocity was a natural consequence of FORCE".
شكرا ❤❤كل تحياتي من جزائر 🇩🇿
Thank you professor. All these lectures are helping me a lot.
Yes
I love how he is so casual with his knowledge
Yes bro
all the coughing makes it a great Halloween watch in 2020
At 06:42 "We can solve this equation very easily and p plus delta, the two graphs, right over" [here] is actually "We can solve this equation very easily for x at t plus delta, let's do that , right over" [here]
For instance, at about 20:38, he's going over what mass is, and the caption says x. Keep in mind that he is from new york, gang. You can also see that he was talking about mass when a few seconds later he says "force divided by acceleration," which is indeed mass in F = ma. So, don't believe everything you read in the captions, everyone.
Thanks for the guy who asked why reversibility is important
ya f prime of Sine is COSx not -Cosx.
Oh well, he is human.
He says that the force law for the spring is -kx. He is assuming the force law of the spring for Newtonian Mechanics and forcing it on Aristotle's Mechanics. Wouldn't the force law for the spring be proportional to the square of the position for Aristotle? Then the resulting trajectory would be the same as derived from Newtonian mechanics.
The force law for the spring (Hooke's Law) is experimental. It is not derived from any equations of motion so it wont change with respect to any equations of motion which we use as our theory is based on experimental knowledge and not vice-versa.
I think i know where you are coming from in the sense that Aristoteles appears to have "defined" what he called force as mv . But therefore we would need to know what he exactly said or wrote or thought .
Why a spring, though? Imagine a different system: a ball rolling up a round hill with juust enough energy to reach the top. In Newtonian mechanics this system is *exactly* as irreversible as the spring-like system Susskind sets up for Aristotlean mechanics -- a stationary ball at the top of a hill could have been at the top forever, or it could been rolled up to the top from any direction at any time in the past.
It's clear enough, then, that the reversibility is a property of the combination of the physical laws *and* the system of forces set up, and Susskind provides no argument in this lecture for the use of the ideal spring system as a litmus test rather than something like the "round hill" (or even stable frictional systems.) If we can ignore the hill system in Newtonian mechanics for not being reversible, we might "let Aristotle off the Hooke" in a similar manner by criticising the choice of the spring system/equation.
by that logic every theory of mechanics is irreversible so you haven't let Aristotle off the hook.
@Rahul Narula - Correct - as Susskind says at the very beginning of Lecture 1, the laws for particular systems, like say a mass on a spring (F=-kx), are independent of the general framework of mechanics (e.g F=ma or F=mv)
Person who wrote or edited subtitles for this video didn't make a very good job. So many errors.
Note: the orbits in phase space that Susskind draws for simple harmonic motion should be moving *clockwise*, not counter-clockwise, as he suggests. (If he had drawn momentum as the x-axis and position as the y-axis, they would have been counter-clockwise.)
does it make any actual difference?
@@1eV ofcourse not
i den watched this lecture too many times
Are these lectures for bsc or msc?
1:23:40 ''it's a law of physics that it's true, you cannot derive it from anything else''
well, not quite, it's because rot(F)=0. That doesn't work in the magnetic field, for example. And you can derive that curl of fields he used is 0 (you must know general relativity to prove for gravitational field though, but it's still provable, it's not just a law of physics we can do nothing about)
but isnt it always true from a math point that such a function will exist? i mean if i have fx, fy and fz, cant i always reproduce the function V irrespective of whether f is a force functon or not?
The problem is that sometimes F won't be equal to a gradient of any function (V). For example (in two dimensions for simplicity), take F(force field) = -y*i + x*j, where i and j are unit vectors.
Then, you want to find V(x, y) such as partial derivative of V with respect to x (w.r.t. x) equals -y and partial derivative of V w.r.t. y equals x. You won't be able to find any V for which that is true. And that's because 2d analogue of curl of F that I gave you doesn't equal 0, it equals 2 (in the other words, the field is rotating with angular velocity curl/2 = 1. Whenever you have rotating fields, you won't be able to find V)
right. thanks much.
Feynman Lectures Vol 2, Chapter 2 is a great read regarding this.
Great catch. Just adding stuff for others.
Basically, when curl is zero, what Susskind says is true.
At 06:12 the caption says "Let's not make the limit, let's just write it this way" and what Susskind actually says is "Let's not TAKE the limit, let's just write it this way"
Can someone tell what does he exactly come to say at 1:23:20?
Thanks in advance.
i think hes wrong there. Clearly such a function exists.
Liam last night I wonder if he was doing because I don’t even care I would F what you doing but whatever are you doing? Stop doing it just effing stop. 6:00 how could I remember unless a lot I hear this 17:22yo 20:17
Lucid, crisp and clear ! simplicity is perfection !
Gonna tell my kids this is god explaining how he made the world.
There's a subtitle/caption error at 05:58 where the caption says "X dot is x times t + delta" when he actually says "X dot is x at time t+delta"
19:36 ...or do/dt =0 .... not happening but you could drive a bus through his maths .... but he’s amazing
At 06:57 "times p" -> "at time t"
Johnson Paul Martinez Kevin Jackson Shirley
40:06 i didnt understand the eqn of X .where the t0 is coming from ?
KRISHNENDU SARATH it’s a second order differential equation, and hence it must have 2 constants. The most general solution to that equation would be Asint + Bcost. Now by basic trigonometry you can see that you can reduce that to Dcos(t-t0), where D=(A^2 + B^2), and tan(t0)=A/B
No, because you changed diapers and that is the original way of being a good parent 21:19
"All the good things."
Mm-hm.
Hall Shirley Hernandez Linda Thompson Maria
1:17:00 Energy conservation
Why when he deal with the derivative he doesn't write the limit ?
But as I know the derivative is a whole part itself it can't be treated like this , because it's a limit and we deal with the limit when we say derivative not with the function itself
You could write in the limit but you would get the same answer so he just leaves it out for the sake of simplicity, sort of like a short hand .
Thomas Larry White William Martinez Jose
Hmmm these students are asking very good questions
That's actually often pointed out when classical mechanics is discussed, be it in textbooks or lectures.
In the theoretical minimum book he says that Aristotle's laws of motion is reversible. And it is off course reversible although he says the opposite in this video. By reversibility what should I understand? If I can get the initial value (let t=0 ) (provided I have an infinite precision and accurate device) from any point from time instant t1 > 0, I am happy to call the process reversible. That indeed means I can predict the past not just future. Please comment on this if I am wrong.
I was confused at that one too. In the book,Susskind describes the force as a function of time and then proved that force to be reversible and deterministic. He also does this in the lecture at around 7:00 too. Later in the lecture, he proves that a force that is a function of position is not reversible as it is not deterministic into the past. This is where the lecture differs from the book.
Professor Susskind on savage beast mode at the end
Gods like Susskind shouldn't have to worry about money. They should be allowed to use whatever resources to advance the knowledge of humanity. It's a sad world we live in.
Jones Frank Moore Donald Martin Deborah
whoever did the caption needs their ears checked....
He is wrong about (dt)^2; it doesn't work like that. You can't say time is -1and it goes positive for that reason it is shortened form of a second derivative. It works because a change of a change is still plus 1.(50.480
Can I have ur not book sir any one plz help me
Excellent lecture. Excellent man. But some absolutely crazy errors on the subtitling throughout. Must have been done by a non-native English speaker with no scientific background. Mass to max, spring to string and instant to instinct picking up on a single minute of it. Becomes quite distracting at times.
Lectures should not be like reading a detailed Book....they should be about clarifying concepts with examples...in,that,he reminds me of his great Pal,the mighty Richard Feynman...he was awesome at clarifying complex and deep ideas 💡 😀
He said relationship between potential energy and force is law of physics and can't be derived from anything... then does it mean potential energy is just discovered and it has the meaning like that???
자막이없구만 영어공부 열심히 해야겠네..
There is no way of acquiring notes, huh?
Regarding the question about importance of reversible nature of physical laws, I think it's because the set of all reversible laws is a tiny subset of the set of all possible deterministic laws, which could be seen by analyzing the graphs presented in the Lecture 1.
on 51:04, I cannot understand about running the acceleration movie backward, same.
I found this youtube video very helpful on reversibility of physics laws.
ruclips.net/video/0Jvpb-c-XfY/видео.html
All it takes to disprove Aristotle's law of motion is throwing a stone in the upward direction lol.
I'm not usually into phisics but all these conservation laws and the way they are proved impress more like properties of the model; they are our way of thinking and viewing reality ( but a good one).
mass is how much resistance a particle will display to change its momentum. I think that schools relate too much mass to volumetric bodies. In a sense that the most important concept of inertia sounds kind of residual, when it is the true essence of mass.
41:40 actually there's a complex solution, x = e^(it)
He is a great physics teacher... I would also recommend a new channel for solving somewhat advanced problems in classical mechanics with thorough discussion... ruclips.net/video/ofTlsMtdB98/видео.html
From 12:52 to 14:50, Prof. Susskind says how Aristotle's law cannot be used to predict the past. I didn't get what he said. Can anyone please explain?
Can somebody also tell me what he means by "reversible" and "irreversible"?
See lecture I at about 27:00-35:00. In classical mechanics, we have to be able to "predict" (= calculate) all past & future states of a closed system from the state information at any given time. That's reversibility (= conservation of information). Aristotle's law is not reversible because, for example, every rolling ball grinds to a halt after a while. Once it's stopped there's no way we can calculate how fast it was going before.
Toby White But the way he explained it, the particle would not in fact reach the 0 position ever. So there is no "loss of information". I am not convinced he correctly showed that Aristotle's low would be irreversible for that case.
To understand it, you can just imagine the way it would be in reality, if you let go of some mass on a string at some location x0 then you can check at some other position it's velocity and from this information you will be able to tell where you started from (because of the total energy). However in this case no matter where you start, the point mass will try to go to zero the same way. To express is mathematically. If you start at two different positions, for every epsilon there will be a t(time), when the difference of x will be smaller then this epsilon. Which means it can be made as small as you want. This way starting from two different position you can choose t such that no matter the original differences the difference at t will be as small as you want it to be, hence you lose information. Hope this helped
The point is that in a truly closed system you could predict the past from Newtonian mechanics *even if* you didn't have perfectly accurate measurements. The mass would continue to oscillate on the spring forever. Obviously the real world is governed by quantum mechanics, which doesn't allow for perfect prediction of the past.
Because no matter where we started, eventually the system will come to rest at the origin. Therefore we can't tell how far the spring was pulled back in the past.
I think we cant prove conservation laws, we can only verify them.
Sir, you haven't discussed the transformation of vectors.
@53:36 "Different orbits of different radii correspond to different tentacles" 🤣
At 35:56 a question is asked. It is very important, and not addressed well. Newtonian Mechanics and Analytical Dynamics are subtlety distinct. The former assumes a coupling between position and time, a priori, the latter asserts that coupling as an additional condition a posteriori. Very few physicist appear to appreciate that distinction. That is the original sin of quantum mechanical epistemology. To paraphrase Schroedinger, we are talking about phase space, not real space.
I don't quite get why the existence of V(x) is a law
the reaction force NEVER acts on the same object as the force that causes the reaction. The initial Action, and the opposing Reaction occur on two different objects. Then how the book placed on a table remains at rest
δύναμης
For the differential equation of harmonic motion, the exponential function works if it is e^(ix) ... Why is that?
讲的比我们老师好太多了。。。我们老师只会念PPT
wonderful!
Precision of measure is not of relevance here. Reversability of a law cannot be determined by the precision we measure outcomes. Even if that would be valid, same would hold for newtonian laws. Both xdotdot = -x and xdot = -x (his examples for aristoteles and newtonian laws of motion) have unique solutions that depend only on initial conditions.
Great lecture but there are some minor things. F.e., when drawing the harmonic oscillator trajectory in the phase space, there is a little mistake made: It cannot go counterclockwise, only clockwise (when the momentum is positive, x is growing etc).
It depends on the initial conditionals. You can throw it towards the equilibrium point with an initial velocity
And count positively the momentum when you go towards the equilibrium point.
@@AdenKhalil now please think about what you have written (and try to plot it)
@@AdenKhalil how could on throw some thing towards something - with the velocity pointing to the OPOSITE direction?
so.. if we watch all these lectures do we earn our degree?
Not sure why he would say that in one dimension any function can always be written as the derivative of another function. What about the case when F(x) = sin(x^2) whose integral cannot be expressed as elementary functions?
A non-elementary function is still a function. You can compute it using numeric methods for integration for instance. A function is simply a mapping, it doesn't have to be computable at all.
Why does he identify F with x? He says that dx/dt = p/m tells us how x changes but dp/dt = F/m tells us how p changes and the system eveloves. But, in order the system to evolve, change of p should determine the change of x and new value of x should affect p new value. So, x must be identified with forsce. But, I do not understand why F this is the case? Why is F identified with x (rather than p, for instance)? Is it because x = cos t and F = -W^2 x in harmonic oscillations?
I think Professor Susskind messed up a bit. Because of the limitations of RUclips comments I will use *bold* for vectors _ to indicate a subscript and ^ to indicate a superscript or taking something to a power.
He should have I think said
*F* = m (d^2 *r* / d t^2)
and not
*F* = m ( d^2 x / d t^2)
That would just be the x component of the force, and is more properly written
F_x = m ( d^2 x / d t^2)
he tells us at least 4 times that x(t)=e^(-at) will eventually come to a rest zero and therefore Aristoteles laws are not reversible. That's wrong for every initial conditions besides x0=0: a trajectory never reaches zero either or it was zero from the start. And in both cases we can compute exactly the location of the trajectory a given dt before.
He sais if you can have an infinite ammount of accuracy (which means counting each coordinate to infinity) you have reversabillity. You can't do that practically. So you take limits.If you take the limit of x as t goes to +infinity, you get zero. Every dt, as the function hovers over the x axis, gives us a certain dx which is practically zero when you compare to infinity.
I still didnt understand why the Aristotle theorem was irreversable? why its irreversable if all particles return to their origin?
Daniel Fisher lets say there are two particles, one at 2 and other at 3 after infinite length of time both end up at 0. Now if we want to move In reverse we don’t know where to go (2 or 3?)
The lectures are pure gold!
Sorry... subtitles here play a twin role: with the existing quality of sound, spontaneous look at the subtitles either helps or just completely ruins the brain from time to time...
how can you retrodict with newton equations
voice quality and the noises are so terrible. its hard to focus on lecture 😡
it's not true that aristoteles' laws would not be reversible.
Shouldn't the general solution to X'' = -X be X(t) = C1 cosX + C2 sinX instead of just C cosX
Simplify it. You get c=sqrt(c1^2 +c2^2)
great❤
voice quality and the noises are so terrible. its hard to focus on lecture 😡
Do you allow downloading videos?
I just fuckin love this guy...I used to watch these series to have a better understanding of my high school Physics...and now that I'm in Med School and do the same shit all over again, Susskind is just a treat :)
I am doing same..
Fiji
what if the particle is on fire?
wouldn' t it excert a force on itself?