I came here to refresh (relearn) things that I learned 30 years ago, but when I studied it then, it was all developed in terms of matrices and applying conditions like isotropy and homogeneity. Susskind develops it in a much more intuitive way. I think I would have had a deeper understanding to see something like this before doing the rigor. Water under the bridge.
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RUclips is trying to subconsciously teach me physics, because I keep landing on these lectures with autoplay when I leave YT playing when I sleep. I gave my friend a physics lesson yesterday, what's going on?
If galaxies past cosmic horizon are not moving at greater than the speed of light w.r.t. to their inertial frame, then how are they moving at faster than the speed of light w.r.t. our frame of reference?
sir when i watch your lectures i feel great because you make it simple. you are the best teacher in my opinion. i have a question; i need exercices and there solution, can you tell me where i can find some.
Consider an event in space-time with all of its spatial coordinates (x1, x2, x3) non-zero integers. How can Lorentz transformation of time for that event will be figured out through this info? Do we have to find the spatial distance X from origin (where X = sqrt(x1^2 + x2^2 + x3^2) ) and then substitute it for length OR something else?
No, you just apply the formulas as given for x and t (remembering that y'=y and z'=z). This assumes that the x-direction is the direction of relative motion. If it isn't, you can rotate the three spatial coordinates so x now points in the direction of motion, do the Lorentz transformations, and then rotate them back. A bit like solving a Rubik cube :-)
Here are the correct equations for relativity. x'=x-vt y'=y z'=z t'=t These are called the Galilean transformation equations because they were derived by Galileo and were the equations used by physicists until 1887, when the Michelson-Morley experiment took place. Then scientists said, The Galilean transformation equations cannot show constant speed of light, as shown in the Michelson-Morley experiment, and they threw the Galilean transformation equations away. Then they substituted the Lorentz equations derived by H.A. Lorentz to describe electromagnetic fields to describe relativity, and the Galilean transformation equations have not been used to describe transmission of light since that time. But the Galilean transformation equations can describe constant speed of light. All you have to do is know the axioms of algebra and follow them in the Galilean transformation equations. If t is the time of a GPS clock on the surface of the earth, then t' in the Galilean transformation equations cannot be the time of a slower or faster clock such as Einstein describes in his theory of relativity. t' also has to be the time of a clock of a GPS clock on the surface of the earth because it is equal to t. The time of a faster or slower clock would have to be shown by a different variable than t'. This set of Galilean transformation equations says nothing about a faster or slower clock in frame of reference S'. These equations say that if time is being kept by a faster or slower clock in the moving frame of reference, then the time of that faster or slower clock would have to be converted to the time shown by a GPS clock on the surface of the earth before using the Galilean transformation equations. But, say scientists, We want to use the time of the slower or faster clock to show that the speed of light is c= 186,000 mi/sec according to the time of the faster or slower clock. Then you have to use another set of Galilean transformation equations with different variables for velocity and time. x = x' - (-vt/n')n' y = y' z = z' n = n' n' is the time of the faster or slower clock in the moving frame of reference. If the clock is in a flying airplane going in a particular direction around the earth, it will be slower than the GPS clock. If the clock is in a GPS satellite and has not been adjusted to agree with the GPS clock on earth, it will be faster than the GPS clock on earth. But, say scientists, The times of all of these clocks show light to be traveling at c = 186,000 mi/sec. It is very simple. Instead of using x=ct and x'=ct' as Lorentz and Einstein did, we use x=ct and x'=cn'. We can use the solar system to show how this works. If there is a clock on the planet Mercury, that clock is slower than a clock on earth because Mercury is in greater gravitation, and its orbital speed is 30 miles per second, ten miles per second faster than earth in its orbit. So then we say, t is the time of a clock on earth, and n' is the time of the clock on Mercury. x'=x-vt cn'=ct-vt n' = t - vt/c This value for n' is the same as the numerator for Lorentz's equation for t'. t'=(t-vx/c^2)/sqrt(1-v^2/c^2) n' = t-vt/c= t-vct/c^2 = t-vx/c^2 Now we consider a clock on one of the outer planets, or non-planets, such as scientists classify Pluto. That clock would be faster than a clock on earth, but would still show light to be traveling at c=186,000 miles per second. I have yet to find a scientist or science enthusiast who will discuss these correct equations for relativity and how they relate to constant speed of light. But if someone thinks they are wrong, go ahead and prove it.
I have attended UIC, and professors probably went through a lot because of the Coronavirus. Hope everyone had Jockey Premium Super Fine Ground Coffee by now.
In the given example here, what happens if the cart moves opposite to the direction of train movement? The equation will be w= (v-u)/(1-uv) . then if u=v=c => w=undefined. But irrespective of direction if cart is moving with C, w should be equal to C.
Jonas la Cour I understand that the cone has 3 dimensions, but the diagram uses the height to represent the time axis; so if we were to graphically represent all four dimensions, we would need a "video" of an expanding sphere... right? Or at least over-lapping spheres of different sizes with each marked for its time signature.
+RunItsTheCat Yeah, that's another way of thinking about. Then you would draw lines between one xyz point in one frame/event/instant and another xyz in a different fram to form the coordinate system. I don't pretend to be an expert on the topic though, hence why I am here.
+RunItsTheCat Yeah you could think of the 3 spatial dimensions mapping to a 3d model where each real dimension maps to itself in the model, and the distance from the center of the sphere would be what is invariant, and of course the evolution of that system with time would be a temporally expanding sphere who's radius grows with time. In general we can only draw 3 spatial dimensions and we get a 4th dimension when we animate over time, it would make sense in this case to use the 3 spatial dimensions to represent themselves and time represent the invariant quantity of proper time. always be careful using these kinds of mappings to try and gain an intuitive understanding of what you're learning, they tend to confuse more than they simplify. Susskind points out this trap in his QM lectures.
The cone is really an expanding circle where we can simultaneously view all the time slices spatially. For the sphere, as you said, we need a video to see all the time slices in actual time.
The Department of Physics at Stanford University held the 2012 Robert Hofstadter Memorial Lectures at 8:00pm on Monday, April 16, 2012. It was given by Prof. Geoffrey West. The talk was entitled: “Searching for Simplicity and Unity in the Complexity of Life: Cells to Cities, Companies to Ecosystems, Milliseconds to Millenia” physics.stanford.edu/events/prof-geoffrey-west-searching-simplicity-and-unity-complexity-life-cells-cities-companies
i have a doubt.. i am standing still. my friend is moving 0.9c towards my right and i see my another friend is moving 0.9c towards left. with respect to my frame everything seems to be ok. but how the einsteins equation agrees for my friends with respect to each other since both are moving 1.8c relative to each other. whether it is violating einsteins assumptions..??
Jayaraman Muniyappan This is a misunderstanding of the Galilean Law of the Addition of Velocities. In this law, we find that for parallel velocities, the speed with respect to each other is (v+u)/(1+v*u). By this, we find these two friends move with a velocity of 1.8/1.81 relative to each other, or .994c. This formula states that two observers will not move at or greater than the speed of light relative to each other unless one observers is moving at the speed of light (i.e. one events are light). This result is a consequence of the speed of light appearing to be the same speed in all inertial frames
@@daccoa I do not get it. I accept that c is a speed-limit for how fast waves move (everything is waves) but I do not grasp that you don't have an actual speed of 2c between wave-fronts in opposite directions. They would cover double the distance in the same time, and hence double the actual speed compared to each other.
@@asgeirnilsen6752 you would indeed see two wave-fronts running away from each other at 2c. but none of them are moving AWAY FROM YOU at speed larger than c. And speed is not really a thing from the wave front reference frame because they are at the speed of light, thus they can't measure any time at all.
@@marcoskunrath5914 I was thinking about a kind of actual speed difference between two mass-objects. Not the possibility to measure. I think a more interesting question is, why the speed of light is c. An electromagnetic wave is a wave that ocillate the energy between a magnetic and an electric field. What is it with the medium of vacuum that set the speed c? Maybe it i a quantum fenomen, to get the energy distribution function to suit a potensial well (C=f*lambda).
if the speed of light is always the same regardless of reverence frame imagine this: If you move away from me with 0.99C and I then shine a light towards you after a while, I would see a beam "slowly" catching up to you with 0.01C but you would see a beam coming at you with speed C relative to you , is that correct? So if I send a message to you I may perceive it taking hours or days to reach you but you get it almost instantly?
That is time dilation, literally. According to your reference frame, my time is running very slowly. Days and Hours in your frame are mere moments in my frame through your perspective.
Really cool, I have never heard of someone calling the "world line" (or Lorentz spatial invariance) length "proper time ". Nonetheless I guess it makes sense as well
"A 3D equilateral triangle on the curved surface of a sphere, has 90° angles". Dear Adam, this statement is not correct. You considered a case with one side is on equator, and the opposite node in a pole. Try to take a very small triangle. Remember we live on an almost sphere, and small flat triangles are not very different from small spherical ones. Another example: make size = 2*pi*R. Therefore, the conclusion is: the angles of a many-D equilateral triangle depends on its size if many > 2.
question at 27:55 answer = the person moving at velocity U and the stationary observer would disagree over time frames on the inner moving object moving at velocity W. the speed of light dictates time and space. also the person inside the train moving at speed U would disagree with the velocity difference of the person moving at velocity W as compared to the stationary observer (do to lorentz contraction). time cannot be separated from space, they go hand in hand. out everyday experiences of time and space are simply misconceptions. illusions created in our mind to make sense of the universe. special relativity is mind breaking concepts because we normally do not experience things at very high speeds.
if you want to fully understand the relativistic effects on matter and time .. itselve- id give you the advice to read he oiginall from einstein, afterwards something about the original from an other person and then an other one about relativity and so on and so forth. because if you hear it from different points of views from different physicists- youll see it in more ways and youll finally get it
S = what colour is Sulphur at room temperature? Sc = what colour is Scandium at room temperature? Sb = what colour is Antimony at room temperature? Sn = what colour is [Tin (is not a can)] at room temperature? In Great Britain s. is the abbreviation for shilling, a coin worth about 14 American cents. This book is S volume 17.
I made some mistakes on my previous comment. So here are the corrections: "A 2D equilateral triangle has 60° angles. (30° per DIMENSION)" "A 3D equilateral triangle on the curved surface of a sphere, has 90° angles. (again, 30° per DIMENSION)" 30° times Nd = the size of each of the three angles in degrees. Where Nd is the Number of dimensions. 30° times 4 = 120° 120° times 3 (the total # of angles a triangle has no matter how many dimensions are taken into account) = 360°. 360° in a circle.
The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For positive curvature with f > 0 sum of angles > 180 deg
Wohoo Master When the direction of motion is ONLY along the X-axis, he defined T^2 = t^2 - x^2 to be the proper time. In this equation, your displacement in space is the sqrt(x^2), which obviously is just x. Now imagine you move in the X and Y direction. Your displacement is now sqrt(x^2 + y^2) aka Pythagorean Theorem. Well, when you move in 3 directions, your displacement is sqrt(x^2 + y^2 + z^2). You can think of the proper time equation as T^2 = t^2 - (displacement in space)^2. So when your displacement in space has an X, Y, and Z components, the equation is T^2 = t^2 - [ sqrt(x^2 + y^2 + z^2) ]^2. Simplify the ^2 and the sqrt(), and you get T^2 = t^2 - (x^2 + y^2 + z^2). Distribute the ' - ' into the parentheses and you get T^2 = t^2 - x^2 - y^2 - z^2.
Donald Timpson I c, thanks ^_^ my problem was grasping why it was T^2 = t^2 - x^2 *Thought it should be a +* but after watching the first lecture it all makes sense
@@wohoomaster9068 I know its too late for you, but somebody else might have this same doubt. So we are getting T^2 = t^2 - x^2 because not the normal (euclidean geometry) which we are used to.This comes from non-euclidean geometry which is a big topic in itself.
@@ayushwithasingle_a In my opinion, stop viewing it as geometry and you shall have more clarity. They are just a bunch of algebraic equations. That's it. Don't mix it up with anything.
L1--------------------X--------------------L2 L1 and L2 are lights. There are 2 ships at X passing each other in opposite directions. L1 and L2 flash simultaneously in the frame of reference that is at rest relative to L1 and L2. For the ship moving towards L1 and away from L2, L1 flashes before L2 flashes. For the ship moving towards L2 and away from L1, L2 flashes before L1 flashes. When L1 flashes is the light from L2 traveling through space or not traveling through space? Has the light from L2 already been emitted or not yet emitted? When L2 flashes is the light from L1 traveling through space or not traveling through space? Has the light from L1 already been emitted or not yet emitted?
Any one else notice a relationship between equilateral triangles & dimensions? A 2D equilateral triangle has 60° angles. (30° per angle) A 3D equilateral triangle on the curved surface of a sphere, has 90° angles. (again, 30° per angle) Can we incorporate the 4 dimension, Time, into this relationship? & if so, would each angle of the equilateral triangle = 120°? 120° times 3 = 360°. The total amount of deg in a circle. Light follows a curved path through 4 dimensional spacetime. Coincidence?
All of this assumes that the speed of light is constant. Of all the methods of measuring the speed of light, over all the years we have been doing so, the speed of light has been slowing down. Infinitesimally, yes, but so far it hasn't become clear whether this slowing is logarithmic, exponential, or linear. Who cares? Well consider for one thing, that in all three foregoing cases of the slowing of light, that if C is not a constant but rather a variable, then our C yardstick for measuring both cosmic distances and the age of the faintest lights is accumulatively skewed. The error is compounded the farther back we look in time, and further out we look in space. An overly dramatic extrapolation would be that of goldfiah, trying to understand the reality beyond the fishbowl. That's analogous to just how distorted our grasp of reality is, when assuming C is a constant. To a May Fly that only lives 24 hours, everything appears to be a constant. In the cosmological time frame, mankind's short lifetime is akin to that of the May Fly, with our skewed assumption of C being a constant.
Al it's mathematically correct BUT everything descends from the ipothesis that nothing and no one can go faster then the speed of light : Lorentz trasformations are strong but are based on the fact that c is an impossible limit
Bah! You'll get a completely different result if the train or the car is stationary and the other two are moving. Momentum is not conserved in these transforms: 1. Stations's perspective: m1 * gamma(0) * 0 + m2 * gamma(v) * v + m3 * gamma(w) * w 2. Train's perspective: m1 * gamma(v) * (-v) + m2 * gamma(0) * 0 + m3 * gamma(u) * u 3. Car's perspective: m1 * gamma(???) * (-???) + m2 * gamma(u) * (-u) + m3 * gamma(0) * 0 You have to find a reference frame where the net momentum is zero because that is the one with the maximum possible lapse of proper time. The station is a good approximation, but it recoils somewhat when the train pushes off, just as the train recoils when the car pushes off. It's easier to analyze if the train and the car push off from one another, leaving the station undisturbed.
@silverrahul Hmmm. I'd forgotten about this one. I was still struggling to reconcile SR with conservation of momentum at the time. The point I was trying to make is that worldlines are kinked by contact forces so you have to look at the history of kinks to find the reference frame with the fastest clock. That resolves the ??? in those equations.
@silverrahul You're right about ??? variable. I can't remember why I thought it was unknown. But the point is, proper time passes at different rates along each worldline (station, train and car) and conservation of momentum is the only way to determine which one has the fastest clock.
@silverrahul Oh yeah! Now I remember. I was struggling to get the velocity addition formula to work out properly in the car's reference frame and I thought the key was to find the fastest clock. It's a nasty bit of math, but I worked it out eventually and it doesn't matter which clock runs fastest (as you say.) I actually conversed with one of the WIkipedia caretakers on this issue and had to apologize after I came to my senses. Too bad Lenny doesn't respond to comments. He would have set me straight on day one. He really should do the calculation in his lecture though because it's bound to come up again. On the plus side, I think this is what compelled me to buy his Theoretical Minimum books so it was a win for both of us. Thanks for keeping me honest.
It is possible to derive 2 contradictory time dilation equations. Imagine that Sally is in a spaceship and moving to the right and is aiming a flashlight straight up and down so that Sally sees the light moving straight up and down and John is outside the spaceship and sees the light forming a triangle with the floor of the spaceship. Now imagine that Sally is aiming a flashlight upwards and towards the left while the spaceship moves to the right. Now the situation is exactly reversed. Sally sees the light forming a triangle with the floor and John sees the light bouncing straight up and down. Here's the details... Sally is in a moving spaceship. John is outside the spaceship. Sally is moving to the right at .6c. The height of her spaceship is .8 light-seconds. If Sally has a light clock with the light bouncing straight up and down the light will make a 3-4-5 right triangle from the viewpoint of John. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T = delta T_o/((1-.6^2)^.5) Now Sally has a light clock but this time she is holding a flashlight at an angle of 53.13 degrees above the horizontal and pointed to the left. Now the leftward movement of the light exactly matches the rightward movement of the spaceship from John's viewpoint. Now the light is bouncing straight up and down from the viewpoint of John and the light is making a 3-4-5 right triangle from viewpoint of Sally. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T_o = delta T/((1-.6^2)^.5) The 2 equations are in direct contradiction to each other. Special relativity is falsified.
either I'm getting the example with the flashlight wrong, but the way I understood it, given your comment, it is not possible. You can't shoot a light beam in a way that when seen from outside the spaceship it will move up and down, at least while the spaceship is moving. It will always form a triangle for that person, but the steeper you put the light, the "flatter" the triangle gets, until it becomes a straight line. If I got something wrong please elaborate.
Sally is moving to the right at .6c. She is holding a flashlight pointed to the left and 53.13 degrees above the horizontal. So the leftward movement of the light is .6c. For someone outside the spaceship looking into the spaceship the light is bouncing straight up and down.
@@vesuvandoppelganger ah now I get whag you are trying to convey. However the Situation you portrayed is not completely possible. For the first move of light to the left it is true that it seems like a straight upward movement for the person outside. However what about the movement back to the origin of the light? It can not be a straight down movement if you think about it. If the spaceship moves to the right the light beam that is now bouncing back has to make a movement that isn't a straight down movement. If it would it would end up on the left side of the ship and not bounce back to the origin.
I got an insight.. Writer , activist and scientist is what I wanted to be... Doing it scientifically is the best way to do it... In India there's a lot of unscientific activism and I just got lucky to be in differnt systems kind of....mostly Indian though... democracy..how bad can it be.. So now based on my Nash's review...what's best for oneself first and then the group...time dependent maybe..... (Btw Nash theories i dunno except movie one) Also Nash dunno his iq but his theory was there before when boardgames warfare etc was going on.....just he wrote it all out neat and tidy orollybin a language that is very specific...and no room for double meanings.
If you know nothing about physics, does that lock you in a prison ? If you simply analyze "motion" to determine what it is and what it is that is required to make motion possible, then you will soon independently discover the SR phenomena, and at the same time you will have independently derived the SR mathematical equations as well, including deriving the Lorentz transformation equations. So the big question is, why did they do not bother to tell you in school, that it was so simple for just about any Joe/Jane Blow to discover SR on his or her own ?
Nice to know I fell asleep to oneyng and woke up to this
Lmao I woke up to this too
Maybe this is telling us something
Same
Same
Wtf.... we are all living the same life
I came here to refresh (relearn) things that I learned 30 years ago, but when I studied it then, it was all developed in terms of matrices and applying conditions like isotropy and homogeneity. Susskind develops it in a much more intuitive way. I think I would have had a deeper understanding to see something like this before doing the rigor. Water under the bridge.
Lies again? Sexist Racist
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Everyone in that damn class should feel ripped off that I’m watching this for free on RUclips
This should be getting 10M views instead of all the other trash they call "educational"...
Is this 8th grade??
RUclips is trying to subconsciously teach me physics, because I keep landing on these lectures with autoplay when I leave YT playing when I sleep.
I gave my friend a physics lesson yesterday, what's going on?
People get dragged in by algorithm since it noticed people sleeping to these cozy/slow and even soundprofiles.
Probably a category of it's own.
If galaxies past cosmic horizon are not moving at greater than the speed of light w.r.t. to their inertial frame, then how are they moving at faster than the speed of light w.r.t. our frame of reference?
These are outstanding lectures.
sir when i watch your lectures i feel great because you make it simple. you are the best teacher in my opinion.
i have a question; i need exercices and there solution, can you tell me where i can find some.
❤agreed
Leonard Suesskind is a genius !!!
very easy to understand, i have learnt so many things
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I think it difficult for me
Consider an event in space-time with all of its spatial coordinates (x1, x2, x3) non-zero integers. How can Lorentz transformation of time for that event will be figured out through this info? Do we have to find the spatial distance X from origin (where X = sqrt(x1^2 + x2^2 + x3^2) ) and then substitute it for length OR something else?
No, you just apply the formulas as given for x and t (remembering that y'=y and z'=z). This assumes that the x-direction is the direction of relative motion. If it isn't, you can rotate the three spatial coordinates so x now points in the direction of motion, do the Lorentz transformations, and then rotate them back. A bit like solving a Rubik cube :-)
@Alec Brady So there can’t be two directions of relative motion?
@@AlecBrady Good old conjugation
Here are the correct equations for relativity.
x'=x-vt
y'=y
z'=z
t'=t
These are called the Galilean transformation equations because they were derived by Galileo and were the equations used by physicists until 1887, when the Michelson-Morley experiment took place. Then scientists said, The Galilean transformation equations cannot show constant speed of light, as shown in the Michelson-Morley experiment, and they threw the Galilean transformation equations away. Then they substituted the Lorentz equations derived by H.A. Lorentz to describe electromagnetic fields to describe relativity, and the Galilean transformation equations have not been used to describe transmission of light since that time. But the Galilean transformation equations can describe constant speed of light. All you have to do is know the axioms of algebra and follow them in the Galilean transformation equations. If t is the time of a GPS clock on the surface of the earth, then t' in the Galilean transformation equations cannot be the time of a slower or faster clock such as Einstein describes in his theory of relativity. t' also has to be the time of a clock of a GPS clock on the surface of the earth because it is equal to t. The time of a faster or slower clock would have to be shown by a different variable than t'. This set of Galilean transformation equations says nothing about a faster or slower clock in frame of reference S'. These equations say that if time is being kept by a faster or slower clock in the moving frame of reference, then the time of that faster or slower clock would have to be converted to the time shown by a GPS clock on the surface of the earth before using the Galilean transformation equations. But, say scientists, We want to use the time of the slower or faster clock to show that the speed of light is c= 186,000 mi/sec according to the time of the faster or slower clock. Then you have to use another set of Galilean transformation equations with different variables for velocity and time.
x = x' - (-vt/n')n'
y = y'
z = z'
n = n'
n' is the time of the faster or slower clock in the moving frame of reference. If the clock is in a flying airplane going in a particular direction around the earth, it will be slower than the GPS clock. If the clock is in a GPS satellite and has not been adjusted to agree with the GPS clock on earth, it will be faster than the GPS clock on earth. But, say scientists, The times of all of these clocks show light to be traveling at c = 186,000 mi/sec. It is very simple. Instead of using x=ct and x'=ct' as Lorentz and Einstein did, we use x=ct and x'=cn'. We can use the solar system to show how this works. If there is a clock on the planet Mercury, that clock is slower than a clock on earth because Mercury is in greater gravitation, and its orbital speed is 30 miles per second, ten miles per second faster than earth in its orbit. So then we say, t is the time of a clock on earth, and n' is the time of the clock on Mercury.
x'=x-vt
cn'=ct-vt
n' = t - vt/c
This value for n' is the same as the numerator for Lorentz's equation for t'. t'=(t-vx/c^2)/sqrt(1-v^2/c^2) n' = t-vt/c= t-vct/c^2 = t-vx/c^2
Now we consider a clock on one of the outer planets, or non-planets, such as scientists classify Pluto. That clock would be faster than a clock on earth, but would still show light to be traveling at c=186,000 miles per second.
I have yet to find a scientist or science enthusiast who will discuss these correct equations for relativity and how they relate to constant speed of light. But if someone thinks they are wrong, go ahead and prove it.
I have attended UIC, and professors probably went through a lot because of the Coronavirus. Hope everyone had Jockey Premium Super Fine Ground Coffee by now.
I reckon you love subscripts. I seen you loving them.
Thank you for your time in effort
In the given example here, what happens if the cart moves opposite to the direction of train movement?
The equation will be w= (v-u)/(1-uv) . then if u=v=c => w=undefined. But irrespective of direction if cart is moving with C, w should be equal to C.
OH WOAH... that's a good pen 😎
+Adam Spears
I think you're a little bit confused
So a cone when only accounting for x and y dimensions, and an expanding sphere when also accounting for the z dimension.
+RunItsTheCat No, a cone already has 3 spacial dimensions you can't exactly draw a space-time diagram with 3 spacial dimensions.
Jonas la Cour I understand that the cone has 3 dimensions, but the diagram uses the height to represent the time axis; so if we were to graphically represent all four dimensions, we would need a "video" of an expanding sphere... right? Or at least over-lapping spheres of different sizes with each marked for its time signature.
+RunItsTheCat Yeah, that's another way of thinking about. Then you would draw lines between one xyz point in one frame/event/instant and another xyz in a different fram to form the coordinate system. I don't pretend to be an expert on the topic though, hence why I am here.
+RunItsTheCat Yeah you could think of the 3 spatial dimensions mapping to a 3d model where each real dimension maps to itself in the model, and the distance from the center of the sphere would be what is invariant, and of course the evolution of that system with time would be a temporally expanding sphere who's radius grows with time. In general we can only draw 3 spatial dimensions and we get a 4th dimension when we animate over time, it would make sense in this case to use the 3 spatial dimensions to represent themselves and time represent the invariant quantity of proper time. always be careful using these kinds of mappings to try and gain an intuitive understanding of what you're learning, they tend to confuse more than they simplify. Susskind points out this trap in his QM lectures.
The cone is really an expanding circle where we can simultaneously view all the time slices spatially. For the sphere, as you said, we need a video to see all the time slices in actual time.
thanks sir for this lecture❤🙏
Susskind seems bored with the material and the questions..well doing this a long time..
agree
May God bless you sir
❤ameen
good seats to what...? I'M SO CURIOUS O.o
me too
@@lunadusk8590 me three
The Department of Physics at Stanford University held the 2012 Robert Hofstadter Memorial Lectures at 8:00pm on Monday, April 16, 2012. It was given by Prof. Geoffrey West. The talk was entitled: “Searching for Simplicity and Unity in the Complexity of Life: Cells to Cities, Companies to Ecosystems, Milliseconds to Millenia” physics.stanford.edu/events/prof-geoffrey-west-searching-simplicity-and-unity-complexity-life-cells-cities-companies
JB
i have a doubt.. i am standing still. my friend is moving 0.9c towards my right and i see my another friend is moving 0.9c towards left. with respect to my frame everything seems to be ok. but how the einsteins equation agrees for my friends with respect to each other since both are moving 1.8c relative to each other. whether it is violating einsteins assumptions..??
Jayaraman Muniyappan This is a misunderstanding of the Galilean Law of the Addition of Velocities. In this law, we find that for parallel velocities, the speed with respect to each other is (v+u)/(1+v*u). By this, we find these two friends move with a velocity of 1.8/1.81 relative to each other, or .994c. This formula states that two observers will not move at or greater than the speed of light relative to each other unless one observers is moving at the speed of light (i.e. one events are light). This result is a consequence of the speed of light appearing to be the same speed in all inertial frames
Ya.. I got it now.. Thank you Anthony D...
@@daccoa I do not get it. I accept that c is a speed-limit for how fast waves move (everything is waves) but I do not grasp that you don't have an actual speed of 2c between wave-fronts in opposite directions. They would cover double the distance in the same time, and hence double the actual speed compared to each other.
@@asgeirnilsen6752 you would indeed see two wave-fronts running away from each other at 2c. but none of them are moving AWAY FROM YOU at speed larger than c. And speed is not really a thing from the wave front reference frame because they are at the speed of light, thus they can't measure any time at all.
@@marcoskunrath5914 I was thinking about a kind of actual speed difference between two mass-objects. Not the possibility to measure. I think a more interesting question is, why the speed of light is c. An electromagnetic wave is a wave that ocillate the energy between a magnetic and an electric field. What is it with the medium of vacuum that set the speed c? Maybe it i a quantum fenomen, to get the energy distribution function to suit a potensial well (C=f*lambda).
if the speed of light is always the same regardless of reverence frame imagine this:
If you move away from me with 0.99C and I then shine a light towards you after a while, I would see a beam "slowly" catching up to you with 0.01C but you would see a beam coming at you with speed C relative to you , is that correct?
So if I send a message to you I may perceive it taking hours or days to reach you but you get it almost instantly?
BillyViBritannia yes
That is time dilation, literally. According to your reference frame, my time is running very slowly. Days and Hours in your frame are mere moments in my frame through your perspective.
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@@kiddmath azzawwz🧖🏾♂️🤳👽😅w. We a. W we ww. Www. Was wasoe TVeseo Tara. Saw ecUeczecoooe CcaOc FewnwEC Cw a C tccC A WE CAezceoW BBCcCZ we car5?5$!aa
@@kiddmath @@kiddmath @@kiddmath
i think those equation are abstraction on a level unseen by humanity
Really cool, I have never heard of someone calling the "world line" (or Lorentz spatial invariance) length "proper time ". Nonetheless I guess it makes sense as well
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536443333363333e
"A 3D equilateral triangle on the curved surface of a sphere, has 90° angles".
Dear Adam, this statement is not correct. You considered a case with one side is on equator, and the opposite node in a pole. Try to take a very small triangle. Remember we live on an almost sphere, and small flat triangles are not very different from small spherical ones. Another example: make size = 2*pi*R. Therefore, the conclusion is: the angles of a many-D equilateral triangle depends on its size if many > 2.
can someone explain to me the column vector math, is it a 2 row column vector on the right filled with x? thanks.
question at 27:55
answer = the person moving at velocity U and the stationary observer would disagree over time frames on the inner moving object moving at velocity W. the speed of light dictates time and space. also the person inside the train moving at speed U would disagree with the velocity difference of the person moving at velocity W as compared to the stationary observer (do to lorentz contraction). time cannot be separated from space, they go hand in hand.
out everyday experiences of time and space are simply misconceptions. illusions created in our mind to make sense of the universe. special relativity is mind breaking concepts because we normally do not experience things at very high speeds.
Susskind is my hero❤
good point about the glass wall
Wonderful lectures
This lecture is really just 54 mins long, unlike the others in the series which are roughly 2 hours.
It seems that there was some function that day. He told "we should go now if we want to get seats"
if you want to fully understand the relativistic effects on matter and time .. itselve-
id give you the advice to read he oiginall from einstein, afterwards something about the original from an other person and then an other one about relativity and so on and so forth.
because if you hear it from different points of views from different physicists- youll see it in more ways and youll finally get it
Thank you for the free college
S = what colour is Sulphur at room temperature?
Sc = what colour is Scandium at room temperature?
Sb = what colour is Antimony at room temperature?
Sn = what colour is [Tin (is not a can)] at room temperature?
In Great Britain s. is the abbreviation for shilling, a coin worth about 14 American cents.
This book is S volume 17.
does anyone know a good excersize sheet fir this course?
I the prime observer read off (VT) that i knew what the observer(u)aka the passenger was about to do.
Thanks a lot!
I don’t know how to explain but he is kinda mike ehrmantraut if studied physics
Where do I get this 'kiddy car' from...?
❤thank you very much
Good basic lecture..walking back and forth is distracting..just listen is ok but miss board calcs..
Prof Susskind looks a bit like mike from BB and a bit like Tywin Lanister frm GoT
If the cart moves in the opposite direction to the train, u is negative in relation to v, so u =/= v. I think that makes sense anyway.
I made some mistakes on my previous comment. So here are the corrections:
"A 2D equilateral triangle has 60° angles. (30° per DIMENSION)"
"A 3D equilateral triangle on the curved surface of a sphere, has 90° angles. (again, 30° per DIMENSION)"
30° times Nd = the size of each of the three angles in degrees.
Where Nd is the Number of dimensions.
30° times 4 = 120°
120° times 3 (the total # of angles a triangle has no matter how many dimensions are taken into account) = 360°.
360° in a circle.
The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For positive curvature with f > 0 sum of angles > 180 deg
Revisit your spherical geometry
If we define the two coordinates so one is left-handed, and other is right-handed, so the sign of v is the same.. perfectly symmetric?
Yeah, that's what I felt. So, all this intuition falls apart then? The derivations have to be done with more rigour and care.
znak równości musi być na wysokości kreski ułamkowej (
the equal sign must be on the same level as the slash)
wooooo! thanks guys
37:05 ~~SAVAGE~~
what was savage? the question or the response?
When did John Malcovich start teaching physics? 😜😜👍👍
Shit never mind, forget that. Misread your comment. I guess my best answer is that things that aren't light just don't go the speed of light.
Speed of light then isn't constant under other action..?
Can someone point me on the right direction or explain why T=t^2-x^2-y^2.... I know I am missing some fundamental maths xD.
Wohoo Master When the direction of motion is ONLY along the X-axis, he defined T^2 = t^2 - x^2 to be the proper time. In this equation, your displacement in space is the sqrt(x^2), which obviously is just x. Now imagine you move in the X and Y direction. Your displacement is now sqrt(x^2 + y^2) aka Pythagorean Theorem. Well, when you move in 3 directions, your displacement is sqrt(x^2 + y^2 + z^2). You can think of the proper time equation as T^2 = t^2 - (displacement in space)^2. So when your displacement in space has an X, Y, and Z components, the equation is T^2 = t^2 - [ sqrt(x^2 + y^2 + z^2) ]^2. Simplify the ^2 and the sqrt(), and you get T^2 = t^2 - (x^2 + y^2 + z^2). Distribute the ' - ' into the parentheses and you get T^2 = t^2 - x^2 - y^2 - z^2.
Donald Timpson I c, thanks ^_^ my problem was grasping why it was T^2 = t^2 - x^2 *Thought it should be a +* but after watching the first lecture it all makes sense
@@wohoomaster9068 I know its too late for you, but somebody else might have this same doubt. So we are getting T^2 = t^2 - x^2 because not the normal (euclidean geometry) which we are used to.This comes from non-euclidean geometry which is a big topic in itself.
@@ayushwithasingle_a In my opinion, stop viewing it as geometry and you shall have more clarity. They are just a bunch of algebraic equations. That's it. Don't mix it up with anything.
+ Test channel. failure.
So far I think you could get away with just following along from the first lecture.
Martinez Melissa Robinson Kevin Anderson Christopher
16:46
L1--------------------X--------------------L2
L1 and L2 are lights. There are 2 ships at X passing each other in opposite directions. L1 and L2 flash simultaneously in the frame of reference that is at rest relative to L1 and L2. For the ship moving towards L1 and away from L2, L1 flashes before L2 flashes. For the ship moving towards L2 and away from L1, L2 flashes before L1 flashes.
When L1 flashes is the light from L2 traveling through space or not traveling through space? Has the light from L2 already been emitted or not yet emitted? When L2 flashes is the light from L1 traveling through space or not traveling through space? Has the light from L1 already been emitted or not yet emitted?
"Even though... blah...blah... you know the rest of the story."
even though this is principle of simple addition. It doesn't work like that
Any one else notice a relationship between equilateral triangles & dimensions?
A 2D equilateral triangle has 60° angles. (30° per angle)
A 3D equilateral triangle on the curved surface of a sphere, has 90° angles. (again, 30° per angle)
Can we incorporate the 4 dimension, Time, into this relationship? & if so, would each angle of the equilateral triangle = 120°? 120° times 3 = 360°. The total amount of deg in a circle. Light follows a curved path through 4 dimensional spacetime. Coincidence?
No, and dumb. Necrocomment revived.
In fact, you might be a fetal alcohol baby, I’m sorry to say.
Garcia Barbara Williams Jessica Martinez Angela
gooo. that's it. THAT'S IT
Get the joke at the end when he asks whose watch has the right time? Good ol' Leonard, always a joker
nice
luv u sir
All of this assumes that the speed of light is constant. Of all the methods of measuring the speed of light, over all the years we have been doing so, the speed of light has been slowing down. Infinitesimally, yes, but so far it hasn't become clear whether this slowing is logarithmic, exponential, or linear. Who cares? Well consider for one thing, that in all three foregoing cases of the slowing of light, that if C is not a constant but rather a variable, then our C yardstick for measuring both cosmic distances and the age of the faintest lights is accumulatively skewed. The error is compounded the farther back we look in time, and further out we look in space. An overly dramatic extrapolation would be that of goldfiah, trying to understand the reality beyond the fishbowl. That's analogous to just how distorted our grasp of reality is, when assuming C is a constant. To a May Fly that only lives 24 hours, everything appears to be a constant. In the cosmological time frame, mankind's short lifetime is akin to that of the May Fly, with our skewed assumption of C being a constant.
41:20
Al it's mathematically correct BUT everything descends from the ipothesis that nothing and no one can go faster then the speed of light : Lorentz trasformations are strong but are based on the fact that c is an impossible limit
hypothesis
Jones Timothy Jones Michael Thomas Maria
Good seats to what?
Hofstadter memorial lecture I think.
Sussy relativity
36:56 Donald Trump?
49:00 Matrix Lorentz transform
Your square root is weird but understandable.
Reduction of v...due to action...-ve
Bah! You'll get a completely different result if the train or the car is stationary and the other two are moving. Momentum is not conserved in these transforms:
1. Stations's perspective: m1 * gamma(0) * 0 + m2 * gamma(v) * v + m3 * gamma(w) * w
2. Train's perspective: m1 * gamma(v) * (-v) + m2 * gamma(0) * 0 + m3 * gamma(u) * u
3. Car's perspective: m1 * gamma(???) * (-???) + m2 * gamma(u) * (-u) + m3 * gamma(0) * 0
You have to find a reference frame where the net momentum is zero because that is the one with the maximum possible lapse of proper time. The station is a good approximation, but it recoils somewhat when the train pushes off, just as the train recoils when the car pushes off. It's easier to analyze if the train and the car push off from one another, leaving the station undisturbed.
@silverrahul Hmmm. I'd forgotten about this one. I was still struggling to reconcile SR with conservation of momentum at the time. The point I was trying to make is that worldlines are kinked by contact forces so you have to look at the history of kinks to find the reference frame with the fastest clock. That resolves the ??? in those equations.
@silverrahul You're right about ??? variable. I can't remember why I thought it was unknown. But the point is, proper time passes at different rates along each worldline (station, train and car) and conservation of momentum is the only way to determine which one has the fastest clock.
@silverrahul Oh yeah! Now I remember. I was struggling to get the velocity addition formula to work out properly in the car's reference frame and I thought the key was to find the fastest clock. It's a nasty bit of math, but I worked it out eventually and it doesn't matter which clock runs fastest (as you say.) I actually conversed with one of the WIkipedia caretakers on this issue and had to apologize after I came to my senses. Too bad Lenny doesn't respond to comments. He would have set me straight on day one. He really should do the calculation in his lecture though because it's bound to come up again. On the plus side, I think this is what compelled me to buy his Theoretical Minimum books so it was a win for both of us. Thanks for keeping me honest.
@silverrahul It's a trilogy: theoreticalminimum.com/
yaay, sound!
It is possible to derive 2 contradictory time dilation equations. Imagine that Sally is in a spaceship and moving to the right and is aiming a flashlight straight up and down so that Sally sees the light moving straight up and down and John is outside the spaceship and sees the light forming a triangle with the floor of the spaceship. Now imagine that Sally is aiming a flashlight upwards and towards the left while the spaceship moves to the right. Now the situation is exactly reversed. Sally sees the light forming a triangle with the floor and John sees the light bouncing straight up and down. Here's the details...
Sally is in a moving spaceship. John is outside the spaceship. Sally is moving to the right at .6c. The height of her spaceship is .8 light-seconds. If Sally has a light clock with the light bouncing straight up and down the light will make a 3-4-5 right triangle from the viewpoint of John. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived:
delta T = delta T_o/((1-.6^2)^.5)
Now Sally has a light clock but this time she is holding a flashlight at an angle of 53.13 degrees above the horizontal and pointed to the left. Now the leftward movement of the light exactly matches the rightward movement of the spaceship from John's viewpoint. Now the light is bouncing straight up and down from the viewpoint of John and the light is making a 3-4-5 right triangle from viewpoint of Sally. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived:
delta T_o = delta T/((1-.6^2)^.5)
The 2 equations are in direct contradiction to each other.
Special relativity is falsified.
either I'm getting the example with the flashlight wrong, but the way I understood it, given your comment, it is not possible. You can't shoot a light beam in a way that when seen from outside the spaceship it will move up and down, at least while the spaceship is moving. It will always form a triangle for that person, but the steeper you put the light, the "flatter" the triangle gets, until it becomes a straight line. If I got something wrong please elaborate.
Sally is moving to the right at .6c. She is holding a flashlight pointed to the left and 53.13 degrees above the horizontal. So the leftward movement of the light is .6c. For someone outside the spaceship looking into the spaceship the light is bouncing straight up and down.
@@vesuvandoppelganger ah now I get whag you are trying to convey. However the Situation you portrayed is not completely possible. For the first move of light to the left it is true that it seems like a straight upward movement for the person outside. However what about the movement back to the origin of the light? It can not be a straight down movement if you think about it. If the spaceship moves to the right the light beam that is now bouncing back has to make a movement that isn't a straight down movement. If it would it would end up on the left side of the ship and not bounce back to the origin.
Why would it not be a straight down movement as viewed from the person outside the spaceship?
math dude
Interesting but is there any practical use for this stuff? Were the Moon Landings Faked ???
Think about GPS, for example.
Even if we r to construct a craft out of photons..it will be slower due to mass of astronaut riding it..will slow it down..
24:02
This isn’t that hard.
I got an insight..
Writer , activist and scientist is what I wanted to be...
Doing it scientifically is the best way to do it...
In India there's a lot of unscientific activism and I just got lucky to be in differnt systems kind of....mostly Indian though... democracy..how bad can it be..
So now based on my Nash's review...what's best for oneself first and then the group...time dependent maybe.....
(Btw Nash theories i dunno except movie one)
Also Nash dunno his iq but his theory was there before when boardgames warfare etc was going on.....just he wrote it all out neat and tidy orollybin a language that is very specific...and no room for double meanings.
😂
He looks like Mike Ehrmantraut from Breaking Bad
If you know nothing about physics, does that lock you in a prison ? If you simply analyze "motion" to determine what it is and what it is that is required to make motion possible, then you will soon independently discover the SR phenomena, and at the same time you will have independently derived the SR mathematical equations as well, including deriving the Lorentz transformation equations. So the big question is, why did they do not bother to tell you in school, that it was so simple for just about any Joe/Jane Blow to discover SR on his or her own ?
This guy needs to work on some novel prize award on time travel instead of teaching wasting time yo
His lectures are not for racist so instead of watching his lectures u need to go to church.
I'm sorry.. What does racism have to do with time travel? Just sayin'.
Thanks sir for this lecture❤❤
32:30