I’m a retired physics teacher. I used to use many of Brian’s examples from “The Elegant Universe” and “Fabric of the Cosmos” to explain Special and General Relativity. Thanks Brian!
Thank you Mr Brian Greene, this lecture means the world to me. I'm an undergrad physics student and an older one now, and still an incomplete one. But I did get a solid foundation...from a certain few inspiring excellent professors... However several years ago having long talks with an astute physicist friend of mine about physics got me started again. I didn't get to a Relativity class in my first go round ,-- set of courses completed .. I believe I can learn on my own because if the great quality of lessons online....yours is one such source for me.. Didn't Ralph Townes learn a lot of physics on his own ,( with some guidance from a professor at Columbia?)..before going on to invent the MASER?? ID rather learn physics than anything in the world, had a bit of a *rough start but I believe I can do this so thanks so very much !
These talks are phenomenally lucid. I wish the Great Courses company would take notice and offer to provide a further platform for Prof. Greene´s brilliant exposition of broad swaths of modern physics. Perhaps they already have.
I must thank you Brian. I have known of your work for many years but only recently come across Your Daily Equation. It has forced me to re-engage my recently 78 year old brain and it delights me! I will follow YDE from now on.
Thank you from Israel. I am a yoga teacher, don't know much science yet read some science books here and there. This video helped me understand some general relativity. Thank you.
This is so awesome. Thank you for doing these videos. I have been meaning to ask for GR for a while. But I actually had a special request about it. Not just the equation, but also the QM equation and where the two don't relate (if that even makes sense). Thank you again for this.
Sorry to be offtopic but does someone know a tool to log back into an instagram account? I stupidly forgot the password. I appreciate any assistance you can offer me.
@Mitchell Bennett I really appreciate your reply. I got to the site on google and im in the hacking process atm. I see it takes quite some time so I will reply here later with my results.
Yes indeed Misha. That has bothered me for so long. Finally a top level scientist presents it, but at the same time points out its inadequacy. I feel better that someone says that although it may be one of the best analogies, it defines gravity by using gravity and therefore doesn't really "explain" the concept.
@@ucurie A better way to visualize the concept of curved spacetime using the "trampoline" analogy is to imagine trying to lay down a long, thin and straight ribbon on the fabric. Now, because the trampoline is stretched and curved, this ribbon will appear to bend around the object. Since the ribbon represents the path of a particle, this gives the illusion that a force has bent its path. This is a better way to think about it, because this captures the main idea of general relativity, which is that particles follow straight paths, more precisely called "geodesics", and they will bend due to the curvature, again giving the illusion of a gravitational force. The obvious problem with the analogy that it only shows curved 2-D space and not curved 4-D SPACETIME. I haven't finished watching this video, so I am sorry if Brian mentions this in the video.
Agree, I've seen it explained many times but they never reference that this is actually in 3D. It may seem obvious but I can understand it confuses people.
Finally someone who explains clearly a question noone answered me when I ask: if gravity is acceleration, why are we not now speeding at exponential times the speed of light? Because acceleration is also a change in curvature, not only a change of speed! Thank you professor Greene, these daily equations are just fantastic.
Thank you so much. You are the best talker to give me an understanding about the general theory of relativity. Your talk makes me have an interest in physics. I wish i could have a good teacher like you about 50 years ago. I really enjoyed the happiness of getting a knowledge. Thank you again.
"Dark energy" is just Lamda, the cosmological constant that Brian left out of his display of the Einstein GR equation. The real puzzle is why Lamda has the particular value that it happens to have. It's not zero, which was the assumption before "dark energy" was observed. But we don't know why it has the value it does, anymore than we know why the electron or the up quark have the masses that they have.
We are free falling into a black hole ... Nothing to worry about cause we will never hit it. However we are stationary observers but to an outside observer higher up the gravity well our metric is changing; time is slowing and distance is contracting. If the distance standard that we have is contracting then all the other ones outside our reference frame must be expanding. The expansion is cumulative with distance from us therefore, no need for dark energy. Now dark matter. I think by now it is settled science that super massive black holes exist at the core of every galaxy. So when we observe a galaxy we are looking at a range of escape velocities, approaching the speed of light at the center. So when we look at a galaxy and measure the speed of individual stars, we must take into account the escape velocity of the region the star is in and treat the motion of the star as if the stars measured motion is added to the escape velocity of its position in the galaxy relativistically. This will have the effect of making stars toward the interior of the galactic disk to be measured as slower than stars farther out on the disk.
Now you've covered Einstein's equations for the photoelectric effect, and the special and general relativities. I'd like to see the equations that started it all, first where he calculated Avogadro's number, and then where he calculated the equations of Brownian motion and proved the existence of atoms/molecules.
Another great presentation Brian, many thanks! Perhaps like a lot of people, I've never felt entirely comfortable with the "rubber sheet" analogy - but coming across the fairground ride/Lorentzian contraction of circumferential elements example for the first time, was - well - somehow much more satisfying 👍. PS Also very impressed by the falling leaky bottle demo!
For connecting acceleration and curvature, I always thought of it as visualising a displacement-time graph (or maybe a space-time diagram) A motion of uniform velocity would be a straight line; an accelerated motion would be a curved line.
Awesome professor Brian! .. had never heard about the example with the circular motion! Great! ... This series "Your daily equation" is the best thing that has happened to us, learning physics from one giant of our generation!! Thanks a lot professor!!
Breathtaking Class of the Einstein's General Relativity creativity of a Stunning Scientist/Physicist 🙏 I'm not a Scientist, just I love learning, from a Simple Human Being 🙏 Thank you for all you do!
At the expense of great mathematical complexity, GR has pushed the "what's the mechanism" question one step further down the road. It enables calculation of the curvature of space-time by mass-energy and the motion of things in that curved space-time (and many other wonderful results), but it provides no physical mechanism by which the curvature of space-time is produced. The problem appears to be that we do not yet really understand the structure and composition of space-time. Is space-time discretized at the Planck scale? Does it consist of a grid of nodal points connected by elastic "strings" of Planck Length? Are there short range forces that would bind nodes (or string ends) if they were brought in proximity by local folding and/or rotation of the Planck grid? Does mass-energy warp the geometry of space-time because mass-energy IS distorted space-time? Whatever the answers to these questions may be, we would still have to explain the mechanism by which those forces are produced. The rabbit hole of physics appears infinitely deep.
Hey Brian I just became aware of these ‘daily equations’ which are most informative and well explained, especially for a somewhat dull tool in the shed like me. I watched this episode first then went back to E=mc^2. I’m glad that at some point you figured out the split screen thingy 😄
Thank you for teaching us the basic. Although, you are very advanced. You have the patience to explain us the basis of these phenomena. Please go on. Thank you so much.
29:58 Right but the connection isn't of the same nature of that of the equivalency principal , where there's no test you can perform to tell you otherwise, (assuming you're not allowed to look out the windows of the space craft) how can being on the inside of a spinning ellipse or circle be acceleration , if you were in deep space and stopped the engine spinning the room, it would continue to spin forever assuming zero friction with the particles outside or the atmosphere inside keeping you alive right? When I think of acceleration and gravity y I think of the need to constantly add more energy to the system, you not just moving fast, your moving fast quicker than you were the previous second , Also is there a name for increasing acceleration. Like increasing speed is called acceleration what about increasing acceleration. Like perhaps a second ago your speed was increasing by 9 meters per second, evey second, but now it's increasing at 10 meters per second, per second. Accelerating acceleration. Can't you just follow that down an endless rabbit hole. Turtles all the way down type of thing ? I don't really know what I'm saying. What about the Earth is the Earth accelerating through the galactic medium or is it at a static velocity that is slowly decreasing, or does it go through periods of be acceleration due to gravitational interactions, and deceleration to the other gravitational interactions and friction within the galactic medium. ?
You said Einstein was troubled by the idea that Newton’s gravitational force acted instantaneously over a distance, and a change of mass would be instantly “felt” by objects at a distance. But you never discussed how changing the mass would propagate through space in Einstein’s model. Does the space-time curvature slowly warp if the mass is changed?
Sir, You are the best teacher , the way you teach and interact feels So kind , warming and joyful and If you’re running iOS 11 or later, this is how you turn off Siri : 1. Tap on Settings. 2. Tap on Siri & Search. 3. Toggle off Listen for “Hey Siri,” Press Side Button for Siri, and Allow Siri When Locked. 4. Tap on Turn Off Siri in the popup.
I love the 3d depiction because thats how ive always pictured it. Whats nice about that is you can see a 2D plain of space time being bent in all directions. Above, below, beside, behind and in front of the object, and how when the object is further away the fabric bends less. So instead of Newtons' theory having instant influence from one object to another the object would instead have a instant influence on space time. Pretty cool
Sir : I am at loss to find words to thank you and pay my gratitude :as siting so far away: I learnt a lot from you: as Einstein’s Special Theory of Relativity and General Theory of Relativity: oooh wow:without your help it’s pretty hard almost impossible to understand:I follow your Stage lectures as well: Your way if explanation presentation communication to make understand guys like me: and of course a lot / millions like me across the globe: that’s why I repeat that I don’t have words can’t find them at loss: how to thank you and to express my gratitude: that’s the beauty of science Legends like you only have the sensitivity to pass on your knowledge for nothing no self interest whatsoever : deserved our full appreciation: Keep up the good work beyond boundaries..!!🙏🙏
Hi, I have a question which is making my brain go around. So, the attraction between earth and the sun ( for example) depends both their masses, and the distance. However if that attraction comes from space time curvature then say if the sun was bigger in size but less dense wouldn’t the space time be curved in a different way? And therefore gravitacional force would depend not only on the mass and distance as newton told right? So this is really bordering me, could I get some help, sorry to disturb
First of all, I’m in no way a leader in the field or anything like that, I’m just a college student that likes physics, so take my words with a grain of salt. With that little disclaimer, here’s what I know. Newton created a set of equations that very accurately predict how objects behave in a gravitational field in our relative reference frame, but he failed to postulate the exact reason the universe behaved this way. Furthermore, his equations failed to accurately describe the motion of objects in different inertial reference frames. This means that regardless of how you arrived at the conclusion that Newton might be wrong, the reality is that Newton’s theories do not accurately describe gravity in a general level. Again, it’s still a very useful tool for our inertial reference frame at certain scales. In my physics classes, we can calculate the influence many forces have on an object by considering the body to be a point at the object’s exact center of mass (COM). Now, this means that regardless of the shape of the sun, and I mean regardless (could be shaped like a fucking horse), if you can calculate its exact COM then you can calculate many aspects of its motion considering the body to be a single point in space. Now, using just the very basic logic of Newton’s equations, we would only need to consider the object’s mass and its geometry, which we’re using to calculate its COM. That means that we really only need two different types of measurements, mass and distance. Now here’s where the big [Restrictions Apply*] sticker comes in. Spacetime is funky, so the shape of whatever object you have in it will most definitely affect the spacetime around it in very specific ways. I’m assuming there’s a limit to the scale of measurements we can make in regards to the curvature of spacetime, whether it be the Planck length or some other value. So I guess that’s just kind of a very long way of saying: TL;DR: The geometry of an object definitely affects the specific curvature of the spacetime around it, however, I don’t know exactly to what scale it does, and I’m not sure anyone really does. However, in most cases, we have current models that much like Newton’s models fail to fully describe the phenomena behind the curvature of spacetime and the nature of the gravitational force, but serve as a very accurate tool for most measurements significant to us at the moment. Btw I wrote this on mobile so I couldn’t really proofread, I hope I didn’t make any big mistakes. Feel free to ask more questions and I’ll answer to the best of my ability.
12:09, why didn't he think about a theory like Maxwell's field equations which care about the speed of light. Like one mass in the field of another mass.
It’s not space that curves, it’s spacetime. That’s important, otherwise one can’t properly understand what’s going on and why. The real answer, that coincidentally has more to do with how Einstein actually arrives at his theory, is the following: As you pointed out, when you are in free fall, you do not feel any force whatsoever. If you held an accelerometer in your hand while falling through a vacuum, it would read 0 in all directions. Now plot the trajectory in a diagram where x is the time axis and y is the spatial axis along which you fall. Coordinates 0,0 are center of the Earth at the time when you start falling. You will see some trajectory that on small time scales bends like a parabola. Now, what’s Earth‘s trajectory in this situation? Well, the center of the Earth moves exactly along the time axis in a straight line. Now plot the same situation, but from the perspective of the falling object/person. Now *its* trajectory becomes the time-axis, while Earth‘s trajectory is minus the trajectory we saw before. How can that be explained without invoking any forces (which we must not do because neither the falling observer nor the observer at the center of the earth measures any force)? Well, it’s quite simple: in their own reference frame, both objects move along their time axis; so the obvious conclusion is that the trajectory of the other object *is* it’s time axis, viewed from our reference frame. The time axis of the distant object is bent (and empirically we can then find that this is thanks to a lot of mass in between us). Space also curves, but this plays a role mostly in other scenarios, e.g. why light curves near large masses. To explain free fall, you mostly need that masses curve time axes.
🍎 Color charge propagation speed is √1√2√3=√6 times the speed of the propagation speed of electromagnetic waves. 8π/c^4 of the Einstein equation is 8π/√6^4= 8π/36=(1/4)(8π/9)=(2π/9), and E =mc^2→m√6^2=m6 , Rμν-(1/2)gμνR= 8πG Tμν /c^4= (1/4)(8π/9)G Tμν, // gluon // or (1/4)(8/9)GTμν (π=1, c=1), ･･･❶ E =mc^2 ⇒ m√6^2=m6, // E=m1c^2, E=m2c^2, E=m3c^2, E =m6c^2 // I think the mass gap problem of Yang-Mills theory was solved with E = m6 . Speed of EM light √1c, ･･･❷ propagation speed of 2 color charges √2c, ･･･❸ propagation speed of 3 color charges √3c, ･･･❹ propagation speed of quark lepton √6c, ･･･❺ 達磨さんが転んだ！ 発音の数は10。 Daruma-san has fallen ! The landscape of the QCD Lagrange Density, which has been decomposed into Gluon and Quark Lepton, has five expressions. A macro example of a membrane space is the solar system. The sun's surface activity becomes D-BRANE. Prominence is an open string. Closed strings are released to the six planets by corona, the solar wind. Quarks and leptons correspond to planets, satellites, asteroids, dwarf planets, exoplanets, and interstellar materials.
Very nice presentation. I have always been wondering, whether the term "curvature" is really correct or maybe misleading. Because curvature in the naive sense or day to day understanding presupposes a curvature into something. A flat plane is curved into the third dimension. However, according to my understanding, Einstein's equations do not imply that the 4D space time must be curved into a 5th dimension. It's not ruled out. The theory doesn't presuppose this. The main thing, which is happening is that the metric tensor changes. The Ricci tensor and curvature tensor are merely fancy functions of the metric tensor. The Ricci tensor and curvature tensor merely tell us that the changes to the metric tensor are substantial. So the main thing in my mind is that the metric is changing? What does that mean? Well the metric defines the distance between objects, it is the yard stick for measuring distances. I have to think of space-time as some kind of continuous expandable substance in order for this to make sense to me. Space time is like a rubber substance, which is invisible to us. A grid is put onto this compressible and expandable substance. The grid is the metric g, which defines the distance between objects in the substance. Whenever the substance is deformed by some form of energy or mass - i.e. expanded or compressed - the grid changes. But, this is not apparent to us mere mortals living within the substance, because we take the grid to be non expandable and the metric fixed. But, since the yard stick changes, we measure acceleration and motion. However, objects still travel on geodesics in this grid, i.e. on the shortest path between two locations - in the absence of additional forces.
I wish you could derive this in an easy way so we could grasp a better understanding, once we understand the math itself I don't think there's a need for long talks....
Natural light is so much better for videography. The last time I saw Dr. Greene in the other room with a bright table lamp, he looked sick. This makes a big difference.
Oleg Jefimenko had resolved Newtonian paradox of infinite speed of Gravity very simply using Maxwell ideas of EM field and applied them to Gravity. Einstein idea of 4 D times-pace curvature is simply wrong. BTW. Whatever you can do in 4D space-time , you can do in Either 3D space + time , or like in QM by using Hamilton 6D phase space of position-momentum
In the UK 🇬🇧 we call the tornado ride the rotor and Einstein uses this analogy in one of his books for a non mathematical reader like me. In other words on the rotor you are stuck or pushed against the wall as though gravity pulls you to it. When it stops gravity is restored to pulling you down in other words there is equivalence between the two.
