Excellent, excellent video as always. I’m so impressed with the content your channel has been putting up - advanced university-level content pitched in a style reminiscent of the very best secondary school lessons. Maximum of intuition and understanding, with maths brought in only as a means to an end, not an end in itself. More universities need to teach like you! I can’t wait for the videos on Einstein’s Field Equations!
This is a nice introduction and very well done. Mathematically accurate, yet succinct enough to give those who don't know Tensor calculus a very good feel for the essentials. Quite an impressive presentation. If they gave awards for best individual video explanation of physics on youtube, this would surely get it. Maybe you should do a series on GR including an introduction to Tensor Calculus, next.
As someone with a physics background, I’d like to say how much I’m enjoying these videos. All the information is so clear and concise and completely accessible to a wide audience. Please keep them coming
Elliot those lessons have been the most impressive videos i have ever gotton I really recommend you'd make complete course for us(the freaky guys) Have a good one!!!!
Most helpful to see the math presented through this pathway. Your explanations of gravity as not a force are succinct and seem to be better informed than most physicists. I wonder if the breach between Newton and Einstein might be resolved by noting that Newton applies bodies and forces whereas Einstein applies geometry and infers frames of reference. To consolidate the calculations we find that it is not the force of attraction which declines at the square of the distance, but the escape velocity.
Very nice introduction. Thank's for that. I like the style of the video. Presenting the math, but avoiding to get bogged down with tensor calculus. The only problem I have with these presentations is, how to derive Newton's law of gravity from the geodesic equation (under the right assumptions). I would like to see a video of that. This would help connect the application of the geodesic equation to what I already know (Newton's law of gravity)
I will add the Newtonian limit to my list of potential future topics! Newton's law comes from the limit of the extra term \Gamma \dot{x} \dot{x} in the geodesic equation. It becomes the Newtonian gravitational potential, and if you move it to the other side the geodesic equation becomes \ddot{x} = -dU in the appropriate limit.
I just discovered your channel and I loved it. I’m currently studying physics and I believe your videos will come in handy. Also, what software are you using for your note-taking? I found really cool that you can bend those lines and simulate space-time curvature.
I am a senior in high school right now, and I am going to college next fall to study physics. However, this was the only time in my life where I felt that I absolutely didn't know anything about mathematics. My brain wasn't registering any of the equations written down even though I understand multivariable calculus lol; guess knowledge in multivariable calc isn't enough for GR.
Great videos, succinct and clear. 👍 One thing which I personally have found useful is to conceive gravity as being density of metric. This makes gravitational lensing simple refraction through a more dense medium.
Question maybe you can address - "proper time" makes sense as the time seen by a particle. But in a pure field theory, what (if anything) does that mean? If you assume particles are just features of fields (like in QFT), how do they "see" a specific proper time?
3:45 ... a tangential thought .. if we are following least action ... and deviation from the speed of light increases action ... would that not be a prescription for how sub-light speeds of matter through spacetime can be accommodated instead of moving at C itself in the first place? I mean ..why do things move at less than C in the first place?
I believe the answer is that massless particles do not interact with the Higgs Boson field, while massive particles do, which slows their speed down in the spatial sense. You still move at c though just through time, look up a Minkowski diagram to see what I mean, also PBS space time has some great videos on this. Ps. I am not an expert so I might be wrong here, just my best interpretation, I hope this helps though.
3:20 - Comparing mass of earth to moon, can we explain why similarly proportionate stones/boulders (81kg:1kg) on flat surface attract each other (or do they? we don't see in real life)
Wouldn't a massive particle change the spacetime curvature (albeit not by much) and hence the action itself? so that the geodesic equation only really applies exactly to light particles?
We haven't done very well with our relationship with this vertical gradiant of time in space. Our dashboard gets in the way even when we desperately try to ignore it lol For the sake of our 2d maps or graphs the trampoline works but I think it confuses more people than it helps as opposed to if its more of a thought experiment in 3d fluidlike with an apple in water. This visual allows you to understand how we are moving up into spacetime and gravity is the by product felt as those we are falling or being pulled down to earth.
Great video! Just a note - the Christoffel symbols are not invariant when changing coordinate maps, so it's not true that they are 0 in flat spacetime. I know that simplification is necessary, but I think it should never be actually false.
Hi Elliott, when astronomers like the guys in Hawaii tracking stars around the Milky Way centre's black hole, would their computer programs apply Einstein's field equations?
Air resistance creates a drag force on the projectile, similar to friction, from ramming into all the little air molecules. It's often proportional to the speed or speed-squared of the object, depending on the circumstances.
I find it interesting that we only 'feel' the force of gravity when we are stationary on a massive body like Earth but if we are in free fall and without air resistance we wouldn't feel any force at all.
Isn't that because when free falling the acceleration is 0 because your speed is constant but when standing stationary the acceleration is trying to increase. Like when you are in a car. You get pulled back when accelerating. But when at a constant speed, you don't get pulled.
@@BboyKeny Hi Kenny, the gravitational acceleration is always acting on anything in a gravitational field, even when the initial speed is zero. A parachutist about to jump out of a plane has zero vertical speed initially but after jumping the vertical speed increases because of the 9.8 m/s/s gravity acceleration. If there was no wind resistance the jumper would keep increasing their speed whereas in reality they reach about 160 km/hr when air resistance balances the gravitational force.
Space time Since space is length x length x length Space9-time must then be Volume-time. What about other combinations of fundamental units, such as: Mass-length, Current-temperature, Light-Length, and Temperature-mol? How do these fit into the reality of nature? Provided, of course, that I understand space time, which I perpetually fail no matter how many times I read or hear it perpetually parroted on the net. I read the 1905 paper, and apart from the prosaic algebra, I fail to grasp how on earth does one draw a curve thru space time... go figure... Thank you in advance.
he just repeats the textbooks BS but here is a more serious problem: they (scientists) do not have any clue on the methodology of their own subject, or in moral general terms, the Philosophy of Science! At 6:50 he (all textbooks' authors use the expression: the proper time=" the time on a particle's watch as it moves through spacetime"- a lot of shit here: at first physically no one makes an experiment with an individual "particle"! This "particle" is just an idealization of the real physical experiment,....a lot of issues are revealed here with "Twin Paradox"( a thought case!) esp. that this Theory (or Relativity) is a field theory and not about a (rigid)particle or even worse, alive matter!
Which is exactly what he explained geometrically as the shortest path being the Largest in Length!. That is precisely the Twin Paradox (Because the each of the other person thinks there path is of shortest length). so yeah all he did was mention the paradox but from pure geometric considerations.
Why is the curvature of both objects not calculated individually ?You still have a geodesic ,but you are calculating curvature from one point relative to curvature from another point ?.The overall curvature is the same but the geodesic path slightly different ?.
You're asking I think why we ignore the fact that the mass of the particle or planet itself curves the spacetime around it? It's true that it does, but nearby a much more massive object like a star, the effect on the curvature due to the planet is much smaller, and so it's a good approximation to ignore it. It's the same idea as a "test charge" you might have encountered in electromagnetism---we ask how a big, external electromagnetic field we've set up affects a tiny charge, without worrying about the "back reaction" of the charge itself
@@PhysicswithElliot Can a single charge not be described as a wormhole in a wormhole with 360 degree surface rotation.Like a 2 sided surface in 4D(the duality stop itself from calapsing ),similar to Geometric algebra ? 3D is causality of 4D space ?
Einstein never said that space-time is curved. This is only a mathematical model that helps us understand it, and gravity is always a force. Motion in a curve is an acceleration due to a force.
"a particle takes a path that maximizes its proper time". can this explain why an apple falls to the ground? when an apple is released 1 m above the ground, as it falls, it's clock slows down as it gets closer to the ground, where gravity is stronger. If the apple moved up 1 m instead, its clock would run faster. It seems that the apple's proper time would be greater if if moved up 1 m rather than moved down 1 m.
Relativity is rotten to the core and anything based on it is affected, including General Relativity and Quantum field theory. Here is simple proof Relativity is just an optical illusion: According to Relativity, two inertial moving observers will see each others space contract and time dilate. This is a complete contradiction and a physical impossibility if the effects are real. Objects and the passage of time can not be both small and large at the same time for the same observer. The only possible explanation is that the observed effects are an optical illusion. Any theory based on Special Relativity, such as General Relativity, must also have the same problem. Again the argument is very simple and it is the argument Einstein used to derive Relativity, and no acceleration is used in the argument. A train traveling at constant velocity relative an observer on a platform. According to Relativity, the observer will see the train contracted, whereas an observer on the train will see it not contracted. So the train is both contracted and not contracted depending on the observer. This is a complete contradiction and can not be true if length is real. The same argument applies to time. Both observers will disagree on the passage of time. If time is real, it can not be both dilated and not dilated. If space and time are observed to be both large and small simultaneously for one frame, such as the train, then it must be an optical illusion. For more information see my paper and a RUclips presentation of the paper: *RUclips presentation of above argument: ruclips.net/video/sePdJ7vSQvQ/видео.html *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145
Vedic math📐📊📚 know about it millions of year's ago in India🇮🇳 very easily🎉🎉so the karma gati ka siddhant become👌 so much accepted through the millions of birth and rebirth cycle🔃 for every partical of universe🌌🎉🎉🎉
Excellent, excellent video as always. I’m so impressed with the content your channel has been putting up - advanced university-level content pitched in a style reminiscent of the very best secondary school lessons. Maximum of intuition and understanding, with maths brought in only as a means to an end, not an end in itself. More universities need to teach like you! I can’t wait for the videos on Einstein’s Field Equations!
This is a nice introduction and very well done. Mathematically accurate, yet succinct enough to give those who don't know Tensor calculus a very good feel for the essentials. Quite an impressive presentation.
If they gave awards for best individual video explanation of physics on youtube, this would surely get it.
Maybe you should do a series on GR including an introduction to Tensor Calculus, next.
Thanks Joe!
love your presentations. outstanding Eliot. Among the best of the best way of explaining physics on the Internet and I've seen many. thanks
As someone with a physics background, I’d like to say how much I’m enjoying these videos. All the information is so clear and concise and completely accessible to a wide audience. Please keep them coming
Great introduction! I’m familiar enough with GR to fill in the details! Thanks for posting!
your channel is so underrated, I love your videos!
Thanks Benjamin!
Elliot those lessons have been the most impressive videos i have ever gotton
I really recommend you'd make complete course for us(the freaky guys)
Have a good one!!!!
Elliott, your videos are great. Please keep producing your content!
Most helpful to see the math presented through this pathway. Your explanations of gravity as not a force are succinct and seem to be better informed than most physicists. I wonder if the breach between Newton and Einstein might be resolved by noting that Newton applies bodies and forces whereas Einstein applies geometry and infers frames of reference. To consolidate the calculations we find that it is not the force of attraction which declines at the square of the distance, but the escape velocity.
This channel is awesome! Keep up the great work!
Thank you Stewart!
Very nice introduction. Thank's for that. I like the style of the video. Presenting the math, but avoiding to get bogged down with tensor calculus. The only problem I have with these presentations is, how to derive Newton's law of gravity from the geodesic equation (under the right assumptions). I would like to see a video of that. This would help connect the application of the geodesic equation to what I already know (Newton's law of gravity)
I will add the Newtonian limit to my list of potential future topics! Newton's law comes from the limit of the extra term \Gamma \dot{x} \dot{x} in the geodesic equation. It becomes the Newtonian gravitational potential, and if you move it to the other side the geodesic equation becomes \ddot{x} = -dU in the appropriate limit.
@@PhysicswithElliot which is now demonstrated in your latest video!
Man, I don’t even study physics but this is pretty cool. Keep up the vids
I just discovered your channel and I loved it. I’m currently studying physics and I believe your videos will come in handy. Also, what software are you using for your note-taking? I found really cool that you can bend those lines and simulate space-time curvature.
Thanks Esaú! Procreate
Very very good introduction
Thanks Christopher!
Can lambda be a space parameter for example y?
I am a senior in high school right now, and I am going to college next fall to study physics. However, this was the only time in my life where I felt that I absolutely didn't know anything about mathematics. My brain wasn't registering any of the equations written down even though I understand multivariable calculus lol; guess knowledge in multivariable calc isn't enough for GR.
Focus on the ideas for now, the math will come with time!
Great videos, succinct and clear. 👍
One thing which I personally have found useful is to conceive gravity as being density of metric. This makes gravitational lensing simple refraction through a more dense medium.
Question maybe you can address - "proper time" makes sense as the time seen by a particle. But in a pure field theory, what (if anything) does that mean? If you assume particles are just features of fields (like in QFT), how do they "see" a specific proper time?
3:45 ... a tangential thought .. if we are following least action ... and deviation from the speed of light increases action ... would that not be a prescription for how sub-light speeds of matter through spacetime can be accommodated instead of moving at C itself in the first place? I mean ..why do things move at less than C in the first place?
I believe the answer is that massless particles do not interact with the Higgs Boson field, while massive particles do, which slows their speed down in the spatial sense. You still move at c though just through time, look up a Minkowski diagram to see what I mean, also PBS space time has some great videos on this.
Ps. I am not an expert so I might be wrong here, just my best interpretation, I hope this helps though.
3:20 - Comparing mass of earth to moon, can we explain why similarly proportionate stones/boulders (81kg:1kg) on flat surface attract each other (or do they? we don't see in real life)
Wouldn't a massive particle change the spacetime curvature (albeit not by much) and hence the action itself? so that the geodesic equation only really applies exactly to light particles?
Great video!
awesome videos..
We haven't done very well with our relationship with this vertical gradiant of time in space. Our dashboard gets in the way even when we desperately try to ignore it lol
For the sake of our 2d maps or graphs the trampoline works but I think it confuses more people than it helps as opposed to if its more of a thought experiment in 3d fluidlike with an apple in water. This visual allows you to understand how we are moving up into spacetime and gravity is the by product felt as those we are falling or being pulled down to earth.
Great video! Just a note - the Christoffel symbols are not invariant when changing coordinate maps, so it's not true that they are 0 in flat spacetime. I know that simplification is necessary, but I think it should never be actually false.
The lambda is just a parameter to parametrize the world line?
Yep!
Did Einstein use the least action principle to derive his equations? Do we know how he derived it?
thanks!
can you please make a whole playlist on general relativity from basics
Hi Elliott, when astronomers like the guys in Hawaii tracking stars around the Milky Way centre's black hole, would their computer programs apply Einstein's field equations?
When a block goes in free gravity including air resistance then resistance act upwards can u know the reason for this please?
Air resistance creates a drag force on the projectile, similar to friction, from ramming into all the little air molecules. It's often proportional to the speed or speed-squared of the object, depending on the circumstances.
If these equations are for particles, what about starts and planets?
Any massive body acts as if all its mass is concentrated at its center, like a particle.
Did Einstein use Hilbert spaces for GR?
I really appreciate for your video and God bless.
I find it interesting that we only 'feel' the force of gravity when we are stationary on a massive body like Earth but if we are in free fall and without air resistance we wouldn't feel any force at all.
Isn't that because when free falling the acceleration is 0 because your speed is constant but when standing stationary the acceleration is trying to increase.
Like when you are in a car. You get pulled back when accelerating. But when at a constant speed, you don't get pulled.
@@BboyKeny Hi Kenny, the gravitational acceleration is always acting on anything in a gravitational field, even when the initial speed is zero. A parachutist about to jump out of a plane has zero vertical speed initially but after jumping the vertical speed increases because of the 9.8 m/s/s gravity acceleration. If there was no wind resistance the jumper would keep increasing their speed whereas in reality they reach about 160 km/hr when air resistance balances the gravitational force.
Space time
Since space is length x length x length Space9-time must then be Volume-time. What about other combinations of fundamental units, such as: Mass-length, Current-temperature, Light-Length, and Temperature-mol? How do these fit into the reality of nature? Provided, of course, that I understand space time, which I perpetually fail no matter how many times I read or hear it perpetually parroted on the net. I read the 1905 paper, and apart from the prosaic algebra, I fail to grasp how on earth does one draw a curve thru space time... go figure... Thank you in advance.
Twin paradox is about both of them thinking that the other is different age, not that one sees the other differently
he just repeats the textbooks BS but here is a more serious problem: they (scientists) do not have any clue on the methodology of their own subject, or in moral general terms, the Philosophy of Science! At 6:50 he (all textbooks' authors use the expression: the proper time=" the time on a particle's watch as it moves through spacetime"- a lot of shit here: at first physically no one makes an experiment with an individual "particle"! This "particle" is just an idealization of the real physical experiment,....a lot of issues are revealed here with "Twin Paradox"( a thought case!) esp. that this Theory (or Relativity) is a field theory and not about a (rigid)particle or even worse, alive matter!
Which is exactly what he explained geometrically as the shortest path being the Largest in Length!. That is precisely the Twin Paradox (Because the each of the other person thinks there path is of shortest length).
so yeah all he did was mention the paradox but from pure geometric considerations.
@@krzysztofciuba271 Literally shows your Scientific Illiteracy.
@@krzysztofciuba271Hi. Interesting point. Please repost removing "shit" references, and I'll reread and take you more seriously. Thanks.
Don't play "serious" Mr. Kid-Moron: U are blind but U play "I am not blind". Go back to ...your comiks @@tim40gabby25
Why is the curvature of both objects not calculated individually ?You still have a geodesic ,but you are calculating curvature from one point relative to curvature from another point ?.The overall curvature is the same but the geodesic path slightly different ?.
You're asking I think why we ignore the fact that the mass of the particle or planet itself curves the spacetime around it? It's true that it does, but nearby a much more massive object like a star, the effect on the curvature due to the planet is much smaller, and so it's a good approximation to ignore it. It's the same idea as a "test charge" you might have encountered in electromagnetism---we ask how a big, external electromagnetic field we've set up affects a tiny charge, without worrying about the "back reaction" of the charge itself
@@PhysicswithElliot Can a single charge not be described as a wormhole in a wormhole with 360 degree surface rotation.Like a 2 sided surface in 4D(the duality stop itself from calapsing ),similar to Geometric algebra ? 3D is causality of 4D space ?
@@BrynSCat You are now writing Bullocks
Einstein never said that space-time is curved. This is only a mathematical model that helps us understand it, and gravity is always a force. Motion in a curve is an acceleration due to a force.
Kudos
"a particle takes a path that maximizes its proper time". can this explain why an apple falls to the ground? when an apple is released 1 m above the ground, as it falls, it's clock slows down as it gets closer to the ground, where gravity is stronger. If the apple moved up 1 m instead, its clock would run faster. It seems that the apple's proper time would be greater if if moved up 1 m rather than moved down 1 m.
Minkowski… the W sounds like an English V, so min-KOV-ski :)
Whoosh...the sound of intelligence going over my head.
If you add the arabic language translation I will be so gratefull for you
Correction
Relativity is rotten to the core and anything based on it is affected, including General Relativity and Quantum field theory. Here is simple proof Relativity is just an optical illusion:
According to Relativity, two inertial moving observers will see each others space contract and time dilate. This is a complete contradiction and a physical impossibility if the effects are real. Objects and the passage of time can not be both small and large at the same time for the same observer. The only possible explanation is that the observed effects are an optical illusion. Any theory based on Special Relativity, such as General Relativity, must also have the same problem.
Again the argument is very simple and it is the argument Einstein used to derive Relativity, and no acceleration is used in the argument. A train traveling at constant velocity relative an observer on a platform. According to Relativity, the observer will see the train contracted, whereas an observer on the train will see it not contracted. So the train is both contracted and not contracted depending on the observer. This is a complete contradiction and can not be true if length is real. The same argument applies to time. Both observers will disagree on the passage of time. If time is real, it can not be both dilated and not dilated. If space and time are observed to be both large and small simultaneously for one frame, such as the train, then it must be an optical illusion. For more information see my paper and a RUclips presentation of the paper:
*RUclips presentation of above argument: ruclips.net/video/sePdJ7vSQvQ/видео.html
*Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145
Vedic math📐📊📚 know about it millions of year's ago in India🇮🇳 very easily🎉🎉so the karma gati ka siddhant become👌 so much accepted through the millions of birth and rebirth cycle🔃 for every partical of universe🌌🎉🎉🎉