Relativity 107a: General Relativity Basics - Equivalence Principle and Proper Acceleration

[@eigenchris]

I skipped a couple videos in Relativity 106 for the tensor review for the time being. I'll come back to them later.

[@nickst2797]

You did 106b private? Is this what you mean?

[@eigenchris]

@@nickst2797 No, it's not fully recorded yet. I'll release it before we talk about the tensors needed for GR.

[@nickst2797]

@@eigenchris Thank you. You are light in the dark alleys of Gr. You are my hope of learning it.

[@Sharikkhursheed]

bro please upload next videos ASAP.. and let's finsh this topic now

[@atikfaysal8189]

we want more joke video...

[@Cosmalano]

The long awaited GR ❤️

[@giulialosi4805]

I don't know if it is because I am an "old fashioned" person who studied on plain paper book, but this bare and simple video, without cool effects and stunning graphics (nor music), is amazingly clear. After the first 4 minutes I was able to unscrambled other videos I was trying to puzzle out for months... 👍🏻👍🏻

[@vitrums]

It's funny how I've been making attempts to understand these concept in past using other sources, but eventually kept returning to square zero for a better explanation time and time again. Learning it by watching your videos feels like someone from Matrix is uploading Kung-Fu into my brain directly ^^

[@RichardLibby]

Reading "Gravitation" by Misner, Thorne and Wheeler was a bit like missing the forest for the trees, but with this sequence of videos the book is much more accessible. Thank you!

[@eigenchris]

Yeah, I heard someone say that book is more of a "reference book" you go to with specific questions, not a "textbook" yo read front-to-back hoping to learn GR, and I agree. Glad my videos helped.

[@slaxer570]

10.42 onward was really eye opening, thank you.

[@cesarjom]

Awesome progression of the topics needed to understand SR and GR. Succinct, complete and masterfully presented.

[@ProfeARios]

This channel is a valuable jewel! Keep up with the good work!! Blessings!!!!

[@wargreymon2024]

most detailed and accurate on KZbin, easily the best video to learn from 👍

[@canyadigit6274]

LETS GOOOO. When I saw the subscription notification I was hoping it was you and it was! ❤️

[@zemm9003]

We don't need to modify Newton's 1st if we write it as: in an inertial frame, an object with no external forces acting on it travels in a geodesic line with a velocity of constant absolute value and maintaining orientation, which means exactly the same thing but can be immediately mathematically generalized to GR if we take the Einstein Equivalence Principle to be true.

[@Astro-X]

I will definitely be leaving a tip for this channel after I do my exam in 2 days... You are awesome

[@fernandogarciacortez4911]

Awesome video as always! Very very very well made. I'm almost over the tensor Calculus playlist which has been an OUTSTANDING aid along with my GR book and my diff. geometry book. I you happen to had something like Patreon, I would without a doubt support you. Thanks a lot.

[@eigenchris]

I have a tip jar here. Thanks! ko-fi.com/eigenchris

[@biblebot3947]

0:46 Gravity: “I’m not like the other forces.”

[@biblebot3947]

@Bullen König yeah man. I can’t believe how being a literal nazi isn’t appreciated nowadays. I wish we could go back to the good old days.

[@cesarjom]

Gravity: "I'm just an tangible consequence of spacetime curvature." 🌌

[@travel_logs]

12:35 proper acceleration of the ball wrt the outer frame is greater than zero in figures 1, 2, 3 (rope, magnetic field, rocket propulsion). Proper acceleration if the ball wrt the outer frame (accelerometer) is zero during free fall on earth (towards the centre of the earth).

[@tcb3901]

Excited for 107!

[@wubyegebre6070]

Thank you. I have followed your videos and my curiosity is better satisfied.

[@rgudduu]

Excellent explanation. For someone who understands this concept but needs more clarity.

[@leonardp8517]

I'm so happy you uploaded the first GR video! One question though: At 7:23, you show the light beam "falling" in a parabola and it goes beyond a 45 degree angle toward the right. Wouldn't the box have to go faster than light for this to happen?

[@eigenchris]

The 45-degree angle rule is for spacetime diagrams. Light's path is purely space-space (xy) inside that box diagram. Although, either way, the image is just supposed to give you an idea of what is going on. You don't need to take it too literally.

[@luudest]

Is there an electromagnetic equivalent to the equivalent principle? Is there „free fall“ in electromagnetic fields?

[@fitness60plus52]

must say: the best video on GR basics I've seen. and I saw many. 👌👍

[@BLEKADO]

Intentaré llegar hasta el último de los videos. Son excelentes.

[@En_theo]

@22:40 When you say "Non-inertial motion due to force is locally indistinguishably from standing on a gravitational mass". But is it not different to be pushed up under your feet compared to being attracted towards the ground ? The pressuring effect will be different and there will be differences for sure.

[@eigenchris]

What would the differences be?

[@En_theo]

@@eigenchris Let's apply the twin paradox rules to a man jumping inside the Box. It is always the accelerating man who is aging slower. In the accelerated box : you have 3 phases. 1) The man jumps and is accelerating (and thus his time is slowing down relative to the ground of the box). 2) He reaches his maximum speed and is not accelerating anymore. His time starts ticking normally (he does not feel any acceleration). BUT the ground of the box is accelerating and thus its time is going slower. 3) He "falls" (the bottom of the box is catching up with his feet). The man starts accelerating again, pushed by the box. In a gravity field : 1) same situation as the 1) of the accelerated box 2) same too except that the ground is not accelerating and its time is not slowed down. 3) now the man is accelerating towards the ground, and during all his fall he sees his time slowing down. In the gravity field, the man should be a little younger than in the box. Unless you tell me that, while he is in the air, his time is going faster because he is slightly farther from the center of the earth (and thus submitted to a smaller gravity pull). Even if that's the explanation and that the math showed the same age in both cases, we see that it would be the same result but for different reasons. How can we have different explanations for the same phenomenon ?

[@eigenchris]

I believe the rule is that "inertial worldlines have the longest proper time". If you are on the floor of a box, being pulled down, either by a rocket force or due to standing on a gravitational mass, you are in a non-inertial frame. When you "jump", you are suddenly in an inertial frame (either freely floating in your rocket with no forces acting on you, ore freely-falling in the gravitational field). Going by the rule, the jumping observer will always experience the longest proper time, whereas someone who remains on the floor of the box will have a shorter proper time since their path is non-inertial.

[@En_theo]

@@eigenchris Thanks for the answer, but did you consider the slowing down of time due to the acceleration of the jumping man ? Sure, after he accelerated, his clock ticks again "normally". But during the acceleration, he is submitted to time dilation. My logic is that with the accelerating box, the kinetic energy is transmitted from the box to the man inside. With gravity, the energy comes from potential energy stored in the man falling and hitting the ground. Since we have at least that difference, there should be a specific case where we could tell who/what communicated his energy to who/what. Since an accelerating object does create an asymmetry in time dilation (as in the twin paradox), my intuition is that (if a specialist was really motivated to explore all the possible cases), we could find a loophole in Einstein reasoning. There is an undeniable difference here, the direction of transmission of kinetic energy. Therefore, there must be a difference that we could exploit.

[@eigenchris]

Back to your first message, in the #2 step for the planet/gravity situation, I think the ground is experiencing proper acceleration. If the ground was in free-fall, then it would fall towards the center of the earth. But the ground doesn't do that... instead it is being pushed "up", away from a downward geodesic. So the ground should be considered to have proper acceleration in GR, just like the floor of an accelerating rocket ship in deep space. Because of this, I think the ground and the rocket ship floor should be treated as equivalent. They are both forcing people away from a geodesic. I'm not sure the concept of "gravitational potential energy" has any sensible meaning in general relativity. Potential energy is usually associated with a force, and since gravity is not considered a force in GR, I don't think it has an associated potential energy.

[@nilakshabarman4560]

There is one paradox of the equivalence principle(EEP) tht has caught my attention 4 quite some time.....if a charge standing on the surface of the earth is equivalent to it being accelerated upwards in deep space, why is the charge on the surface of the earth not emitting electromagnetic radiation.....or m I missing something here regarding the observer????your response would b greatly appreciated....thank you!!!

[@eigenchris]

Sorry for the late response, I missed this comment. I admit I don't know the answer and you may have to google this further to learn more. My guess is that, since we (the observers) are in the same frame as the charged particles on the surface of the earth, we do not observer any radiation. The existence of an electric field is "relativity". An electric field might exist in one inertial frame, but will not exist in another inertial frame. The same might be true when observing radiation in accelerated frames.

[@Chicken_Little_Syndrome]

Einstein's equivalence is not fundamental. His work is nonsense.

[@SambarAbbayi]

I have watched all your videos. Big fan. Can't wait for more GR.

[@-_Nuke_-]

I FINALLY UNDERSTOOD THAT THE DIFFERENCE BETWEEN SPECIAL AND GENERAL RELATIVITY, ISN'T THAT SPECIAL RELATIVITY CAN'T EXPLAIN GRAVITY, BUT THE FACT THAT IT CAN'T EXPLAIN TIDAL FORCES. So many videos online "explaining" Gravity, and yest nobody ever mentioned that. WOW... (And I'm obviously angry because of that.)

[@redbel2624]

Finally completed all of your videos

[@Mikey-mike]

Great lecture ! "Gravity is not a Force." This fact is why all attempts to find Quantum Gravity are mere folly. Also, concerning the folly of Quantum Gravity, have you ever wondered how one would ever detect or measure a Quantum Gravity Graviton ?

[@alwaysdisputin9930]

Gravity is a force. A wizard curved spacetime using magic Forces & then objects move together like 2 people heading N move closer as they approach the N pole.

[@jorriffhdhtrsegg]

Still looks more like a force than the weak nuclear force looks.. but yes i think we have to see how it arises from energy and the nature of spacetime, which we don't actually describe whatever that field REALLY is. Or even do we have a description of mass, i mean fair enough to say 'such a coincidence that inertia and gravity from same property and relativistic effects from both speed and mass' but no one finds a like beyond the energy-momentum-tensor just 'does stuff' to a 4d grid used to model something. Depends whether by gravity you mean "mass is drawn to mass" or "mass curves 4d spacetime" because often the latter is considered kind of forcey by those who know GR Intuitively though it does seem like an emergent property that needs some adjustment of an axiom rather than a new boson in the standard model to me.

[@-_Nuke_-]

Quantum Gravity might explain why? mass curves space, so hold your horses!

[@SpontaneityJD]

16:15 Does this mean that accelerometers can "prove" that the Earth is actually accelerating upwards?

[@eigenchris]

The proper acceleration of object's on the earth's surface is directed "upwards". This doesn't mean the earth's surface is actually moving outward compared to the core, though.

[@user-dialectic-scietist1]

4:34 Your suggestion speaks about similarities between mass and charges. Is this correct?

[@jorriffhdhtrsegg]

Well, they are forces so produce an acceleration....a kinetic movement. The rope does it with charge anyway, its what holds it together btw, now the thing pulling the rope has charge maybe too..

[@user-dialectic-scietist1]

@@jorriffhdhtrsegg There are not forces. Force is only a mathematical and geometrical human's invention for describing material interactions!

[@luudest]

Do you know what lead Einstein to start describing Graviton by curved spacetime? How important were tidal forces im this process?

[@eigenchris]

I'm honestly not sure what the exact historical sequence of events is that lead Einstein to the concept of curved spacetime. This wikipedia article might be worth reading: en.wikipedia.org/wiki/History_of_general_relativity It makes reference to these papers: 1907 paper on acceleration in special relativity: einsteinpapers.press.princeton.edu/vol2-trans/266 1911 paper equivalence principle (downward gravity = upward acceleration): einsteinpapers.press.princeton.edu/vol3-trans/393 It also mentions that Einstein considered the "Ehrenfest Paradox", which involves measuring lengths in a rotating reference frame, and how this caused him to believe spacetime would be curved. Although I think this is an incorrect conclusion, as spacetime is still flat in a rotating reference frame if gravity is ignored. But he eventually ended up asking his friend Marcel Grossman for help with curved geometry for the purposes of generalizing relativity to include gravity.

[@luudest]

@@eigenchris Found this interesting summary: “The attempt to include gravitation in the special theory had to be abandoned. Prof. Einstein came to the conclusion that the key to the real understanding of inertia and gravitation was the experimental result that all bodies in a gravitational field were subject to the same acceleration. From 1908 until 1911 he endeavoured to apply this, but a dilemma arose from which he did not escape until 1912, when he conjectured that the space-time continuum had a Riemann metric. The development of this hypothesis by the aid of the absolute differential calculus of Ricci and Levi-Civita kept Einstein and Grossmann busy from 1912 until 1914. They found the correct gravitational equations, but failed to recognise their physical validity, and thus wasted two years of hard work. Finally Einstein “returned penitentially to the Riemann curvature”. Source: www.nature.com/articles/132021d0 I just love the stories and history of all the theories of physics.

[@luudest]

@@eigenchris PS. Thank you very much for all immediate replies on my questions. Very much appreciated.

[@DanSternofBeyer]

10:08 I'm a little confused how Proper Acceleration (alpha) can be an invariant quantity. I guess I assumed that the curvature of spacetime, and/or the relativity of simultaneity, would change what different observers see, and such a change would also effect apparent acceleration. Clearly I've missed something somewhere. Can someone link me a lecture or paper that goes a bit more in depth about why Alpha is invariant in all reference frames?

[@eigenchris]

In relativity, the things that observers disagree on are the COMPONENTS of vectors (or tensors, more generally). So people will disagree on the x-component of your 4-momentum, or they will disagree on the t-component of your 4-momentum, or disagree on the z-component of your 4-acceleration. But they will not disagree on the LENGTH of 4-vectors. For example, everyone in the universe will agree the length of your 4-velocity vector is c (the speed of light). Everyone in the universe will agree the length of your 4-momentum vector is m*c where "m" is your rest mass. And everyone in the universe will agree the length of your 4-acceleration vector is alpha, your proper acceleration α. "c", "m*c" and "α" are all tensors because everyone agrees on them. As for a source, if your trust wikipedia you can see this article: en.wikipedia.org/wiki/Proper_acceleration "In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant."

[@Onegod40-v4h]

Here we are 😁♥️♥️

[@russellstephan6844]

Of course, it's rather easy to break the Equivalence Principle. Since in a gravitational field, all objects are accelerating towards a central point. Objects in freefall will have an apparent attraction to each other due to their convergent freefall paths. Hence the need for the nebulous and fudge-factor "localized" footnote.

[@dorothyyang8590]

Thank you very much! I'can't wait to learn more about GR!

[@amulyasrivastava2985]

When you were explaining tidal force, you shown the bulge in water body opposite to the moon. The region opposite to the moon is Day region. So , we can have high tide during the day time?

[@eigenchris]

There are 2 high tides and 2 low tides every 24 hours. You can look up time lapse videos of the tide in the Bay of Fundy in Canada to see this happen. Also, it's possible to see the moon during the day, depending on its position. It's just harder.

[@jaydenwilson9522]

3:40 .... if true. Then why does F=mg??? shouldn't F=g or F=M ??? Why do we still refer to Newtons principles as "Laws"

[@samuelmcdonagh1590]

Hey Chris, it's easy to imagine that an object in a non-uniform field would experience tidal force-related distortion. So are tidal force therefore built into electromagnetism on a simpler level?

[@marcomuscogiuri1243]

Hello Chris, I am failing to grasp exactly why we are forced to introduce curvature to describe gravity. I know that it works and that it is consistent. But I am not catching strongly what makes it imnpossible to describe gravity in flat spacetime. In other words, why can we not describe it in flat Minkowsky spacetime using some kind of vector/tensor field? This field could produce worldlines for massive particles, would produce hyperbolas and other lines. For instance an object falling in the field generated by a mass that is moving in an inertial frame would be described by a hyperbola. What makes it incoherent? Where in this picture does this inconsistency emerge? Do you have an easy way to picture this in the spacetime diagram or to show its mathematics? You say tidal forces imply curvature, still I cannot picture why we cannnot treat them in SR, as tidal forces are even present and consistent in Newotnian Gravity. Won't the different hyperbolas describe tidal forces correctly? What am I missing? Is the line of reasoning as simple as this? : if you are subject to gravity hence in free fall, you measure zero proper acceleration so you must be on a straight line if you are in flat space, but sooner or later you will come accross another people's worldline in a non uniform way. Therefore either you are not both on straight lines or your space is to be curved. Still I am not convinced. I am missing the inconsistency as to why gravity as a force cannot be treated in some way in SR.

[@eigenchris]

I think your 2nd last paragraph is a good summary of how I view things. Two inertial people in flat spacetime can have worldlines "pointed toward each other", but this means the distance between them should decrease linearly overtime if they are in flat spacetime. With gravity, we don't see a linear decrease in distance overtime, so curvature of spacetime seems like a good explanation. The Riemann and Ricci tensors I talk about in video 107c describe how two inertial lines can come together in curved space while IGNORING linear effects that are due to the initial angles of the two worldlines. I haven't explored any alternatives to GR so my ability to answer this question might be limited. But as I said in the video, the "standard forces" that we're used to in Newtonian mechanics all result in an accelerometer reading that's non-zero. Gravity is "special" because it leaves an accelerometer reading zero. If we placed accelerometers at top, bottom, and sides of a ball experiencing tidal effects, they would all measure zero. If tidal effects were caused by a standard "force" vector that we're used to seeing in the cases of ropes, rockets, and E&M forces, then these accelerometers would read non-zero values. So "force vectors" are not sufficient to explain tidal effects. There's also no reference frame in SR that can explain tidal effects. We need another way to explain why the distance between objects shrinks/expands in the presence of mass. I guess I don't have a way to prove curvature is the only way to explain gravitational effects, but we know that curvature works and that forces/reference frame changes fail.

[@charlievictor6552]

TC≈ 18:15 start. “In deep space these balls would float-“ Are you certain? It seems to me that they will interact gravitationally with each other and come together?

[@imaginingPhysics]

Somehow I have always felt that an accelerometer relies a lot on the fact that "gravitational charge has always the same sign". Then its sort of trivial that gravity acts uniformly on every particle of the accelerometer equally, and the springs will not register anything. If I made an accelerometer with a uniform electric charge, I could accelerate it with an electric field without the strings registering it. Right? It was assumed in the video that the ball should be neutral, but its not "neutral gravitationally" , so why can we assume it to be neutral electrically? I do not mean to critize the equivalence principle. I am just wondering about this detail. Thanks.

[@eigenchris]

Your 2nd paragraph isn't quite right. I tried to address this at 4:30. The acceleration on electrically charged particles due to electric fields depends on both their charge and their mass. So different accelerometers with different central masses and different charges would each behave slightly differently in the same situation. For gravity, the acceleration of massive (or massless) particles is identical and doesn't depend on mass at all. So different accelerometers with different central masses would all behave the same in the same situation. The idea behind GR is that nothing in the universe is "gravitationally neutral". Everything in the universe feels gravity and it cannot be avoided.

[@imaginingPhysics]

I meant that the whole accelerometer with its springs, balls, and walls have a uniform charge-mass ratio. Then yes the accelerometer as a whole has a positive or negative charge and its reaction to EM field will depend upon the sign of the charge. But the springs will not compress, wil they? Since each part will accelerate in unison. Right? I guess my point is that you can in principle accelerate an accelerometer (or a human, or a space ship) without itself "feeling it". Okay this may not be the deepest insight, but I like to keep it in mind. I like this channel alot. A suitable combination of details and intuition. And the pace is fine.

[@eigenchris]

@@imaginingPhysics In a uniform electric field, that would be true. But you could still detect the existence of the electric field by using different accelerometers with different charge/mass ratios. When it comes to gravity, it's impossible to detect a "local" gravitational field (where "local" refers to being in the tangent plane of the spacetime manifold). The effects of gravitational fields are only visible when you do some kind of integral or comparison between to different spacetime points. Any two accelerometers with any masses at the same place in spacetime will because the exact same way. So locally, gravity is not detectable. But an electric field is locally detectable.

[@imaginingPhysics]

Yes, agreed. The detection of the source of acceleration, other than gravity, would be possible.

[@fratkaymak1271]

First of all, thank you very much for the videos. I will ask you a question about the principle of equivalence. The starting point of Gr is this principle; In other words, the formation of gravity in the world argues that the world is due to the fact that the world travels with fixed acceleration at a curved space time. For that reason, we feel like there is gravity because of this acceleration like an elevator. So this attraction is felt on the surface of the orbit in the direction of the orbit, but in the opposite direction on the other surface, there is an acceleration towards space, which is not in the world direction. How do you explain this? In other words, this gravity should be felt in the direction of going. is not it?

[@lourencoentrudo]

Hell yeah!!! GR has arrived

[@tomgraupner171]

Thank you so much for these videos!!! I saw that part "107f" is now online - YEAH! Please allow me one question to this part 107a. At 8:05 you explain the accelerometer with the sample of a car. A car - standing on the earth's surface is not an inertial system, right? "It's" accelerometer would already show a 9.81m/s**2 downwards. And pushing the gas padal would just add a second accelation in a second direction. A person - watching the car from the outside - is also not in an inertial system. Thus, a car is not the best way to explain "proper acceleration". Wouldn't it be better to show the accelerometer in "deep space" with an astronaut inside a rocket being watched by a second one outside? As a newby to this, I maybe completely wrong - but then I could need a hint to get a better understanding. Thanks again for the series. Have a great time and take care!

[@pavolgalik499]

All experiments show: mi = mg? However, this is not true when we are standing on the surface of the globe and the ball has the weight of the globe. The local acceleration in the case of an accelerating spacecraft is different from the local gravitational acceleration with which the ball and the globe fall on each other.

[@MasterHigure]

13:50 I remember the Heraeus Winter School lecturer pointing out that Newton was no fool. Why make a first law that is just a special case of the second law? He argued that no, the first law is meant to DEFINE what "straight line at constant velocity" means. It is any path that an object under the influence of no forces will travel. Then the second law relates deviations from this newly defined type of paths to the forces that act. This way, you don't really need a new formulation of the first law for general relativity. We will just have to make sure that we have a metric on our spacetime such that our geodesics correspond to the "straight lines at constant speed" that Newton's first law defines (not counting gravity as a force). But that correspondence will be a mathematical convenience, not a matter of the laws we base our entire model on.

[@eigenchris]

Yeah, I've seen some people claim that the 1st law is a special case of the 2nd law, but Newton was just trying to make it clear that objects don't naturally come to rest, as Aristotle believed. I've seen others claim the 1st law gives the definition of an inertial frame, as you say, and the 2nd law keeps track of the deviations. I haven't looked at the history enough to know. Either way, I'm hoping the way I phrased it is acceptable.

[@MasterHigure]

@@eigenchris I'm not really disagreeing with your presentation. It's just not my personal preference among several viable options.

[@salvatoreventre8193]

Best video ever.

[@ZingZang]

Just adding my voice to the opposition of ‘no force in a gravitational field’ Also adding that I have enjoyed your series way more than I have ever experienced an offering of GR, so I’m not just objecting for the sake of it. At 15:53 you concede that ‘molecular forces force the object(apple) upward’. How is this different to the application of any other force? It always comes down to the molecular forces and it’s always the electrons that keep you from walking through a wall or falling through your chair right now. Can we agree that you just offer this stance so you can offer geodesic paths as ‘an alternative viewpoint’ to conventional forces? If so, then we have no further argument. However, mainstream science sells this now as ‘the only correct viewpoint because there is no force’ and I think this has caused some unnecessary conflicts. Accelerating a box in your car is very different to accelerating the box in gravity. The ball is not accelerated by the car; the ball is accelerated by the spring, which is accelerated by the box. The closest analogy to falling in gravity I can make is that the box in your car must be tied to the seat, and so must the ball. Result is the ball ‘doesn’t move relative to the box’ but this is silly because we know why it doesn’t move. The reason gravity is not detected by an accelerometer (yes, you do accede to that), it that gravity works on every item that has mass in the object. Every atom, including neutrons, protons and electrons are subjected to gravity simultaneously. This is why the ball or spring won’t move relative to the box, because their atoms are all attracted ‘equally’ in a small region of spacetime. In summary, the box on the surface in a gravitational field is exactly like the box in an accelerating car. A ‘falling’ box cannot be compared to either of these. Here’s a ‘thought experiment’. Hang a rope with the accelerometer attached from the ISS to close above the earth surface. Adjust the velocity of ISS so it doesn’t crash to earth from the box and rope’s weight. *Cough .. ignore air friction. Inside the box the ball is pulled down and the spring compressed by gravity, just as when it was resting on the surface. Yet the box is not pushed up ‘by molecular forces’, it is pulled up by the end of a floating rope, by a force on the rope, for which force you also had to adjust ISS speed else the 'weight' of the box would make it crash to earth. From your viewpoint the box is prevented from falling into its geodesic. From my point of view curved space causes a directional force on all mass (pushing/pulling it toward earth), and the force on the rope prevents the box from falling. The same force of gravity, or the force from curved space, compresses the ball onto the spring. Notwithstanding my above argument, I will go ahead and enjoy the remaining videos on GR, and then return to earlier videos to thoroughly enjoy the maths in each one. You’ve done a sterling job, Sir!

[@eigenchris]

In your thought experiment, you said "From my point of view curved space causes a directional force on all mass". This sentence bothers me a bit. I think I should clarify what I mean by "force". There's a general sense in which a "force" is something that "makes things move". In this sense gravity in GR is a force. But mathematically, the "force" I'm talking about is a 4-vector that changes the direction of a particle's worldline in spacetime. So I think the issue you're getting at is: do we model gravity using curved spacetime and no 4-force vectors, or do we model gravity using flat spacetime and use 4-force vectors instead (or phrase another way: can we model gravity in flat spacetime using some kind of field on that flat spacetime that produces 4-force vectors)? My reason for believing that gravity should be modelled by curved spacetime and not 4-force vectors is that (by the equivalence principle), it's impossible to distinguish a freely floating accelerometer in the absence of gravity (no 4-force vectors) from a freely falling accelerometer in the presence of gravity (implying that this should also involve no 4-force vectors). This hints that we need another explanation for gravity that does not involve 4-force vectors, and using curved spacetime to explain gravity does the job. Now, the above isn't a formal mathematical proof. You might still wonder if there is a way of using flat spacetime + a force field to describe gravity in an equivalent manner. That's a question I don't know the rigorous answer to. I saw this discussion on the physics stack exchange that you can read if you like: physics.stackexchange.com/questions/32544/can-general-relativity-be-completely-described-as-a-field-in-a-flat-space . You might need to do more googling to fully resolve this issue and explore all the different mathematical structures that could possibly be used as an alternative to curved spacetime. I'm sorry that I don't have a better answer than that right now.

[@ZingZang]

Well answered, thank you.

[@user-dialectic-scietist1]

9:51. Yes, but the inertial and the not inertial referring frames are both subjective systems. There isn't such a thing like objective frame. Relativity, is everywhere and everything. That means that couldn't exist in real, constant things in every frame. Because referring frames are subjective a conception of a constant for any frame is also subjective.

[@herwig160265]

Hi Chris, great Video like usual. I have a question rgd. your accelerometer falling freely towards earth. let´s say the walls are made of glas so an observer at a constant distance to earth would see a box accelerating towards earth with a ball inside but the spring in the back ist not squeezed. What would his conclusion be? That the ball lost its inertia? Thanks for a short explanation.

[@eigenchris]

I think the easiest conclusion to make would be to say the observer/accelerometer are stationary and that the earth is accelerating towards them. But really, as I say at 9:00, the concepts of "stationary"/"constant velocity"/"acceleration" are meaningless on their own. Each of these must be measured relative to something else. You could say the accelerometer is accelerating towards the stationary earth, or you could say the earth is accelerating towards the stationary accelerometer. Both are equally valid. But both the accelerometer and the earth will consider their own proper accelerations to be zero because gravity does not cause proper acceleration.

[@herwig160265]

@@eigenchris Hi Chris, I was thinking carefully about your answer and I can see my mistake now. The ball in the accelerometer is in free fall towards earth and doesn´t feel acceleration at all, so the concept of inertia and squeezed springs is not applicable. This is also backed by your statement that gravity is not a force. Hope I got it right. Looking forward to 107b :-)

[@fernandogarciacortez4911]

Chris, do you mind sharing which program do you use to make the slides? Is it LaTeX (Beamer class). I can't imagine doing something like this in PowerPoint. Edit: I love the effort done to color code characters. Really makes it a lot easier to read things when equations get messy (which is pretty frequent!)

[@eigenchris]

Yeah, it's all powerpoint. All microsoft office products have an equation editor in the "insert" tab (or you can press Alt + "=" when inside a textbox). You can either click equation symbols from the UI or use LaTeX-style code like \alpha or \Omega or \vec, and after you hit the space bar, the code will auto-convert to the corresponding symbol (can also use ^ and _ for super/subscripts). The colour-coding is all manual though, and it's a bit time-consuming, but I think it pays off. It also has a recording option, along with export-to-video. (Recording might be a paid-only option... I'm not actually sure.)

[@user-dialectic-scietist1]

12:38 α=0, but the g=10 m/s2 I hope you are realizing what are you being saying. Don't forget that the "great" Einstein uses the constant G in his field equations, but the G measurement by Cavendish, couldn't be done if g = α=0. I hope that you realized that the falling accelerometer is a different referring frame from the Galileo observer. Because Galileo founds α=g= 10 m/sec2 for his observation frame. Also, a Martian if he saw your falling accelerometer through a telescope probable he will measure a different α suitable for his referring observation frame, because this is the meaning of relativity. But if you insist that gravity isn't a force, I agree with you, because objectively there aren't subjectively things like force but only objective interactions between material things.

[@user-dialectic-scietist1]

9:57. In a relativistic world like our Universe, where every moment, everything moves and changes, it is impossible to have objective referring frames, inertial or not inertial. This is a flow of logic if you accept that the Universe is relativistic. So, SR disapproves GR just only for this reason that Einstein thought that c and also space and time are constant values the same time they are relativistic. And a lot of others wrong conceptions like the belief that matter is a kind of energy and also that when mass is absent he thought that this means matter is absent (Ricci's tensor=0) but Reimann's tensor isn't and this is the absolute not curved space-time fabric with have energy the energy of empty space. Now we know that there isn't empty space and also the mass of all the visible Universe, isn't enough to bend visible space.

[@se7964]

Awesome job, these keep getting better! I can’t say however that I belong to the “gravity is not a force” camp. Mostly this is from counterfactual conjecturing: if mass curves spacetime in different ways, and different types of curved spacetimes produce different trajectories, then certain motion would not occur were it not for certain masses behaving certain ways. Two objects converging under tidal forces, for instance, would not do so if whatever mass warping spacetime in that neighborhood were removed. There exists therefore very much a “cause-effect” relationship between the motion of some masses and the motion of other masses, i.e. a force of gravity. Though it’s most people’s intuition to throw out gravity as a force because it disappears locally, I think this is the wrong instinct. I mean, we could have a bunch of particles with equal charges and equal masses attracted to a central charge, and then suddenly the electromagnetic force would disappear too. Rather I think we should be expanding our notion of what a force actually is.

[@eigenchris]

When I say "gravity isn't a force", I'm not saying that "gravity doesn't make stuff move". I'm trying to say that the traditional view of forces involving f=ma (or more correctly f = dp/dt) doesn't apply to gravity. When gravity changes an object's trajectory, there's no 4-Force vector, no 4-acceleration vector, and no proper acceleration (which is the length of the 4-acceleration vector). When an object is following a geodesic in curved spacetime, its 4-momentum is not changing, so F = dP/dτ = 0. The object is just travelling "as straight as possible" in curved spacetime. In order for two objects to converge, we don't need forces, we just need spacetime to be curved in such a way that when they both "move forward" in spacetime, they get closer together. In my Tensor Calculus series, I give the example of two people on the moon about 100m apart, both walking due north. They will get closer and closer together overtime, not because there is a force pulling them together, but because the curvature of the moon's surface causes "straight" paths to converge.

[@se7964]

@@eigenchris “In order for two objects to converge, we don’t need forces, we just need spacetime to be curved...” I think there’s a subtle point in there being overlooked. For in order for spacetime to be curved, we need a mass. Mass/energy is the source of curvature, and hence it ultimately provides the cause that furnishes tidal accelerations. If mass can cause motion that would not otherwise occur, were it not there, this makes it a source of force. In your traveling north example for instance, there’s nothing we can do to make the earth not a sphere. But in spacetime, we can always remove the mass that is causing the curvature, and thereby abolish the tidal forces at the same time. Then two objects “traveling north” will never have the possibility of meeting. Yes, under the specific localized differential form of force, gravity will not qualify; but gravity/spacetime curvature still matches our intuitive idea of what a force should or shouldn’t do, which is cause things that were apart to come together.

[@kylelochlann5053]

Gravity is not a force as it cannot produce an acceleration, as shown in the video (assuming EEP is valid). Specifically, all free-fall objects move along geodesics. This can verified with a smartphone accelerometer. We get the same result associating the massless spin-2 boson with the graviton (EEP comes about as a theorem rather than a postulate as in GR). Gravity, specifically, the existence of a non-uniform metric, is an effect. Similar effects would be the centrifugal and Coriolis effects.

[@se7964]

@@kylelochlann5053 I think you’re missing my point here - it cannot produce acceleration in the local sense as can be measured by an accelerometer. But it still produces acceleration in a global sense, acceleration that would not otherwise occur were there not masses there warping spacetime. In fact, if you think about it, curvature is sort of a “hack” to get around the equivalence principle. We can’t measure the acceleration due to gravity locally so we have to stitch it together over more global regions. Gravity still makes things come together. If mass/energy didn’t warp spacetime (i.e. cause gravity) then objects wouldn’t come together. This makes it a force in the “cause - effect” sense for which the idea of force was initially fashioned. This is why I stated in my first comment that’s people’s intuition to throw out the idea of gravity as a force simply because it doesn’t match a localized differential criteria is a mistake and an example of backwards, restrictive thinking.

[@kylelochlann5053]

@@se7964 There isn't any such thing as a "global" or "local" acceleration. A worldline is a geodesic or it isn't, and all free fall worldlines are geodesic, so there isn't any force. I think you may getting coordinate acceleration confused with physical acceleration. Sure, you can define a coordinate acceleration for gravity, but this does not suddenly turn it into a physical force. I never said anything about curvature. I'm perfectly fine discussing this without reference to curvature, for example, as is done in Weinberg's classic text on gravitation and cosmology. Besides, there isn't any "hack" anyway. You may wish to get that sorted out here: arxiv.org/pdf/1403.7377.pdf Gravity is a Fundamental Force in the sense that it's a phenomenon that shapes the distribution of matter - gravity just shapes the world without having to apply forces on anything. This is a tremendously beautiful thing once it's understood. If you're using gravitational force metaphorically, as in say, "the force of the Federal Reserve on interest rates" then, okay.

[@mentalgaming4558]

Hi i don't know anybody will reply yo me or not. But can someone tell me that either rocket is already in the acceleration and going upwards and the we drop the ball or the rocket is suddenly accelerated and if we leave the ball freely it will fall down. Please if anybody knows, answer me.

[@eigenchris]

The ball will not "drop" until the rocket accelerates. If the rocket is in an inertial frame, the ball will appear to float in the middle of the rocket and not change position.

[@nickst2797]

Since this channel heavily focuses on GR, i want to ask a question here. I have Ray Dinverno's book which is a good book for Gr newbies. There was a webpage called "physicspages" Which had a lot of the solutions to that book (solved by the man himself). The man got worried on copyright infringements (which is absurd, he had uploaded his solutions to gr exercises. Can you trademark math?) Most of them were solutions to the math of gr like tensors. But anyway, this resource is gone now. I want to ask, if by any chance someone has the solutions, of someone saved them, can someone upload them? If yes, please respond to this comment. Thank you in advance.

[@edwardmacnab354]

Equivalent for extremely small spaces with extremely small test masses perhaps but in no way equivalent for larger spaces or for larger test masses whose Gravitational force intrinsic to that larger mass changes the picture . Also , the electric force is no different except that the electron has no mass relative to the magnitude of it's force . If the electron had a larger mass , then the electric force would behave like the gravitational force . And whatsmore , for a large electric charge , I'm sure there are tidal forces just like for gravity , and the electrons , if they had larger mass and therefore inertia , you might not be able to see a difference , in fact , I challenge you to construct a model of the electric force with electrons that fit the gravitational profile for a real demonstration of equivalence .

[@annas8079]

Hello! Amazing explanation. Could I use a portion of this video in my own video where I talk about zero-gravity flight? I will give clear credit.

[@eigenchris]

Sure!

[@deadman7770]

when acceleration is caused by upwards acceleration of earth, shouldnt the earth be faster then the speed of Light?

[@eigenchris]

In the 105a/b videos, I show that a rocket with constant acceleration never goes faster than light (it travels in a hyperbola instead of a parabola... hyperbolas have "asymtotes"/"speed limits", so we don't violate the rule that nothing can go faster than light).

[@rohitbhatia7573]

Hats off to you.... Sir Can We say Apple is not falling towards earth but the earth is coming upward to touch the apple 🍎

[@foxhound1008]

Really nicely done. I especially enjoyed the tidal forces. So, with that said, would a linearly accelerating rocket have a gravity gradient? In other words, would gravity at the base of the rocket be slightly greater than gravity at the top of the rocket? I would say no, as this was explained in your video as the constraint of “locally” and “uniform”. In addition, if someone had a definition of a real force, is that a real force obeys Newton’s third law, which is tantamount to conservation of momentum, then wouldn’t gravity be considered a real force? Two objects orbiting each other are orbiting their common center of mass, pulling on each other continually exchanging momentum. An apple falling to the earth, is also pulling up in the earth, albeit imperceptible. A basketball “falling” to the bottom of an accelerating rocket, is not pulling up on the rocket ( not counting the gravitational force of the basketball itself)

[@eigenchris]

For the "linearly accelerating rocket" question, the concept of acceleration in SR is tricky, as you may have seen in my video on Bell's spaceships. If you have a spaceship accelerating in a "born rigid" way, this means that all points on the spaceship have slightly different proper acceleration, with the highest at the rear and the lowest at the front... in this sense there would be a "gravity gradient", although I think it changes with 1/r instead of 1/r^2. For the 2nd question, you could debate what is and isn't a "real" force. It's a matter of definition. My goal with this video was just to point out that gravity is unlike any other force because it is impossible to detect with an accelerometer. In the long run, it will make more sense to think of gravity as the shape of spacetime itself (which changes the paths of geodesics) instead of a vector. It's also the case that it's not just mass that creates gravity, but energy and momentum as well. Electric and magnetic fields can cause gravity as well: en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor . The Newtonian view of gravity as a vector that's proportional to mass really just doesn't work for these cases.

[@DoniSholk]

What is an inertial reference frame I'm GR tho?

[@eigenchris]

It's one where all spring-mass accelerometers in all directions have no compression, so it's a state of zero proper acceleration.

[@filmattic7907]

the example with the ball in the iron box with springs on each side can be seen as misleading in some cases because you did not mention the springs composition if it is metal it would be attracted to the magnet I understood but some people might not I have no problem with the video I am only mentioning this because my sister mentioned it and would not leave me alone about it

[@eigenchris]

Yeah, I could see that being confusing. I'm assuming the springs and ball are not magnetic.

[@longsarith8106]

Why the proper acceleration of International space station is equal to zero ? How about centripetal acceleration?

[@Mysoi123]

the centripetal acceleration of the International space station is caused by gravity and gravitational acceleration cannot be felt inside and therefore it is not proper.

[@johneonas6628]

Thank you for the video.

[@sam-u8y9j]

but what exactly is gravitational mass??

[@eigenchris]

It's the mass used in Newton's Law of Gravity. It's what causes objects to be gravitationally attracted to each other.

[@sam-u8y9j]

can you explain it in depth cuz i didn't get it ?@@eigenchris

[@y0n1n1x]

where is 101c?

[@eigenchris]

I started making it, but I realized I didn't understand GR well enough to explain it properly, because I had made a serious conceptual mistake in it. I'll make 101c when I feel I understand GR well enough..

[@y0n1n1x]

@@eigenchris thanks u the best

[@MS_PrithwirajMaity]

PLZ SHARE BOOK PDF ON GR

[@brianleake7762]

Freefalling in a strait line to the ground is not gravity(spacetime curvature)Not a geodesic.

[@tahamishoaib9836]

amazing explanation..thanks a lot

[@-_Nuke_-]

Wait wait wait... At 9:59 we have: "constan't velocity" "acceleration" That are relative / coordinate depended And then "inertial observer" "non-inertial observer" That are objective / agreed upon by all observers But at 10:13 you say that everyone in the universe will agree that my acceleration is the same that I measure and that a is invariant... WHAT? I don't understand ... :/ Isn't being inertial (so, at rest or traveling with constant speed) allways relative? How is it objective as you said? Also why do you say that acceleration is relative but then directly contradicting yourself by saying that its invariant and thus objective? Also when you say "non-inertial observer" isn't that an accelerated observer? What is going on here?

[@eigenchris]

Accelerometer measurements are objective, because it doesn't depend on coordinates. But the m/s^2 value measured for an object from the origin of a coordinate system will depend on a coordinate system. For example, a car's acceleration relative to my house will not be the same as the car's acceleration relative to a nearby accelerating cyclist.

[@viniciusneves9988]

Great video! Can you make a list of some books to study *special* relativity?

[@alwaysdisputin9930]

I'm not sure about books but apart from eigenchris's videos I found DrPhysicsA's vid 'Spacetime & The Twins Paradox' to be great for explaining time dilation & light clocks. & then you can combine that idea with ScienceClic's visualising of space flowing into the ground & what you get is that clocks tick more slowly near to Earth because the light in the light cock is like a fish trying to swim away from the edge of a waterfall but the current is too strong so it gets stuck & can't reach the top of the light clock. Thus clocks seem to freeze at the BH's event horizon

[@ritikrai7423]

Can we assume that black holes are STAR made of ANTI-MATTER Material? And can this answer any question related current physics, not taking account that the singularity exists.

[@eigenchris]

I don't know much about anti-matter but, the idea of black holes was around before anti-matter was proposed. The standard concept of a black hole from early general relativity is a mass that's so dense that it creates a radius (called the "event horizon" , or "schwarzschild radius") that prevents anything inside of it from escaping (including light).

[@ritikrai7423]

@@eigenchris neither do I know much about them :p Now hear me out for this. Let’s have a massive enough star and on collapse it comes out to be a neutron star. In this type of stars, electron and protons are merged together to form all neutrons, that’s why called a neutron star. now further more massive and we have a black hole, here why can’t fermions(quarks) rearrange in such a way that we get an anti-matter atom. And by a simultaneous chain, an anti matter black hole? This can answer one question that comes in my mind that coming in contact with the event horizon any matter will vanish destroying itself and some part of the black hole(a very very tiny amount as it is way too dense), call it Hawking radiation if you like. can this assumption stand even near 1% out of 100%. I'm really sorry if I'm bothering you.

[@narfwhals7843]

@@ritikrai7423 you can't just turn matter into anti matter. There are conservation laws that forbid this. But even if you could, it doesn't matter for the black hole what it is made of. And as far as general Relativity is concerned you can't come into contact with a black hole. The event horizon of not a solid surface. It is just a region in spacetime nothing can come out of. Whatever made the black hole is always falling toward the center.

[@tomkerruish2982]

"A long horizontal room..." kind of like a railroad boxcar?😁 Philosophically, does motion along a geodesic correspond to Aristotelian natural motion? Fantastic video! I'm glad Andrew Dotson recommended your channel.

[@eigenchris]

Thanks. Yeah, it was nice of Andrew to direct people my way. I probably got 1 or 2 thousand subscribers because of him.

[@eigenchris]

As for your "aristotelian natural motion", I'm not sure what you mean. When I say "natural motion", I just mean motion without any forces acting on something.

[@tomkerruish2982]

@@eigenchris I was thinking out loud. Aristotle held that there were two types of motion: natural and violent. Natural motion arose from the nature of the object; violent motion was that imposed by an external force. Given the era, he was wrong in the particulars, but not outrageously so; examples of natural motion were terrestrial bodies falling (only) straight down and celestial bodies executing their circular orbits about the (stationary) Earth. While listening to your video, I was struck with the realization that these correspond to geodesic motion. IMO, if Democritus can be considered the father of atomic theory, then one could make a case for Aristotle providing the foundation for general relativity. Or maybe not; it's a rather half-baked idea.

[@tensorific]

@@tomkerruish2982 I think if you speak generally enough, you can always bend the interpretation of your ideas to match the prevailing theory of a given paradigm. Aristotle's "natural motion" is as "correct" in the Newtonian universe as it is in the Einsteinian universe. It's the double-edged sword of metaphors.

[@tomkerruish2982]

@@tensorific Very true. It was a fleeting thought of mine. Thank you.

[@Potassium697]

hi guys I have already solve the equivalence principles and I have the answer why inertial mass and gravitational mass the same I am sure 100% my idea is correct Where can I pass my article or my papers ? it’s big lot help if you can give an advice

[@kanikapathak2040]

Is it okay for me to study tensors as multilinear maps?

[@eigenchris]

Yes, from a mathematician's point of view, tensors are multilinear maps (this is how I talk about them in my "tensors for beginners" videos). But in physics, tensors are important because they are agreed on in all reference frames, so I wanted to stress this fact..

[@MS_PrithwirajMaity]

which BOOK is good for beginer in GR?

[@eigenchris]

You can look at Sean Carroll's free online GR notes. You can also look at Edwin F Taylor's free PDF called "Exploring Black Holes".

[@sanjibkarjee7998]

Kindly send the details calculation of Einstein field equations of 10 comments. I have been waiting for your this videos.

[@-_Nuke_-]

So If I understand this right, the Earth is an inertial refference frame because its in orbit around the Sun. So everyone in the Universe will agree on that too right? Which means, that we can always know if a random object is inertial or not by comparing its motion to the motion of the Earth or any other thing in free fall right? That means, that if we were able to map every object in the Universe, relativity would go away... Nothing would be relative anymore, because we would have perfect knowledge of the motion of all objects... Even though we would still experience relative phenomena like time dilation and lenth contraction. So, in that framework - these phenomena (time dilation and lenth contraction) are calculation errors... For example, according to the above, if I travel at 91% the speed of light relative to the Earth, and I measure my proper velocity to be 2.4 times faster than light - my speed isn't 218% the speed of light but 91% instead (91%C*2.4 = ~ 218%C) (γ=2.4) Also if I travel with that speed towards a 1 light year away star, I will reach it in 5 months from my point of view and not in 13 months which is the Earth's view. That means that my 5 months measurement was wrong - and my proper time was not a "relativistic effect" but a calculation error instead. So the time dilation that I experienced was asbolute time dilation, but the time dilation that I measured for the Earth was apparent time dilation. So I can't really claim that my watch was running normally and the Earth's watch was running faster... We know that the only normal way for a clock to run is by being on the Earth. We know that because it was established from the above that the Earth is an absolute inertial frame. I won't lie - that makes relativity all that more clear but also all that less relative too. Also, I can't anymore claim to be stationary either, because relative to the Earth I am moving at 91% the speed of light and everyone in the Universe agrees on that. So, again I'm so confused... Does that mean that relavity dies when we introduce general relativity?

[@eigenchris]

I don't fully follow your comment. In general relativity, it's possible for 2 objects to be inertial and to also be getting closer together, or farther apart (both are allowable with tidal effects seen with gravity). Two bodies being inertial tells you nothing about the distance between them or their relative velocities. It just tells you that each object measures zero on their accelerometer.

[@WilliamCacilhas]

Relativity would not go away. If someone is moving at some constant V with respect to the Earth, they would also be an inertial observer. The person on Earth can insists they are stationary and person V is moving and person V can also insists he is stationary and the person on Earth is the one that is moving. You still can’t measure absolute velocities. So how exactly is Earth being in an inertial reference frame get rid of relativity?

[@vwcanter]

I'm still a little skeptical about the tidal bulge of the oceans. It's true that the moon's gravitational attraction should be weaker on the far side of the earth. But that doesn't mean the moon pushes away on the far side. It just pulls less. And the earth's own gravity should matter much more than the moon's. I don't see how the weakness of the moon's attraction could be enough to overcome the earth's gravity, and raise all of that water in the earth's gravitational field. And also, if the bulge was only on the moon side of the earth, it would still be stretching the earth's shape. So I suspect it is a result of the rotation, together with the tidal forces. I suspect if the moon were merely suspended above earth, and the earth was not rotating, the tides would only bulge on the moon side.

[@eigenchris]

The earth's gravitation affects all the oceans roughly equally due to spherical symmetry. The moon's force on the ocean is what causes the asymmetric bulging. I don't see how rotation of the earth would play a role, because again that would affect all points on a given latitude approximately equally. It wouldn't explain the bulging effect on opposite sides of the earth.

[@manta567]

Awesome! Thanks a lot.

[@maurpine]

seems confusing to refer to ‘tidal forces’ and ‘gravity as a force’ where in relativity there are no ‘forces’

[@Chicken_Little_Syndrome]

If free-fall were truly equivalent to Zero gravity, in other words, if free-fall could magically turn gravity off, the object that was falling would now be moving towards Earth's center of mass at a fixed velocity. Falling is the result of being in a gravitational field. Weight becomes falling when an object has no support. Einstein's equivalence is a shallow one that is not a fundamental feature of Nature. It might be mathematically true when examined in a very limited way, and it might look or even feel the same, but in terms of energy, it is logically false. But of course, most people do not think in a logical manner and fall for the circularly-reasoned explanation instead. And his General Relativity thought experiments are easily shown to be wrong with a compass or Michelson-Gale-Pearson experiment performed in the windowless elevator. We can do experiments that can discern whether we are on Earth (falling) or in an imagined area of outer space devoid of all other matter. Besides, his genie-pulled elevator thought experiment is absolute nonsense. What mechanism allows an elevator to be pulled with 9.8 m/sec acceleration in an (imagined area of the) Universe that lacks a gravitational field? What leverage would allow this to occur? What kind of magical rocket can have an endless supply of fuel, and how did Einstein engineer it so it accelerated at the constant rate it would need to? We should just assume that he employs a magical genie, right? Not all thought experiments are created equal. Some of them are nonsense.

[@fazilnajeeb]

SUPERB !!!

[@mahmoudmaher00]

Thank you

[@vanikaghajanyan7760]

Real gravitational fields are variable in space and time, so there is no global equivalence between them and non-inertial reference frames. In the case of a gravitational field, no global transformation can exclude it and thereby bring the metric to the form of an inertial Cartesian system. This can be done only in an infinitesimal 4-volume in the vicinity of the event P. That is, the strong equivalence principle (the same flow of natural phenomena in the gravitational field and the corresponding non-inertial systems) turns out to be just a dream; and the principle of general covariance, which holds for all 4-coordinate systems without exception, is unreasonable.

[@eigenchris]

I agree the equivalence principle only holds locally and not globally. I don't see why this is a problem, though.

[@vanikaghajanyan7760]

@@eigenchris According to the equivalence principle, a Lorentzian system (a free-falling system) can be introduced at any world point by a suitable transformation of 4-coordinates, where there is no gravitational field anymore. Thus, thanks to the equivalence principle (!), only a pseudotensor of energy-momentum can be attributed to the gravitational field. "There are "true" gravitational fields; however, the meaning of this word in general relativity is different than in classical mechanics... The question of in which cases, by choosing a reference point, the gravitational field is destroyed throughout its entire length can, of course, be resolved only by a complete theory." (Max Born, Theory of Relativity, Chapter VII, paragraph 2).

[@vanikaghajanyan7760]

P.S. "The objective is to establish a theory based on the principle of equivalence for the case of inhomogeneous gravitational fields: already Einstein and Abraham tried to characterize the total static gravitational field by the value of the speed of light c at each point in space-time, which would thus play the role of the gravitational potential, and they looked for differential equations that the speed c must satisfy. But even if we set aside the fact that these theories take into account only gravitational fields of a special kind, they had already led to difficulties.” (Pauli, RT). "The geometry of space in general relativity theory turned out to be another field, therefore the geometry of space in GR is almost the same as the gravitational field.” (Smolin). P.P.S. Developing Einstein's hypothesis of a cylindrical world, Einstein's theory of gravitation "migrates" into phase space: due to this, it is quantized. Final formula: ф(G)=-(½)[w/w(pl)]c^2, where ф(G) is Newtonian gravitational potential, w - the frequency of the quanta of the gravitational field (space-time); - can be tested experimentally in the laboratory at the moment.

[@vanikaghajanyan7760]

@@eigenchris In 1907 Einstein started with the classical equivalence principle (gravity/inertia), but soon modified it: gravity suddenly "became equivalent" to the curvature of 4-space, and was replaced by it. P.S. The starting point of physics is the idea of inertia, but "The knowledge of the straightness of the movement of a body left to itself does not follow from experience. On the contrary!" (Einstein). The fundamental difference between inertia forces and ordinary forces of interaction of bodies is that for inertia forces it is impossible to specify the action of which specific bodies on a material point they describe, they cannot be confused with the Dalembert force of inertia, and they are always external forces. (Newton's first law is not a special case of Newton's second law.) GR reduced gravity to inertia by generalizing the first law: the free movement of test bodies occurs along geodesic lines, but the theory did not find out anything new about the nature of the cause of inertia forces. "... the complete geometrization established by GR introduces a hierarchized cosmos on the plane, indicating indirectly the presence of an elusive source." (Tonnelat). It seems that this source of external (external) inertia forces is an "absolute vacuum" - instead of Newtonian "absolute space", which "... as a cause, does not satisfy the need for a causal explanation." (Born). Finally, the search for the root cause became possible after Friedmann spoke for the first time in a scientific way about the "creation of the world", and even then there was an opportunity to abandon the a priori nature of the law (more precisely, the axiom) of inertia, and build physics on a more reliable basis. P.P.S. GR was QG: docs.google.com/document/d/1PKsO3vuXu7XJUhwjgpCR-a8Bwdi24B89QkE9RsKABOU/edit?usp=drivesdk

[@freefreepalestine360]

According to the general relativity it allows a non rotating earth in the center of the universe 🙏

[@fkeyvan]

Why does your voice get deeper at the end of sentences?

[@eigenchris]

Gravitational pitch dilation.

[@eigenchris]

Realistically, I guess it's just my speech pattern. I don't know why I talk the way I do.

[@akhilreddy3771]

Very very useful

[@VortekStarling]

Actually there IS a reason why inertial mass and gravitational mass should be exactly the same, because it's just mass, period. With inertia, you're talking about how much acceleration you get from a certain amount of force on a certain amount of mass, the equation would be Force divided by mass equals acceleration, in units of Newtons, kg and meters per second squared, a= F/m . When talking about gravity, you know that the acceleration is a constant on earth's surface so what you're looking for is the force which that acceleration produces on a certain amount of mass, F= m*a. Let's try it out. We'll do this in two sets of of the two equations. Equations A pertain to inertia and equations B pertain to gravity. Set 1: We use a 10 kg mass. Equation A: We want to find the unknown value of how much acceleration is produced on the known value 10 kg of mass from the known value 100 Newtons of force. Force (100 N) divided by mass (10 kg)= 10 m/s2 acceleration, the previously unknown value. Equation B: Now we want to find the unknown value of force produced on the known value 10 kg mass from the known value acceleration (gravity) of 10 m/s2. So acceleration (10 m/s2) * mass (10 kg)= 100 N of force, the previously unknown value. Now comes the part that confused physicists, apparently, since they seem to be amazed that inertial mass is the same as gravitational mass, like it's a remarkable coincidence. Set 2: We use a 2 kg mass Equation A: We have known value force (100 N) divided by known value mass (2 kg)= 5 m/s2 acceleration, the previously unknown value. Equation B: We have known value mass (2 kg) times known value acceleration (10 m/s2)= 20 N of force, the previously unknown value. Now notice that in both Equations B, the gravity related equations, the acceleration, ie: gravitational (10 m/s2), are the same and only the force values differ when you change the mass from 10 kg to 2 kg. That's why the 10 kg and the 2 kg masses fall at the same rate though they have different weights on a scale. In both Equations A, the force was the same but the acceleration was different when the masses were changed, which is how inertia differs from gravity while inertial mass is the same as gravitational mass. The known and unknown values differ but in both cases the value for mass is one of the knowns, it's just that the other known values, for force and acceleration, differ and you're looking for different unknown values.

[@drbonesshow1]

Special relativity takes into account those special relatives in your family.

[@changarturo]

Please post your videos faster! Thank you!

[@alwaysdisputin9930]

Zoltan said to me: "No. Your flight to Pluto involves acceleration. Pluto doesn’t accelerate. Acceleration is not relative." I said to him: 7:53 of eigenchris's YT vid 'Relativity 107a: General Relativity Basics - Equivalence Principle & Proper Acceleration' says: "If you're inside a car & the driver steps down hard on the gas pedal causing acceleration, you will feel as if you're being pulled towards the back of the car. This feeling of being pulled backwards is your body feeling proper acceleration... & proper acceleration is measured with an accelerometer. An accelerometer is made of a rigid outer box with an inner ball ... balanced on springs that are attached to the outer rigid box. ... The larger the spring compression, the larger the proper acceleration felt by the accelerometer. Throughout this video series, I've used terms like 'constant velocity' & 'acceleration'. It's important to remember that, technically speaking, these terms are relative & depend on the reference frame that we're in. I could say that when we step hard on the gas pedal, our car is accelerating with respect to the ground; but I could also say that the car is stationary with respect to the driver. So concepts like constant velocity & acceleration are relative & they will depend on who you ask. Talking about constant velocity & acceleration on their own without a reference point does not make any sense. However an inertial observer will always measure 0 proper acceleration on an accelerometer that they are carrying with them by definition. Similarly, a non-inertial observer will always measure a non-zero proper acceleration on an accelerometer they're carrying with them. The concepts of inertial & non-inertial frames are objective & can be agreed upon by all reference frames & all observers. This is because an observer's proper acceleration (⍺) is an objective number that is agreed upon by all reference frames. If your personal accelerometer measures 10 msᐨ² then everyone in the universe will also agree your accelerometer measures 10 msᐨ². This means that the number ⍺ is an invariant quantity, or a tensor, because everyone in the universe agrees on it."

[@narfwhals7843]

At 16:00 "because of its own weight" seems a bit handwavy without defining what weight even is when gravity isn't a force. But i suppose otherwise you would have just repeated what you said on the previous slide. Great video otherwise!

[@metastephen8252]

Momentum joke is fire

[@RITIKPALPHD2410]

A frame of an object kept on the floor of the earth is a non-inertial frame. Tell that to my classical mechanics teacher.😂

[@redbel2624]

Please don't tell me that you will continue on the 106 videos in an upcoming video

[@eigenchris]

106 will have parts b and c. They will probably be uploaded out of order though.

[@redbel2624]

I cannot believe that you know all this and you have not read books. If you have not read books, it means that you studied all this at university.

[@eigenchris]

It's not that I don't read books.... it's more that I don't read them front-to-back. I tend to just look at small sections at a time.

[@drvidya7350]

@@eigenchris Which books/resources are you basing these series on? You've mentioned 'Gravitation', but are there any others. I get the impression you're using more recent book/lecture notes.

[@eigenchris]

@@drvidya7350 There's Sean Carroll's notes, which are the description. But as I said... it's largely me just devouring anything I find on google until I understand it. Is there something in particular you want a source for?

[@drvidya7350]

@@eigenchris Is there a good book which uses the matrix notation for Lorentz transforms as you've been doing. Most of the books I've read don't keep things as neat.

[@eigenchris]

@@drvidya7350 Writing the basis vectors in a row and the components in a column is not something I've seen in any textbook before, so unfortunately I can't recommend a another source that does this. I only realized it was a good way of doing things a couple years ago, when I was making my tensor videos. It's pretty non-standard, though.

[@Persueurdreams]

Hey eigenchris, I don’t mean to demean the value of your educational videos, but you’re also really funny. I think you should make comedy videos more often. It will have more people realize your channel, but it will also bring many laughs to people who have no interest in actually learning these useless subjects

[@abrlim5597]

I appreciate your introduction to GR. Here's a more comprehensive introduction I found: kzbin.info/aero/PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_ But at some points some topics or ideas were being glossed over. I am hoping maybe you can cover them in your series.

[@eigenchris]

Which parts in particular did you feel they glossed over?