The TRUE Cause of Gravity in General Relativity

even with all our modern theories the nature of gravity is still such a mystery to us what is it where does it come from unfortunately if you ask youtube these questions you're going to get some wrong answers some very wrong answers namely you're likely to come across an explanation which purports that time dilation is the cause of gravity indeed almost as mysterious as the origins of gravity are the origins of this popular yet confoundingly incorrect explanation where did it come from what does it mean exactly and what can we learn about the actual nature of gravity from it this is dialect with the true cause of gravity [Music] understanding general relativity is no easy feat the central concept it relies upon curvature though mathematically well-defined often eludes clear interpretation indeed nowhere is this more apparent than in a recent spate of youtube videos all of which erroneously attempt to attribute gravity and curvature to time dilation gravity does not warp the flow of time it's the other way around the warping of time causes gravity that's what i'm going to show you right the type of time dilation involved in that building experiment is called gravitational time dilation not because it comes from gravity but because it causes gravity on the surface these videos and their explanations seem pretty cool and convincing each video starts out by noting that the further out you are from a gravitational mass the faster clocks tick this causes the clocks near the earth to run slower than clocks far away for example time passes more slowly the closer you are to the earth when charted out on a space-time diagram this leads to a time gradient or temporal flow about a gravitational mass we have this sense of time flowing in a gradient faster stream is distant from the earth slower streams near it and just like an object caught in a river with an eddying current any smaller mass near the central one will be forced to rotate towards it meaning rotated out of the time direction and into the spatial direction over time it points more and more toward the earth parts of the object will want to move through time at different rates hence we have the appearance of a gravitational attraction if you were like us your first reaction upon hearing this explanation was probably whoa dude yeah whoa that's freaking awesome mind blowing mass and energy cause time dilation gradients and time dilation gradients rotate the paths of objects through space-time so that they come together that's gravity it all seems to make so much sense but then on further reflection you might have started scratching your head wait is the whole current gradient thing supposed to imply that there's like an inter-temporal force binding an object to its future self and which causes it to hold together after being rotated by another sort of strange temporally directed torque like what suddenly you're lost in a very murky analogy even matt from pbs space-time admitted he was still a little confused by this interpretation well speak for yourself i'm still quite confused this raises thorny questions well the reason for your confusion is simple you're confused because the explanation is wrong one hundred percent unequivocally completely wrong it's astounding that not one of these videos did their homework properly because this entire interpretation with its multitude of youtuber proponents and its millions of beguiled viewers comes undone with just a few simple considerations now before we begin we need to make some important distinctions there are three different phenomena under consideration here curvature gravity and gravitational attraction [Music] now in newtonian physics gravitational attraction and gravity are one in the same thing masses are the source of a gravitational force gravity which thereby causes gravitational attraction in general relativity however gravitational attraction is only an apparent phenomenon it's fake meanwhile gravity and curvature become one and the same thing where you have curvature you have gravity where you have no curvature you have no gravity and lastly where you have accelerating frames of reference you have apparent gravitational attraction so the first important takeaway here is that this apparent gravitational attraction is not gravity that is it is not space-time curvature now half of these videos don't understand whether they're trying to explain the cause of apparent gravitational attraction or the cause of actual gravity i.e space-time curvature being separate phenomena these two concepts actually require separate explanations and we'll get to that later but at the moment this doesn't matter because none of these videos succeed at explaining either phenomenon they're all wrong on all counts to see why let us first consider a uniform gravitational field now the argument in all these videos hinges on the fact that time dilation gradients that is clocks ticking at different rates at different places will cause different masses and objects to come together remember time passes at different rates in different places the heights of the clocks don't have to be that different though any difference will do so imagine we attach two clocks to a squirrel one on his head and one on his feet they should tick at different rates too the squirrel's head moves faster through time than his feet this gradually turns his motion arrow the squirrel falls to the ground simply because time dilation exists now a uniform gravitational field has a time dilation gradient and certainly at a place like near the surface of the earth where the gravitational field is essentially uniform objects seem to be drawn together so all good right nope why because the equivalence principle the equivalence principle tells us that a uniform gravitational field is actually just an accelerating frame of reference imagine being on a rocket ship in outer space undergoing constant acceleration according to your perspective there arises a uniform gravitational field filling all of space causing clocks that are further and further out from you to tick faster and faster now imagine coming to rest suddenly all those clocks resume ticking at the same rates and the time dilation gradient abruptly vanishes if we accept the explanation purported by these videos that time dilation gradients are the cause of gravity this would mean every time you accelerated you would be inducing gravity that is inducing space-time curvature not only in your immediate vicinity but across the entirety of the universe curvature which would vanish as soon as you stopped accelerating this is patently absurd of course space-time curvature is not an observer dependent phenomenon it is something that according to the theory of general relativity all observers will agree upon no matter what their frame of reference and a uniform gravitational field in fact has zero curvature because there is no gravity there it's just an accelerated frame of reference alright let's return to the surface of the earth you're probably most accustomed to experiencing gravity here in your day-to-day life it might shock you to learn then that at the surface of the earth there is no gravity none whatsoever the reason the apple falls to the earth isn't due to the fact that clocks at the top of the apple are from the perspective of an individual on the ground ticking slightly faster than clocks at the bottom of the apple rather it's due to the fact that you the observer are accelerating upwards through space at 9.8 meters per second squared you and the ground beneath you are literally rushing up to meet the apple as well as towards anything else that might happen to be falling at that moment and that is the true cause of apparent gravitational attraction the fact that you're accelerating when you believed yourself to be stationary time dilation is a relative phenomenon gravity as in real space-time curvature gravity is not the fact that clocks tick faster at higher elevations is certainly true for observers who are observing those clocks while on the ground accelerating however if we transform into the inertial frame of the free falling apple the clocks at both its top and bottom will be ticking at exactly the same rate thus the fact that all these videos attempt to assert that apparent observer dependent time dilation gradients are responsible for real observer independent gravity is absurd and doesn't make any sense but what makes even less sense is that in promoting this idea all these youtubers somehow managed to completely forget the basic fundamentals of general relativity yet they're obviously not unintelligent individuals so that leaves a whole new mystery where did this explanation come from and why was it so convincing the answer lies in a pretty simple fact everyone who pushed for this explanation mistook a space-time diagram for actual space time to see what we mean let's turn to idea lists video despite being a smaller channel the level of explanatory power and clarity evident in idealist's video far exceeded that of all the other channels and we thank him for that because without his video we wouldn't have been able to get to the bottom of this enthralling mystery the white lines show that for an equal amount of bottom floor hours higher up clocks travel further in time an intuitive way to estimate the geodesic between two lines in this curved spacetime is to start at a point on a time grid line then use a circle to find the shortest path to the next time grid line let's think about an apple hanging from a tree in this new context it will follow its geodesic through space-time its shortest path which just so happens to coincide with the apple falling towards the center of the earth in space as you can see idealist notes that at higher elevations where clocks tick faster the world line of an object on the space-time diagram will be forced to curve if that object wants to take the shortest path between coordinate grids but idealist's mistake here like all the others is that he interprets the space-time diagram as being actual space-time that is he thinks these objects are actually curving through time and space simply because they're curving on the diagram he conflates curved lines on a space-time diagram with space-time curvature this is the sense in which space-time is curved here because the space time is curved geodesics through it will also be curved the space time is curved space time is current [Music] now a space time diagram is a tool it is not actual space-time like taking the curved surface of the earth and making a flat map of it it is a representative depiction an aid to assist in understanding so if we want to know where and how curvature appears we need a mathematical test more precise than simply pointing at curved lines on a space-time diagram and going space-time curvature so here's what we'll do let's note first that mathematically speaking curvature arises wherever geodesics on a surface are either converging or diverging consider two great circles on this sphere for instance note that as we traverse them the separation between these geodesics either grows or shrinks this indicates curvature if the surface were flat the geodesics would remain parallel and the separation distance between them would never change now let's return to the surface of the earth position a bunch of apples at different elevations and release them simultaneously with respect to the accelerated observer on the ground next construct a space-time diagram from the perspective of this accelerated observer since the gravitational field that the observer perceives here is uniform all of the apples will fall at the same rate and their trajectories will form a series of staggered parabolas because the paths of all the apples were inertial paths we know that these parabolas are all geodesics on the space-time manifold now let's examine the separation between these geodesics notice something despite all these paths curving the separation between them never changes this means there is no space-time curvature here and thus no gravity now if we zoomed further out and dropped our apples from higher and higher elevations we would start to notice that the separation between geodesic world lines would begin to grow this would indicate space-time curvature this is where true gravity finally makes its appearance so when idealist and others thought they were looking at space-time curvature they were in fact looking at something else what exactly well let's trace this idea back to its origins you see pbs space-time acknowledges borrowing this idea from the silence asylum who probably borrowed it from eugene kurtarianski who probably got it from this dude who in turn likely got it from this 2013 video after that the trail goes cold but this early video is enough to show us what's really going on here ready watch as you can see it's just a simple coordinate transformation specifically it's a coordinate transformation mapping a parabola to a straight line and this curving on the diagram which results from the rotation of the coordinate system of the accelerated observer and not from the rotation of actual world lines of objects through space or time everyone has confused for either actual space-time curvature or apparent gravitational attraction so basically all of youtube got tricked by a coordinate transformation forgetting to remember that in relativity coordinates don't always mean what you think they do okay now back to gravity if all these videos are wrong then what is the true cause of gravity well that answer is the same one einstein and essentially newton gave mass and energy density that's the only factor which determines the amount of space-time curvature or gravity in a given region interestingly enough this means time dilation has nothing to do with curvature in fact you can build a theory of curved space time without time dilation using only the classical concepts of time and space from newtonian mechanics it's called newton carton physics and what it demonstrates is that general relativity actually has a lot less to do with relativity then its name might lead you to believe but that's a topic for another day okay but the question that you've been really asking yourself since this video started is what causes two objects seemingly at rest with respect to one another to become drawn together well to explain that you simply need to invoke gravity the internal pressures within a mass and apparent gravitational attraction you see no single mass is truly ever at rest with respect to itself this portion of the surface of a spherical mass for instance is accelerating out from the opposite portion of that mass by a certain amount while that opposite portion is also accelerating away but in the opposite direction in fact every portion of a given mass is accelerating away in a radially outwards fashion from the rest of the mass now such masses don't blow apart into a hundred pieces because real gravity space-time curvature steps in here to ensure the space-time manifold is warped in just the right way as to compensate for all that outward acceleration and thus produce a stable configuration hence we have the appearance of a universal attraction affecting all bodies because every single mass in the universe is literally accelerating towards every other single mass granted this is a very abbreviated explanation but it's a much closer step towards understanding the truest cause of the attraction between bodies lastly we'll note that there is a way to interpret an accelerating observer's rotating planes of simultaneity as a sort of one-dimensional temporal curvature however this curvature would not be space-time curvature rather it would be a coordinative curvature which we could transform away unlike real curvature nor would it explain apparent gravitational attraction since the attraction between bodies in this case is again obviously explained by the fact that objects are just accelerating towards one another well this has been a lot so to conclude for today we will say that general relativity is obviously confusing and we can forgive these youtubers for getting it wrong but the question remains will science asylum pbs space-time or any of these other big league bad boys acknowledge their mistake and help to rectify the misconceptions they've propagated unto their millions of viewers well we appeal to you our viewers to take up this mantle and help spread the word because frankly we're exhausted after sorting through this mess and we need a vacation but don't worry we'll be back this has been dialect thanks for watching you

Channel: Dialect

Views: 289,813

Keywords: general relativity, physics, myths, gravity, space, spacetime

Id: PjT85AxTmI0

Length: 25min 52sec (1552 seconds)

Published: Sat Jun 18 2022