The River Model of General Relativity

a solitary Mass sits in empty space very far out from it we release a ring of neutral particles followed shortly thereafter by another ring and then another if we repeat this process in a continuous fashion we will soon have a sea of particles flowing faster and faster inwards towards the mass what would you say this is a picture of exactly a large number of particles all subject to an inwardly attractive Force well what if it weren't these particles which were moving at all but rather space itself that was truly flowing sweeping the particles other masses and even light along with it this is dialect with the river model of general relativity when is an analogy merely a tool for comprehension and when is it something more indeed there's an analogy in general relativity that asks us to imagine space to be like a river a sort of flowing background against which all matter is swept into sinks of mass and energy at first glance this may not strike you as a great analogy how the heck can an abstract construct like space flow into itself what would such a statement even mean but when we start to peel back the layers to this analogy we'll find there's something highly suggestive going on okay but first where does such an analogy even come from well start by imagining that you're on a rocket ship blasting through outer space next Imagine dropping a loose object off of yourself that object will fall to the floor of course the object didn't really fall the second You released it it stopped accelerating and began traveling at a constant velocity while the rocket ship continued accelerating up to meet it foreign now rather than a single object Imagine You released a set of tiny particles in the shape of a grid in the same manner as before this grid will also fall to the ground this grid of course is a stand-in for our traditional conception of space so if we're accelerating we can make a sort of funny sounding statement about space that is we can say space is Flowing past us getting sucked into the rocket ship floor as though that floor were a sink or drain loose objects floating on the current of this space likewise get carried towards the floor and even a light beam itself will Arc downwards as if with the current of course if we weren't accelerating but rather we're at rest or traveling at constant velocity we wouldn't be able to make such a statement because our space grid would simply stay put now if you're familiar with general relativity at all you know there's another kind of statement we can make about being in an accelerating rocket ship we can claim that we perceive ourselves to be in the presence of a homogeneous gravitational field this is the equivalence principle by flipping it around we can also claim that any frame in which we perceive a gravitational field can likewise be treated as accelerating meaning we can make the same funny assertion about being in a gravitational field that we did about being in an accelerating rocket ship that is we can say that space itself is Flowing past us getting sucked no longer into the floor but rather into the mass or source of the field now the primary place we perceive a gravitational field is at the surface of the Earth okay but this is just a clever analogy space isn't really flowing into the Earth is it well now comes the incredible fact that you aren't actually at rest on the surface of the Earth the ground is in fact accelerating you upwards at 9.8 meters per second squared through space if you drop an object off of yourself it falls to the ground for the same reason it did in the accelerating rocket ship because the ground rushed up to meet it if you're skeptical of this fact you can prove it to yourself by stepping off of a tall building we said by stepping off of a tall building there we go now this action will cause the gravitational field in your immediate vicinity to vanish before any light signal has a chance to reach it this is a violation of causality for in a true force field such as the electromagnetic one any disturbance to the field can only propagate at the speed of light this fact in conjunction with an empirical inability to measure the field you are supposedly falling in forces you to conclude that the field you perceived the moment before you stepped off the building was indeed a fictitious one and that implies that it must be the ground which is accelerating not you but this incredible fact immediately raises a whole host of other questions how can one part of the Earth's surface be accelerating upwards while miles away another part is also accelerating upwards but in a slightly different direction and meanwhile at the untipital end of the planet that same surface is somehow accelerating in the completely opposite direction it becomes even more mind-boggling when you realize that even though the Earth is hurtling apart in every direction it somehow remains stationary with respect to itself even though there is no force acting to pull it together but this is where the idea that space is Flowing becomes something more than just an explanatory analogy to answer the question of how we can all be accelerating and yet all remain in place it becomes useful to reinterpret gravity not as a force that acts on matter but rather as a force that acts on Space itself causing it to rush and flow in towards sinks of mass and energy remaining stationary with respect to a mass means different observers will have to accelerate in different directions and with different strengths in order to overcome this flow or Rush to make this clearer imagine that you are motorboating along a river near a waterfall the closer you get to the waterfall the faster and faster the current begins to rush now if you want to stay stationary with respect to the shore you'd have to fire up your Motors and start accelerating this acceleration wouldn't need to be very great if you were far out from the waterfall's edge but as you got closer the increase in current will precipitate a greater and greater acceleration of your boat relative to the shore meaning you are required to run your Motors harder and harder in order to stay put indeed within a certain distance of the waterfall's edge you may not be able to accelerate hard enough to overcome the current and you'll be swept over meanwhile if you simply drifted along with the current you wouldn't feel any force on your boat at all even though you're clearly accelerating relative to the shore you would however feel a tidal pressure stretching your boat apart since the downstream end of your boat would be getting pulled towards the waterfall faster than the Upstream end this tidal gradient also means that other boats drifting along with you will steadily see their distance with respect to you increase over time now instead of a linear River let's imagine a large flat Basin of water which is draining through a single hole in the middle in this setup boats will have to accelerate not only with different strengths but also in different directions if they want to remain stationary with respect to the basin boats that aren't accelerating but just drifting with the current will now experience tidal pressures not only in the radial Direction but also in the tangential direction as water rushing in from all sides towards the drain will act to squeeze the boat inwards this will also cause boats that are drifting along adjacent radial Avenues to see their respective separations steadily shrink over time of course in this visual the Basin is relatively small and drains fast so these tidal effects will be very brief and very strong but a different picture might invoke a very large very shallow body of water draining through a comparatively small Outlet something like a 360 degree river which was headed towards a waterfall in every direction indeed in such a situation the supply of water would be endless enough and the accumulation of tidal forces subtle enough that an observer accelerating in place might not notice the motion of the river at all and rather think that objects floating on it were being attracted inwards by a radial force field that fell off with distance now these pictures essentially sum up how gravitation as modeled by flowing space works to see this let's start at the model of the classic gravitational field where we have vectors drawn in for the strength and direction of the field at every point thanks to the equivalence principle we can now take every one of these vectors and flip it around to find the respective strength and direction of acceleration that an observer located there would need to exert in order to remain stationary with respect to the Central Mass from our earlier considerations we know that this means for each tiny area in the region we can say space is Flowing past our Observer there just as on the spaceship before we'll let grids fall in these areas to give us a general idea of how much speed the current of space is picking up at each location now if we drop neutral particles from a far distance the velocity of these particles will be boosted as they cross over from one tiny area to the next this produces the so-called River of space which rushes faster and faster as it nears the Central Mass of course the true River of space is three-dimensional but for ease of both the visuals and the analogy we're gonna stick to two dimensions now this River resembles our physical rivers from earlier and indeed between these various pictures we can observe many similar phenomena the downstream end of space rushing ahead faster than the Upstream end for instance gives rise to Tidal forces that cause radially aligned inertial observers to drift apart similarly space rushing in from all sides causes those same observers if they occupy different radio Avenues to drift closer together for something such as a grid of neutral particles the total tidal deformation produced upon it by the flow of space will be the same as the deformation produced upon a grid of say rubber duckies by the flow of our 360 degree River but the most powerful aspect of the river picture is furnished by the simple intuition that any matter within this River will be subject to its movement and Flow just as how objects cut on the current of an actual River are subject to its flow this idea applies to even light itself yes light always travels through space in a straight line at 300 000 kilometers per second but as we saw earlier on the rocket ship that space can itself be in motion and indeed close enough to a spherical Mass the converging flow of the river indicates space is likewise converging in every direction resulting in the deflection or bending of the trajectory of that light beam as it passes by now by the time the river of space reaches us at the surface of the Earth it will have obtained to a velocity of approximately 11 000 meters per second In classical physics this value is known as our planet's escape velocity but in the river model it's the velocity at which you are traveling through space indeed your continual acceleration of 9.8 meters per second squared at the surface of the Earth ensures that you are always traveling through the river of space at this velocity similar to how accelerating in place in a river ensures that you are always traveling the same speed over the water now at last we can understand how the Earth can be accelerating outwards in every direction at once and yet remain stationary every point of its surface is merely fighting against a different inflow of space this also explains why the earth's surface is accelerating in the first place if we imagine a bunch of boats in our Basin all getting stuck together atop the drainage point they will be forced to accelerate over the in-rushing water due to their Mutual blockage likewise we can view the mass of the earth as being all jammed up over the inflow point of space forcing a radially outwards acceleration across all parts of the mass lastly just as there comes a point in our physical River where the current becomes so strong we won't be able to run our Motors hard enough to overcome it there comes a point where the current of space becomes so overpowering that no amount of acceleration will negate it this is the Event Horizon of a black hole or the place where the river of space reaches the speed of light two observers outside this Horizon here at this location the inward Rush of space exactly matches the outward movement of light making it appear as though that light itself were frozen in place and that time had ground to a halt in Falling observers meanwhile are transported to a realm where space is now traveling possibly faster than the speed of light technically if we don't want to think of space as having a single preferred speed we should rather say that at the Event Horizon of a black hole observers are being boosted by an amount equal to the speed of light of course thanks to the special additive properties of velocities in special relativity any velocity that is boosted by the speed of light simply becomes equal to the speed of light so indeed at the Event Horizon of a black hole all and every possible conception of space is traveling there at the speed of light this is indeed like approaching a massive current gradient in a river a place where over a very short distance the speed of the water and all objects on it will increase drastically in other words a black hole is to space what a waterfall is to a river how far can an analogy take us obviously the comparison of space to a physical River breaks down at numerous points and is only intended to be illustrative but the concept of flowing space on the other hand can be made formally precise via the use of the gold strand pun Levy metric moreover it can be extended to other metrics to help us describe rotating black holes and more but is all this just an illustrative way of interpreting space-time curvature or is there a deeper underlying connection indeed how is all this supposed to relate to the warping of space and time well our journey down this particular River has only just begun so climb aboard now because boy Revelations are coming this has been dialect thanks for watching foreign [Music] [Applause] [Applause]

Channel: Dialect

Views: 33,488

Keywords: general relativity, space, time, physics, black holes, spacetime, curvature, river, education, learning, waterfall

Id: hFlzQvAyH7g

Length: 19min 34sec (1174 seconds)

Published: Sat Mar 11 2023