The River Model of General Relativity 

Have you perchance received a reference to the paper I sent you a couple weeks back? The river model even handles Kerr spacetime.

@@cykkm Oh I had missed your email I just found it! Yes actually after making my video on this topic, I discovered that the river model was actually a thing, and that it's actually very useful in many situations, especially when studying black holes. It's funny because Andrew J. S. Hamilton who co-published the paper you sent me actually advised me on my video about falling into a black hole. Another thing the river model is good for is gravitational waves : they can be viewed as a sort of waves within the river, that stretch and squeeze the spaces between the rest masses that form the inertial grid of space.

Thanks ScienceClic! Your channel deserves a HUGE shout-out since your videos were the first to originally tackle the River Model, and thus furnished us with the understanding from which we were able to make this video. We very much wanted to reference the amazing visuals you pioneered in your Visualizing General Relativity series and connect them explicitly to the river model -- but it proved too much for one video, and we're gonna save that for a future work! Also, hopefully we didn't butcher the pronounciation of "Painlevé" too badly. Best!

​@@dialectphilosophy Haha the pronunciation was actually pretty good :) Since I didn't know about the river model my video was very blurry when interpreting the "falling grid", you rectified that in yours which is much more rigorous and precise on what it does (and does not) represent!

The physical concepts and the visual realizations with the nicely balanced sight-gags are truly astonishing. I don't know any other channel on any other topic that even comes close to the melding of such a diverse array of elements.

yeah. Action Labs white hole video is really good for demonstrating this. When we pee into the sink it creates a circle called a hydraulic jump. This is because: 1) when the pee lands it flow very quickly towards the walls of the sink. 2) The wave rebounds & tries to reach the centre of the sink i.e. where the pee is landing. 3) However it can't reach the centre because the pee in 1) is too fast. 4) Therefore the wave gets stuck. It just stands there & looks like a circle. If you try to send morse code waves to the centre they will also get stuck. Thus we can't send information into a white hole. & if time is reversed the urine flies into our penises. & thus it is like a black hole.

Indeed! Theoretical physicist Bill Unruh discusses this in some of his work, arguing that the waterfall 's edge is a "sonic horizon" analogous to a black hole's event horizon. A fish that has fallen down the edge of a waterfall cannot send a message (in the form of a sound wave) upstream of the waterfall's edge/sonic horizon: their sound wave travels at a constant speed, but the waterfall sweeps the flowing water (and the sound wave traveling in it) down faster than the wave's speed. Analogously, an observer that has passed a black hole's event horizon cannot send a message (in the form of a light signal) outside (or "upstream") of this event horizon: their light signal travels at a constant speed, but the black hole sweeps the space (and the light signal traveling in it) in (or "down") faster than the signal's speed.

​@@sannyid, I am by no means an expert on this topic, but I dare to say that the analogy, whereby the edge of a waterfall would correspond to the event horizon of a black hole, is wrong. The edge of the waterfall is rather an analogy for the centre of a black whole. The event horizon of a black hole in the river/waterfall model correponds to any point UPSTREAM, i.e. BEFORE the waterfall, where the flow of water is so high, that not the even the fastest (or highest accelerating) ship could prevent from inevitably being drifted towards the edge of the waterfall. (Actually, this is addressed in 8:29.)

Light is the agent and enemy here. It gave us the knowledge of existence, but can't overcome it's limitations on which we make most all of our assumptions or theories. A waterfall is no longer an unbroken chain of molecules - put that water into a pipe with the same flow and it all changes.

​@@alwaysdisputin9930a black hole is kinda like when someone unpisses

Thank you so much -- appreciate the support and stay tuned!

Yea recently O saw a Ted Talk on black holes where everything started making sense once I knew that space time flows! Before youtube videos would have space time being warped but not flowing. It makes it all make sense

I still can’t imagine how earth surface can accelerate in all directions. For me this will cause it to explode.

If we imagine that the earth is made of particles (atoms, subatomic particles) those particles can be seen to expand together, so earth stays in one piece. Although the fact that some particles like electrons are supposedly point size, this seems impossible so maybe they have an event horizon like the blackhole

If the speed of space against Earth surface is 11000 m/s as shown in video, then the surface is NOT accelerating, it moves in space with CONSTANT speed. So, the video is logically inconsistent with itself.

Yeah they should give him a parachute so he can pull the cord after he has free fallen for a while

Why did he miss the mattress?!?

Gravity Monkey and Shroedinger's cat should unionize

Oh, you're about to run into some major problems when trying to combine Quantum Mechanics with Gravity...

@@juliavixen176yeah, seems everyone has that problem. So, makes me think that’s he’s right.

Miles Mathis charge recycling

... with more and better answers ...

you actually think that the black holes are constantly devouring space? this guy makes it seem like there is an infinite amount of water. there isn't.

​@@RobertoCarlos-tn1iqBro we don't even know what space is. We can only observe very subjective effects and play with our symbols. What I'm talking about is visualizing effects of gravity with moving coordinates of space. This might not have anything to do with real space, it's just a mental tool.

Not sure what you mean but this isn't the first time anyone has used this analogy. Have you never tried searching the internet for this analogy?

@@nektu5435 no not rlly tbh

@@thetenrings Do you find it strange that you proclaimed “FINALLY someone addressed this” about a this that you never bothered Googling to see if it had been addressed?

@@timjohnson3913I never saw it being discussed in youtube

On my side, I thought that the floor was accelerating up. I am happy this analogy was addressed too. What I don't get though is why the heavier the floor, the faster its acceleration towards us is? If the floor keeps accelerating towards us, why have we not reached the speed of light yet :p ?

As it turns out, it’s more expensive to create a whirlpool in a classroom

Well, tbh, this video was made mostly to respond to the deluge of questions we got in the comments section after our "Sky is Falling Up" and "True Cause" video, but glad it helped clarify things and thank you!

I like your analogy better than the one where the boat is using it's motor to stay in one place. Your analogy better represents a person standing on the Earth. In the 360° river analogy 10:40 we could imagine a floating ring over the drain. If the ring were too large to fit down the drain it would remain in one place. Then you could brace your feet against it and it would be like standing on a planet.

Thank you for watching!

"the Earth is accelerating upwards" could be replaced with "the Earth is accelerating us up/outwards". Most people think acceleration = motion, but it's not, in general relativity. Proper acceleration is any force that causes an object to deviate from its geodesic.

@@jddang3738 I think that would be more appropriate, actually. I even tell my physics 1 students that you don't feel your weight, you feel the normal force of the chair pushing on your butt. That's a familiar idea, the Earth pushing against you. In general relativity, you would "fall" in a straight line geodesic, but the Earth's surface gets in your way and that's what you feel when you're on the Earth.

Thank you for the kind words and for watching! There wasn't enough time in this video to address the connection to the spacetime-block view, but hopefully we'll get to it soon in another video. As to the point about acceleration = motion, it all depends on how you choose to view the concept of "motion" of course. If you interpret motion as the necessary consequence of a force, then the river view is rather indispensable. Indeed, one might argue that the assertion "acceleration causes an object to deviate from its geodesic" is nothing further than this view, just wrapped in mathematical lingo, since objects traveling along geodesics through spacetime are technically at rest in space. Of course, you could choose to define motion with respect to some globally stationary coordinate system, in which case spacetime curvature begins to look a whole lot like a regular force. The real problem seems to boil down to the fact that there appear to multiple ways to interpret GR, as a certain mathematical structure doesn't necessarily imply a unique singular interpretation of that structure.

@@dialectphilosophy yeah that whole topic opens up quite the can of worms lol. Interestingly, it's similar to how there are many ways to interpret quantum mechanics. I always pictured general relativity as having a much clearer ontology than the quantum theory, but perhaps that was a naïve viewpoint. Of course, quantum mechanics is mathematically incomplete, as well as ontologically incomplete. But maybe relativity has a richer interpretation than I thought, since it's not just spacetime geometry we have to worry about, but also the observer and their coordinate choices. In any case, this is a fascinating pedagogical topic for physics professors to reflect upon when teaching relativity, and I'm excited for the next video!

Elaborating on something someone else posted in the comments, I think the "upwards" acceleration becomes completely intuitive: Imagine a disc floating big enough to no fit inside the river's drainage in the animations. That disc is equivalent to earth's matter pushing against each other's mass (the boats clogging the drain). Now each side of the disc is pushed by the river (accelerated) in the opposite direction... every opposite side from where water if flowing in, is accelerating at the same speed. It's so simple and beautiful.

Thank you so much!

it's only a mental image, space is not a material thing that goes anywhere, gets created or destroyed.

Good questions! I would add why spacetime "falls" towards matter?

3. Matter gets stuck because of (mainly electromagnetic) repulsion between the bits of matter. You could say that every bit of matter is like a little mobile space drain trying to flow into the other space drains, but ultimately being forced to keep a distance by repulsive forces.

The space, and time, don't "go anywhere" or even move at all.... those are arbitrary coordinates that we map onto a four dimensional shape (spacetime) that describes the "distance" between any two points in spacetime. Any arbitrary 4D chunk of spacetime will always have the same hypervolume, but some of the space and time edges will get longer or shorter when compared to an identically sized hypervolume of spacetime located next to any large concentration of mass (and energy). General relativity is literally just geometry. It's literally just describes a (4D) shape.

I should add... light, by definition, follows a straight line. And material objects, being held together with electrostatic forces (i.e. light) will consider a straight line to be whatever light is doing, and follow along with the light. As long as you observe light to be following a straight line in your own reference frame, you are therefore in an inertial reference frame. (Because your ruler and clock, the atoms of which are held together with light, are going to bend with the light, and never measure any bend. You need to compare with rulers and clocks located far away.)

That's what coming up next

It's just an analogy to help people understand the concept of how the Earth's surface, can be accelerating us up/outward. Notice in the video, nothing really moves towards the center of the mass until he drops a ring of particles around it, and another ring, and another ring, etc. It's the particles which are flowing like a river.

@@jddang3738 Literally the first sentence in his description of the video: “Does space “flow” like a river?” It’s not just the particles bud; he’s claiming it’s the space that’s flowing and the particles are just floating along for the ride.

Inertia and "inertial reference frames" are what this is based on... and inertia is kinda non-intuitive if you've lived your whole life as a human on the surface of the Earth. I don't want to write a long comment here about Galileo and Newton's first law of motion... but mechanically inertia comes down to the subatomic particles that compose material objects being held together with electrostatic forces -- the electric force is essentially "light". You're body is partially made out of light, to put it bluntly. And when the light takes the same amount of time to travel between all of your atoms in every direction equally, you will measure yourself as being "at rest", i.e. in an inertial reference frame. If the light needs to travel a further distance through "space" in one direction than in other directions, you will measure this as acceleration, a "force". Newton's second law of motion is that anything which is not straight line motion through space is by definition involving acceleration (a force for constant mass). General relativity is curving the "straight line" path of light, and material objects fallow the path of light, because material objects are held together with "light".

How far can an analogy take us?... stay tuned...

Hey, sorry for missing this earlier! But thank you for your support and your kind words :-) If we want to extrapolate the analogy and treat space as something physically real, then indeed the space must "vanish" somewhere. Newton actually proposed such a "mass-eat-space" theory of reality once in a letter he wrote, so such a possibility is not as new-sounding as it seems. Some proponents of the river interpretation conjecture that each proton in each atom functions as a sort of miniature black hole, so that the river, as it flows into a body of mass, slowly dissipates. There are number of other issues to be considered with such a model, but we certainly plan on exploring it further down the line!

Gosh -- thank you for your generosity and support, it means a lot to the channel!

Haha thank you! Won't even begin to mention how many hours were wasted playing with the water simulator... never again!

@@dialectphilosophy not wasted! The product is at least well-appreciated!

thanks for your support! And we're returning to the Twin Paradox very soon (and we know we keep saying that, but this time we mean it)

@@dialectphilosophy I'm eagerly waiting for it! In fact, all the content produced by Dialect has been exceptional, so I'm excited to see any content you make, whether it be in theoretical physics, logic, or philosophy.

That makes us thrilled to hear! So glad our videos are helping!

No, the waterfall and river source just needs to narrow the closer you get to the fall.

@@timjohnson3913 The water volume right above the fall is usually shallower than the stream/river leading up to it.

@@jddang3738 It doesn't need to be shallower... when it isn't all the water falls out faster and you just have an empty valley or salt flat with a broad cliff, or something... this is more of a Geology thing, and the "waterfall" model of gravity is an analogy, and not a real waterfall.

Our depiction of a waterfall isn't very physically accurate, and was intended to create a picture which mirrored the linear picture of approaching a body of mass. Now, there are several reasons why water flows faster near the edge of a waterfall and the discussion of why that is, is actually quite illuminating for the river model. Unfortunately it was too much for one video, so it'll come up at a later date.

Same!

Have you consider to join that "sink" of space, where "mass eats space", wirh the opposite "source" in empty space (with no mass), where "space creates space", giving place to a number of phenomena, from universe accelerated expansion to limited speed of light (although photons seem to move instantaneously, with no time flowing)?

@@manueldaniel2371 I've wondered whether the space is destroyed or separated off like droplets of water into their own separate universes, or into a shared parallel universe, perhaps with inverted spacial dimensions (a mirror-verse) - and that could have interesting implications for quantum-entanglement or a realm for dark matter to hide. As for space coming back into our dimensions causing expansion, I've seen it suggested that antimatter might expand space but I don't think that's possible, as it appears to falls the same as regular matter. An idea I prefer, inspired by holographic, information and simulation theories of the universe, is that as particles consist of information, in order for a quantum interaction to create a new particle, new space must be created to store it in, but perhaps when a particle is annihilated that space is left behind and not deleted. Think then of the interactions in the quantum foam, where photons split into electron-position pairs then recombine into photons, and this process could result in ever-expanding space. This could theoretically be tested if you could rapidly create and destroy antimatter underneath a super-sensitive scale or some other gravitational measure, but perhaps not in practice! 🙃

To introduce acceleration (which is needed for "apparent gravitational force") the mass should eat space with more and more speed over time. So, it should eat more space in each next second compared to the corresponding previous second.

@@balabuyew I don't think so. Constant speed of "amount" of space eaten would transmit (in time) along 3-dimensional space (spherecally), resulting in a "space falling speed", in every point, inversely proportional to the square of the distance, just for geometrical reasons.

Stop it. We're in 2023, not the 1823. Go back and re-watch his videos on relativity, so that you can catch up with the rest of his audience.

That is a common objection against the River Model, that is creates a substantialist view of space. There are several further analyses to be made about such a statement, and we'll probably follow up on them in future videos.

There was nothing to do with dark energy or spacetime in this video.. just space.

Absolutely... He even said near the last that this river model is just for subtle understanding or to build a good easy picture,but not the exact reality. You highlighted the exact unmatching points...👍👍👍👍

Now you've thrown a spanner in the works. Just when all this starts to make a glimmer of sense suddenly I'm right back where I started, confused. The stones may pass you on the 1st floor at different speeds, but they will be experiencing the same rate of acceleration. Isn't that the point?

Another huge red flag with this idea is that we must assume matter is somehow attached to space, and when space is moving the matter must move along with it. It is far from clear how this interaction can work. When we travel through space, it’s not like we drag along the bits of space our matter sits on with us. Instead, traveling matter is moving into new bits of space (space atoms, if you like) as it travles.I would love to see Dialect provide the details as to why moving space would drag matter with it.

@@kevconn441 Right, same acceleration but not same speed. Unlike a river. IMHO to get somewhat intuitive understanding of GR it's best to stick with geometry of curved spaces, a static 4D manifold, not some flowing space which may be easy to imagine but quite misleading.

@@thedeemon I suppose you are right. Problem, for me at least, is the math is hard and it's hard to get an intuitive grip on it, if you know what I mean. I will, however, accept you are right and keep stumbling along. Thanks for the reply.

We found that same paper during our research for this video! It was extremely enlightening. How we'd interpret the rotational vorticity without a global vortex is like having tiny "eddying" currents in your river... for instance, if you pass a floating stick over a very small eddy in your river, its rotation will change, but not its direction of flow, which produces the description that occurs in Hamilton's paper.

Thank you for your support, and glad it made a difference for you!

*incorrectly

Thank you for the kind words and support! ScienceClic is our hero too -- don't think we'll ever out-do him (not that we won't try 😏)