https://www.youtube.com/watch?v=wrwgIjBUYVc
This uses Adobe tools to visualize and take advantage of video format.
Why though? Would it help if the sheet were in a centrifuge?
It bothers me too, why? because it's circular reasoning: acceleration can't explain acceleration.
> Would it help if the sheet were in a centrifuge?
No, for the same reason. (You're imagining a tube-shaped membrane?)
To make it worse, it's developing a wrong idea that hides the right and deeply strange idea: when an object passes a mass and its path seems to deflect what's really happening is that the object is moving in a straight line the whole time and space itself is curved. (The situation is actually a little stranger than that, but I'm no physicist so I won't try to explain any further.)
And anyway explaining gravity v2 in terms of v1’s first approximation isn’t that strange when recursive definitions are going to play a part in lots of higher education anyway. When you’re a kid, 5 is just a concept useful to describe every instance of 5 apples, but later, a number N is perhaps best understood as the successor of N-1.
The actual description of gravity isn't hard to understand, it's just really strange. There is no good reason to introduce confusing and intrinsically incorrect models.
Well, teaching is the usual reason, otherwise physics with trig would all just wait for calculus, and calculus wouldn't get covered before real analysis, etc. Incorrect, or more charitably "useful, prerequisite, & intentionally not rigorous" models are a pretty standard tool for walking students closer to real understanding. Clearly no one is proposing trampolines and bowling balls models because they are expecting to win a Nobel.
> The actual description of gravity isn't hard to understand, it's just really strange.
Hmm, Einstein thought it was pretty hard, and I didn't know that you and Witten had finished quantum gravity or the other latest and greatest.
> Gravity is one of the fundamental forces, there's no recursion in it's definition, indeed we don't "define" it we describe it.
Unpacking this to a first approximation it actually sounds like you're looking for The Truth instead of useful models, that you always know Truth when you see it, that you don't believe that apparently different descriptions can result in formally equivalent stuff. I'm also guessing that you might be strongly inside a "only cares about math because physics" camp whereas I sympathize more with "only cares about physics because math". Lots of interesting conversations in there, but it'll all just be philosophy at that point anyway and you probably wouldn't like it.
> Well, teaching is the usual reason,
Introducing confusing and intrinsically incorrect models is the opposite of teaching.
> "useful, prerequisite, & intentionally not rigorous" models are a pretty standard tool for walking students closer to real understanding.
The funnel model of gravity isn't useful, prerequisite, or rigorous.
> Unpacking this to a first approximation it actually sounds like you're looking ...
A bunch of projection on your part follows.
I'm sorry to be rude, but to me you seem to be intelligent yet deeply confused.
I'm going to bow out of this thread now, again I apologize.
until we crack it.
It's fun to try to peel away defects in the "ball on a rubber sheet" in an effort to arrive at Newtonian limit equations of motion for balls in placed around it. (First advanced question: how do we adapt Einstein-Hilbert to reflect trapping onto the sheet? Does dimensional reduction work?) What sort of membrane in constant acceleration could generate scaled 2+1 timelike geodesics for model solar system objects placed on it? Can one scale this to a model of the solar system with all orbits flattened onto the membrane? For instance, what do the IVs look like for a ~ 1050:1 mass ratio between a model sun and a model Jupiter that is shrunk down to classroom size and retains a good match to Jupiter's real orbital parameters (or if you prefer, lengths and angles) across many orbits? Without destroying this scale model orbit, can we add the inner solar system? Can we get sensible orbits of scale model Galilean moons?
(And of course all of the above has completely neglected the rotations of these bodies about their axes, which is clearly always very wrong with a typical in-classroom rubber sheet + balls demonstration. We can blame friction for that.)
I'm not sure what you're representing on silly putty: are the drawn lines solutions to geodesic equations? What would the twists-pulls of the putty in a scale model ~kg:g Sun and Jupiter system look like? Or are you thinking about a relativistic regime somewhere in the right half of this diagram : <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...> ?
The balls on a rubber sheet model is actually really great, but not in the way it's typically presented (rolling a ball down the curvature). Instead, just use a pen to draw lines to show the concept of geodesics.
Start like this:
1. Imagine that you can move without friction if you stay at the same vertical level.
2. Draw a line on a flat rubber sheet, that's a line in free space. It's just a straight line that can go on to infinity.
3. Now put a ball onto the rubber sheet, so you get some curvature. Now the lines near the ball that stay on the same level are not straight lines, but circles.
Ok, you brought in the "g" word. I think that makes it fair to ask how you plan to calculate the analog of spacetime intervals along your rubber sheet.
The general curves (not just geodesics) down to the heavy central ball all end up where the ball and sheet are in contact unless blocked by earlier contact with the central ball. How do you recover anything like the behaviour of a smaller ball bound to a non-spacelike radial geodesic with one end normal to the central ball's surface and the other "at infinity" (or at least in the part of the sheet that is asymptotically parallel to the ground)?
How do we show students, using your adapted rubber sheet, that spacetime curvature around a spherically symmetrical mass is symmetrical in all the spatial dimensions and that there is a curvature induced on the timelike dimension too.
What's the relationship between your pen lines and the Christoffel symbols (notably \Gamma^{1}_{00}) or Euler-Lagrange?
How does your "3." work with highly eccentric elliptical orbits? How about a grazing hyperbolic orbit? Think Halley's comet and 1l/`Oumuamua.
Describe it as an artistic representation of the theorized behavior.
Pull a Maxwell, whose theory of electromagnetism only worked when he got rid of the imaginary levers; get rid of descriptions in terms of physical things.
As a visual it’s fine. The debate here is the language. Only one aspect needs to change.
I like to imagine a sponge. If you could somehow make dense lumps inside the sponge (may be apply heat in its center somewhere using microwaves?) everything around that lump will be feel a tension/attraction towards that lump. That's my mental model.
When you see those stretched rubber sheets, they rarely/never show the grid lines moving. So let's say you place a small *stationary* object at a specific grid point (coordinate), and there's a large object that deforms the grid itself. Nothing about that visual provides any new intuition about why the small object would leave it's current grid position and move towards the larger one.
The visual tries to explain gravity by appealing to your existing notion of gravity.
Afaiu, the answer is that moving through time in a gravitational gradient makes you constantly “fall flat” on an x/time 2d graph due to time dilation gradient, thus affecting x and spatial momentum. Apparently mass affects time and time creates gravity. Idk if that’s a fringe idea or mainstream.
"using gravity" in the experiment is convenience of the experiment - gravity is freely abundant to use, both as a source of curvature and source of "making objects not leave the sheet"
if you want to hold the sheet by yourself, and hold the objects to the sheet by yourself - you are free to do it, enjoying your victory of "not using gravity"
but the point is not in the means, but in the end - create curvature, keep contact
An inert object will sit on it kissing it and never go anywhere. The curvature of a sheet doesn’t matter cause there’s no “down” and no forces. If you push it “in” a little and release, the sheet tension will push it back out but not “to” the well. You may start accelerating the system to create gravity-like situation, but that’s the point.
These models are also an intuitive way to illustrate why the speed of light is a limit.
A ball rolling on a rubber sheet, or a boat on a lake, etc, can travel faster than waves in the rubber or water. So why can't matter travel faster than light? With ball-on-sheet type models, you need to resort to abstract relativity arguments about mass going to infinity, time slowing, causality, etc.
But if particles are actually just waves or knots or whirlpools or whatever, they clearly can't possibly travel faster than the speed of waves in the medium.
For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surrounding putty. So, if you drew lines on the putty then pulled it into lumps, you’d see the distortion to the lines.