## Experiments Reveal That Deformed Rubber Sheet Is Not Like Spacetime 264 264

KentuckyFC writes

*"General relativity is mathematically challenging and yet widely appreciated by the public. This state of affairs is almost entirely the result of one the most famous analogies in science: that the warping of spacetime to produce gravity is like the deformation of a rubber sheet by a central mass. Now physicists have tested this idea theoretically and experimentally and say it doesn't hold water. It turns out that a marble rolling on deformed rubber sheet does not follow the same trajectory as a planet orbiting a star and that the marble's equations of motion lead to a strangely twisted version of Kepler's third law of planetary motion. And experiments with a real marble rolling on a spandex sheet show that the mass of the sheet itself creates a distortion that further complicates matters. Indeed, the physicists say that a rubber sheet deformed by a central mass can never produce the same motion of planet orbiting a star in spacetime. So the analogy is fundamentally flawed. Shame!"*
## Why did they bother? (Score:4, Interesting)

## All analogies are fundamentally flawed (Score:5, Interesting)

It only illustrates the

basic concepts. After that, one has to go beyond the analogy and do themath.I remember a poster on a door at the math department of my university (parafrazing from memory): "Do not try to visualize a space with more than 3 dimensions. Nobody can do that, trying will just twist your mind. Just use the formulas with the correct number of variables and leave it at that."

## The experts have spoken (Score:4, Interesting)

In other news, experts pointed out that rubber sheets provide a two-dimensional surface, while the real spacetime continuum provides three spatial dimensions and one of time. Experts also pointed out that rubber sheets have nonzero friction with rolling marbles, while empty space has zero friction; and that the rubber sheets do not provide the time dilation effects that gravity provides.

Experts also pointed out that the whole rubber sheet thing is what is known as an "analogy" and pretty much by definition is inexact.

Personally, I found the article interesting, but the tongue-in-cheek "Shame!" of the summary a bit over the top.

P.S. From TFA:

## Re:Um... (Score:4, Interesting)

In the analogy of the rubber sheet, the earth's gravitational acceleration is the passage of time.

## Re:Um... (Score:5, Interesting)

The dented rubber sheet (done in earth's gravity) is a not too bad analogy for Newtonian gravity.

Let me try the "ant" analogy in a bit more detail:

The "orange" is curved space time. here we have 1 space like dimension and one time like dimension, curved into 3d.

The "ants" walk forward. This walking is the analogy to moving forward in time.

On a big flat surface, two ants that started near each other walking on parallel paths (both moving forward in time and at rest relative to each other) would stay the same distance apart.

On the curved orange though as the ants walk forward, they wind up getting closer: Imagine they start at the equator and both head due north. The start out parallel, and both walk in as straight a line as is possible on the surface. After a while they find themselves closer together - as if some mysterious force (gravity) is attracting them. (this is as they get to the north pole.

The orange analogy isn't all that great either because the curvature isn't shaped right for GR. Unfortunately humans aren't good at imagining curved 4-dimensional space.

If the rubber-sheet demo is done without earth's gravity it isn't a terrible analogy, but I don't think I've ever seen it show that way. It seems to always be shown as this curved surface where the EARTH's gravity causes the marbles to roll to the center.

## Re:Um... (Score:5, Interesting)

The problem is the rubber sheet is a 2D surface. It can represent two dimensions. It can be two of space (as is normal), one space and one time, etc.

Real spacetime is a 4D entity - 3 (elongated) space, 1 time. The reason we use the rubber sheet analogy is because visualizing the distortions in spacetime (a 4D entity) is quite... difficult. Even visualizing a 3D representation is quite hard (pick your mix of space and time dimensions you want to show).

However, a 2D representation is quite easy to demonstrate and show to a class so they can visualize that happens. Sure, gravity is the biggest reason why the rubber sheet curves and what causes the marble to follow the curves, but it's a remarkably intuitive image of the warping of spacetime. (Then again, gravity is what causes the warping to begin with, and while we're using the earth to warp a rubber sheet because it's convenient...).

To be honest, it isn't a rigorous mathematical model, but it was never supposed to be. It's a practical demonstration on the weirdness of spacetime and gravity, illustrated on a 2D plane because we, despite being 4D entities have a hard time imagining it.

No one's going to derive equations for general relativity based on the rubber sheet analogy (or model - our physics class had a real model and we all had a chance to play with it). But it's certainly a great "a ha!" style of demonstration to solidify what is happening from dozens of equations and dry text.

And face it - modern physics is really damn hard to show people what is happening - either things are too big (relativity) or too small (quantum physics) that most people do not have any sort of grasp of it. At best, you have a model or an analogy. And never mind gravity is an extremely weak force to deal with.

So no, you aren't going to be mathematically correct. You are, however, going to get a lot of "I get it now!" reactions. Because in normal everyday life, gravity is not like what the theory says it is. We experience gravity like what Newton said it is. We don't see gravitational lensing or other such things

I say the rubber sheet model is more adept at getting the public to understand relativity than anything else.