The trampoline of gravity

courtesy of Analogies are an important part of understanding, as well as the popularisation of physics.

However, analogies are analogies and at some point always fail to capture the full picture of what is going on. More than that, taking analogies too seriously can lead to misunderstandings.

Einstein’s general relativity basically tells us that massive objects bend the space-time they are sat in and that this is the origin of gravity. To really understand this one has to pull apart the Einstein field equations in all their tensorial beauty. I won’t do that here and now.

A common analogy here is that of a heavy bowling ball placed on a trampoline. The bowling ball deforms the elastic trampoline surface, it sags, and this is similar to how a massive object, say a star, bends the space-time around it.

One can now “model” photons or test particles by using light balls, say ping-pong balls. The point is that these near weightless balls will not deform the trampoline’s elastic surface. When the bowling ball is not on the trampoline the light balls move in straight lines when given a light initial push. When the bowling ball is on the trampoline the light balls no longer follow straight lines, but curved paths. These light balls are attracted to the bowling ball: thus we have gravity!

This is a great analogy for light rays or photons in general relativity. Light is bent around massive objects like stars. If you have access to a trampoline and some heavy and light balls, play around and experiment for yourself.

However, This analogy seems to be the principle source of misunderstandings and even scepticism of general relativity for the untrained.

Conceptionally the analogy breaks down because the trampoline does not represent the three dimensional space we inhabit, or rather a time slice of our four dimensional world. All we have is an embedding of a two dimensional geometry in our three dimensional flat world.

The trouble is that the space-time of general relativity does not require any such embedding in a higher dimensional flat space. It is of course true that mathematically we can always find (isometric) embeddings in higher dimensional spaces of the geometries found in general relativity, but this does not imply that nature uses such things.

The other issue is that the trampoline analogy really misses the curvature of space-time and only highlights space curvature. The ping-pong balls move about the sheet being “attracted” to the bowling ball because of the depression in the elastic sheet. The trouble is that in general relativity test particles, say photons, move in the “straightest possible path” in four dimensions, including time. This fact is missed by the analogy.

So however useful this analogy is, and I say it is useful, it cannot really describe general relativity. Objections, philosophically or otherwise to general relativity cannot be founded on the trampoline analogy.

The great man himself. Moreover, there is plenty of direct and indirect experimental verification that general relativity is a good model of gravity. This fact seems rather inescapable: there are no consistent repeatable experiments that, taking into account the domain of applicability and experimental errors, that suggest that general relativity is not a good model. I may say more about this another time.

In short, love analogies, use analogies, tell other people about analogies, however remember they are analogies and no replacement for mathematical models.

4 thoughts on “The trampoline of gravity”

  1. I’ve always hated the picture of the earth warping a ‘sheet’ of coordinated space–it was the least sensible thing I had ever seen as a teenager.

    One statement you have made is another source of discomfort for me, “Einstein’s general relativity basically tells us that massive objects bend the space-time they are sat in and that this is the origin of gravity.” This bothers me because it implies that mass curves space-time and so we have gravity. But then what is the difference between this and saying we are looking for the Higg’s Boson, the transmitter of gravity? I’ve always concluded in my own mind that as a cause of gravity objects of mass warp space-time, but in fact we do not know what the cause of gravity is. I’ve always concluded in my mind that Einstein’s General Relativity modeled or explained the behaviour, but not necessarily the source.

  2. The Higgs is believed to be the origin of mass for fundamental particles. It is not the “main component” of the mass of composite objects, for instance stars and planets. So on this classical level we do not need to think about the Higgs when thinking about gravity.

    My statement; “Einstein’s general relativity basically tells us that massive objects bend the space-time they are sat in and that this is the origin of gravity.” is intentionally a bit fluffy. To really get to grips with the relation between curvature and matter content you need to examine the field equations in detail.

  3. I will, after I pick up the book you recommended and maybe a few others depending on its contents. It might also take me another five years of learning math, which kind of sucks.

    Thanks as always ajb! 🙂

  4. I don’t think the analogy completely misses the point that photons travel in the straightest line possible. If the rubber sheet analogy was demonstrated in zero-g, with “sticky” ping pong balls that rolled freely while adhering to the surface, they would also travel the straightest line possible along the curved surface and their paths would curve along with the rubber sheet. No uniformly “downward” force is needed.

Leave a Reply

Your email address will not be published. Required fields are marked *