# How to resolve confusions on the rubber sheet analogy of the spacetime curvatures?

How to resolve confusions on the rubber sheet analogy of the spacetime curvatures?

I am a newbie to spacetime curvature. I have watched several youtube videos on Einsteins GR and spacetime curvature where most people used the analogy of the rubber sheet and ball on the sheet. However, I cannot realize that rubber sheet analogy with my reality. For example,

1. The rubber sheet is a two dimensional sheet on the other hand I see our universe is a three dimensional.
2. The balls on the rubber sheet are placed from one direction to other (top to bottom) but in reality I see out planets and stars are flying on the space.
3. Light flows over the rubber sheets and curves around the balls in its world line, but in reality we know everything themselves are travelling with the speed of light in their world line.

How can I resolve these confusions? I am really interested to know detail about them.

• Analogies are intended to be similar to something; they are not the same thing. So they are always imperfect and partial. Not every aspect of the analogy will be reflected in reality. The rubber sheet analogy has many serious problems, as several earlier questions on this site show. – Anders Sandberg Nov 10 '20 at 21:39
• I can't understand the English in your third point. Please clarify. – James K Nov 10 '20 at 21:40
• @JamesK I tried to edit 3rd point – Sazzad Hissain Khan Nov 10 '20 at 21:52

The rubber sheet only is not meant to be a qualitative model, it gives one concept and one concept only: Mass causes curvature of spacetime.

You can't get any more than that from the rubber sheet. If you have that idea in your head already then you are ready to drop the image because:

• The sheet is 2d but spacetime is 4d
• The 2d sheet is embedded in 3d space. Space-time isn't embedded in a 5d or higher dimension (or at least, if it is, it is irrelevant)
• The sheet has two space-like directions with no time dimension. Space-time has a time-like dimension.
• The basic way of finding distances on a flat sheet is $$(x^2+y^2)^\frac12$$. The basic way of finding distances in 4d spacetime is $$(x^2+y^2+z^2-t^2)^\frac12$$ (where units are chosen to make the speed of light = 1, eg time in seconds, distance in light-seconds)

You can't create a simple image of curved 4-d space-time. The rubber sheet analogy will hinder further understanding if you try to use it to understand why an object will travel in an apparently curved path in space when in a gravitational field. It's only purpose is to embed the notion that "space-time is curved" it can't tell you anything else about what that implies.