B Visualizing Spacetime: 3 Dimensions Not Enough?

[Patrick Murphy]

I've tried to imagine and draw the effect of a large object would have on space time in 3d but it just doesn't seem right. Would I be right to assume that maybe spacetime has more than 3 dimensions?

 

[Nugatory]

It has four.

 

[Patrick Murphy]

Yes the 4th being time. But you can't draw that onto paper. If I draw the effect of gravity that a planet has on the fabric of space I would come up with a much larger sphere of space/time around the planet that is distorted/warped. But if gravity pulls you to one point in 3d space then what I see in the drawing is an illusion?

 

[Charles Kottler]

If I draw the effect of gravity that a planet has on the fabric of space I would come up with a much larger sphere of space/time around the planet that is distorted/warped. But if gravity pulls you to one point in 3d space then what I see in the drawing is an illusion?

"Rubber sheet" diagrams are often used to illustrate the distortion of space-time. They usually show a large three dimensional mass above a stretched 2D plane, with the vertical axis representing time, so the plane should be imagined to be moving 'upwards' at the speed of light. The closer the 2D plane is to the planet the further it lags in time, hence the stretching effect. What is less clear in these diagrams is that the choice of units we use depends on the local speed of light - where time is 'running slower' the local distances are also smaller by the same degree, so 1 light year close to a large mass would in co-ordinate terms be smaller than a light year far from a mass. Whether what you see could be described as an illusion therefore depends very much on your interpretation of what you are looking at.

 

[Orodruin]

Please do not give rubber sheet illustrations more importance than they have. At best they are illustrations of the spatial geometry of the situation. In GR, the geometry of space-time is the important thing.

 

[PeterDonis]

Yes the 4th being time. But you can't draw that onto paper.

Sure you can. What you can't do is draw time and all three dimensions of space. You have to leave out some space dimensions. That means you can't capture all of the effects of a massive body on the curvature of spacetime around it in one drawing. But that just means you need multiple drawings to capture all of the effects; it doesn't mean you can't draw them at all.

 

[A.T.]

Yes the 4th being time. But you can't draw that onto paper.

Yes you can. And you have in order to correctly understand how gravity works in GR.





The problem is that to show orbits, you need 2 spatial dimension, makes 3 with time. But then you have to show a distortion of that 3D space-time, so the illustration would need to be more than 3D for an isometric embedding. As Peter notes, you can draw multiple diagrams to show the different aspects, as shown in the below link:

http://demoweb.physics.ucla.edu/content/10-curved-spacetime