Gravity is Time? | General Relativity Explained

[Ralph Spencer]

While reading through Halliday & Resnick, I came across a brief introduction to General Relativity in the gravity chapter. It gives the example of two boats starting off on the equator heading towards the south pole in parallel paths. However, they MEET at the south pole. While sailors can believe this to be a force between the boats, from a higher dimension (as 'flat' surface of Earth curved around its center is viewed from space), we notice that it is only because the surface is curved. But the actual motion is caused not by the curvature of the surface but by ROWING the boat - which corresponds to time in the real world. Thus significance of gravity is nothing but passage of time i.e. gravity is time?

EDIT: Request to Moderator: I believe this thread is more appropriate on the 'Cosmology' board.

 

[CompuChip]

The point is that they do move, but to them the movement is exactly parallel. Nothing in the motion they produce has a perpendicular component to push them closer together, and yet they meet in a single point.

You can probably also look at it another way. Suppose that the water is completely frictionless... you could give them both a single push at the equator such that they get the same constant velocity with respect to earth. Then relative to each other they are at rest (in the special relativistic sense). And still there is some mysterious force that accelerates them with respect to earth, just like an apple falling to the ground.

 

[Ken G]

Indeed, the connection with time is closer than you might imagine. In the analogy of the Earth, we have the concept of "geodesics" on the spatial surface. A geodesic is the analog of a "straight line" when there is inherent curvature, like the curved surface. But that's all spatial-- in GR, the geodesics are through spacetime, not space. What's more, for the person traversing the "straight line" through the "curved spacetime", it's all time-- they aren't going anywhere, they are always where they are, because there's no "water" to give them an absolute frame of reference. If they are, for example, inside a freely falling black box in which they can do experiments, they are, as far as they are concerned, perfectly stationary. That's the "equivalence principle."

So if the observers transiting the geodesic are stationary, as far as they are concerned, then they experience and measure no change in spatial location-- only a change in elapsed time. What's more, the geodesic is the path of maximum elapsed proper time (analogous to how straight lines in Euclidean space are the minimum distance). Since the role of gravity in GR is simply to determine what the geodesics are, this means the role of gravity is to determine the paths along which we have maximum proper time. So yes, in a way, gravity is time.

 

[Ralph Spencer]

you could give them both a single push at the equator such that they get the same constant velocity with respect to earth. Then relative to each other they are at rest (in the special relativistic sense). And still there is some mysterious force that accelerates them with respect to earth, just like an apple falling to the ground.

So it should correspond to some initial force applied on what was available back then at the beginning of time?