# Curved Space and Acceleration

*Most recent answer: 09/02/2010*

Q:

Einstein said that gravitation is not a force like Newton said but rather the curvature of the space-time continuum. I have no trouble to accept this. What bothers me is this : why do we see it as a force? Why things get accelerated in the first place if it's just a curvature of space-time? Think of it as a car on the freeway. The freeway goes to Chicago. Since the car has to follow the freeway, it will end up at Chicago even though it would like to go to New-York let's say. But something is accelerating the car towards Chicago (the engine). The freeway only guides the car to Chicago. So if gravitation was just mere space-time curvatures, like the freeway, they would only guide already accelerated objects towards the massive body. They would not accelerate anything just like the freeway doesn't accelerate cars. Does it?

- Anonymous

- Anonymous

A:

I like the way you first phrased the question- "why do we see it as a force?", i.e. why do we perceive acceleration. The questions about whether it really is acceleration are more semantic.

I believe the answer is this. Take two objects, say you and the earth, which are traveling in parallel. That means that their distance isn't changing. A situation like that exists if you jump, when you're right at the top of the jump. Follow the paths, and these two parallel-moving objects collide. So either one or both accelerated, or what looked like parallel lines intersected, in which case the space is curved.

Our spacetime is only mildly curved near here. That means that it can be approximately pictured as a flat space, so long as you add some extra acceleration effects (called gravity). Our minds seem to naturally grab on to the mathematically simplest picture which does an adequate job of describing things. Flat space is much simpler than curved space, so that's how we see it.

Mike W.

I believe the answer is this. Take two objects, say you and the earth, which are traveling in parallel. That means that their distance isn't changing. A situation like that exists if you jump, when you're right at the top of the jump. Follow the paths, and these two parallel-moving objects collide. So either one or both accelerated, or what looked like parallel lines intersected, in which case the space is curved.

Our spacetime is only mildly curved near here. That means that it can be approximately pictured as a flat space, so long as you add some extra acceleration effects (called gravity). Our minds seem to naturally grab on to the mathematically simplest picture which does an adequate job of describing things. Flat space is much simpler than curved space, so that's how we see it.

Mike W.

*(published on 09/02/2010)*

## Follow-Up #1: electrical geometry?

Q:

I've been wondering about this myself. I think I have an explanation—but best to check it with you.
Firstly, by definition, the path of two stationary objects are two stationary points in a 3D space.
Now, consider the following two scenarios:
Scenario 1, the objects are too small to have much gravitational effect on each other: The world lines of these objects (i.e., their 4D paths) are approximately two parallel lines.
Scenario 2, one or both objects are massive and hence, curve the 4D space: The (4D) world lines of these objects trace the curvature of 4D space. These world lines ultimately converge.
Now, (and here is my doubtful assumption) the "engine" that the writer speculated is the forward-moving time dimension. Time does not stop (why? I don’t know!). In other words, the (4d) world lines are not static. Every object (as it is on some world line) is moving forward in time. And if the world lines converge (as in Scenario 2) the objects moving on them also converge (i.e., collide).
The curvature of the space forces the objects toward each other in the same manner as an oddly-shaped railroad track with converging rails forces the wheels of a moving train towards each other.
Question: As we accept that mass concentrates space, why not similarly accept that two charged particles expand it?

- Mehran (age 59)

Miami, Florida

- Mehran (age 59)

Miami, Florida

A:

The problem is that if another particle, with a different charge (e.g. zero) were to come along, it wouldn't behave in the way that either of those charged particles would. Two such neutral particles going through there would neither converge nor diverge. So you can't summarize the behavior of all particles by postulating a changed geometry. The Galilean universality of gravity (more generally, the Equivalence Principle) is the key to getting into the General Relativistic arguments.

Mike W.

Mike W.

*(published on 09/22/2010)*