# What is it that forces an object down curved space time?

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• vincent

#### vincent

To explain the concept of curved space time, we often use analogy of rubber sheet. If we put a heavy ball at the centre of sheet then it creates a depression and now a smaller ball will fall towards that heavy ball because of depression. But in this analogy smaller ball is falling down the slope because of gravity itself and the whole analogy was introduced to prove that gravity is an illusion. Also, this analogy will fail in space.

Now in space time because of mass space time will curve and a moving object will move along the curved path. But what is causing that movement in the first place. What is that force which pushes an object along the curved path?

To explain the concept of curved space time, we often use analogy of rubber sheet. If we put a heavy ball at the centre of sheet then it creates a depression and now a smaller ball will fall towards that heavy ball because of depression. But in this analogy smaller ball is falling down the slope because of gravity itself and the whole analogy was introduced to prove that gravity is an illusion. Also, this analogy will fail in space.

Now in space time because of mass space time will curve and a moving object will move along the curved path. But what is causing that movement in the first place. What is that force which pushes an object along the curved path?
You have inadvertently succumbed to pop-science non-sense, basically. The "curvature" you speak of is actually a straight line, it's just that it's a straight line (more correctly a "geodesic") in Riemann Geometry which is what is used to describe space-time (except in pop-science which can't be bother with such correctness because it's too complicated for them). SO ... there IS NO "force". Objects follow straight lines and they lead to massive objects, so other objects tend to move along these geodesics to the massive objects. A different way of saying this is that the "force" you think exists is just the geometry of space-time.

vincent
To explain the concept of curved space time, we often use analogy of rubber sheet.

No. The rubber sheet analogy only illustrates curved space, not curved spacetime. The time part is completely left out--which makes the analogy highly limited and often misleading. One common misunderstanding it causes is the question you ask:

What is that force which pushes an object along the curved path?

There is no force required. Objects moving in a curved spacetime and feeling no force, i.e., in free fall, move along geodesics of the curved spacetime; the reason they move is that they are moving into the future, which everything does automatically.

OK. So, can I say that space time curve in a way changes relative distance between objects with passage of time although objects are following straight lines themselves. If there was no space time curve objects would have remained at same relative distance with passage of time.

No. The rubber sheet analogy only illustrates curved space, not curved spacetime. The time part is completely left out--which makes the analogy highly limited and often misleading. One common misunderstanding it causes is the question you ask:

There is no force required. Objects moving in a curved spacetime and feeling no force, i.e., in free fall, move along geodesics of the curved spacetime; the reason they move is that they are moving into the future, which everything does automatically.
Thanks a lot. I think I have moved closer to grasping general relativity now.

can I say that space time curve in a way changes relative distance between objects with passage of time although objects are following straight lines themselves

More precisely: take two objects that are both in free fall and start out at rest relative to each other. In flat spacetime, they will stay at rest relative to each other forever. But in curved spacetime, in general, they won't: they will acquire a relative motion (exactly what relative motion depends on the details of the spacetime curvature). This is, in fact, the physical definition of what it means for spacetime to be curved.

vincent
More precisely: take two objects that are both in free fall and start out at rest relative to each other. In flat spacetime, they will stay at rest relative to each other forever. But in curved spacetime, in general, they won't: they will acquire a relative motion (exactly what relative motion depends on the details of the spacetime curvature). This is, in fact, the physical definition of what it means for spacetime to be curved.
OK but for free fall what are these objects falling towards and why?

OK but for free fall what are these objects falling towards and why?
Free fall just means they aren't subject to forces like electromagnetism, or friction, or whatever. They're not going anywhere in particular, they're just going. In the absence of gravity free fall is literally Newton's first law - things keep going in a straight line.

Einstein's insight was that gravity didn't look like other forces. If you are inside a box in free fall there is no way to tell if you are in deep space, or in orbit, or falling towards the surface of the Moon. For example you can detect an electromagnetic field in your box by letting a charged and an uncharged particle fall. They will move differently. But everything interacts the same way with a gravitational field, so there is no "gravitationally uncharged" thing to let fall.

Coupled with Minkowski's realisation that Einstein's equations for Special Relativity imply that spacetime was a 4d manifold, this opens the door to the notion that spacetime is a curved 4d manifold. In such a spacetime, the "natural path" for things to follow is not a straight line (it's not really possible to define a straight line in a curved space) but a geodesic (note: in flat spacetime, geodesics are straight lines).

So, basically, free-fall in general relativity is a generalisation of Newton's first law. Things move along geodesics unless acted on by a force. And gravity is not a force.

They're not going anywhere in particular, they're just going.
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Ok, This is where I have reached now. They are just going through time and not falling to anything.
Under no gravity, they are going through time in straight line with no change in physical space location( as we perceive it). And under gravity, space gets curved with time, so their physical space location keeps changing with time and this is what we see as effect of gravity.

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Ok, This is where I have reached now. They are just going through time and not falling to anything.
Under no gravity, they are going through time in straight line with no change in physical space location( as we perceive it). And under gravity, space gets curved with time, so their physical space location keeps changing with time and this is what we see as effect of gravity.

Personally, I never saw much value in describing a geodesic as a straight line. Not least because "straight" carries strong preconceived notions that may not generalise to a geodesic.

In particular, in this case, we are taking about a geodesic through spacetime. Not a straight line through space.

If you are standing on the Earth and fire a projectile, then clearly it moves in a curved path relative to you. But, if you are fired with the projectile, then it appears stationary to you. So, whether something is moving in a curved physical path depends on your reference frame.

However, the projectile is following a "natural" or "unforced" or "inertial" path through spacetime. While you standing on the Earth are not following a natural path through spacetime, as you experience a force from the Earth's surface that prevents you "falling" in a natural path (geodesic) towards the centre of the Earth.

vincent
Under no gravity, they are going through time in straight line with no change in physical space location( as we perceive it). And under gravity, space gets curved with time, so their physical space location keeps changing with time and this is what we see as effect of gravity.

There is no such thing as "physical space location" in any absolute sense; it depends on your choice of coordinates.

Also, gravity is spacetime curvature; that is not the same as "space curves with time".

They are just going through time and not falling to anything.
Under no gravity, they are going through time in straight line with no change in physical space location( as we perceive it).
Whether something is stationary or not is a matter of perspective. I'm on a train; I regard my phone as stationary. Someone standing by the track would say it was doing 60mph.

In the absence of gravity, objects in free fall move in straight lines. A special case of this is not moving with respect to you (or some chosen reference object).
And under gravity, space gets curved with time, so their physical space location keeps changing with time and this is what we see as effect of gravity.
This makes it sound like space is changing, which isn't the case. Space and time are mot uniquely defined; spacetime is curved and you can choose to slice up into space and time in many different ways. There really isn't a better explanation for why the paths are curved in curved space than for why paths are straight in flat space: those are just the paths objects follow in such spaces.

vincent