[Outcast (OP)]

A bowling ball on a rubber sheet to illustrate how "warped space" makes orbits work is OK as far as it goes.
What if the two bodies have no relative motion? They are sitting there occupying each other's curved space, but neither is moving thru that curved space. Is there no gravity?

[Janus]

A bowling ball on a rubber sheet to illustrate how "warped space" makes orbits work is OK as far as it goes.
What if the two bodies have no relative motion? They are sitting there occupying each other's curved space, but neither is moving thru that curved space. Is there no gravity?

The rubber sheet analogy only works even for the orbits if you assume that the orbiting object tends to want to "roll down hill" in the dip made by the bowling ball. Just placing an object somewhere in that dip will result in it rolling down the slope towards the bowling ball.

It isn't just warped space that's involved, it is warped space-time.  There is a time component involved in the warping that lends to the "down hill" aspect of this model. 

[Origin]

A bowling ball on a rubber sheet to illustrate how "warped space" makes orbits work is OK as far as it goes.
What if the two bodies have no relative motion? They are sitting there occupying each other's curved space, but neither is moving thru that curved space. Is there no gravity?

It is just an analogy so it will only approximate the actual phenomenon.
How could it be possible to have 2 massive objects near each other and have no relative movement?  Certainly they would move towards each other.

[Outcast (OP)]

It is just an analogy so it will only approximate the actual phenomenon.How could it be possible to have 2 massive objects near each other and have no relative movement?  Certainly they would move towards each other.

Certainly they move towards each other...but curved space doesn't explain it.

[Janus]

It is just an analogy so it will only approximate the actual phenomenon.How could it be possible to have 2 massive objects near each other and have no relative movement?  Certainly they would move towards each other.

Certainly they move towards each other...but curved space doesn't explain it.

Again, Gravity is a result of curved Space-time, not just curved space.

[alancalverd]

Two massive bodies in free space will move towards each other - that's the everyday observation of gravity. Their motion is neatly modelled by the ball-and-sheet analogy.

[Outcast (OP)]

Two massive bodies in free space will move towards each other - that's the everyday observation of gravity. Their motion is neatly modelled by the ball-and-sheet analogy.

We certainly agree on the observation...what made them start moving toward each other with no previous relative motion? Curved spacetime initiated motion between them? By what mechanism?

[Janus]

Two massive bodies in free space will move towards each other - that's the everyday observation of gravity. Their motion is neatly modelled by the ball-and-sheet analogy.

We certainly agree on the observation...what made them start moving toward each other with no previous relative motion? Curved spacetime initiated motion between them? By what mechanism?

One way to look at it is that in curved space-time, the natural tendency for things to go from past to future is partially transformed in a tendency to move towards a lower gravitational potential. In other words, movement through time becomes spatial movement to a certain degree. 

[geordief]

One way to look at it is that in curved space-time, the natural tendency for things to go from past to future is partially transformed in a tendency to move towards a lower gravitational potential. In other words, movement through time becomes spatial movement to a certain degree.

By describing a "natural tendency for things to go from past to future" are you in any way saying that there is an absolute nature to time ? It sounds to me as though time is primordial and that space-time  is  something  that developed from it

Are you saying ,or implying that this attribute of time is ever present(an odd choice of words on my part)  and somehow independent of space-time itself (well space-time is just  a  highly successful model,I think I have heard)

Time is perhaps no model ,whereas space-time is?

[Colin2B]

It sounds to me as though time is primordial and that space-time  is  something  that developed from it

Why would you assume that?

Janus was describing how space and time are inextricably linked, movement through one affects movement through the other (relatively).

In other words, movement through time becomes spatial movement to a certain degree.

[geordief]

 

Why would you assume that?

Janus was describing how space and time are inextricably linked, movement through one affects movement through the other (relatively)

Well "the natural tendency for things to go from past to future" as Janus described it  seems to involve phenomena
(a phenomenon) that lie outside the spacetime model .

I mean ,the spacetime model would ,I suspect work as well if time ran backwards ,but I think we are taking it as an axiom that time runs in the direction of increasing entropy.

That is why I was wondering if this question of the "mechanism" of the unfurling of time (eg its direction) might be more fundamental than the outworkings we see in the spacetime relativistic effects when relative distances become involved.

I notice you seem to talk of things moving through space as well as through time (in their inter related way) but wonder can we really talk of things "moving through space" when all they are doing ,arguably is to change their positions  relative to each other and not "through" anything

I am musing rather than prescribing

[Outcast (OP)]

Janus was describing how space and time are inextricably linked, movement through one affects movement through the other (relatively).

Are you saying nothing can be stopped in space because it's moving forward in time? I disagree. The linkage of space to time has led many to believe that makes these dimensions equal.They are not. I can stop in space. I can go backwards in space. I can do neither in time.

[Colin2B]

Well "the natural tendency for things to go from past to future" as Janus described it  seems to involve phenomena
(a phenomenon) that lie outside the spacetime model .

Not if you take the Minkowski model of spacetime.

I think we are taking it as an axiom that time runs in the direction of increasing entropy.

Axiom or observation?

That is why I was wondering if this question of the "mechanism" of the unfurling of time (eg its direction) might be more fundamental than the outworkings we see in the spacetime relativistic effects when relative distances become involved.

not sure what you mean, can you expand?

I notice you seem to talk of things moving through space as well as through time (in their inter related way) but wonder can we really talk of things "moving through space" when all they are doing ,arguably is to change their positions  relative to each other and not "through" anything

it seems easier to talk of things moving rather than ‘changing their positions relative to each other or relative to a coordinate reference point’

Are you saying nothing can be stopped in space because it's moving forward in time?

no

I can stop in space.

how would you know?

[Fishreeler]

Imagine an iron ball. When the space in which it is located begins to contract and stretch, the atoms of which it consists begin to converge in one direction and move away in the other. However, the forces between them prevent them from moving as freely as they should. As a result of this, the deformation of the ball lags somewhat behind the deformation of space-time. Regarding space-time, the ball begins to vibrate, contracting and stretching. And such vibrations can let us know that right now GW pass through the ball. Unfortunately, the deformations are very small: the relative change in size under the influence of the GW recorded in September 2015 is ten to minus twenty-first degrees.

[alancalverd]

what made them start moving toward each other with no previous relative motion?

Gravity. Acceleration = force/mass. Force = GMm/r^2. You can measure the force anywhere in the vicinity of a large mass, and calculate it for a small mass.

[geordief]

not sure what you mean, can you expand?

I have been thinking about this.I am handicapped by my lack of knowledge in this area but I will have to try and explain what I  may have been  thinking.

Time seems to me like it could be more fundamental than spacetime (space/distance  perhaps ,also)

I know Minkowski said that henceforth we should consider spacetime rather than space or time independently and of course that has led to predictions that we wouldn't have otherwise.

But I am wondering whether ,in some way spacetime  might have emerged from space and time  and that space and time do/did have independent existences before we had the spacetime that we now observe.

Of course ,if spacetime is completely fundamental  then I would accept that but is it accepted generally that it is the case? Do all  potential theories of Quantum Gravity approach spacetime ,time and space in the same way as current classic and quantum theories do?

[Paul25]

It's using gravity to define itself.

[David Cooper]

The problem with the rubber sheet analogy is that it simply moves the gravitational pull which it's trying to eliminate to a pull from below the sheet to drag things down into the dip, so it provides an empty explanation which merely hints at the idea of curved space. If you actually move things on the straightest path across such a sheet without the gravitational pull from below being involved, the path they'll follow will be the path that a roller would follow, and two rollers moving through the same point on the sheet in the same direction at different speeds would follow the same path instead of following different orbits, and they can't even orbit on a rubber sheep either unless the surface has been bent all the way to the vertical to provide a wall-of-death geometry.

To visualise how the curving would actually work (and I use the word "would" because I think Spacetime is just a mathematical abstraction and nothing to do with how the universe actually works), you have to get the whole idea of circular and elliptical orbits out of your head and replace them with helical paths. When an orbiting object completes one orbit, it hasn't returned to the place it started in, but has travelled a vast distance from there along the "time" dimension, and the time-wise distance that it's covered is orders of magnitudes greater than the length of the orbit through the space dimensions. This means we're dealing with a path which, if we imagine the time dimension running upwards and just use two space dimensions, it looks almost like a string hanging vertically from the ceiling to the floor with just a tiny amount of helical wandering from side to side as it goes up. This means that the orbiting object is following a path that's almost straight even if you include the curving of Spacetime as part of the curvedness of that path - it never curves back to return to where it was in the past, so nothing anything like a circular or elliptical path exists for anything in Spacetime.

To create an orbit, it is thus sufficient just to deflect the path of the object a little in order to make the path helical. Objects moving at different speeds through the same location in the same direction from the 3D perspective are not passing through that location in the same direction from the 4D perspective because they are following different time-length paths due to their different speeds through the space dimensions, so that's how they're able to follow different orbits.

If you want to understand how a stationary object placed near a planet would accelerate towards the planet, you need to realise that it is not stationary, but is racing along the time dimension at the speed of light, so it is already moving and only needs its path to be deflected to guide it towards a collision with the planet, so everything in the Spacetime model is driven by deflection of the paths of things that are all moving all the time already. Nothing can ever sit still.

[Outcast (OP)]

A non-Euclidian geometry has been posited to describe how parallel lines converge in curved spacetime. This is one explanation for gravity between bodies with no relative motion. Can parallel lines not also diverge in this non-Euclidian geometry? Why would we not observe repulsive gravity?

[David Cooper]

A non-Euclidian geometry has been posited to describe how parallel lines converge in curved spacetime. This is one explanation for gravity between bodies with no relative motion. Can parallel lines not also diverge in this non-Euclidian geometry? Why would we not observe repulsive gravity?

I'm sure they can diverge too, in principle, but you need to have something to cause them to diverge, just as you need to have something cause them to converge. The universe only seems to do the latter because its content always produces the conditions for attraction-gravity, but that doesn't mean it's impossible for Spacetime to do the former - it might merely be impossible to create the kind of stuff that would produce the desired effect.