[yor_on (OP)]

" f space-time is infinite ,how gravity extends to infinity?
 we know infinity is unreachable because it continues forever and no-one reach a finite point.How gravity extends to infinite distances while  infinity is unreachable? how gravity bends and curve space-time everywhere while space time end is unreachable? for gravity to bend space-time everywhere it should reach its end , how gravity bends space-time end while this end is unreachable? " By  Yahya A.Sharif

[yor_on (OP)]

You're perfectly correct,
It can't, everything breaks down at 'infinity'

Although it also involves a arrow.
And it´f the arrow is'c' while 'space' is 'ftl'`?

[Colin2B]

He is however incorrect to say that gravity has a finite range. The reduction in the effect is asymptotic and never reaches zero.
He plays word games eg “for gravity to bend space-time everywhere it should reach its end”. Garbage as well as being logically incorrect.

[yor_on (OP)]

I don't know Collin, what it made me think of was the example in where you place a circle over a infinity. You can't, a infinity has no 'edge' and so it can't fit a circle (or any other geometrical figure I guess? Although depending on 'dimensions' introduced possibly?). And Yahya do agree that science define gravitys reaches 'infinitely' but then ask how it is supposed to work. Also how it can 'bend space'.

[yor_on (OP)]

Now, that's a funny thought?
How about a sphere, isn't that a infinity too, bounded but boundless in all directions (two dimensionally at least). I'm not that happy with dimensions myself. Then again, the same could then be argued for a circle (one dimensionally at least, maybe two dimensionally too?  If a infinite amount of one dimensional circles described from a 'higher space' could become a 'sphere', crazy thoughts :) )

But 'gravity' the way I see it Yahya is not a 'force', it belongs to laws and properties and so must be of a infinite reach if the universe is infinite.
=

You could think of gravity as one of the properties intrinsic to any 'space' defined. Introduce a mass inside a space and you will introduce dimensions. A perfect vacuum without any mass has no dimensions as far as I can imagine it. No distance either.

[Colin2B]

The problem with infinity is that it isn’t a real place, it’s a shorthand/concept for a very, very, very long way away.
In practical terms no matter how far we move away from a single mass its gravitational influence will always be greater than zero. We all accept that it might be so close to zero that we can’t measure it, but that doesn’t make it zero.
The rubber sheet is always curved 

Of course, with multiple masses there will be points where the curve is at a cusp, and those will be a lot closer to us than infinity 

[yor_on (OP)]

Think of those super massive black holes Collin. Inside their 'event horizon' as defined from their inside gravity becomes infinite, doesn't it :) At the same time as its gravity outside that event horizon also is infinite, although maybe not measurably so.You could think of its inside as a 'folded space' from my point of view in where all directions becomes one, at least it seems reasonable to presume so. We need mass to define both space and gravity. And then we have 'accelerations'. so weird stuff thinking of it in terms of relative motion.
=

You could think of it this way too.
What comes first, mass or acceleration?

[yor_on (OP)]

I actually don't expect accelerations to be provable without introducing mass. And that puts acceleration in the same category as gravity, it becomes a property, doesn't it?

Think of a 'spaceship coasting' (uniform motion) inside a 'empty space'. Make it do a turn as defined from its inside (by using thrusters etc) will it feel a acceleration?
=

Then think of the light paths taken inside that event horizon. Although we might define them as 'bending' there are no accelerations involved inside the event horizon. The lightpaths do not blue and redshift intrinsically, only relative a observer. To see how you could imagine yourself just inside a event horizon watching one light path coming towards you. It should redshift to you, but as it's also traveling a 'curved path' as defined from an outside, which then if we think of it as a analogue to the 'spaceship' above, it also should blue shift.

so those lightpaths are not bent, and there are no accelerations involved intrinsically. Introducing mass it becomes different, then a acceleration is immediately provable intrinsically, and should be so even in a otherwise 'totally empty space'. And that is the way gravity acts on a space. When we talk about masses we say that gravity acts and get acted upon by other masses. But I don't think the same could be said about space, space doesn't exist without mass, or expressed otherwise mass defines Space. When we discuss uniform (relative) motions we use one way of looking at it, formed through the way we grow up and the way we see it around us.Was it Wheeler that said that space tells mass where to 'move' and mass told space how to 'curve'? Well, if a uniform motion is indistinguishable from being still to all terms except observer dependently then mass is what creates relative motion. And they should all be 'straight paths', just as that 'light path'.

Then again, let's use the spaceship once more in a otherwise 'empty space'. This time we first accelerate it in a 'straight motion' to then let it 'coast' again. Here's the tricky part, as we now make the same turn as last time (apply the same force to our thrusters etc) will we now find a stronger intrinsic acceleration acting upon us, aka 'gravity'? We should, shouldn't we?

So is a relative motion indistinguishable from being still?

[Yahya A.Sharif]

I think the probelm here is associated with two points:
1) the gravitional equation F=GmM/r²:
The gravitional equation is experimental at the distances it was tested for but it is not at infinite distance and can't be tested infinitely:
a) The equation could be wrong at the places it is not tested in, but true where it has been tested the fact of infinite gravity is only a prediction according to the equation since for each value of r we have a non-zero value for F, the fact the gravity ( where it has been tested)is inversely proportional to the squared r does not not necessarily validate the equation for each r till infinity. There might be another model that says the equation is true where it has been tested or for a specific range and it is not true elsewhere, an example is the "rubber sheet" at a time it is not fully bent , there is a delay in its bending; it spreads out with a delay, at a time there are places where the rubber bending is zero and places where the bending is non-zero, if we compared space-time curvature with rubber sheet bending then there is places where gravity is governed by the inverse squared law and there is other places which are not'zero gravity"" all this in case mass poped out from nowhere at a time before the big bang.

b) Is it possible that gravity suddenly drop to zero while it is governed by the inverse squared law? This depends on how the space-time is curved .Since gravity is an effect of space-time curvature for gravity to exist everywhere its cause"space-time curvature " must exist everywhere as well, is space-time curvature everywhere? that depends on the mass itself which causes space time curvature.
If space time curvature exists everywhere then gravity exists everywhere till infinity as well, if space-time curvature exists within a range so does gravity.

2) Does space-time curvature exist everywhere untill infinity? it is simple as this: non-zero mass causes spacetime curvature , no mass no space time curvature.
a) Lets suppose mass poped out from nowhere, In physics events happens gradually , that is mass m can't jump from quantity zero grams to let say 3 grams at 2 seconds! 'supposing mass is possible to exist from no where' it starts to increase gradually until it reaches the quantity 3 grams during the 2 seconds. Did space time extend in range gradually 'from zero meters' after the mass poped out  or it existed everywhere  ? is that physical, an example is the 'rubber sheet' its bent delay to reach every part of the sheet.

b) The negation of number a option is a unique other option which is mass existed infinitly in the past and never poped out from nowhere, there was mass one miliion years ago, 1 billion years,→infinite time, there is not a law that says mass didn't pop out from nowhere ,  energy conservation law governs our universe , but what if our universe which is governed by this law itself poped out from nowhere and the laws started to apply within our universe but not beyond our universe?
Did mass exist infinitely in the past or just the universe poped out from nowhere before the big bang? But could we say something spent ∞ time while ∞ is not a real number ? Is that physical?

[alancalverd]

I actually don't expect accelerations to be provable without introducing mass. And that puts acceleration in the same category as gravity, it becomes a property, doesn't it?

Gravity bends the path of (i.e. accelerates)  and alters the energy of (i.e. accelerates) photons, which have no mass.

There is no problem if you define infinity as the distance at which F_grav = 0

[Yahya A.Sharif]

There is no problem if you define infinity as the distance at which F_grav = 0

You can't define infinity such way, infinity is not a fixed number, you cant say " at which"  there is not a point " at which "we could measure infinity as distance with a ruler, if force could be measured with a scale with a value of 0 we can't find a ruler to measure infinite distance.

[yor_on (OP)]

I don't have a good answer to the idea of a infinity.
More than it is is more than our measurements

Infinity may be described mathematically, but practically it never ends.

[alancalverd]

There is no problem if you define infinity as the distance at which F_grav = 0

You can't define infinity such way, infinity is not a fixed number, you cant say " at which"  there is not a point " at which "we could measure infinity as distance with a ruler, if force could be measured with a scale with a value of 0 we can't find a ruler to measure infinite distance.

Nor will you ever find a point at which F = 0. Hence the validity of my definition.

It is a very practical concept, which we use to define gravitational and electrical potential, among other things.

[Yahya A.Sharif]

The reduction in the effect is asymptotic and never reaches zero.

Light intensity is also asymptotic but it reaches zero. when light delay in reaching a place its intensity there is zero.
Although light intensity is proportional to 1/d² , where d is the distance , we can't substitute all possible values of d

[pensador]

You are all missing a small point.

The cosmological constant (or maybe dark energy) is causing the accelerating expansion of the universe. This is not factored into newtons equations. Without the cosmological constant( Einsteins greatest blunder ) the universe would end up in a big crunch and galaxies would not be accelerating apart.

Infinity is just a thing/value that can not be calculated or attained, it helps in maths that it enables equations to be simplified. ie anything/∞ = 0 and anything/0 = ∞ .

Newtons theories are very accurate but were replaced for accurate calculations by Einsteins SR and GR.Einsteins equations predict the existence of Dark matter, which might or might not exist. Likely some of the alleged dark matter might be H2. Most exotic substances have been ruled out. Perhaps Einsteins equations will be replaced by some other gravitational theory in the future, that better explains the rotation of galaxies, without the need for random amounts of Dark matter to be inserted.

[alancalverd]

The reduction in the effect is asymptotic and never reaches zero.

Light intensity is also asymptotic but it reaches zero. when light delay in reaching a place its intensity there is zero.
Although light intensity is proportional to 1/d² , where d is the distance , we can't substitute all possible values of d

It doesn't "reach" zero at a place where it hasn't yet arrived. You just have to wait for it. Buses don't disappear at Grantham en route from York to London, but they take a couple of hours longer to get to London. And the intensity of York buses in London is low because some of them go to Birmingham.

Same thing with photons.

[Yahya A.Sharif]

The reduction in the effect is asymptotic and never reaches zero.

Light intensity is also asymptotic but it reaches zero. when light delay in reaching a place its intensity there is zero.
Although light intensity is proportional to 1/d² , where d is the distance , we can't substitute all possible values of d

It doesn't "reach" zero at a place where it hasn't yet arrived. You just have to wait for it.

Light has a limited range extendable with c speed , even though 1/d² works for it.
If there is another model for gravity where you have to wait for gravity"extendable limited range", the gravitational equation will then be valid for that model , just like 1/d² is valid for light

[alancalverd]

As far as we know, the speed of gravity is the same as the speed of light. It is certainly an inverse square force and cannot logically be anything else since the gravitational field of a point source must be spherically symmetrical.

[Yahya A.Sharif]

The current fact is that the initial singularity of the universe contained infinite gravity density, the universe and space-time were created by the big bang, all gravity contained by this singularity " gravity of all matter of the universe "expanded to infinity.

[pensador]

The initial singularity of the universe contained infinite gravity density, the universe and space-time were created by the big bang, all gravity contained by this singularity " gravity of all matter of the universe "expanded to infinity.

Your view of the big bang is out dated, all mass did not appear from a singularity. It appeared from inflating areas of space where mass did not exist. Have a look at inflationary theory Guth > Linde etc