[Spacetectonics (OP)]

Sounds like a stupid question !
But,
According to general relativity mass curves space-time giving the effect of gravity,
Why light follows a curved path as the shortest possible path between two points,when crossing ,say a huge mass ?and not a straight line ?
OK ,we may say it is because of the space-time "curved" and its intrinsic characteristic!now my question is what caused space to curve"bend"?
Lets be straight forward,HOW matter could "curve" the space-time?Under what physical regime,what formula?!

[Pmb]

Sounds like a stupid question !

You asked

Why Light follows the space-time curve?

It follows a spacetime curve by definition. That is to say that the name we give to the set of events through which light passes is defined as a worldline.

But,
According to general relativity mass curves space-time giving the effect of gravity,

Its more accurate to say that mass can curve spacetime. It’s conceivable to have a distribution of matter and the spacetime region near the matter still be flat. It’s quite possible to have a gravitational field in flat spacetime.


Whether the spacetime is flat or curved, any particle, free or not, will my on a worldline by definition. A free particle moves on a geodesic.

Why light follows a curved path as the shortest possible path between two points, when crossing ,say a huge mass ?and not a straight line ?

A particle follows a path on which the proper time is extremal. It can be shown from this that such a particle follows a geodesic. The derivation is pretty mathematical so if your mathematically inclined you can follow the derivation I placed on my website at
http://home.comcast.net/~peter.m.brown/math_phy/geodesics.htm

It shouldn’t call it the “shortest possible path” because that phrase refers to a spatial trajectory, not a spacetime trajectory. And that it does it a postulate so it can’t be derived from more fundamental facts.

OK ,we may say it is because of the space-time "curved" and its intrinsic characteristic!now my question is what caused space to curve"bend"?
Lets be straight forward,HOW matter could "curve" the space-time?Under what physical regime,what formula?!

Nobody knows the “why”’s of your questions. We just know the “how”’s and they’re given by general relativity. Einstein’s field equations describes how spacetime curvature is related to matter. For more on Einstein’s field equations please see
http://home.comcast.net/~peter.m.brown/gr/einsteins_field_equations.htm

[Spacetectonics (OP)]

Thanks BMP,

I have read about GP.B and have some inquires!!

Einstein's theory of General Relativity predicts that Earth, by rotating, twists space and time around with it, forming a mild vortex in the fabric of spacetime around our planet. Researchers call this "frame dragging." Most physicists believe the spacetime vortex is real, but no experiment to date has been sensitive enough to detect it unequivocally.

Until this has been done:   http://science.nasa.gov/science-news/scien.../26apr_gpbtech/

"Einstein’s field equations describes how space-time curvature is related to matter"

Does that mean everything defined as "mass ",could effect Space-T?!
-----------------------

When saying :  "by rotating, twists space and time around with it, forming a mild vortex"

And considering  that  "Sun rotates once every 27 days at the equator" and solar system rotates at the center of M.W galaxy  ,then should not we observer effect of a huge vortex at about our sun?and consequently on the light received from outside of the milky way?from other stars,including ones at these experiments?

In another world, have these vortexes affected the "light observation experiments"including the one you have mentioned?
What happen to the light crossing these vortexes?!(or by expanding this into "even" milky way, this effect is still negligible?)

Cheers,

[lean bean]

It’s conceivable to have a distribution of matter and the spacetime region near the matter still be flat. It’s quite possible to have a gravitational field in flat spacetime.

Perhaps I'm being pernickety.
Some time ago on a NASA site there was a question... '' is spacetime a thing'' the answer given was... ''Yes, it's another name for the gravitational field of the universe''
Is it in this sense that you mean you can have a gravitational field even though spacetime may be flat?  i.e. a flat spacetime is still a gravitational field?
Or is it something to do with the evenness of the distribution of mass/energy in a region ?

[yor_on]

To me it is energy dependent

Our universe is picky, and don't want to spend more energy than it must. So if the cheapest 'way' is bent, then that is the way it will follow. As for what is a straight line I'm not sure. I would call that observer dependent too.
=

Or geometry dependent?
Or all of the above possibly?

[Pmb]

Perhaps I'm being pernickety.
Some time ago on a NASA site there was a question... '' is spacetime a thing'' the answer given was... ''Yes, it's another name for the gravitational field of the universe''

Then that NASA site is wrong. Another name for the gravitationall field is not the universe. That's just plain silly.

Is it in this sense that you mean you can have a gravitational field even though spacetime may be flat?  i.e. a flat spacetime is still a gravitational field?
Or is it something to do with the evenness of the distribution of mass/energy in a region ?

Spacetime curvature is the same thing as tidal forces. Tidal forces cannot be transformed away. For that reason some relativists like to think of spacetime curvature as being the true signature of the presense of a gravitational field. Einstein disagreed with that perspective and so don't I.

[evan_au]

Re: mild vortex in the fabric of spacetime around our planet. Researchers call this "frame dragging."

The Earth, the Sun and the Galaxy have a relatively low density, and a fairly low rate of spin, so frame dragging was undetectable (until Gravity Probe B).

Neutrons stars have the have the mass of the sun in a diameter of about 10km, and can spin at up to 1000 revolutions per second. Frame dragging would be more easily detectable in this environment.

But the environment where it has the biggest impact is in the vicinity of a spinning black hole, which could have a mass much larger than the Sun in a smaller volume than a neutron star, with a greater angular velocity, with no risk of flying apart.

Some links to this story:
Frame Dragging due to Earth http://science.nasa.gov/missions/gravity-probe-b/
Frame Dragging due to a Black Hole http://science.nasa.gov/science-news/science-at-nasa/1997/ast06nov97_1/

[lean bean]

Spacetime curvature is the same thing as tidal forces. Tidal forces cannot be transformed away. For that reason some relativists like to think of spacetime curvature as being the true signature of the presense of a gravitational field. Einstein disagreed with that perspective and so don't I.

I think I can understand how comparing different points in a region leads to the idea of tidal forces and so to the idea of curvature. But, you say like Einstein you don’t agree with that idea?
If it’s not too mathematical could you explain the grist of what Einstein would agree with in defining gravity in a region if it’s not comparing different points of that region?

To me it is energy dependent
Our universe is picky, and don't want to spend more energy than it must. So if the cheapest 'way' is bent, then that is the way it will follow. As for what is a straight line I'm not sure. I would call that observer dependent too.

 Yes I can see something of where your coming from. A rock will take the path that will give the rocks wristwatch the maximum proper time in spacetime, that maybe the straightest path in spacetime but not necessarily a straight path in just space. Something like...in the rock's frame there's no energy expended.
I think!

[Pmb]

I think I can understand how comparing different points in a region leads to the idea of tidal forces and so to the idea of curvature. But, you say like Einstein you don’t agree with that idea?

No. In essence, what Einstein said was that the presence of a gravitational field was not the non-vanishing of tidal forces (Reimann tensor) but the non-vanishing of gravitational acceleration (affine connection).

[lean bean]

I think I can understand how comparing different points in a region leads to the idea of tidal forces and so to the idea of curvature. But, you say like Einstein you don’t agree with that idea?

No. In essence, what Einstein said was that the presence of a gravitational field was not the non-vanishing of tidal forces (Reimann tensor) but the non-vanishing of gravitational acceleration (affine connection).

Thanks for getting back.
Now, you have made me really pernickety and allowing me to display my ignorance here...
I thought, when talking of GR, it was because of the differences at difference points we get acceleration?
What is causing a rock to accelerate, if all it is doing is moving in a spacetime which is the same at all points?
Not too mathematical please

[Pmb]

I think I can understand how comparing different points in a region leads to the idea of tidal forces and so to the idea of curvature. But, you say like Einstein you don’t agree with that idea?

No. In essence, what Einstein said was that the presence of a gravitational field was not the non-vanishing of tidal forces (Reimann tensor) but the non-vanishing of gravitational acceleration (affine connection).

Thanks for getting back.
Now, you have made me really pernickety and allowing me to display my ignorance here...
I thought, when talking of GR, it was because of the differences at difference points we get acceleration?
What is causing a rock to accelerate, if all it is doing is moving in a spacetime which is the same at all points?
Not too mathematical please

There is no theory of what causes objects to accelerate.

Picture yourself in a uniform gravitational field. When standing in such a field you can't tell that you're in a uniform g-field or at rest in a uniformly accelerating frame of reference. in flat spacetime. However if there were tidal forces present then you'd b able to tell the difference. If tidal forces are present then you know its caused by a gravitational field. There is no way to simply change your frame of reference to mimic a frame of reference in which there are tidal forces.

[lean bean]

The concept of mass is only metaphysically tied to matter. The idea of "curved space-time" is gibberish. "Time", "space" and "space-time" are abstract coordinate systems invented to help describe reality, they are not somethingreal you can manipulate or "curve" in any fashion.

If from experiment and observation we create our reality and so our models (GR), then in what other way do you wish to explain reality if not by models?
 Observation, and so our models, suggests something about mass/energy alters spacetime in their vicinity.
Can you suggest a way of getting to the fundamental ''truth'' (whatever that means) and how we will know it is the fundamental ''truth'' and not just a very good model?

[AndroidNeox]

Actually, light does follow a straight line, from its own perspective. Imagine you have a long string that doesn't weigh anything but is very strong pulled tightly. Shoot a light beam alongside it and the light and string will remain parallel, even as they pass through bent spacetime.

I was surprised to read that the NASA site says spacetime is a thing. Not only is it not a thing, but the universe appears to have no net gravity, when you add up all of the positive and negative energies the result seems to be zero.

[lean bean]

I was surprised to read that the NASA site says spacetime is a thing. Not only is it not a thing, but the universe appears to have no net gravity, when you add up all of the positive and negative energies the result seems to be zero.

I have spent a little time googling for that Nasa site where the question was asked,it was some time ago when I first saw it...

Bit more googling and Nasa site ...
Where does space come from?

Essentially, space is what we refer to as three of the four dimensions to a more comprehensive entity called the space-time continuum, and this continuum is itself just another name for the gravitational field of the universe. If you take away this gravitational field -- space-time itself vanishes!

http://www.nasa.gov/centers/kennedy/about/information/science_faq.html#46

These are interesting saying the same...
http://www.astronomycafe.net/qadir/BackTo283.html

http://www.astronomycafe.net/qadir/BackTo289.html

Don't shoot the messenger.

[Pmb]

Actually, light does follow a straight line, from its own perspective.

In what way does light does have a perspective? Light follows a geodesic if that’s what you mean but in a gravitational field its spatial trajectory is curved.

Imagine you have a long string that doesn't weigh anything but is very strong pulled tightly. Shoot a light beam alongside it and the light and string will remain parallel, even as they pass through bent spacetime.

Not in general. E.g. in a uniform gravitational field a taught string will have the shape of a catenary. The more tension in the string the less it sags but regardless of how strong the tension is there will always be some sag.

Shoot a light beam alongside it and the light and string will remain parallel, even as they pass through bent spacetime.

That’s incorrect. If you tied a string between two walls in a gravitational field the shape of the string will be a catenary. Now aim a laser beam starting off parallel with the string at one end. The string and laser beam will diverge. This happens because light falls in a gravitational field and thus the beam of light will be deflected downwards just as if you were throwing a ball parallel to the ground and it dropped as if moved and eventually hits the ground

[lean bean]

 Android

Actually, light does follow a straight line, from its own perspective. Imagine you have a long string that doesn't weigh anything but is very strong pulled tightly. Shoot a light beam alongside it and the light and string will remain parallel, even as they pass through bent spacetime.

Android
I think your find the idea is rocks, light and anything else unpowered follow a curved spacetime path in the vicinity of massive bodies such as the sun/ black holes. Powered things like rockets can travel in straight line paths ignoring curved spacetime.
Your ''pulled tightly'' straight rope has been pulled straight, that is, the work done in pulling, has stopped the rope from following a curved spacetime path. So light would not follow the rope parallel
I think

[AndroidNeox]

Maybe I didn't make it clear that I was presenting a thought experiment in which a string of zero weight were under tension. Since it has no weight, it will not sag. It will be perfectly straight, locally, just as a light beam is. A light beam always follows a straight line, from its own perspective. I presume one can meaningfully speak about the perspective of a light beams since Einstein depended upon such thought experiments in forming Relativity. In thought experiments, one should ignore every inconvenience of real physics, so long as the logical basis of the argument isn't invalidated.

[Pmb]

Maybe I didn't make it clear that I was presenting a thought experiment in which a string of zero weight were under tension. Since it has no weight, it will not sag. 

So you're not talking about a real string and thus not a real lsitiation but merely an approximation to the real thing. In anycase the string and beam of light will not remain parallel if there is a gravitational field present which is perpendicular to the beam of light.

In any case you still have given no meaning to the statement "A light beam always follows a straight line, from its own perspective." What does this mean? What is the perspective of light? What does it mean for light to have a perspective?.On what basis are you justifying this assertion? Are you speaking about a straightline in spacetime or in space? Is this spacetime curved? Is the space curved? If so then "straight line" has no meaning for curved surfaces.

[AndroidNeox]

In any case you still have given no meaning to the statement "A light beam always follows a straight line, from its own perspective." What does this mean? What is the perspective of light? What does it mean for light to have a perspective?.On what basis are you justifying this assertion? Are you speaking about a straightline in spacetime or in space? Is this spacetime curved? Is the space curved? If so then "straight line" has no meaning for curved surfaces.

Here's a wikipedia reference that might help: http://en.wikipedia.org/wiki/Geodesics_in_general_relativity

"In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime."

[Pmb]

In any case you still have given no meaning to the statement "A light beam always follows a straight line, from its own perspective." What does this mean? What is the perspective of light? What does it mean for light to have a perspective?.On what basis are you justifying this assertion? Are you speaking about a straightline in spacetime or in space? Is this spacetime curved? Is the space curved? If so then "straight line" has no meaning for curved surfaces.

That is true only for null worldliness, i.e. for particles moving at the speed of light.

The point is that only particles that move at the speed of light have speed c. The other person was talking about the speed of objects in spacetime where I was speaking about the speed of objects in space. The term “speed of an object in spacetime” is meaningless. There are a few people here and there who like to say that all objects move at the speed of light in spacetime but no relativist would ever make such a statement. In fact when they hear that they sigh and say that its wrong.
." What does this mean? What is the perspective of light? What does it mean for light to have a perspective?.On what basis are you justifying this assertion? Are you speaking about a straightline in spacetime or in space? Is this spacetime curved? Is the space curved? If so then "straight line" has no meaning for curved surfaces.
[/quote]

Here's a wikipedia reference that might help: http://en.wikipedia.org/wiki/Geodesics_in_general_relativity

"In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime."
[/quote]
I'm well aware of what a geodesic is and how its viewed as the 'straightest possible line in a curved space". The phrase "light beam always follows a straight line, from its own perspective." is not something that has been used to mean that by anybody else I've ever seen. If we were to use that kind of terminology then It can always be said that that all free particles move in straight lines from their own perspective. That holds true because all free particles move on geodesics