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Sounds like a stupid question !

Why Light follows the space-time curve?

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 ?

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 ?

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

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.

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.

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?

Quote from: lean beanI 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).

Quote from: Pmb on 06/01/2013 14:26:26Quote from: lean beanI 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

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.

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.

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!

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.

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

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.

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.

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.

Quote from: lean beanPerhaps 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.

Why is the gravitational field of the universe another name for space-time?The development of any mathematical theory of natural phenomena such as gravity requires that the mathematical symbols defining the theory must be related to qualities of the phenomena such as the symbol T representing temperature, V representing velocity or M representing mass. In general relativity, a similar association had to be made by Einstein. We have seen how Einstein defined the gravitational field to be identical to the so-called metric tensor, g mu,nu used by Riemann to describe the geometry of a space. This means that where Newtonian gravity dealt with one quantity to measure the gravitational field, Einstein's theory in the guise of "g-mu-nu" required a total of 10 unique quantities to more completely define how the gravitational field behaved. The force of gravity defined as changes in the gravitational field from place to place in Newtonian mechanics, was replaced by changes in the geometry of space from place to place in spacetime measured by the degree of curvature symbolized by "C-mu-nu" at each point. Einstein's minimalist adoption of "g-mu-nu" as the embodiment of the gravitational field was significant and has far-reaching ramifications. Before Einstein, the metric tensor "g-mu-nu" was a purely geometric quantity that expresses how to determine the distances between points in space. Geometers from the time of Gauss knew nothing about forces, mass and momentum, they did however use the metric tensor to uncover new and bizarre spaces resembling nothing that humans have ever experienced.Einstein's appropriation of the metric tensor so that it also represented the gravitational field led to an inevitable, logical conclusion: If you took away the gravitational field, this meant that "g-mu-nu" would be everywhere and for all time equal to zero, but so too would the metric for spacetime. Spacetime would lose its metric, the distance between points in the manifold would vanish, and the manifold itself would disappear into nothingness. In Relativity: The Special and General Theory page 155, Einstein expressed this quality of spacetime as follows,"Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field"

I have found another site where a Dr Sten Odenwald goes into more detail as to why he thinks...

Why is the gravitational field of the universe another name for space-time?The development of any mathematical theory of natural phenomena such as gravity requires that the mathematical symbols defining the theory must be related to qualities of the phenomena such as the symbol T representing temperature, V representing velocity or M representing mass. In general relativity, a similar association had to be made by Einstein. We have seen how Einstein defined the gravitational field to be identical to the so-called metric tensor, g mu,nu …Einstein's appropriation of the metric tensor so that it also represented the gravitational field led to an inevitable, logical conclusion: If you took away the gravitational field, this meant that "g-mu-nu" would be everywhere and for all time equal to zero, but so too would the metric for spacetime.

The case of the ordinary theory of relativity arises out of the here case considered if it is possible, by reason of the particular relations of the g-mu-nu in a finite region, to choose the system of reference in the finite region in such a way that the g-mu-nu assume the constant values diag(1, -1, -1, -1)

The force of gravity defined as changes in the gravitational field from place to place in Newtonian mechanics, was replaced by changes in the geometry of space

I do not agree with the idea that the general theory of relativity is geometerzing physics or the gravitational field. The concepts of physics have always been geometrical concepts and I cannot see why the g_ik field should be called more geometrical than f.i. the electromagnetic field or the distance of bodies in Newtonian mechanics. The notion probably comes from the fact that the origin of the g_ik field is the Gauss-Riemann theory of the metrical continuum which we are wont to look at as a part of geometry. I am convinced, however, that the distinction between geometrical and other kinds of fields is not logically founded.

Space-time does not claim existence on its own, but only as a structural quality of the field.

On the basis of the general theory of relativity, on the other hand, space as opposed to "what fills space", which is dependent on the co-ordinates, has no separate existence. Thus a pure gravitational field might have been described in terms of the gik (as functions of the co-ordinates), by solution of the gravitational equations. If we imagine the gravitational field, i.e. the functions gik, to be removed, there does not remain a space of the type (1), but absolutely nothing, and also no "topological space". For the functions gik describe not only the field, but at the same time also the topological and metrical structural properties of the manifold.

A space of the type (1), judged from the standpoint of the general theory of relativity, is not a space without field, but a special case of the gik field, for which – for the co-ordinate system used, which in itself has no objective significance – the functions gik have values that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a space without field.

There is no such thing as an empty space, i.e. a space without field.

In any case he did not mean that such a field was a gravitational field.

If we imagine the gravitational field, i.e. the functions gik, to be removed, there does not remain a space of the type (1), but absolutely nothing, and also no "topological space". For the functions gik describe not only the field, but at the same time also the topological and metrical structural properties of the manifold.

And as he says, if you remove the gravitational field, your not even left with a type one space, your left with but absolutely nothing…

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of coordinates.

In his text Einstein identifies the presence of a gravitational field with the spacetime variability of the copmponents of the metric tensor. Thusds^{2} = (1 + gz/c^{2})^{2} (cdt)^{2} - dx^{2} - dy^{2} - dz^{2}denotes the presence of a uniform gravitational field whileds^{2} = (cdt)^{2} - dx^{2} - dy^{2} - dz^{2}denotes the absence of a gravitational field.

In accordance with classical mechanics and according to the special theory of relativity, space (space-time) has an existence independent of matter or field.

On the basis of the general theory of relativity, on the other hand, space as opposed to "what fills space", which is dependent on the co-ordinates, has no separate existence.

A question about observer dependencies?If I assumed that 'gravity' always need to be observed in some coordinate system to 'exist' as a global phenomena, including all observers description. Can we then assume a 'space' that no observers would be able to define a 'gravity' too?If we can then 'space' clearly exist on its own, gravity not needed. If we can't?

Can you link to anywhere where that's shown. google's not helping me.

Gravity is observer dependent to me. It has to do with what coordinate system you use.

Gravity is observer dependent to me. It has to do with what coordinate system you use. But that's also because I think of it as local definitions.

Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations. A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it. This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.

I'm wondering here, does Einstein mean a uniform gravitational field when he refers to special form? ''but only for those of quite special form''

No. He means those gravitational fields in flat spacetime. Consider a rotating frame of reference. In that frame there will be two inertial forces, The Coriolis force and the centrifugal force. Since there is an inertial force in the rotating frame there are gravitational forces/gravitational field in such a frame. But you can transform the field away by the proper coordinate transformation. The "special kind" that Einstein refers to are gravitational fields in which the spacetime is flat.

It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same! You have not transformed away the acceleration - you have changed the physical situation. an accelerated frame of reference is not an inertial frame

I can look at a rock travelling at a constant velocity from my "fixed" position or I can mathematically show what I look like from the rest frame of the rock (ie the rock is no longer moving).

What I cannot do is a mathematical operation that allows me to say that the one point of view the earth has a gravitational field - but from another frame of reference, or coordinate system describe the earth without that field

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same!

"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same! You have not transformed away the acceleration - you have changed the physical situation. an accelerated frame of reference is not an inertial frame I can look at a rock travelling at a constant velocity from my "fixed" position or I can mathematically show what I look like from the rest frame of the rock (ie the rock is no longer moving). What I cannot do is a mathematical operation that allows me to say that the one point of view the earth has a gravitational field - but from another frame of reference, or coordinate system describe the earth without that field

Quote from: imatfaal on 30/01/2013 16:25:58"Transformed away" in physics normally means that you perform a mathematical operation, or change coordinate systems but keep whats happening the same! When it comes to GR it means the following: Suppose there is a gravitational field in the current frame of reference, The presence of the gravitational field manifests itself by letting an object go free by dropping it. If the body accelerates with respect to the current frame of reference it means that there is a gravitational field present. Now invoke a change of the system of coordinates corresponding to a locally inertial frame of reference, If a body is let free and it remains at rest and doesn’t accelerate then there is no gravitational field present. That is what it means to “transform the gravitational field away.” At least according to Einstein. Obviously the reverse is true in that you can produce a gravitational field by an appropriate change in coordinate systems.

Equivalence principle allows one to equate a gravitational field with linear acceleration only if the field is uniform... for example, for someone standing on an infinitely wide plane of mass in an otherwise empty universe. Real world gravitational fields only approximate this, locally.

Sorry Pete but can you run that again? How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away.

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

Thanks Pmb,Would it it be possible for you, to define "Appropriate"; where you have mentioned "an appropriate change in coordinate systems" please?

If you were in a frame of reference in which there was a gravitational field of the Earth’s gravitational field then you can only transform the gravitational field away locally (i.e. in a small region of spacetime). Please explain what your objection is and what the talk about the elevator has to do with it? I.e. please explain why it can’t be transformed away? You do understand, don’t you, that when the spacetime is curved then you can only transform the field away locally? What local means has to do with the precision of the instruments that you’re using to detect the tidal forces.

That’s answered something I was wondering about earlier.Those tidal gradients are still there, it’s just a question of the precision of the instruments that you’re using to detect the tidal forces. Thanks.

The strong principle of equivalence is usually formulated as an assertion that in a sufficiently small, freely falling laboratory the gravitational fields surrounding the laboratory cannot be detected. We show that this is false by presenting several simple examples of phenomena which may be used to detect the gravitational field through its tidal effects: we show that these effects are, in fact, local (observable in an arbitrarily small region). Alternative formulations of the strong principle are discussed and a new formulation of strong equivalence (the "Einstein principle") as an assertion about the field equations of physics, rather than an assertion about all laws or all experiments, is proposed. We also discuss the weak principle of equivalence and its two complimentary aspects: the uniqueness of free fall of a test particles in arbitrary gravitational fields ("Galileo principle") and the uniqueness of free fall of arbitrary systems in weak gravitational fields ("Newton's principle").