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### Author Topic: Why Light folows the space-Time curve?Not the the shorthest Line?  (Read 12371 times)

#### Spacetectonics

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##### Why Light folows the space-Time curve?Not the the shorthest Line?
« on: 04/01/2013 14:10:13 »
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?!

« Last Edit: 04/01/2013 14:16:29 by Spacetectonics »

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #1 on: 04/01/2013 20:50:10 »
Quote from: Spacetectonics
Sounds like a stupid question !
Quote
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.

Quote from: Spacetectonics
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.

Quote from: Spacetectonics
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.

Quote from: Spacetectonics
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #2 on: 05/01/2013 07:54:29 »
Thanks BMP,

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,

« Last Edit: 05/01/2013 08:03:25 by Spacetectonics »

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #3 on: 05/01/2013 10:47:12 »
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 ?
« Last Edit: 05/01/2013 10:51:19 by lean bean »

#### yor_on

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #4 on: 05/01/2013 19:14:56 »
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?
« Last Edit: 05/01/2013 19:17:32 by yor_on »

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #5 on: 05/01/2013 19:58:40 »
Quote from: lean bean
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.

Quote from: lean bean
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #6 on: 05/01/2013 21:55:09 »
Quote
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.

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/
« Last Edit: 06/01/2013 15:06:21 by evan_au »

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #7 on: 06/01/2013 12:10:41 »
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #8 on: 06/01/2013 14:26:26 »
Quote from: 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).

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #9 on: 06/01/2013 17:28:10 »
Quote from: 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?

« Last Edit: 06/01/2013 17:30:59 by lean bean »

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #10 on: 06/01/2013 20:34:46 »
Quote from: 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?

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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #11 on: 12/01/2013 12:14:55 »
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?
« Last Edit: 12/01/2013 16:14:04 by lean bean »

#### AndroidNeox

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #12 on: 13/01/2013 01:11:33 »
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #13 on: 13/01/2013 18:34:58 »
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?
Quote
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!

These are interesting saying the same...

Don't shoot the messenger.

« Last Edit: 13/01/2013 19:12:24 by lean bean »

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #14 on: 13/01/2013 18:54:30 »
Quote from: AndroidNeox
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.

Quote from: AndroidNeox
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.

Quote from: AndroidNeox
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
« Last Edit: 13/01/2013 23:35:34 by Pmb »

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #15 on: 13/01/2013 21:50:21 »
Android
Quote
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 :)

« Last Edit: 14/01/2013 18:21:16 by lean bean »

#### AndroidNeox

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #16 on: 15/01/2013 01:32:08 »
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #17 on: 15/01/2013 02:13:38 »
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #18 on: 15/01/2013 17:02:13 »
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

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #19 on: 15/01/2013 21:20:26 »
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

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #20 on: 20/01/2013 15:42:14 »
Quote from: lean bean
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.

I have found another site where a Dr Sten Odenwald goes into more detail as to why he thinks...
Quote
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"
The article continues...
http://einstein.stanford.edu/content/relativity/q2442.html

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #21 on: 20/01/2013 16:34:59 »
Quote from: lean bean
I have found another site where a Dr Sten Odenwald goes into more detail as to why he thinks...
He’s quite wrong. I explain why below.

Quote
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 reason why he’s wrong is because he’s misquoting Einstein. Einstein never said such things.

Einstein said in describing gravity the following (by “ordinary theory” he mean SR and the absence of gravity)
Quote
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)
Its only when the metric tensor components are not constants and the coordinates Cartesian that when the system of reference leaves the components of the metric tensor as variables will there be a gravitational field. When g-mu-nu = diag(1, -1, -1, -1) there exists no gravitational field, just spacetime. So gravity and spacetime are quite different, but related, things. You can certainly have spacetime with no gravitational field.

He also said
Quote
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

Compare this with what Einstein said in a letter to Lincoln Barnett date June 19, 1948
Quote
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.
« Last Edit: 20/01/2013 16:37:47 by Pmb »

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #22 on: 20/01/2013 18:35:58 »
From "Relativity and the Problem of Space" Albert Einstein (1952)
http://www.relativitybook.com/resources/Einstein_space.html
Quote
Space-time does not claim existence on its own, but only as a structural quality of the field.
If we imagine the gravitational field, i.e. the functions gik, to be removed...

Quote
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.
Quote
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.

I take it that the space of type (1) here is Minkowski space.
If I'm misquoting or what may seem like selective quoting then it's unintentional...it's not my field(pun)
« Last Edit: 20/01/2013 18:50:19 by lean bean »

#### Pmb

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #23 on: 20/01/2013 20:37:20 »
Quote from: lean bean
There is no such thing as an empty space, i.e. a space without field.
Frankly I find that to be just plain creepy. What could he possibly have had in mind for the definition of the term “field” when he wrote that.

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

#### lean bean

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##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #24 on: 21/01/2013 17:56:28 »
In any case he did not mean that such a field was a gravitational field.
He seems to be  referring to a gravitational field.
Look at the first sentence here ( quote below)…
Quote
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.
''If we imagine the gravitational field, i.e. the functions gik, to be removed,''
So here he is associating the gravitational field with the functions gik.

Then he goes on to make a point about type one space
Quote
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.
So there his saying a space of type one is a special case of a gravitational field. And the very next sentence you have ''There is no such thing as an empty space, i.e. a space without field.''
So I think he is referring to a gravitational field.

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…
« Last Edit: 21/01/2013 18:05:18 by lean bean »

#### The Naked Scientists Forum

##### Re: Why Light folows the space-Time curve?Not the the shorthest Line?
« Reply #24 on: 21/01/2013 17:56:28 »