OPTICS and GRAVITY

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My guess isn't wrong based on this ignorant comment by you "Kevin Brown is a good bloke, but it would be wrong to discard some concept on his say-so."'
Kevin Brown wasn't discarding any concept. He derived a 'model' from the 'Fresnel equation', at 8.4 Reflections on Relativity, that has a first order one to one correlation with the weak field derivation 'gravitational bending of light' from the Schwarzschild Geometry [metric]. I think I've said that to you three times. Maybe it's your turn to describe 'which concept Kevin Brown discards on his say so'. I haven't read
http://iopscience.iop.org/0256-307X/25/5/014

But this is what the author says in the abstract introduction,

"This result provides a simple and convenient way to analyse the gravitational lensing in astrophysics."

So what would that mean? Think it might include 1/1 correlation with gravitational bending of light to the first order? Duh?

 

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Look it up or ask around about it. A uniform gravitational field is simply one where the force of gravity doesn't diminish with distance. Beware of irritation. Sometimes it's a psychological response associated with the irrational rejection of something that is not in accord with your preconceived assumptions. Set emotions aside.

Look at the plot on the gravitational potential article on wiki. It's a Newtonian article, but nevertheless the slope indicates the strength of gravitational force, and the curvature represents tidal force, which is associated with the Riemann curvature tensor. Without that, the centre of the plot, which is little flat spot, can't curve up as you move away from the centre. The whole plot would therefore be flat.

 

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This demonstrates my point exactly! The author presents his preconceived ideas and conclusions based on an analysis of how Thorne's statement fits with an imaginary gravitational field. He does not begin by saying that he is exploring a hypothetical. They way he proceeds assumes that a "uniform gravitational field" is something that exists......, somewhere.

The definition you provide and the author implied does not exist in any practical gravitational system associated with observation..., and yet the author continues, to draw conclusions....

And yes it may be my own preconceptions that lead me to the conclusion that, your definition of a "uniform gravitational field", is a ficticiuos hypothetical situation, but it is consistent with even Newton's understanding of gravity.

The plot you refer to models the gravitational field of a uniform spherical mass..., not a "uniform gravitational field" — as you described. Even within the context of GR uniform spherical masses are used to model gravitational fields, but they do not result in "uniform gravitational fields", consistent with your definition or what seems implied in the author's paper.

It would have been possible to define a "uniform gravitational field" in a manner that would be consistent with experience and both Newtonian dynamics and GR, but the conclusions drawn would then be nonsense.

The author first quotes Thorne and then refutes the intent of the quote... The way I read his intent in the use of "uniform gravitational field" and your definition, do not seem to be consistent with observation or reality. There is no observed example where, "A uniform gravitational field is simply one where the force of gravity doesn't diminish with distance.".

 

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You're misreading this. The author agrees with Thorne. Look carefully:

"There is a well accepted definition of space-time curvature. As stated by Thorne: space-time curvature and tidal gravity are the same thing expressed in different languages, the former in the language of relativity, the later in the language of Newtonian gravity."

Einstein used the principle of equivalence to develop GR. When you accelerate continuously, you still see light curving down. You see what looks like gravity even though there's no tidal force and thus no spacetime curvature. In effect your spacetime is tilted rather than curved. Einstein then referred to a small region, such as the room you're in. Ask around and say something like this: "I'm in a room and I drop a ball. Why does the ball fall down? People will say it's because the spacetime in the room you're in is curved. That's wrong. The ball falls down because there's a gradient in gravitational potential in that room, a "tilt" rather than a tidal-force curvature. Yes the gradient is there because the curvature gets the gravitational potential off the flat and level like I was saying above. But it isn't spacetime curvature in your room that makes the ball fall down.

 

I don't think so! The context of the contradiction is that Thorne was comparing space-time curvature and tidal gravity as two ways of describing the same thing! Keep in mind both are imperfect descriptive models not explanations for the origin of gravity.

From P.M. Brown's paper,
As stated by Thorne

space-time curvature and tidal gravity are the same thing expressed in different languages, the former in the language of relativity, the later in the language of Newtonian gravity.​

However one of the main tenants of general relativity is the Principle of Equivalence: A uniform gravitational field is equivalent to a uniformly accelerating frame of reference. This implies that one can create a uniform gravitational field simply by changing one’s frame of reference from an inertial frame of reference to an accelerating frame, which is rather difficult idea to accept. A uniform gravitational field has, by definition, no tidal forces and thus no space-time curvature. Thus according to the interpretation of gravity as a curvature in space-time a uniform gravitational field becomes a contradiction in terms (i.e. no tidal forces where there are tidal forces).

In the bold portion Brown is comparring apples and oranges. Broken down, the Principal of Equivalence only compares the inertial resistance of an object to constant and uniform acceleration with an equivalent fixed position in a gravitational field. As soon as you begin to try and compare an accelerating frame with the tidal forces associated with a changing location within the gravitational field of a massive object, you are no longer dealing with a constant and uniform acceleration... Apples and Oranges.

 

Here it seems as though you are attempting to define some kind of origin for gravity, through the use of models that only describe the dynamics of objects exposed to gravity.

No one has yet developed a compelling arguement for what causes gravity. Though there have been some attempts, mainly approaching the problems from QM.

You are correct when you say, "people say....". And I would include, in those people, some noted physicists cashing in through the popular media. But I don't think you will find many physicists seriously suggesting that the curvature of space, is any better description of the why of gravity than Newton's action at a distance.

Again, no one has an answer to that one yet.

 

And he was right. The defining feature of a gravitational field is the Riemann curvature tensor. Look it up on wikipedia:

"It is a central mathematical tool in the theory of general relativity, the modern theory of gravity, and the curvature of spacetime is in principle observable via the geodesic deviation equation. The curvature tensor represents the tidal force experienced by a rigid body moving along a geodesic in a sense made precise by the Jacobi equation."

Look around elsewhere and you can find articles like this where you can read:

"The metric tensor determines another object (of tensorial nature) known as Riemann curvature tensor. At any given event this tensorial object provides all information about the gravitational field in the neighbourhood of the event. It may, in real sense, be interpreted as describing the curvature of the space-time. The Riemann curvature tensor is the simplest non-trivial object one can build at a point; its vanishing is the criterion for the absence of genuine gravitational fields..."

If there's no Riemann curvature tensor there's no tidal force and no spacetime curvature. When you're accelerating, there's no Riemann curvature tensor. But inside your spaceship, things still "fall down".

It isn't apples and oranges. The tidal force isn't something that arises from changing location, it's the differences between the force of gravity at your feet as opposed to at your head. If there isn't any there's no spacetime curvature. The whole point is that if you're in an accelerating rocket there's no spacetime curvature, and that is comparable to being in a room where you can discern no difference between the force of gravity at your feet as opposed to your head. But you can discern when you fall down. So you don't fall down because "the spacetime is curved in the room you're in".

I'm not, I'm trying to explain something to you. The force of gravity at some location is the first derivativee of potential, the tidal force is the second derivative. Look it up.

Einstein did. He said this:

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty."

The ten functions ten functions concern energy density, flux, pressure, and shear stress. See for example this web page. In a nutshell, a concentration of energy in the form of a massive star stresses the surrounding space. It doesn't curve it, it stresses it such that light moving through it curves. The stress diminishes with distance in line with the Riemann curvature tensor.

Curved spacetime, not curved space.

Newton rejected action at a distance. He said this in a letter to Dr Richard Bentley on 25 February 1692:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”.

 

The portions of your leading statement and the quote, in bold above do not imply the same thing. Your statement suggests some real substance is involved, as if the Riemann curvature tensor is describing the origin..., while the quote indicates it as a tool that can be used to represent, the curvature of space-time. Space-time itself is really a conceptual model, a tool we use to better describe the dynamic geometry of objects in/and space(space-time). (Note, I often use "space/space-time" rather than just space-time to emphasize the fact that space-time is a tool we use to describe the interaction of objects, and objects and space.)

The geometries we use to describe gravity, space-time, and what we observe of the universe, are only special to the extent that they accurately describe some observation or concept.

I believe while the application of the Riemann curvature tensor may not apply in the case of an accelerating frame, meaning it may not be able to model what occurs, that does not mean there is no curvature in an accelerating frame.

The association of, the principal of equivalence and constant and uniform acceleration, is misleading in that superficially it suggests a purely hypothetical situation. In practice an constant and uniform acceleration, would not — over time, duplicate a uniform gravitational field. It does so only when and where the distance and time involved can be treated as flat. Even within the context of SR, uniform acceleration over time will result in conditions, where the Lorentz factor becomes significant. As the absolute change in velocity increases, an object's inertial resistance to further acceleration also increases, and the rate of acceleration required to maintain 1 G, decreases... This suggests that space-time for the accelerated frame is "curved".

Your example in bold above does involve a change in location within a gravitational field, even if that change is only 5 or 6 feet. But it is a bad example in any case because unless we were dealing with a strong or extreme gravitational potential, the electromagnetic properties of atoms and molecules, dominate. Any effective force or difference in gravitational potential from head to foot is insignificant and completely dominated by the QM of matter...

But set that aside for a moment and assume that we can use a uniformly accelerating box, to demonstrate the principle of equivalence. We take a test object, inside the box and on the earth, and drop them from the same height above the floor and the ground. The relative accelerations between the test objects and the floor and ground, in each case is identical. If we assume that space-time curvature is involved, or at least descriptive of the case involving gravity, it again suggests space-time curvature, in the accelerating frame... And while it is difficult to define the origin of what we experience as gravity.., in the case of the uniformly accelerating box, we can provide some explanation. The test object's relative acceleration compare to the floor is defined by, its initial state of acceleration and its inertial resistance to a change in its state of motion, when dropped. Keep in mind also that as far as the test object and the box are concerned, though they are both accelerating, they share the same accelerating frame and so are relative to one another — inertial.

I believe that in the end, it will be from the perspective of QM that the origins of both inertia and gravity will be explained. It seems at present that there may be at least some conceptual changes required to reach that goal, but though pains me to say so, I don't see the fundamental answers as comming from either SR or GR.

Oh.., and space-time is a conceptual tool, not a description of why or from where the geometry originates. There is nowhere, that how space and matter interact is defined within SR and/or GR, just what that interaction looks like.

 

I didn't suggest that, you're reading too much into The defining feature of a gravitational field is the Riemann curvature tensor.

Agreed.

No problem.

In your accelerating frame you see light curving. But note that that's only how you see it. A reference frame is something of a conceptual model too.

But that's the principle of equivalence for you. Einstein used it to say that when you're accelerating you see light curving, just as you see light curving when you're standing on the surface of the Earth.

To emulate the curved spacetime of a real gravitational field you just change your acceleration, from say 9.8m/s/s to zero.

The point is that Riemann curvature is associated with curved spacetime and tidal force. The latter is so negligible as to be undetectable within a room, but things still fall down.

This is wrong I'm afraid. In the accelerating box things fall down because conceptually speaking "spacetime is tilted". In a real gravitational field things fall down because "spacetime is tilted", not because it's curved. The point is that in the real gravitational field, you can't get that tilt without the spacetime curvature. If there's no spacetime curvature you start with flat level spacetime, and that's what you're stuck with.

Simple stuff.

They came from SR and GR!

OK re spacetime, but I don't quite agree on the latter point.

 

For the uninitiated, Farsight and a number of actual physicists including myself have been going back and forth over this. Specifically, physicists often use space and spacetime synonymously and Farsight objects to this, citing this very quote above. The current status is that Farsight has been asked to describe the origin of the "ten functions (the gravitation potentials \(g_{\mu \nu}\))," and explain why Einstein in this quote refers to both space and spacetime. To make things simple for farsight, I have explained that \(g_{\mu \nu}\) is the metric tensor. It is a rank two tensor as it has two indicies and it's dimension is the number of spacetime dimensions in nature (ie, d = 3 + 1 = 4). In general, a rank two tensor has \(d^2 = 16\) components, so at first sight it's is not clear that this is what Einstein was talking about. Add in a bit of extra information though, and everything crystallises: The metric tensor is symmetric, in other words \(g_{\mu \nu} = g_{\nu \mu}\) and one can convince oneself that a symmetric tensor has \(\frac{1}{2}d(d + 1)\) components. In four dimensions this number is the 10 that Einstein referred to.

So, given that rather long preamble, how can you possibly object to anyone using space and spacetime interchangeably and repeatedly provide this quote from Einstein to "support" your view when Einstein does exactly what you object to.

I'm sorry, it looks from this like you are arguing against the equivalence principle. You can't possibly be that stupid and arrogant can you?

 

I think Farsight has problems understanding derivations associated with physics. He couldn't understand Kevin Brown's derivation which I last commented on in post #81. I've never come across a 'crank' who was actually interested in science. It's always about finding something wrong with stuff they don't understand to begin with.

 

Don't. I give informative explanatory posts with references, and all you do is play the naysayer troll. You throw out perjoratives like crank and you don't understand the math because you can't find something wrong with something you don't understand.

 

For the uninitiated, prometheus tries to play the "actual physicists including myself" authority card when he knows jack sh*t. Check out John Baez's website, where you can read this: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

Au contraire, the current status is that prometheus tries on a pathetic blind 'em with maths argument that convinces nobody, and doesn't mention that the ten functions concern energy-momentum density, flux, pressure, and shear stress. The way to understand this is go back to basics and imagine a gedankenexperiment where you place parallel-mirror light-clocks at various locations through an equatorial slice through the Earth and the surrounding space. Then after a suitable interval you plot all your clock readings on a "spacetime chart" or coordinate system, which ends up looking like the depiction of Newtonian gravitational potential on wiki:

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CCASA image by AllenMcC, see http://en.wikipedia.org/wiki/File:GravityPotential.jpg

It's similar to the "bowling ball" depiction on the right of the wiki spacetime page where the caption says this:

"The grid lines do not represent the curvature of space but instead the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime"

The slope at some location indicates the gravitational force at that location, in that the steeper the slope the faster you start to fall. The "curviness" of the slope indicates tidal force, which relates to what's called the Riemann curvature tensor, which is the defining feature of a real gravitational field. Basically, that curviness is spacetime curvature. It's the curvature of your spacetime chart aka coordinate system rather than the curvature of space. In our example, it's merely a curvature in a plot of your clock readings. And those clocks were just parallel-mirror light clocks, with light going back and forth like this |-|. What you're plotting is "the coordinate speed of light", which varies in a non-inertial reference frame like a gravitational field. It varies from place to place in space. You certainly aren't plotting curved space, and since all you're dealing with is light moving between mirrors, you aren't really plotting curved time either. There's no actual thing called time flowing between those mirrors, it's just light moving through space. Yes, people try to bamboozle you by talking about "the metric tensor", but don't be fooled. A metric is a word associated with measurement, and a tensor is a matrix. So in truth a metric tensor is a measurement matrix. That's what our plot is. It's curved, and people refer to it as curved spacetime, but it isn't curved space.

See above. We use the motion of light through space in our parallel-mirror light clocks and call the reading "the time". We also use the motion of light through space to define distance: "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.". It all comes back to the motion of light through space, and since you use the motion of light to define your coordinates, the coordinate speed of light is the speed of light. Einstein referred to this varying with gravitational potential many times over the years up to including 1916. And Einstein's words in 1920 are quite clear: “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty. He doesn't say spacetime, he said space. And he gave the equations of motion not the equations of curved spacetime. He used geometry, but that motion is motion through space, and the map is not the territory.

Not me. I was explaining the significance of the equivalence principle. The Riemann curvature tensor is synonymous with curved spacetime, and is associated with the tidal force, which is the second derivative of gravitational potential. This is so slight as to be undetectable in the room you're in. But drop a ball, and you can detect that very easily. What that means is this: in the room you're in, your ball doesn't fall down because the spacetime in that room is curved. That's what the equivalence principle tells us. So why does it fall down? Magic?

I do so love our little chats prometheus.

 

Um, no, those are the \(T_{\mu\nu}\)s, not the \(g_{\mu\nu}\)s.

As for "blinding", any text on general relativity, including Einstein's own, will tell you that \(\mu\) and \(\nu\) run over four index values corresponding to four coordinates needed to map spacetime. So:

\( (g_{\mu\nu}) = \begin{bmatrix} g_{00} & g_{01} & g_{02} & g_{03} \\ g_{10} & g_{11} & g_{12} & g_{13} \\ g_{20} & g_{21} & g_{22} & g_{23} \\ g_{30} & g_{31} & g_{32} & g_{33} \end{bmatrix} \,. \)​

"Symmetric" means that \(g_{01} = g_{10}\), \(g_{12} = g_{21}\), and so on. How many independent components does that leave you with?

 

The fact the metric tensor is symmetric has a physical reason - if \(g_{12} \neq g_{21}\) the distance from point a to point b would be different than the distance from point b to a. The metric tensor is just the curved space

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P) statement of pythagoras after all. I'll respond to the rest of Farsight's post later.

 

Farsight said:

"Not me. I was explaining the significance of the equivalence principle. The Riemann curvature tensor is synonymous with curved spacetime, and is associated with the tidal force, which is the second derivative of gravitational potential. This is so slight as to be undetectable in the room you're in. But drop a ball, and you can detect that very easily. What that means is this: in the room you're in, your ball doesn't fall down because the spacetime in that room is curved. That's what the equivalence principle tells us. So why does it fall down? Magic?"

That's probably one of the dumbest comments I've ever come across. Learn some physics. Or put a cork in the nonsense.

 

Actually, I think "magic" is closer to a description of the fundamental mechanism, than his earlier post.

At least a part of what I have been trying to point out, is that the various geometries we use to describe experience and observation, are not explanations of the fundamental mechanisms that lead to those geometries.

GR does a very good job of describing the geometry and dynamics, but the origin or mechanism from which they (gravity, the dynamics and geometry) emerge, will most likely be found itself to emerge from QM, rather than relativity.

 

It's about domain of applicability. GR is a classical theory of gravity so it was never intended to explain quantum phenomena. For GR the origin, in it's domain of applicability, is spacetime geometry. Since our universe is a quantum universe then it won't be surprising that we find out something more about gravity when 'all the details' emerge. I mean 'we' in a general sense that we can all read the literature as the theoretical and experimental physicist provide it for us.

 

Here http://prd.aps.org/abstract/PRD/v85/i2/e024035 is another paper related to Optics and GRavity. Here also only abstract can be read from the link. A quote from the abstract of this paper is as follows: "It is shown that the energy of an elliptically polarized wave does not propagate along a geodesic, but in a direction that is rotated with respect to the gravitational force."




Can 'gravitational lensing' be considered as 'acceleration of particle photon' towards the cg of the mass causing gravitational lensing?


If another massive particle travels along the path of light where 'gravitational lensing' is hapenning, it will experience a force( or accelerate) towards the cg of the mass causing gravitational lensing.

 

You're trying to explain it using Newtonian physics. The Newtonian prediction is ~ 1/2 the empirically confirmed GR prediction of

dphi=4M/r.