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Thread: The God's eye global gist of general relativity

  1. #1 The God's eye global gist of general relativity 
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    A while back I was saying time travel is a fantasy because clocks clock up motion, and you "travel" to the future by not moving whilst everything else does. Once that clicks, IMHO it’s easy to appreciate the varying speed of light. There no actual time flowing inside a clock. It isn't some kind of cosmic gas meter which literally measures the flow of time. So when an optical clock goes slower when it's lower, it's because light goes slower when it's lower, just like Einstein said.

    Then when it comes to gravity, you give some priority to the global "God's eye view" wherein the coordinate speed of light varies in a gravitational field. And wham, you suddenly get this visceral understanding, the likes of which you have never known. You suddenly get this simple picture of general relativity that's different but elegant. So much so that you can't say where it's wrong. At least I don't think you can. But let's see.

    You’ll have seen the bowling-ball analogy. The Earth is likened to a bowling ball in a rubber sheet, like this:


    GNUFDL image by Johnstone, see wikipedia

    You probably know already that one problem with this picture is that the Earth looks like it’s being pulled down by gravity. It’s no good using gravity to explain gravity, that’s circular. But the picture isn’t totally wrong. Imagine you’ve placed an array of parallel-mirror light-clocks in an equatorial slice through the Earth and the surrounding space. When you plot all the clock rates, your plot resembles the rubber-sheet picture because clocks go slower when they’re lower. Then the curvature you can see relates to Riemann curvature which relates to curved spacetime. And yes, you measured those clock rates, so yes, it’s a curvature in your metric. But it’s important to remember that the curvature is just a curvature in your plot of clock rates, and those clocks measured the motion of light through space. So what the rubber-sheet analogy is really depicting, is the varying speed of light.

    It’s also important to note that the clocks nearer the Earth don’t run slower because your plot is curved. In other words, they don’t run slower because spacetime is curved. Spacetime is a mathematical model, and it is static. It’s the plot, the map, and the map is not the territory. It isn't what space is. The clocks run slower when they’re lower because the space down there is different. That’s because a concentration of energy in the guise of the matter of the Earth “conditions” the surrounding space, the effect of this diminishing with distance. Einstein talked about this in his 1920 Leyden Address, where he also talked about inhomogeneous space. I think that’s the physical reality that underlies curved spacetime. And like I was saying, Einstein didn’t say light curves because spacetime is curved. He said light curves because "the speed of light varies with position".

    Another issue with the rubber-sheet picture is that it depicts tension instead of pressure. Einstein’s stress-energy tensor has an energy-pressure diagonal, and to envisage pressure you need to step up from a rubber sheet to three-dimensional space. Imagine it’s like some gin-clear ghostly elastic jelly, then you insert a hypodermic needle and inject more jelly to represent the mass-energy of the Earth. The surrounding jelly is pressed outwards rather than being pulled inwards. Like this picture but the other way round. A further issue is that the Earth is spherical, which really muddies the water re inhomogeneous space and curved spacetime. To clarify that, we need to zoom in a little, like this:


    Image credit: NASA (I removed the moon and added the lattice lines)

    You can think Ricci curvature and volume if you like, and you could plot the volumes and draw a curve. But keep it simple: the height of each rectangle relates to your clock rate at that location. Remember they’re light-clocks, so the height of each rectangle relates to the coordinate speed of light at that location. And because this speed of light varies smoothly from top to bottom, a beam of light going across the picture will curve like a car veers when it encounters mud at the side of the road. Like this:



    Hence Professor Ned Wright’s Deflection and Delay of Light wherein "the delay experienced by light passing a massive object is responsible for the deflection of the light”.



    That’s easy to understand. And once you understand why light curves, it’s easy to understand why matter falls down. There’s only one other thing you need to know about, and that’s the wave nature of matter. We can make an electron along with a positron out of light waves in pair production. And we can diffract an electron. Plus in atomic orbitals electrons "exist as standing waves". And they have their magnetic dipole moment. And then there's the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies". Then annihilation gets you the light back. De dah de dah. To cut to the chase, just think of an electron as light going round and round. Then simplify it to light going round a square path. Draw it, like this:



    Now imagine it’s in a gravitational field. The vertical parts of the light path are still vertical, but the horizontal parts bend down a little. So the electron falls down. Like this:



    In essence the reducing speed of light is transformed into the downward motion of the electron. You can diffract protons and neutrons too, and buckyballs. So the same principle applies to matter in general. From this you can even understand why the general-relativity deflection of light is twice the Newtonian deflection of matter. It’s because for matter, only the horizontals bend down.

    Yes, it’s pretty simple really. But as for why this isn’t common knowledge, I don’t know. It could have been common knowledge for about three hundred years, because in Opticks query 20 Newton said this: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?" That’s Newton telling you why light curves, and it's pretty much what Einstein said. And in Opticks query 30 Newton said "Are not gross bodies and light convertible into one another?" So I imagine he had an idea about why matter falls down. I hope that now you do too. Get the gist of time, then the speed of light, and you can get the gist of gravity too.

    After that, well I think black holes are simple as well. But that's one for another day.
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    Quote Originally Posted by Farsight View Post
    You suddenly get this simple picture of general relativity that's different but elegant. So much so that you can't say where it's wrong. At least I don't think you can. But let's see.
    Again, I must ask you to actually do a physics problem with your supposed Farsight-General-Relativity. As it stands, you have a lot of pretty words but there is no evidence that what you are discussing bears any relation to a physics application.

    So, please, to actually provide some evidence, show us how to do a problem with FGR. You are well known for declaring yourself a physics expert, help us learn how to do physics better.
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    Farsight, I am interested in what mechanism would slow down light near massive objects. Do you have any views on this?
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    Farsight has written a book called Relativity +.

    This is a review from Amazon.

    This is a work of pure imagination. The author has come up with an imaginative idea (that does NOT meet the criterion for being considered a theory) about what comprises the universe we live in. This book claims that matter, energy and space are the same thing, with the particles we observe being 'knots' of space.
    Unfortunately, his ideas simply don't work. When one creates even the most rudimentary mathematical model of his theories, one finds predictions that contradict what we know about the universe. Even without doing any math, it is possible to find errors and false predictions in his ideas based on simply finding the logical conclusions of his claims.
    This book is self-published, after having been rejected by a number of publishers. I find it quite telling that even a company that would publish works by Deepak Chopra would turn down this author.
    Duffield has been shopping this theory around the internet for several years now. In that time, he's been banned from numerous science forums for various reasons, including refusing to accept correction, presenting his ideas as established science, and even attempting to intimidate others by describing his claimed prowess at boxing and willingness to travel.
    In short, this book is a waste of time, for the author as well as any reader. I would recommend that anyone wishing to learn more about physics purchase a book by an actual physicist. If one is determined to read this work, it was available on the web in HTML format as of 2008. An archival search would likely provide a free copy, which would be a far more appropriate price than what is listed.
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    Alex, I have seen this review before. ; )
    Critics should always be taken with a pinch of salt. Everyone has a salt cellar to grind!
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    Quote Originally Posted by AlexG
    Farsight has written a book...
    It's not on sale any more, apart from a few used copies that I can't control. And yikes, that review is full of mistruth.

    Quote Originally Posted by PhysBang
    Again, I must ask you to actually do a physics problem with your supposed Farsight-General-Relativity. As it stands, you have a lot of pretty words but there is no evidence that what you are discussing bears any relation to a physics application. So, please, to actually provide some evidence, show us how to do a problem with FGR. You are well known for declaring yourself a physics expert, help us learn how to do physics better.
    Like I've said previously, Einstein gave the maths of general relativity "from the local viewpoint" rather than "from the global viewpoint". Hence we see c in . I'm afraid I don't know how to give the maths from the global viewpoint.

    Quote Originally Posted by Jilan
    Farsight, I am interested in what mechanism would slow down light near massive objects. Do you have any views on this?
    Yes. In mechanics a shear wave travels at a speed v = √(G/ρ) where G is the shear modulus of elasticity and ρ is the density. There's something akin to this going on for space wherein c = √(1/ε0μ0). The simplest thing I can think of that has a gravitational field is a photon. It's so slight as to be unmeasurable of course. But rather than mass it's a concentration of energy that causes gravity, and whilst the photon has a zero rest mass, it has a non-zero active gravitational mass. And it has its action h in E=hf. So when Einstein talked about a concentration of energy "conditioning" the surrounding space, I think of that as the reaction to the action.
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    Quote Originally Posted by Farsight View Post
    Like I've said previously, Einstein gave the maths of general relativity "from the local viewpoint" rather than "from the global viewpoint". Hence we see c in . I'm afraid I don't know how to give the maths from the global viewpoint.
    Then it seems that you don't actually have any physics; your claims are baseless.
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    For a stationary metric, the acceleration of a stationary object depends only on the time dilation. The curvature of the three-dimensional space is irrelevant. In other words, your claim that gravity is caused by three-dimensional spatial curvature is provably incorrect. This more than anything else is what is wrong with the rubber sheet analogy of gravitation.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Farsight View Post
    Like I've said previously, Einstein gave the maths of general relativity "from the local viewpoint" rather than "from the global viewpoint". Hence we see c in . I'm afraid I don't know how to give the maths from the global viewpoint.
    There is no global maths. Tensors live in the tangent space at each point of the manifold, so they are inherently local objects; the objects you see appearing in the field equations are technically tensor fields, since the tensors are defined at each point of space-time - picture them as position-dependent functions ( maps ) that map vectors and 1-forms into real numbers, at each point.
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    Quote Originally Posted by Farsight View Post
    In mechanics a shear wave travels at a speed v = √(G/ρ) where G is the shear modulus of elasticity and ρ is the density. There's something akin to this going on for space wherein c = √(1/ε0μ0). The simplest thing I can think of that has a gravitational field is a photon. It's so slight as to be unmeasurable of course. But rather than mass it's a concentration of energy that causes gravity, and whilst the photon has a zero rest mass, it has a non-zero active gravitational mass. And it has its action h in E=hf. So when Einstein talked about a concentration of energy "conditioning" the surrounding space, I think of that as the reaction to the action.
    This might suggest that the permittivity is akin to a density, but a density of what? Maybe if we knew the answer to this question we might understand why the speed of light is what it is.
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    Quote Originally Posted by Markus Hanke View Post
    There is no global maths. Tensors live in the tangent space at each point of the manifold, so they are inherently local objects; the objects you see appearing in the field equations are technically tensor fields, since the tensors are defined at each point of space-time - picture them as position-dependent functions ( maps ) that map vectors and 1-forms into real numbers, at each point.
    As you state GR is not coordinate dependent. Because we can choose to represent the physics using coordinates Farsight thinks Einstein chose the 'wrong' coordinates. He essentially thinks the Schwarzschild bookkeeper coordinates are 'preferred'. As evidenced by the Farsight comment on Einsteins choice.
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    Quote Originally Posted by KJW
    For a stationary metric, the acceleration of a stationary object depends only on the time dilation. The curvature of the three-dimensional space is irrelevant. In other words, your claim that gravity is caused by three-dimensional spatial curvature is provably incorrect.
    Huh? I didn't claim that at all. I said a gravitational field was inhomogeneous space, not curved space. Why did you think I claimed that gravity is caused by three-dimensional spatial curvature? Only it sounds to me as if I have to clarify something somewhere.

    Quote Originally Posted by Jilan
    This might suggest that the permittivity is akin to a density, but a density of what?
    Energy? If you seen me talking to KJW about space and energy, well, I can't separate them at the fundamental level. Space is like some gin-clear ghostly elastic jelly, then you insert a hypodermic needle and inject more jelly to represent the mass-energy of the Earth. In this analogy space is jelly, and energy is jelly too.

    Quote Originally Posted by Markus Hanke
    There is no global maths. Tensors live in the tangent space at each point of the manifold, so they are inherently local objects; the objects you see appearing in the field equations are technically tensor fields, since the tensors are defined at each point of space-time - picture them as position-dependent functions ( maps ) that map vectors and 1-forms into real numbers, at each point.
    Fine. But there's nothing that maps out the coordinate speed of light around the Earth. Is there?
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    Ok, so you have a jelly and the local prescence of mass increases the jelly density, bit why would it follow an inverse square law?
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    Because it's like you're injecting jelly in the middle which presses out against the surrounding jelly. See hyperphysics:

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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    For a stationary metric, the acceleration of a stationary object depends only on the time dilation. The curvature of the three-dimensional space is irrelevant. In other words, your claim that gravity is caused by three-dimensional spatial curvature is provably incorrect. This more than anything else is what is wrong with the rubber sheet analogy of gravitation.
    Huh? I didn't claim that at all. I said a gravitational field was inhomogeneous space, not curved space. Why did you think I claimed that gravity is caused by three-dimensional spatial curvature? Only it sounds to me as if I have to clarify something somewhere.
    Perhaps you didn't explicitly say that gravity is caused by three-dimensional spatial curvature, but the many things you have said here and in other threads very much suggests gravity being caused by three-dimensional spatial curvature.


    Quote Originally Posted by Farsight View Post
    I said a gravitational field was inhomogeneous space
    Inhomogeneous space is space that is not the same everywhere. Without specifying the way that space differs from one location to another, it is rather meaningless. However, one can ask what properties characterise a location in space.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Farsight View Post
    Because it's like you're injecting jelly in the middle which presses out against the surrounding jelly. See hyperphysics:

    Farsight, the problem I have with this picture is that pressure does not tend usually to follow an inverse square law. It tends to even itself out. In a liquid for example the pressure quickly becomes distributed throughout the incompressible fluid. But thinking on I guess if it were more like a rubber ball this might be correct.
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    Quote Originally Posted by KJW
    Perhaps you didn't explicitly say that gravity is caused by three-dimensional spatial curvature, but the many things you have said here and in other threads very much suggests gravity being caused by three-dimensional spatial curvature.
    You've misread something. I've suggested that electromagnetism is three-dimensional spatial curvature. not gravity.

    Quote Originally Posted by KJW
    Without specifying the way that space differs from one location to another, it is rather meaningless.
    Einstein referred to a gravitational field as inhomogeneous space. The permittivity and the permeability differs, so the vacuum impedance differs along with the speed of light.

    Quote Originally Posted by KJW
    However, one can ask what properties characterise a location in space.
    Yes. Look to the EFE and the stress-energy-momentum tensor.

    Quote Originally Posted by Jilan
    Farsight, the problem I have with this picture is that pressure does not tend usually to follow an inverse square law. It tends to even itself out. In a liquid for example the pressure quickly becomes distributed throughout the incompressible fluid. But thinking on I guess if it were more like a rubber ball this might be correct.
    It's definitely "elastic" rather than a fluid. Look at the stress-energy-momentum tensor. See that shear stress?
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    Quote Originally Posted by Farsight View Post
    Yes. Look to the EFE and the stress-energy-momentum tensor.
    If all you mean by "inhomogeneous space" is the EFE, then nothing that you have said about electromagnetism and stress bears any relation to physics. It seems clear that what Einstein meant by "inhomogeneous space" was the EFE.
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    Fine. But there's nothing that maps out the coordinate speed of light around the Earth. Is there?
    Remember that the exterior Schwarzschild metric is not solely about black holes - it is about the vacuum outside any stationary, spherically symmetric body. As such, the Schwarzschild metric is also what you use for the vacuum outside of the Earth, so long as your problem allows you to neglect the rotation. So to answer your question - if you have a far-away observer who looks back onto Earth, and performs experiments similar to the ones at a black hole, he will see the coordinate speed of light around Earth to be reduced. The Schwarzschild metric makes reference only to the total mass in your space-time, it does not distinguish what form that mass has.

    Einstein referred to a gravitational field as inhomogeneous space.
    "Inhomogeneous" here means only that space-time has degrees of freedom, as captured by the metric tensor, which we can obtain from the field equations. As for permittivity and permeability, GR does not make any reference to that. We understand that coordinate speed varies ( that's kind of the point of having a metric theory of gravity ! ), but we also understand that this is only one particular way to label events in our space-time, and by no means physically privileged. If it were, the field equations as they stand would not be valid.
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    Quote Originally Posted by Farsight View Post
    You've misread something. I've suggested that electromagnetism is three-dimensional spatial curvature. not gravity.

    Einstein referred to a gravitational field as inhomogeneous space. The permittivity and the permeability differs, so the vacuum impedance differs along with the speed of light.

    Yes. Look to the EFE and the stress-energy-momentum tensor.
    All this points to gravitation being curvature, and since you reject time, one can only infer that the curvature is of three-dimensional space.

    The speed of light does not vary. You've already acknowledged that the local speed of light does not vary, but in fact there is no other kind of speed of light. The notion of "coordinate speed of light" is not valid because coordinates do not have units of length and time and therefore cannot form units of speed.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    The notion of "coordinate speed of light" is not valid because coordinates do not have units of length and time and therefore cannot form units of speed.
    That's a remarkable point of view, but it seems to contradict most textbooks on the subject matter. For example, Taylor/Wheeler in their text "Exploring Black Holes" ( chapter 3 ) specifically refer to the notion of coordinate velocity, and derive an expression for this, which does come out in m/s in terms of units. The thing is that coordinate velocity is purely a bookkeeper concept - it is what an external observer determines the speed of light in a remote frame to be, as opposed to what is locally measured in that frame. As such, coordinate speed of light goes asymptotically to zero at the event horizon.
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    Quote Originally Posted by Markus Hanke View Post
    That's a remarkable point of view, but it seems to contradict most textbooks on the subject matter. For example, Taylor/Wheeler in their text "Exploring Black Holes" ( chapter 3 ) specifically refer to the notion of coordinate velocity, and derive an expression for this, which does come out in m/s in terms of units. The thing is that coordinate velocity is purely a bookkeeper concept - it is what an external observer determines the speed of light in a remote frame to be, as opposed to what is locally measured in that frame. As such, coordinate speed of light goes asymptotically to zero at the event horizon.
    Could you give a brief outline for the Schwarzschild metric if this differs from simply ? It should be noted that and cannot have units since this would be inconsistent with the definition of the metric.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Could you give a brief outline for the Schwarzschild metric if this differs from simply ?
    Yes, this is exactly it :



    from rest at infinity, in geometrised units as everywhere in Taylor's text. I don't really understand why this is inconsistent, because once converted back into standard units



    it all seems to come out in m/s...?
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    Quote Originally Posted by Markus Hanke View Post
    Yes, this is exactly it :



    from rest at infinity, in geometrised units as everywhere in Taylor's text. I don't really understand why this is inconsistent, because once converted back into standard units



    it all seems to come out in m/s...?
    The problem isn't within the dimensional analysis but with what and actually are... coordinates. They are not themselves distances... that is what the metric is for... to convert the coordinates to distances. For example, if had units of metres, then the interval would be an interval of 1 metre, which is not true in general because of the metric. Also, the notion that coordinates have units goes against the principle of general covariance which requires that all coordinates be on equal footing, but examples of coordinate systems exist where the different coordinates appear to have different units (eg and of the polar coordinate system).
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    The problem isn't within the dimensional analysis but with what and actually are... coordinates. They are not themselves distances... that is what the metric is for... to convert the coordinates to distances. For example, if had units of metres, then the interval would be an interval of 1 metre, which is not true in general because of the metric. Also, the notion that coordinates have units goes against the principle of general covariance which requires that all coordinates be on equal footing, but examples of coordinate systems exist where the different coordinates appear to have different units (eg and of the polar coordinate system).
    Ok, I see what you are saying. For all practical purposes though you would be integrating this expression over some domain to obtain either a "true" radial distance, or a coordinate in-fall time. As it stands it is merely an instantaneous measure.
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    Quote Originally Posted by KJW View Post
    Could you give a brief outline for the Schwarzschild metric if this differs from simply ? It should be noted that and cannot have units since this would be inconsistent with the definition of the metric.

    A choice of units doesn't have any consequences on the physics. There's no requirement for the metric components to be dimensionless.
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    Quote Originally Posted by KJW View Post
    The problem isn't within the dimensional analysis but with what and actually are... coordinates. They are not themselves distances... that is what the metric is for... to convert the coordinates to distances. For example, if had units of metres, then the interval would be an interval of 1 metre, which is not true in general because of the metric. Also, the notion that coordinates have units goes against the principle of general covariance which requires that all coordinates be on equal footing, but examples of coordinate systems exist where the different coordinates appear to have different units (eg and of the polar coordinate system).
    A position in spacetime.

    2M/r

    This is the remote coordinate speed of light derived from the metric

    dr/dt_bkkpr = 1-2M/r [radial remote coordinate speed of light]

    Markus wrote down how to convert the conventional unit mass to geometric unit mass. Mass expressed as a length.

    r=nM is a distance.

    All coordinates are on equal footing. All the metric solutions to the EFE are coordinate solutions. None are preferred over any other.
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    Quote Originally Posted by brucep View Post
    A choice of units doesn't have any consequences on the physics. There's no requirement for the metric components to be dimensionless.
    There is no physics to consider. The original issue is whether the coordinate speed of light has any significance whatsoever. It has already been pointed out that the answer is no because coordinate systems are arbitrary. I pointed out another reason based on the notion that coordinate speeds aren't speeds.

    It should be noted that has dimensions (by definition) and therefore each term of the metric will also have dimensions . If the coordinate differentials are dimensionless (my claim), then the metric tensor components must have dimensions . But note that giving the coordinate differentials the dimensions of is still not in agreement with many coordinate systems such as the spherical coordinate system.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    There is no physics to consider. The original issue is whether the coordinate speed of light has any significance whatsoever. It has already been pointed out that the answer is no because coordinate systems are arbitrary. I pointed out another reason based on the notion that coordinate speeds aren't speeds.

    It should be noted that has dimensions (by definition) and therefore each term of the metric will also have dimensions . If the coordinate differentials are dimensionless (my claim), then the metric tensor components must have dimensions . But note that giving the coordinate differentials the dimensions of is still not in agreement with many coordinate systems such as the spherical coordinate system.
    It has significance to me. We use this physics to predict the path of light reckoned from remote coordinates [for this case]. This particular prediction will help in the analysis of the dying pulse train which is natural phenomena predicted by GR.
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    Don't forget the varying speed of light. The coordinate speed of light is not the same throughout the room you're in. If it was, light wouldn't curve and your pencil would not fall down. You might claim that the speed of light is always 299,792,458 m/s, but don't forget gravitational time dilation. The seconds at one elevation are not the same as the seconds at a different elevation, so one 299,792,458 m/s is not the same as another. If they were, those NIST optical clocks would run at the same rate. They are two super-accurate clocks, one a mere 30cm above the other. And they don't run at the same rate. If they did, light wouldn't curve and your pencil wouldn't fall down. There wouldn't be a gravitational field in the room you're in. And of course, whatever happens to the optical clocks will happen to parallel-mirror light clocks. Like this:



    So the coordinate speed of light does have significance. You can see it in action in those NIST optical clocks. And in the gif above, where each parallel-mirror light-clock can be likened to a frame of reference. Only to get the picture you have to look at both frames at once. Then you can see the significance of the coordinate speed of light. Of the the varying speed of light.
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    So does light slow down because the vacuum is more dense then?
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    And can you put this slowing down in precise mathematics?
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    Quote Originally Posted by Farsight View Post
    So the coordinate speed of light does have significance.
    We already know that. The point is that its significance is the exact same as the local proper speed; one is not any more or less significant than the other.
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    Quote Originally Posted by Farsight View Post
    The coordinate speed of light is not the same throughout the room you're in.
    The coordinate speed of light is not a physical speed of light. The physical speed of light is same throughout the room I'm in and indeed everywhere. You can't actually say the coordinate speed of light is not the same throughout the room I'm in because this presumes some particular coordinate system within the room I'm in, whereas there is no coordinate system until one is defined.


    Quote Originally Posted by Farsight View Post
    If it was, light wouldn't curve and your pencil would not fall down. You might claim that the speed of light is always 299,792,458 m/s, but don't forget gravitational time dilation.
    No one is forgetting gravitational time dilation.


    Quote Originally Posted by Farsight View Post
    The seconds at one elevation are not the same as the seconds at a different elevation

    A second is a second.


    Quote Originally Posted by Farsight View Post
    If they were, those NIST optical clocks would run at the same rate. They are two super-accurate clocks, one a mere 30cm above the other. And they don't run at the same rate. If they did, light wouldn't curve and your pencil wouldn't fall down. There wouldn't be a gravitational field in the room you're in.
    General relativity requires more careful consideration than you are providing. For example, saying the clocks don't run at the same rate is flawed because they are separated by 30cm and therefore not comparable to each other because they are not local to each other.


    Quote Originally Posted by Farsight View Post
    So the coordinate speed of light does have significance.
    It doesn't because the coordinate speed of light is not a physical speed of light. It depends on the coordinate system which is arbitrarily chosen.



    Farsight, I have a seemingly unrelated question I'd like you to answer: What direction is north?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Jilan
    So does light slow down because the vacuum is more dense then?
    Kind of. Space isn't some material so "density" in the usual sense doesn't apply. But we do talk of energy density when it comes to space. Where the energy density is higher the light goes slower.

    Quote Originally Posted by PhysBang
    And can you put this slowing down in precise mathematics?
    It's already there, you just don't recognise it as such. There's no actual time flowing in a light clock, so the t represents the moving light:



    Quote Originally Posted by Markus Hanke
    We already know that. The point is that its significance is the exact same as the local proper speed; one is not any more or less significant than the other.
    It's more significant, Markus. Without a variation in the coordinate speed of light there is nothing to make light curve and nothing to make an electron fall down. You always measure the local proper speed to be the same because of the wave nature of matter. It's that "same essence" thing that's mentioned in GR time dilation on wiki. The local motion of light defines your second and your metre. Then you use them to measure the local motion of light. When light goes slower you don't notice because you and your clocks are going slower too.
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    Quote Originally Posted by KJW
    The coordinate speed of light is not a physical speed of light. The physical speed of light is same throughout the room I'm in and indeed everywhere.
    Noooo! If it was, those two NIST optical clocks would stay synchronised, light wouldn't curve, and your pencil wouldn't fall down.

    Quote Originally Posted by KJW
    You can't actually say the coordinate speed of light is not the same throughout the room I'm in because this presumes some particular coordinate system within the room I'm in, whereas there is no coordinate system until one is defined.
    Then I'll say this: the speed of light is not the same throughout the room you're in.

    Quote Originally Posted by KJW
    A second is a second.
    And a second is the duration of 9192631770 periods of radiation. The duration of 9192631770 light waves coming at you at the local speed of light. When a second at one location is bigger than a second at another location, it's because light goes slower there.

    Quote Originally Posted by KJW
    General relativity requires more careful consideration than you are providing. For example, saying the clocks don't run at the same rate is flawed because they are separated by 30cm and therefore not comparable to each other because they are not local to each other.
    They don't stay synchronised because they don't run at the same rate. Not for any other reason. It's that simple. It isn't flawed.

    Quote Originally Posted by KJW
    It doesn't because the coordinate speed of light is not a physical speed of light. It depends on the coordinate system which is arbitrarily chosen.
    I only called it the coordinate speed of light because that's what everybody is familiar with.

    Quote Originally Posted by KJW
    Farsight, I have a seemingly unrelated question I'd like you to answer: What direction is north?
    It's lots of directions. For example, you and I and Markus and Jilan could stand around the North Pole, all pointing North. I point at you, you point at me, Markus points at Jilan, Jilan points at Markus. Or we could stand around the South Pole with our backs to it all pointing in outward directions like this: ←↑→↓. We're all pointing North.
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    Remember the post I made to you before:

    Quote Originally Posted by Beer w/Straw View Post
    Anyway, a neutral pion decays into two gamma rays ie light. In 1964 at CERN whether these pions were moving at 0.999 75c or stationary in the lab, the gamma rays that came from them were all measured to be the same speed.

    Farsight is out to lunch like no other on this one. He may be challenging that light is not an electromagnetic wave that travels at a finite speed, or he wants to re-write Maxwell's equations.
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    Quote Originally Posted by Farsight View Post
    It's already there, you just don't recognise it as such. There's no actual time flowing in a light clock, so the t represents the moving light:

    That is a non-answer bordering on insult.

    As others have said, you have no physics here, only speculation that you cannot even tie to a single physical measurement.
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    It's no insult, as you know full well. You also know full well that the gedanken parallel-mirror light-clock is employed extensively in relativity. And you know full well that t=time is merely the count of reflections. There is no time flowing in this clock. All we have, is light, moving. So you surely know that t depends on the local speed of light:

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    Yes well, light goes through space-time.

    Stop posting that stupid gif. all over the internet.
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    Quote Originally Posted by Farsight View Post
    It's no insult, as you know full well. You also know full well that the gedanken parallel-mirror light-clock is employed extensively in relativity. And you know full well that t=time is merely the count of reflections.
    No, that would be something that you tell people that isn't true.

    If it were possible to count the reflections, then one could use the mirrors and light as a clock. The assumption behind GR is that all physical systems are effected in the same way by the presence of mass-energy and that it is in principle possible to compare the operation from one moment to the next of one physical system to another, regardless of what the physical system consists. (I.e., the various versions of the equivalence principle.)

    You are trying, deceptively, to argue that all that exists is photons. This is a ludicrous idea that a few crackpots have considered. You want us to beg the question in your favor by simply accepting that all there is to GR is the movement of light when this is not the case.

    If you want us to accept your alternative physics, then you first have to show that it is physics, i.e., you must show that you can do physics with your alternative system.

    If you cannot do this, then you can be a pleasant speculator. You cannot, however, lie here and elsewhere that you have some special understanding of physics that the entire physics community lacks.
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    Quote Originally Posted by Beer w/Straw View Post
    Yes well, light goes through space-time.
    No it doesn't. It goes through space. Spacetime is just a static mathematical model. We can draw worldlines in it to represent the motion of light through space over time, but nothing goes through or moves through spacetime. Imagine I throw a red ball across the room and you film it with a cine camera. Then you develop the film and cut it up into individual frames, and form them into a vertical block. There's a red streak through the block which you can liken to the ball's worldline. But the ball isn't moving through the block.

    Quote Originally Posted by Beer w/Straw
    Stop posting that stupid gif. all over the internet.
    No. It isn't stupid. It brings home the simple fact that speed of light is not the same throughout the room you're in. Just like Einstein said.



    Quote Originally Posted by PhysBang
    No, that would be something that you tell people that isn't true.
    It's true.

    Quote Originally Posted by PhysBang
    If it were possible to count the reflections, then one could use the mirrors and light as a clock.
    The parallel-mirror light-clock isn't something I've dreamt up. It's a gedanken favourite amongst relativists, all of whom know that "the time" on such a clock is a cumulative count of the number of reflections.

    Quote Originally Posted by PhysBang
    The assumption behind GR is that all physical systems are effected in the same way by the presence of mass-energy and that it is in principle possible to compare the operation from one moment to the next of one physical system to another, regardless of what the physical system consists. (I.e., the various versions of the equivalence principle.)
    You can compare clocks at different elevations. Read the OP where I explain how one can derive the Riemann curvature depiction from light-clocks. It's very simple.

    Quote Originally Posted by PhysBang
    You are trying, deceptively, to argue that all that exists is photons. This is a ludicrous idea that a few crackpots have considered. You want us to beg the question in your favor by simply accepting that all there is to GR is the movement of light when this is not the case.
    I didn't invent this "same essence" thing or the wave nature of matter.

    Quote Originally Posted by PhysBang
    If you want us to accept your alternative physics, then you first have to show that it is physics, i.e., you must show that you can do physics with your alternative system. If you cannot do this, then you can be a pleasant speculator. You cannot, however, lie here and elsewhere that you have some special understanding of physics that the entire physics community lacks.
    I'm not lying. But you are casting unfounded ad-hominem allegations. Please desist. It might take your mind off your bitterness if you tried to point out any problems with the OP. When you can't, accept it. And apologise.
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    Another review of Farsight's book.

    This is a work of pure imagination. The author has come up with an imaginative idea (that does NOT meet the criterion for being considered a theory) about what comprises the universe we live in. This book claims that matter, energy and space are the same thing, with the particles we observe being 'knots' of space.
    Unfortunately, his ideas simply don't work. When one creates even the most rudimentary mathematical model of his theories, one finds predictions that contradict what we know about the universe. Even without doing any math, it is possible to find errors and false predictions in his ideas based on simply finding the logical conclusions of his claims.
    This book is self-published, after having been rejected by a number of publishers. I find it quite telling that even a company that would publish works by Deepak Chopra would turn down this author.
    Duffield has been shopping this theory around the internet for several years now. In that time, he's been banned from numerous science forums for various reasons, including refusing to accept correction, presenting his ideas as established science, and even attempting to intimidate others by describing his claimed prowess at boxing and willingness to travel.
    In short, this book is a waste of time, for the author as well as any reader. I would recommend that anyone wishing to learn more about physics purchase a book by an actual physicist.
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    Quote Originally Posted by Farsight View Post
    You can compare clocks at different elevations. Read the OP where I explain how one can derive the Riemann curvature depiction from light-clocks. It's very simple.
    Man, it is so stupid obvious that you don;t even know what the equivalence principles are. It is also stupid obvious that you have never shown a derivation of anything; you haven't shown us anything that we can do to determine any physical value.

    I didn't invent this "same essence" thing or the wave nature of matter.
    No, many crackpots have argued that everything is made of some one substance. Many of them do far more than you and try to actually do physics.

    I'm not lying.
    You are clearly lying. While you can't do physics, you can't be dumb enough to know that some of what you are saying isn't true.
    But you are casting unfounded ad-hominem allegations.
    While I am discussing your character, you are doing nothing other than trying to bolster the appearance of your character as someone who knows physics without doing physics. Thus discussion of your character is all that is on topic for your threads.

    It might take your mind off your bitterness if you tried to point out any problems with the OP. When you can't, accept it. And apologise.
    As many have said, the problem is that it isn't physics: you can't show anyone how to do anything with a physical system. All you can do is try to make yourself look better.
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    Quote Originally Posted by Farsight View Post
    Noooo! If it was, those two NIST optical clocks would stay synchronised, light wouldn't curve, and your pencil wouldn't fall down.

    Then I'll say this: the speed of light is not the same throughout the room you're in.
    What varies within the room is the interval of time between two given isometric spacelike slices in spacetime. This explains the gravity we experience including the gravitational redshift, doing so without a variable speed of light or a variable rate of time, and without the optical clocks staying synchronised.


    Quote Originally Posted by Farsight View Post
    And a second is the duration of 9192631770 periods of radiation. The duration of 9192631770 light waves coming at you at the local speed of light. When a second at one location is bigger than a second at another location, it's because light goes slower there.
    A second is the same size as any other second. There are no bigger or smaller seconds.

    I think you are neglecting the principle of relativity, which basically says that the laws of physics are the same in all frames of reference everywhere.


    Quote Originally Posted by Farsight View Post
    They don't stay synchronised because they don't run at the same rate. Not for any other reason. It's that simple. It isn't flawed.
    They don't stay synchronised because they are different intervals of time at the different locations.


    Quote Originally Posted by Farsight View Post
    I only called it the coordinate speed of light because that's what everybody is familiar with.
    It doesn't matter what you called it because the only speed of light that is physical is the local speed of light that is the same everywhere.


    Quote Originally Posted by Farsight View Post
    It's lots of directions. For example, you and I and Markus and Jilan could stand around the North Pole, all pointing North. I point at you, you point at me, Markus points at Jilan, Jilan points at Markus. Or we could stand around the South Pole with our backs to it all pointing in outward directions like this: ←↑→↓. We're all pointing North.
    I apologise for neglecting that the question I asked is open to different interpretations with some interfering with the point I am trying to make. I was referring to a particular direction is space rather than directions on the earth's surface. My point wasn't about the ambiguity of the definition of "north", but about how to specify a direction in space.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    What varies within the room is the interval of time between two given isometric spacelike slices in spacetime.
    No! Spacetime is a static mathematical model. There is no spacetime in the room. Your isometric spacelike slices are abstract things. What isn't is those optical clocks or the light moving in them. Which is what defines the interval of time. When the light goes slower the interval is bigger. That's it. That's all there is to it. Sometimes I think it's almost too simple to understand.

    Quote Originally Posted by KJW View Post
    This explains the gravity we experience including the gravitational redshift, doing so without a variable speed of light or a variable rate of time, and without the optical clocks staying synchronised.
    I'm sorry KJW, but with respect, that confuses cause and effect. Remember what I said in the OP:

    "It’s also important to note that the clocks nearer the Earth don’t run slower because your plot is curved. In other words, they don’t run slower because spacetime is curved. Spacetime is a mathematical model, and it is static. It’s the plot, the map, and the map is not the territory. It isn't what space is. The clocks run slower when they’re lower because the space down there is different..."

    Quote Originally Posted by KJW View Post
    A second is the same size as any other second. There are no bigger or smaller seconds.
    I'm sorry and again with respect, gravitational time dilation says you're wrong. If you're close to a black hole and I'm not, one of your seconds lasts for ten of mine.

    Quote Originally Posted by KJW
    I think you are neglecting the principle of relativity, which basically says that the laws of physics are the same in all frames of reference everywhere.
    I don't think I've neglected it. Your clock slows down and so do you because of that "same essence" thing, so things look the same to you.

    Quote Originally Posted by KJW
    They don't stay synchronised because they are different intervals of time at the different locations.
    Those intervals of time defined by the motion of light at those locations.

    Quote Originally Posted by KJW
    It doesn't matter what you called it because the only speed of light that is physical is the local speed of light that is the same everywhere.
    That's the tautology that Magueijo and Moffat referred to:

    "The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition".

    Quote Originally Posted by KJW
    I apologise for neglecting that the question I asked is open to different interpretations with some interfering with the point I am trying to make. I was referring to a particular direction is space rather than directions on the earth's surface. My point wasn't about the ambiguity of the definition of "north", but about how to specify a direction in space.
    I'm not sure, but there's mention of something in the CMB article on Wiki:

    "From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 369±0.9 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB) in the direction of galactic longitude l = 263.99±0.14°, b = 48.26±0.03°."
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    That's all there is to it.
    Except that light never "goes slower". Everyone measures the speed of light to be exactly c in his own frame; variances arise only if one attempts to determine the speed of light in a remote frame. What changes is not the local speed of light, but only the global relationship between frames. That is the point of GR, as mentioned several times previously.
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    It deserves mention that it is in fact impossible to measure light to propagate at anything other than exactly c in a given medium; no experiment one can dream up can do that, just as no observer will ever see his own clock slow down. Of course you can look upon a distant frame and use your own local methods of assigning labels to events to come up with a figure for the speed of light in that remote frame; and you will find that it differs from what you measure locally. However, what you actually measured is not the speed of light, but simply how your local frame is related to that other remote frame. It's still valid, but only for you, not for the remote frame itself.
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    Quote Originally Posted by Farsight View Post
    Spacetime is a static mathematical model.
    So?


    Quote Originally Posted by Farsight View Post
    There is no spacetime in the room.
    I can choose to define an -coordinate system within the room. That is sufficient. If you don't think it is sufficient, then you place excessive burden on what spacetime is.


    Quote Originally Posted by Farsight View Post
    Your isometric spacelike slices are abstract things.
    No more abstract than geometry. Modern theories of physics are quite abstract but that is not a shortcoming if it provides a deeper understanding. Standard general relativity is not abstract because the elements of the theory (the metric, curvature, etc) are directly measurable.


    Quote Originally Posted by Farsight View Post
    What isn't is those optical clocks or the light moving in them. Which is what defines the interval of time. When the light goes slower the interval is bigger.
    If one is using a light clock, then the speed of light is required to be invariant. Otherwise, how does one know what the speed of light is under the given conditions?


    Quote Originally Posted by Farsight View Post
    Sometimes I think it's almost too simple to understand.
    Don't presume that we don't understand just because we disagree.


    Quote Originally Posted by Farsight View Post
    I'm sorry KJW, but with respect, that confuses cause and effect.
    The gravity we experience and the gravitational redshift are concomitant. One is not the cause or effect of the other.


    Quote Originally Posted by Farsight View Post
    The clocks run slower when they’re lower because the space down there is different.
    Are you sure about that? In particular, are you sure that the differences in the space down there are of the appropriate form for clocks to run slower? Can you mathematically justify this (hand-waving explanations will not be good enough)?


    Quote Originally Posted by Farsight View Post
    gravitational time dilation says you're wrong. If you're close to a black hole and I'm not, one of your seconds lasts for ten of mine.
    The flaw in this statement is the underlying false assumption that your second is being compared to my second. Just because the interval of time at my location is one second and the interval of time at your location is ten seconds doesn't mean that the seconds themselves are different.


    Quote Originally Posted by Farsight View Post
    I don't think I've neglected it. Your clock slows down and so do you because of that "same essence" thing, so things look the same to you.
    You've neglected the principle of relativity by your claim that the speed of light varies and that the second varies, in conflict with the same laws of physics for everyone.


    Quote Originally Posted by Farsight View Post
    Those intervals of time defined by the motion of light at those locations.
    The problem is that it is the observer who is comparing the time intervals at the two locations.


    Quote Originally Posted by Farsight View Post
    That's the tautology that Magueijo and Moffat referred to:

    "The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition".
    The metre wasn't always defined in terms of distance light travelled in an interval of time. In Einstein's time, the metre was defined by a particular rod.


    Quote Originally Posted by Farsight View Post
    I'm not sure, but there's mention of something in the CMB article on Wiki:

    "From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 369±0.9 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB) in the direction of galactic longitude l = 263.99±0.14°, b = 48.26±0.03°."
    I shall defer discussion of this until a later time.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Markus Hanke View Post
    Except that light never "goes slower". Everyone measures the speed of light to be exactly c in his own frame; variances arise only if one attempts to determine the speed of light in a remote frame. What changes is not the local speed of light, but only the global relationship between frames. That is the point of GR, as mentioned several times previously.
    You've missed the crucial point, which is the speed of light varies with position. Einstein said it repeatedly. It varies in the room you're in. If it didn't, things wouldn't fall down. Like I was saying on the other thread, when you appreciate time then the speed of light you appreciate that one optical clock 30cm lower than another is showing you the varying speed of light. It's an optical clock. It doesn't go slower when it's lower because time goes slower. It goes slower because light goes slower. And a curvature of rays of light can only occur when the speed of light varies with position. Not because spacetime is curved. Spacetime curvature is associated with tidal force, which isn't detectable in the room you're in. But your pencil falling down is detectable.

    Quote Originally Posted by Markus Hanke View Post
    It deserves mention that it is in fact impossible to measure light to propagate at anything other than exactly c...
    Because as Magueijo and Moffat said, it's a tautology. You use the motion of light to define the second and the metre. Then use them to measure the motion of light.

    Quote Originally Posted by Markus Hanke View Post
    just as no observer will ever see his own clock slow down.
    Just as no observer will ever see his own clock stop. Because he stops too.

    Quote Originally Posted by Markus Hanke View Post
    Of course you can look upon a distant frame and use your own local methods of assigning labels to events to come up with a figure for the speed of light in that remote frame; and you will find that it differs from what you measure locally. However, what you actually measured is not the speed of light, but simply how your local frame is related to that other remote frame. It's still valid, but only for you, not for the remote frame itself.
    Einstein said the speed of light varies with position. And when you use the NIST caesium clock to define your second, what you effectively do is count nine billions waves passing you by, then you say "that's a second".
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    Quote Originally Posted by Farsight View Post
    You've missed the crucial point, which is the speed of light varies with position. Einstein said it repeatedly.
    This seems like a falsehood. You showed one citation where Einstein said this, prior to the development of GR, which, as you have admitted, only uses the constant speed of light in its equations.
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    Quote Originally Posted by KJW View Post
    So?
    You said this: what varies within the room is the interval of time between two given isometric spacelike slices in spacetime. And there is no spacetime in the room. Spacetime is an abstract thing. It's space in the room. And you define your time using the motion of light. So what really varies in the room is the motion of light. It goes slower when it's lower. Like Einstein said, the speed of light varies with position.

    Quote Originally Posted by KJW View Post
    I can choose to define an -coordinate system within the room. That is sufficient. If you don't think it is sufficient, then you place excessive burden on what spacetime is.
    You can define anything you like, but a coordinate system is an abstract thing too. And you define your coordinate system using metres and seconds which are in turn defined using the motion of light. Only if your seconds at the top of the room were exactly the same as the seconds at the bottom, things wouldn't fall down.

    Quote Originally Posted by KJW View Post
    No more abstract than geometry. Modern theories of physics are quite abstract but that is not a shortcoming if it provides a deeper understanding. Standard general relativity is not abstract because the elements of the theory (the metric, curvature, etc) are directly measurable.
    My argument here is that Einstein provided a deeper understanding of how gravity works by saying the speed of light varies with position. All you need to add to that is the wave nature of matter, and you know why the electron falls down. But it's been expunged. The deeper understanding has gone. It's been replaced by a myth: light curves because spacetime is curved. It isn't true. Curved spacetime is nothing more than a curvature in your plot of measurements. Your metric.

    Quote Originally Posted by KJW View Post
    If one is using a light clock, then the speed of light is required to be invariant. Otherwise, how does one know what the speed of light is under the given conditions?
    You don't know what the speed of light is. You might claim it's 299,792.458 m/s, but you used light moving to define your second and your metre. And when light goes slower you go slower along with everything else, so you think it isn't going slower.

    Quote Originally Posted by KJW View Post
    Don't presume that we don't understand just because we disagree.
    See the above. It is such a simple point, but people seem unable to grasp it.

    Quote Originally Posted by KJW View Post
    The gravity we experience and the gravitational redshift are concomitant. One is not the cause or effect of the other.
    There is no gravitational redshift. Really. When you ascend we did work to raise you. We added energy to you. Your mass-energy is increased. So when you measure an ascending photon, it looks like it has lost energy even though it hasn't. You must know this is true because you surely know about the mass deficit, and that a 511keV photon falling into a black hole increases its mass by 511keV/c².

    Quote Originally Posted by KJW View Post
    Are you sure about that? In particular, are you sure that the differences in the space down there are of the appropriate form for clocks to run slower? Can you mathematically justify this (hand-waving explanations will not be good enough)?
    I can point to optical clocks running slower and to mechanics, where a shear wave travels at a speed v = √(G/ρ) where G is the shear modulus of elasticity and ρ is the density. Then I can point you to c = √(1/ε0μ0) and vacuum impedance Z0 = √(μ0/ε0) and remind you that light is alternating displacement current and that impedance is resistance to alternating current. And that Einstein said this in his Leyden Address:

    "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..."

    Quote Originally Posted by KJW View Post
    The flaw in this statement is the underlying false assumption that your second is being compared to my second. Just because the interval of time at my location is one second and the interval of time at your location is ten seconds doesn't mean that the seconds themselves are different.
    It definitely does. We define event1 as your departure and event2 as your return, and compare clock readings. Your clock reading is one zillion seconds, mine is ten zillion seconds. Your seconds were bigger than mine.

    Quote Originally Posted by KJW View Post
    You've neglected the principle of relativity by your claim that the speed of light varies and that the second varies, in conflict with the same laws of physics for everyone.
    It's just the God's eye global viewpoint as opposed to the local viewpoint.

    Quote Originally Posted by KJW
    The metre wasn't always defined in terms of distance light travelled in an interval of time. In Einstein's time, the metre was defined by a particular rod.
    Light is the purest way to define it because of the electromagnetic "essence" of matter.
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    Quote Originally Posted by Farsight View Post
    And you define your time using the motion of light. So what really varies in the room is the motion of light.
    The reason that "time" is "defined" using light (not its motion, but how much of it is emitted in a certain process), is because of the practical use of certain types of physical systems. In physics as currently practiced, the composition and particular interactions of a physical system do not matter for time. Only in Farsight-Relativity is this so. And we have no good reason to accept Farsight-Relativity.
    Like Einstein said, the speed of light varies with position.
    As many have pointed out, this is a deceptive claim.

    My argument here is that Einstein provided a deeper understanding of how gravity works by saying the speed of light varies with position.
    That is your claim, not your argument. Your argument is that in one place before GR Einstein said this. That is the extent of your theological argument. You have admitted that nowhere in GR or in any other physics can we use your idea to describe a physical system. So you have a lot of semi-religious claims and dogma, but no reasoning.


    And that Einstein said this in his Leyden Address:

    "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..."
    Yes he did say this, and he explained what he meant using equations that, by your own admission, rely on the constant speed of light. So it appears that your citation here gives the lie to your claim.
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    Quote Originally Posted by PhysBang View Post
    This seems like a falsehood. You showed one citation where Einstein said this, prior to the development of GR, which, as you have admitted, only uses the constant speed of light in its equations.
    It's no falsehood. Einstein said this repeatedly during and after the development of general relativity:

    1911: "If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c²)”.

    1912: "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential".

    1913: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis".

    1915: "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned".

    1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position”.


    As I said in the other thread, the word velocity is the common usage, not the vector quantity.

    Have a look at Is The Speed of Light Everywhere the Same? on Baez's website. It's been updated recently by Don Koks, whom I spoke to about an issue. Here's some excerpts:

    So consider the question: "Can we say that light confined to the vicinity of the ceiling of this room is travelling faster than light confined to the vicinity of the floor?". For simplicity, let's take Earth as not rotating, because that complicates the question! The answer is then that (1) an observer stationed on the ceiling measures the light on the ceiling to be travelling with speed c, (2) an observer stationed on the floor measures the light on the floor to be travelling at c, but (3) within the bounds of how well the speed can be defined (discussed below, in the General Relativity section), a "global" observer can say that ceiling light does travel faster than floor light...

    I collate their measurements and find that in this "global" uniformly accelerated frame, ceiling light travels faster than floor light...

    Still, we can say that light in the presence of gravity does have a position-dependent "pseudo speed". In that sense, we could say that the "ceiling" speed of light in the presence of gravity is higher than the "floor" speed of light...

    Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers.
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    Quote Originally Posted by PhysBang View Post
    The reason that "time" is "defined" using light (not its motion, but how much of it is emitted in a certain process), is because of the practical use of certain types of physical systems. In physics as currently practiced, the composition and particular interactions of a physical system do not matter for time. Only in Farsight-Relativity is this so. And we have no good reason to accept Farsight-Relativity.

    As many have pointed out, this is a deceptive claim.

    That is your claim, not your argument. Your argument is that in one place before GR Einstein said this. That is the extent of your theological argument. You have admitted that nowhere in GR or in any other physics can we use your idea to describe a physical system. So you have a lot of semi-religious claims and dogma, but no reasoning.

    Yes he did say this, and he explained what he meant using equations that, by your own admission, rely on the constant speed of light. So it appears that your citation here gives the lie to your claim.
    Read the Baez article updated by Don Koks, and then you might like to apologise:

    Is The Speed of Light Everywhere the Same?
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    No apology, since it appears to be saying the same thing I have been saying. If you can show me where in Einstein's equations he uses this change in the speed of light as the fundamental means of understanding physics, then I would certainly apologize. Until then, I will continue to believe that you are deceiving us by hiding behind the local speed and coordinate speed difference that you do not fully understand.
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    All you need to add to that is the wave nature of matter, and you know why the electron falls down. But it's been expunged.
    This is clearly just a personal idea of yours - GR does not require any assumptions about the nature of matter. It is purely classical, always has been since its publication, and explains perfectly well why the electron ( or anything else ) falls down. Now you mightn't believe that it does, but that's hardly a problem with GR, now is it
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    It isn't a personal idea of mine. It's detective work. Read the Baez article updated by Don Koks after I raised an issue:

    Still, we can say that light in the presence of gravity does have a position-dependent "pseudo speed". In that sense, we could say that the "ceiling" speed of light in the presence of gravity is higher than the "floor" speed of light...

    Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers...
    Light curves because the speed of light varies with position. That's what Einstein said. The electron falls down for the same reason. You can find other people saying something similar elsewhere on the internet. Light doesn't curve because spacetime is curved. Einstein never said that, and it confuses cause and effect.

    I notice you haven't said much about the OP. Can you point out some flaw with it? Alternatively can you explain why an electron falls down? If you can't do either, please think carefully about why not. If you think you can do the latter, pay special attention to this:

    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.
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  59. #59  
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    So?
    You said this: what varies within the room is the interval of time between two given isometric spacelike slices in spacetime. And there is no spacetime in the room. Spacetime is an abstract thing. It's space in the room. And you define your time using the motion of light. So what really varies in the room is the motion of light. It goes slower when it's lower. Like Einstein said, the speed of light varies with position.

    Quote Originally Posted by KJW View Post
    I can choose to define an -coordinate system within the room. That is sufficient. If you don't think it is sufficient, then you place excessive burden on what spacetime is.
    You can define anything you like, but a coordinate system is an abstract thing too. And you define your coordinate system using metres and seconds which are in turn defined using the motion of light. Only if your seconds at the top of the room were exactly the same as the seconds at the bottom, things wouldn't fall down.
    You say that coordinate systems and spacetime are mathematical or abstract as if this somehow invalidates the notions, and as if the invalidation of the notions is self-evident. It is not self-evident... you need to justify it.


    Quote Originally Posted by Farsight View Post
    And you define your coordinate system using metres and seconds
    This represents a misunderstanding of what a coordinate system is. A metric requires measurement of distance and time, a coordinate system is simply a smooth mapping from physical events (points) to 4-tuples.


    Quote Originally Posted by Farsight View Post
    My argument here is that Einstein provided a deeper understanding of how gravity works
    Einstein is not god and what he said should not be taken as gospel. A deeper understanding of how gravity works is best obtained from a deeper understanding of the underlying mathematics.


    Quote Originally Posted by Farsight View Post
    ... and you know why the electron falls down
    I already know why the electron falls down.


    Quote Originally Posted by Farsight View Post
    Light curves because spacetime is curved. It isn't true.
    You are correct here. Spacetime curvature is not directly the cause of gravity. One has artificial gravity in an accelerated frame of reference in flat spacetime.


    Quote Originally Posted by Farsight View Post
    Curved spacetime is nothing more than a curvature in your plot of measurements.
    Perhaps the most significant aspect of our disagreement is that I take measurements at face-value, whereas you reject the face-value in favour of hidden caveats. For example, to me, a clock simply measures time, whereas you want to engage in lengthy debate about how a clock works to deny the existence of time.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    If one is using a light clock, then the speed of light is required to be invariant. Otherwise, how does one know what the speed of light is under the given conditions?
    You don't know what the speed of light is. You might claim it's 299,792.458 m/s, but you used light moving to define your second and your metre. And when light goes slower you go slower along with everything else, so you think it isn't going slower.
    You appear to have missed my point, which is that if one wishes to have a clock based on light travelling between mirrors, then it is necessary to have a value for the speed of light. Also one needs a value for everywhere the clock is to be used. This value can't be measured because that would require a clock that isn't based on light travelling between mirrors. Therefore, one fixes the value and defines it to be the same everywhere.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    Don't presume that we don't understand just because we disagree.
    See the above. It is such a simple point, but people seem unable to grasp it.
    Again, you assume that people are unable to grasp what you are saying simply because they disagree with you.


    Quote Originally Posted by Farsight View Post
    gravitational time dilation says you're wrong.
    Quote Originally Posted by Farsight View Post
    There is no gravitational redshift. Really.
    Well, which is it? Is there gravitational redshift or not?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Why isn't the John Duffield (Farsight) troll banned?
    Send him to spew his tripe elsewhere.
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    I'm no troll, I provide interesting and challenging discussion. What's your name by the way?
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    Quote Originally Posted by KJW View Post
    You say that coordinate systems and spacetime are mathematical or abstract as if this somehow invalidates the notions, and as if the invalidation of the notions is self-evident. It is not self-evident... you need to justify it.
    It's a matter of ontology and empiricism and hard scientific evidence. You can see a space between your outstretched hands, and when you waggle them, you can see motion. You can see space and motion through it, but you can't see time, or spacetime, or a coordinate system. I could take you out into my back garden tonight and say "look, that's space". But I couldn't say "look, there's a coordinate system". IMHO a large part of gaining understanding is learning to distinguish what's actually there from the abstractions that aren't, and giving priority to the former instead of the latter.

    Quote Originally Posted by KJW View Post
    This represents a misunderstanding of what a coordinate system is. A metric requires measurement of distance and time, a coordinate system is simply a smooth mapping from physical events (points) to 4-tuples.
    I know what a coordinate system is. Note that people talk of "the metric" as if it's space. It isn't. It's an abstract "plot" or "map" of your measurements. See the OP about how the Riemann-curvature depiction can be obtained from light-clock readings.

    Quote Originally Posted by KJW View Post
    Einstein is not god and what he said should not be taken as gospel. A deeper understanding of how gravity works is best obtained from a deeper understanding of the underlying mathematics.
    I will not be told to ignore what Einstein said in a discussion of gravity or relativity because "we know better". Because we don't. Two out of the three authors of MTW believe/d in time travel.

    Quote Originally Posted by KJW View Post
    I already know why the electron falls down.
    Then explain it. And note that magical mysterious action at a distance is not permitted.

    Quote Originally Posted by KJW View Post
    You are correct here. Spacetime curvature is not directly the cause of gravity. One has artificial gravity in an accelerated frame of reference in flat spacetime.
    Spacetime is an abstract static mathematical model in which motion does not occur. A frame of reference is another abstract thing.

    Quote Originally Posted by KJW View Post
    Perhaps the most significant aspect of our disagreement is that I take measurements at face-value, whereas you reject the face-value in favour of hidden caveats.
    I only reject it when it demands the impossible. I say my measurement has changed, why? If I measure something repeatedly and I find that my measurements change, I say either it's changed or I have. When it's a pulsar and I'm falling, I know it's me changing. When it's a stream of identical photons and me accelerating, I know it's me changing. And so on. What's not to like?

    Quote Originally Posted by KJW View Post
    For example, to me, a clock simply measures time, whereas you want to engage in lengthy debate about how a clock works to deny the existence of time.
    I want you to look inside the clock in order to establish what it really does. By the way, I say time exists like heat exists. Heat burns you. It exists all right.

    Quote Originally Posted by KJW View Post
    You appear to have missed my point, which is that if one wishes to have a clock based on light travelling between mirrors, then it is necessary to have a value for the speed of light.
    You don't. You simple say "when this clock has ticked 9192631770 times one second has elapsed".

    Quote Originally Posted by KJW View Post
    Also one needs a value for everywhere the clock is to be used. This value can't be measured because that would require a clock that isn't based on light travelling between mirrors. Therefore, one fixes the value and defines it to be the same everywhere.
    You just say "when this clock has ticked 9192631770 times one second has elapsed". Then when you're lower you still measure the speed of light to be 299792458 m/s. Even though the light's going slower, and so are you because of your electromagnetic "essence".

    Quote Originally Posted by KJW
    Again, you assume that people are unable to grasp what you are saying simply because they disagree with you.
    Sorry.

    Quote Originally Posted by KJW
    Well, which is it? Is there gravitational redshift or not?
    No. Your mass-energy increases when you are raised. Ditto for your measuring equipment. The ascending photon doesn't change, but your measurement of its energy is less than it was when you were lower. Flip it around, and a 511keV photon falling into a black hole increases the black hole mass by 511keV/c². A photon doesn't gain any energy when it descends, and it doesn't lose any energy when it ascends. If this isn't what textbook says, your textbook is wrong.
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    Quote Originally Posted by Farsight View Post
    It's a matter of ontology and empiricism and hard scientific evidence. You can see a space between your outstretched hands, and when you waggle them, you can see motion.
    If this is empiricism, then please explain how one can see motion by waggling one's hands. Please explain how one can distinguish this from a lack of motion.
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    Quote Originally Posted by Farsight View Post
    I could take you out into my back garden tonight and say "look, that's space". But I couldn't say "look, there's a coordinate system".
    Actually, you could draw a coordinate grid over your back garden and say "look, there's a coordinate system". Altenatively, you could take a photograph of your back garden and draw the grid on that. However, one doesn't need an actual drawn grid, one can consider an imaginary grid. A coordinate system is simply a description of the set of locations. But note that one must distinguish between the same location at different times.


    Quote Originally Posted by Farsight View Post
    Note that people talk of "the metric" as if it's space. It isn't. It's an abstract "plot" or "map" of your measurements.
    That makes it more valid, not less. A description may not be the thing it describes, but it still describes the thing, and what more does one need other than the description in order to have a theory?


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    Einstein is not god and what he said should not be taken as gospel. A deeper understanding of how gravity works is best obtained from a deeper understanding of the underlying mathematics.
    I will not be told to ignore what Einstein said in a discussion of gravity or relativity because "we know better". Because we don't. Two out of the three authors of MTW believe/d in time travel.
    I didn't refer you to the authors of MTW. I referred you to the mathematics.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    I already know why the electron falls down.
    Then explain it. And note that magical mysterious action at a distance is not permitted.
    I have no intention of posting a complete explanation, but I will say that objects fall in gravity for the same reason they fall from an accelerated observer: the object has an inertial trajectory while the observer accelerates away from it. I will also mention the following formula:



    where is the acceleration of a stationary observer and is the relative magnitude of the corresponding time-like Killing vector. This formula is the direct relationship between time dilation and gravity. Although this formula is expressed in kinematic terms, it is in fact based on pure geometry.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    Perhaps the most significant aspect of our disagreement is that I take measurements at face-value, whereas you reject the face-value in favour of hidden caveats.
    I only reject it when it demands the impossible.
    What impossibility is being demanded? If one has obtained the measurement, then that measurement obviously can't be an impossibility.


    Quote Originally Posted by Farsight View Post
    When it's a pulsar and I'm falling, I know it's me changing.
    If you are in a box from which you cannot see out, how do you know you are falling?


    Quote Originally Posted by Farsight View Post
    me accelerating, I know it's me changing.
    If you are constantly accelerating, then you are not changing.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    For example, to me, a clock simply measures time, whereas you want to engage in lengthy debate about how a clock works to deny the existence of time.
    I want you to look inside the clock in order to establish what it really does. By the way, I say time exists like heat exists. Heat burns you. It exists all right.
    If time exists, what is the point of looking inside the clock?


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    You appear to have missed my point, which is that if one wishes to have a clock based on light travelling between mirrors, then it is necessary to have a value for the speed of light.
    You don't. You simple say "when this clock has ticked 9192631770 times one second has elapsed".
    But in order to construct a clock based on light travelling between mirrors, it is necessary to specify how far apart the mirrors are. Then the value of the speed of light becomes specified (even if implicit).


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    Also one needs a value for everywhere the clock is to be used. This value can't be measured because that would require a clock that isn't based on light travelling between mirrors. Therefore, one fixes the value and defines it to be the same everywhere.
    You just say "when this clock has ticked 9192631770 times one second has elapsed". Then when you're lower you still measure the speed of light to be 299792458 m/s. Even though the light's going slower, and so are you because of your electromagnetic "essence".
    If the speed of light is 299792458 m/s everywhere, then it has the same speed everywhere because 299792458 m/s is the speed.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW
    Well, which is it? Is there gravitational redshift or not?
    No. Your mass-energy increases when you are raised. Ditto for your measuring equipment. The ascending photon doesn't change, but your measurement of its energy is less than it was when you were lower. Flip it around, and a 511keV photon falling into a black hole increases the black hole mass by 511keV/c². A photon doesn't gain any energy when it descends, and it doesn't lose any energy when it ascends. If this isn't what textbook says, your textbook is wrong.
    It isn't just the energy that decreases, it is also the frequency, hence the term "redshift". This connects it to time dilation.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    Actually, you could draw a coordinate grid over your back garden and say "look, there's a coordinate system". Altenatively, you could take a photograph of your back garden and draw the grid on that. However, one doesn't need an actual drawn grid, one can consider an imaginary grid. A coordinate system is simply a description of the set of locations. But note that one must distinguish between the same location at different times.
    No problem.

    Quote Originally Posted by KJW View Post
    That makes it more valid, not less. A description may not be the thing it describes, but it still describes the thing, and what more does one need other than the description in order to have a theory?
    Ditto.

    Quote Originally Posted by KJW
    I didn't refer you to the authors of MTW. I referred you to the mathematics.
    Noted.

    Quote Originally Posted by KJW View Post
    I have no intention of posting a complete explanation, but I will say that objects fall in gravity for the same reason they fall from an accelerated observer: the object has an inertial trajectory while the observer accelerates away from it. I will also mention the following formula:



    where is the acceleration of a stationary observer and is the relative magnitude of the corresponding time-like Killing vector. This formula is the direct relationship between time dilation and gravity. Although this formula is expressed in kinematic terms, it is in fact based on pure geometry.
    I'm afraid it's no explanation at all. Note that the principle of equivalence applies to an infinitesimal region. And actually, that means it doesn't apply at all. Heresy I know, especially coming from an amateur relativist, but's that's the size of it. Have a look at the Synge quote on page 20 of this essay:

    "I have never been able to understand this principle…Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line … The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time faced".
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    Quote Originally Posted by KJW
    What impossibility is being demanded? If one has obtained the measurement, then that measurement obviously can't be an impossibility.
    That energy leaps through space via some unseen instant mechanism.

    Quote Originally Posted by KJW
    If you are in a box from which you cannot see out, how do you know you are falling?
    You don't. But what I was talking about was being able to see a pulsar as you're falling.

    Quote Originally Posted by KJW
    If you are constantly accelerating, then you are not changing.
    You are. It takes energy to accelerate, just as it takes energy to lift you up.

    Quote Originally Posted by KJW
    If time exists, what is the point of looking inside the clock?
    To understand what clocks really do. It all starts with that. Once you understand that a clock "clocks up" some kind of regular cyclical motion, you appreciate that when the clock goes slower it's because that motion goes slower. Then you apply that to a light clock and you start noticing what Einstein said.

    Quote Originally Posted by KJW
    But in order to construct a clock based on light travelling between mirrors, it is necessary to specify how far apart the mirrors are. Then the value of the speed of light becomes specified (even if implicit).
    You're getting things back to front. You don't start by specifying how far apart the mirrors are. You start by counting some number of reflections and declaring that a second has elapsed. Then you let light move for some period of time and declare the distance moved to be a metre. Then the distance between the mirrors is some fraction of that, depending on your count and your period. By definition. And the speed of light is then 299792458 m/s by definition, regardless of how fast it moved. Hence the parallel-mirror gif.

    Quote Originally Posted by KJW
    If the speed of light is 299792458 m/s everywhere, then it has the same speed everywhere because 299792458 m/s is the speed.
    It's a tautology because you use the motion of light to define your second and your metre, then you use them to measure the speed of light. Again see [0705.4507] Comments on "Note on varying speed of light theories" :

    "Following Ellis [1], let us first consider c as the speed of the photon. Can c vary? Could such a variation be measured? As correctly pointed out by Ellis, within the current protocol for measuring time and space the answer is no. The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition."

    Quote Originally Posted by KJW
    It isn't just the energy that decreases, it is also the frequency, hence the term "redshift". This connects it to time dilation.
    The frequency doesn't decrease either. You measure a lower frequency because your clock goes faster when you're higher. You go faster too, so you don't notice your clock going faster. There is no unseen instant mechanism by which energy leaps through space and drains out of the photon. Conservation of energy applies, and E=hf.
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    Quote Originally Posted by Farsight View Post
    Note that the principle of equivalence applies to an infinitesimal region. And actually, that means it doesn't apply at all.
    So that means you are rejecting calculus?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Farsight seems to confuse coordinate distances and times with physical distances and times. Coordinates are arbitrary, thus, coordinate distances and times are arbitrary. In practice, coordinates are often selected to make calculations easier, like making various symmetries manifest. For flat space, an obvious choice of coordinates is one that makes the metric constant. That's rectangular or Cartesian coordinates.

    Furthermore, he seems to believe that there is some absolute, universal time that all observers experience. That is contrary to relativity, and in fact, relativity got its name from time not being absolute in it. Furthermore, there are many observations of time not being absolute. This relativity of time is associated with positions in space, so that is why we speak of space-time, with time treated as something like an additional space dimension.

    Newtonian mechanics is, in a sense, a relativity theory. Like special relativity, it posits space-time as having a full set of symmetries, but with different boosts: Galilean boosts instead of Lorentz ones.
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    lpetrich: I don't confuse coordinate distances and times with physical distances and times. Nor do I believe that there is some absolute, universal time that all observers experience. I don't know where you get that from. And note that this Baez article 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."


    Quote Originally Posted by KJW View Post
    So that means you are rejecting calculus?
    No, not at all. I'm essentially saying that a real gravitational field just isn't the same as accelerating through space. Of course if you were in a box you couldn't tell the difference, but there is a difference. See paragraph 82 of Relativity: The Special and General Theory where Einstein says this:

    "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."

    What I'd call a real gravitational field is what Einstein said is a gravitational field of quite special form. What Einstein is saying is the same as what Synge essentially said, you can't transform a real gravitational field away. It isn't exactly equivalent to accelerating through space.
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    And when I said light goes through spacetime, you replied to me with this:

    No it doesn't. It goes through space. Spacetime is just a static mathematical model. We can draw worldlines in it to represent the motion of light through space over time, but nothing goes through or moves through spacetime. Imagine I throw a red ball across the room and you film it with a cine camera. Then you develop the film and cut it up into individual frames, and form them into a vertical block. There's a red streak through the block which you can liken to the ball's worldline. But the ball isn't moving through the block.
    And now you're quoting something like 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."
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    There's no contradiction. See the OP. You could plot curved spacetime using light clocks. What you're plotting is the "coordinate" speed of light through space. Space is the territory, spacetime is the map. See Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime which relates curved spacetime with inhomogeneous space. Einstein talked about inhomogeneous space in his 1920 Leyden Address. Space isn't curved where a gravitational field is, it's inhomogeneous. When you plot out this inhomogeneity using light clocks, your plot is curved. Like this:


    GNUFDL image by Johnstone, see: Riemannian geometry - Wikipedia, the free encyclopedia
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    "Chinese Physics Letters"? "An Alternative Interpretation of Curved Spacetime"?

    I really don't know what to say. Or, even if I should report your post to have it moved to the alternative subsection.
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    Quote Originally Posted by Farsight View Post
    lpetrich: I don't confuse coordinate distances and times with physical distances and times. Nor do I believe that there is some absolute, universal time that all observers experience.
    In a sense, this is true: you don't really have any coherent beliefs about spacetime. You use language about "motion", but since you have never learned how to do physics, you don't really understand that your claims about motion assume an absolute space and time. Since you don't ever explain any details about how physics actually works given your ideas, you don't really have to face the implications of the claims that you make.

    You are attempting to reduce the kinematics of physics to a single standard of motion. This requires a single standard of time and space, even though you do not understand this. If you would ever take the time to work out your theory, then you might learn this.
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    Quote Originally Posted by Farsight View Post

    No, not at all. I'm essentially saying that a real gravitational field just isn't the same as accelerating through space. Of course if you were in a box you couldn't tell the difference, but there is a difference. See paragraph 82 of Relativity: The Special and General Theory where Einstein says this:

    "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."

    What I'd call a real gravitational field is what Einstein said is a gravitational field of quite special form. What Einstein is saying is the same as what Synge essentially said, you can't transform a real gravitational field away. It isn't exactly equivalent to accelerating through space.
    I guess it all comes down to that inverse square law resulting in acceleration is not uniform. To model the real equivalence you would need a constant field strength. A spherical underground cave should do the job nicely.
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    I'm afraid it's no explanation at all.
    Refer to the other thread - this is exactly what I mean. You accuse me and others of not providing justification, but when sound justification is given ( as is the case here by KJW ), you declare it insufficient and meaningless. We will not ever get anywhere like this.
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    Farsight seems to confuse coordinate distances and times with physical distances and times.
    Indeed.
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    I have no intention of posting a complete explanation, but I will say that objects fall in gravity for the same reason they fall from an accelerated observer: the object has an inertial trajectory while the observer accelerates away from it. I will also mention the following formula:



    where is the acceleration of a stationary observer and is the relative magnitude of the corresponding time-like Killing vector. This formula is the direct relationship between time dilation and gravity. Although this formula is expressed in kinematic terms, it is in fact based on pure geometry.
    I'm afraid it's no explanation at all. Note that the principle of equivalence applies to an infinitesimal region. And actually, that means it doesn't apply at all. Heresy I know, especially coming from an amateur relativist, but's that's the size of it. Have a look at the Synge quote on page 20 of this essay:

    "I have never been able to understand this principle…Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line … The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time faced".
    Quote Originally Posted by Farsight View Post
    I'm essentially saying that a real gravitational field just isn't the same as accelerating through space. Of course if you were in a box you couldn't tell the difference, but there is a difference. See paragraph 82 of Relativity: The Special and General Theory where Einstein says this:

    "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."

    What I'd call a real gravitational field is what Einstein said is a gravitational field of quite special form. What Einstein is saying is the same as what Synge essentially said, you can't transform a real gravitational field away. It isn't exactly equivalent to accelerating through space.
    You asked me to explain why an object (an electron) falls down in gravity and that is what I explained. The distinction between an accelerated frame of reference and true gravitation due to spacetime curvature is not relevant to this specific issue. That is why I said in an earlier post that "spacetime curvature is not directly the cause of gravity". Although one can distinguish between an accelerated frame of reference and true gravitation by means of the tidal effect for true gravitation, the tidal effect is not important to the issue of why objects fall. That's not to say that spacetime curvature isn't important, but you didn't ask about that.

    An important issue to come to terms with is how one is being constantly accelerated upward while standing on the ground and apparently not going anywhere. But then, this is relativity.

    The equivalence principle is important because it says that local physics is special relativity. Thus, special relativity is not merely a weak field approximation to general relativity, but has an important position within general relativity as the local physics regardless of the field strength. It means that one can form a curved spacetime by patching together, albeit imperfectly, Minkowskian spacetime patches. It also means that a straight line in curved spacetime locally looks like a straight line in flat spacetime.
    x0x likes this.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Jilan View Post
    I guess it all comes down to that inverse square law resulting in acceleration is not uniform. To model the real equivalence you would need a constant field strength.
    Then you've got a uniform gravitational field, which means you've got no Riemann curvature, so you haven't got a gravitational field. The moot point is that standing on the surface of the Earth is like accelerating through space, but you aren't actually accelerating. So it isn't actually equivalent.

    Quote Originally Posted by Jilan
    A spherical underground cave should do the job nicely
    If it's in the centre of Earth you just float around, because there's no local gradient in gravitational potential. See the purple-blue plot of gravitational potential on Wikipedia. Right in the middle there's a little bit that's flat and horizontal. And note this: if you don't have any Riemann curvature the plot can't get off the flat and level. Also note that the gradient of the plot at some location relates to the strength of the force of gravity at that location.


    Quote Originally Posted by Markus Hanke
    Refer to the other thread - this is exactly what I mean. You accuse me and others of not providing justification, but when sound justification is given ( as is the case here by KJW ), you declare it insufficient and meaningless. We will not ever get anywhere like this.
    No we won't. Let's take a look at what KJW said:

    "I have no intention of posting a complete explanation, but I will say that objects fall in gravity for the same reason they fall from an accelerated observer: the object has an inertial trajectory while the observer accelerates away from it".

    Now drop your pencil. Do you really accelerate away f rom it? No. Was your pencil really accelerating when it was lying on your desk? No. Was one electron within your pencil constantly accelerating upwards? No. So why does the electron fall down? Because spacetime is curved? No - curved spacetime relates to the tidal force, which you cannot detect in the room you're in. Instead it falls down because that gradient is there. So what kind of gradient is it?
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    Quote Originally Posted by KJW View Post
    You asked me to explain why an object (an electron) falls down in gravity and that is what I explained.
    But the observer doesn't really accelerate away from it. The observer stays put, and the electron moves. The electron falls down.

    Quote Originally Posted by KJW View Post
    The distinction between an accelerated frame of reference and true gravitation due to spacetime curvature is not relevant to this specific issue. That is why I said in an earlier post that "spacetime curvature is not directly the cause of gravity".
    Good. See what I said above to Jilan about curvature and gradient.

    Quote Originally Posted by KJW View Post
    Although one can distinguish between an accelerated frame of reference and true gravitation by means of the tidal effect for true gravitation, the tidal effect is not important to the issue of why objects fall. That's not to say that spacetime curvature isn't important, but you didn't ask about that.
    Fair enough.

    Quote Originally Posted by KJW View Post
    An important issue to come to terms with is how one is being constantly accelerated upward while standing on the ground and apparently not going anywhere. But then, this is relativity.
    You aren't being constantly accelerated upward. You are subject to a force, but no work is being done, and you aren't going anywhere. However work is being done when I lift you up.

    Quote Originally Posted by KJW View Post
    The equivalence principle is important because it says that local physics is special relativity. Thus, special relativity is not merely a weak field approximation to general relativity, but has an important position within general relativity as the local physics regardless of the field strength. It means that one can form a curved spacetime by patching together, albeit imperfectly, Minkowskian spacetime patches. It also means that a straight line in curved spacetime locally looks like a straight line in flat spacetime.
    Noted. You could divide the plot of gravitational potential into little squares and say each was "flat but tilted". Like I was saying, the gradient of the plot at some location relates to the strength of the force of gravity at that location. The steeper the gradient the more your light beam curves downward. Now think of pair production and the wave nature of matter as to why that electron falls down. Have a look at this by Albrecht Giese. I don't like everything he says, and I've nagged him about the "relativity without Einstein", but it's worth a look.
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    Quote Originally Posted by Farsight View Post
    But the observer doesn't really accelerate away from it. The observer stays put
    So the relativistic notion that there is no absolute velocity means nothing to you?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    So the relativistic notion that there is no absolute velocity means nothing to you?
    I wouldn't say that. I've said motion is relative plenty of times. But the point is that when you're standing on the ground you aren't moving relative to me or the Earth. You aren't accelerating. Yes you feel a force on your feet like you would if your were accelerating through space, but you aren't, and again, no work is being done. The two situations aren't exactly equivalent. When you let go of your electron you aren't accelerating away from it acquiring kinetic energy. Instead the electron appears to acquire kinetic energy, but conservation of energy applies, gravity is not a force in the Newtonian sense. The electron's kinetic energy comes from its mass-energy. We call it gravitational potential energy. We did work on the electron when we lifted it, we increased its mass. When we drop it that extra mass-energy is converted into kinetic energy and its mass is reduced. Hence the mass deficit.
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    Quote Originally Posted by Farsight View Post
    I wouldn't say that. I've said motion is relative plenty of times. But the point is that when you're standing on the ground you aren't moving relative to me or the Earth. You aren't accelerating.
    For the ground beneath my feet and the objects near me, they are accelerating with me. For the people on the other side of the globe, don't forget that the spacetime is curved and the equivalence principle is applied locally, which being on the other side of the globe isn't.


    Quote Originally Posted by Farsight View Post
    Yes you feel a force on your feet like you would if your were accelerating through space, but you aren't, and again, no work is being done. The two situations aren't exactly equivalent. When you let go of your electron you aren't accelerating away from it acquiring kinetic energy. Instead the electron appears to acquire kinetic energy, but conservation of energy applies, gravity is not a force in the Newtonian sense. The electron's kinetic energy comes from its mass-energy. We call it gravitational potential energy. We did work on the electron when we lifted it, we increased its mass. When we drop it that extra mass-energy is converted into kinetic energy and its mass is reduced. Hence the mass deficit.
    If instead of an object resting on the ground, what about an object hovering a few metres above it?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Farsight View Post
    Then you've got a uniform gravitational field, which means you've got no Riemann curvature, so you haven't got a gravitational field. The moot point is that standing on the surface of the Earth is like accelerating through space, but you aren't actually accelerating. So it isn't actually equivalent.

    If it's in the centre of Earth you just float around, because there's no local gradient in gravitational potential. See the purple-blue plot of gravitational potential on Wikipedia. Right in the middle there's a little bit that's flat and horizontal. And note this: if you don't have any Riemann curvature the plot can't get off the flat and level. Also note that the gradient of the plot at some location relates to the strength of the force of gravity at that location.
    You misunderstand me, the cave is not at the centre of the earth, it's just a little way underground. The acceleration due to gravity within the cave is constant between the bottom and the top of the cave. There is gradient in potential alright, but it's uniform, so no inverse square law would apply. Notice that I said a constant field strength, not a constant potential (there is a difference!). Objects would still fall, but they would not converge. A free falling frame in such an environment would be equivalent to a frame under constant acceleration.
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    Quote Originally Posted by Jilan
    You misunderstand me, the cave is not at the centre of the earth, it's just a little way underground. The acceleration due to gravity within the cave is constant between the bottom and the top of the cave. There is gradient in potential alright, but it's uniform, so no inverse square law would apply.
    I don't think that the above is correct. If you have a cave of height located at radial distance from the center of the Earth, the gravitational force on a probe of mass varies from (at the bottom of the cave) to (at the top of the cave). So, the acceleration varies from to
    Note: this correction should not be misconstrued as a support for the Farsight (John Duffield) crackpot claims.
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    Quote Originally Posted by x0x View Post
    I don't think that the above is correct. If you have a cave of height located at radial distance from the center of the Earth, the gravitational force on a probe of mass varies from (at the bottom of the cave) to (at the top of the cave). So, the acceleration varies from to
    Note: this correction should not be misconstrued as a support for the Farsight (John Duffield) crackpot.
    No, that formula only works outside of the earth. Inside the earth it's just the mass inside the shell you are on the counts. There is an easy way to solve it. Consider the whole sphere then take away the smaller sphere. Compare the results you get at the top of the cave to the bottom.
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    Quote Originally Posted by Jilan
    No, that formula only works outside of the earth. Inside the earth it's just the mass inside the shell you are on the counts. There is an easy way to solve it. Consider the whole sphere then take away the smaller sphere. Compare the results you get at the top of the cave to the bottom.
    This is incorrect, the formula that you are thinking about is for a shell, indeed inside a shell, the force is zero. Inside the solid ball formed by the Earth, the solid ball of radius r acts exactly like an "Earth" of radius . It is the shell above the cave is the one that contributes a zero force.
    Last edited by x0x; 06-28-2014 at 02:44 PM.
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    x0x, you are correct that the contributions from mass outside the shell cancel, but I never mentioned the mass outside the shell. You just consider the contributions inside the shell. You can find lots of reference as to how there will be zero gravity inside a spherical cavity at the centre of a body, BUT I am talking about a cavity that is not in the centre.
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    Quote Originally Posted by Jilan
    x0x, you are correct that the contributions from mass outside the shell cancel, but I never mentioned the mass outside the shell. You just consider the contributions inside the shell. You can find lots of reference as to how there will be zero gravity inside a spherical cavity at the centre of a body, BUT I am talking about a cavity that is not in the centre.
    I think that you keep missing the point that your claims are valid for a cave inside a "shell". Your claims are false for a cave inside a solid ball.
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    Ok a challenge for you Consider a solid sphere of radius R and density d which had a spherical hole of radius a, at a distance distance A from the centre of the solid sphere. If I am I inside the hollow sphere at a distance A+r from the centre of the solid sphere what is my gravitational potential energy? I get an expression that when I differentiate it is independent of r.
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    If I am I inside the hollow sphere
    But what I explained to you (three times now) is that a cave inside the Earth is NOT a cave inside a "hollow sphere", it is a cave inside a solid ball.
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    Quote Originally Posted by KJW View Post
    For the ground beneath my feet and the objects near me, they are accelerating with me.
    Standing on the ground can be likened to accelerating through space, but you aren't actually accelerating, nor is the ground, nor are the objects near you.

    Quote Originally Posted by KJW
    For the people on the other side of the globe, don't forget that the spacetime is curved and the equivalence principle is applied locally, which being on the other side of the globe isn't.
    I don't know what the other side of the globe has got to do with spacetime curvature. I tried to remove the confusion caused by the curved surface of the Earth in the OP by "zooming in".

    Quote Originally Posted by KJW
    If instead of an object resting on the ground, what about an object hovering a few metres above it?
    Let's say it's a rocket that has enough exhaust to keep it hovering. A force is being exerted. Energy is being expended. But because there's a gravitational field present the rocket isn't accelerating. It's like it's accelerating through space when there's no gravitational field present. But the two situations are not the same.
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    John (Farsight)


    You are obviously ignorant of the fact (among many other things) that Newtonian mechanics and GR have opposing views on what constitutes accelerated motion. You need to stop posturing and start learning. All this posturing makes you the butt of all jokes.
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    Quote Originally Posted by Jilan View Post
    You misunderstand me, the cave is not at the centre of the earth, it's just a little way underground. The acceleration due to gravity within the cave is constant between the bottom and the top of the cave. There is gradient in potential alright, but it's uniform, so no inverse square law would apply. Notice that I said a constant field strength, not a constant potential (there is a difference!). Objects would still fall, but they would not converge. A free falling frame in such an environment would be equivalent to a frame under constant acceleration.
    Fair enough. You could say much the same for the room you're in. Regardless of or shells or balls, if you can't detect any tidal force or any difference in field strength between the floor and ceiling, you might think the gravitational field was uniform.
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    Quote Originally Posted by x0x View Post
    You are obviously ignorant of the fact (among many other things) that Newtonian mechanics and GR have opposing views on what constitutes accelerated motion.
    Not me.

    Quote Originally Posted by x0x
    You need to stop posturing and start learning. All this posturing makes you the butt of all jokes.
    No it doesn't. But you do need to read the OP and discuss it sincerely instead of sniping.
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    Farsight,

    Based on the gross errors you posted about acceleration, it is obvious that you are clueless. Despite all your posturing.
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    Quote Originally Posted by x0x View Post
    Farsight,

    Based on the gross errors you posted about acceleration, it is obvious that you are clueless. Despite all your posturing.
    I think that we might be charitable and say that until Farsight is able to show how to address a physical system in a way that can assign actual measurements to forces and velocities, Farsight-Relativity is neither physics nor a review of physics. It could be preliminary work towards an understanding of physics. Now it is little more than performance art.
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    x0x: I haven't posted any errors about acceleration. By the way, are you the same x0x as the guy on TSR?

    PhysBang: read the OP. If there's anything that's not clear please point it out. If you think there's anything wrong, please point it out. If you can offer a better explanation of how gravity works, please do. If you can't do any of those things, well, anonymous sniping is not a useful substitute for a physics discussion.
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  98. #98  
    x0x
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    Quote Originally Posted by Farsight
    I haven't posted any errors about acceleration.
    No, you have posted laughable errors. Despite your posturing, your posts demonstrate your crass ignorance.
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  99. #99  
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    Quote Originally Posted by x0x View Post
    But what I explained to you (three times now) is that a cave inside the Earth is NOT a cave inside a "hollow sphere", it is a cave inside a solid ball.
    I don't think you are quite getting it. I am talking about a hollow spherical cave inside a solid spherical body.
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  100. #100  
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    Quote Originally Posted by Farsight View Post
    PhysBang: read the OP. If there's anything that's not clear please point it out.
    OK:

    How do we use the varying speed of light to predict the motion of an orbiting body? It is not clear how this works from your statements.

    How do we use inhomogeneous space to predict the falling speed of a body? In detail?

    Nothing that you have said bears any resemblance to physics, so it might be helpful if you made it look something like physics.

    If you think there's anything wrong, please point it out. If you can offer a better explanation of how gravity works, please do. If you can't do any of those things, well, anonymous sniping is not a useful substitute for a physics discussion.
    Again, you have no theory that can even be considered to be worse than existing physics.
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