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

  1. #201  
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    The wave nature of matter is not in doubt. Nor is electron spin or magnetic moment or the Einstein-de Haas effect.
    What is in doubt is why you keep mentioning quantum effects in a thread that deals with General Relativity - a purely classical theory that describes the macroscopic effects of gravity perfectly well without recourse to quantum mechanics.
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    I'm not. I'm referring to Einstein.
    No, you are referring to what you think Einstein's theories mean. You are referring to your personal understanding of these matters. That is not the same thing !
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    Quote Originally Posted by Markus Hanke View Post
    No, you are referring to what you think Einstein's theories mean. You are referring to your personal understanding of these matters. That is not the same thing !
    Don Koks shares my understanding of some matters, as does Ned Wright: light curves because the speed of light varies with position. That's what Einstein said. It doesn't curve because spacetime is curved. Resist the urge to dismiss something new as "my personal understanding". Consider your own understanding, and consider where it came from and whether you can defend it.

    Quote Originally Posted by Markus Hanke
    What is in doubt is why you keep mentioning quantum effects in a thread that deals with General Relativity - a purely classical theory that describes the macroscopic effects of gravity perfectly well without recourse to quantum mechanics.
    The wave nature of matter is why we always measure the local speed of light to be the same, and why matter falls down. It's crucial to understanding why relativity works. Gravity is not some magical mysterious action-at-distance force. There are no gravitons flying around, just as there are no photons flying around in the hydrogen atom. Virtual particles are field quanta, and like Einstein said, a gravitational field is inhomogeneous space. The electron falls down because of it's dynamical Dirac bispinor. It's like you have a little motorboat with the steering locked left so it goes round and round in circles. When you set it going in a pool which is salty on the left and fresh on the right, you find it works its way over to the left. Again see Albrecht Giese's take on it here. There's things I don't like about it, like "a particle is made up of two sub-particles". But it's basically how gravity works. Don't reject it out of hand. Try to fault it, or try to better it. And most of all, try to understand why an electron falls down. Try explaining it to your grandmother.


    Quote Originally Posted by KJW
    The definition of acceleration that you are using does not come from general relativity. Therefore, you are not entitled to say that the falling observer's frame is not more correct.
    You are declaring the falling observer's frame to be a preferred frame I reject that.

    Quote Originally Posted by KJW
    The definition of acceleration that you are using assumes preferred frames of reference, and applying the equivalence principle indicates that the falling observer's frame is the more correct frame from which to determine acceleration. If you were to apply the definition of acceleration that comes from general relativity, then it wouldn't matter which frame to consider because they all say that the person standing on the ground is accelerating.
    I'm sorry KJW, but that's Humpty Dumpty logic. I can only re-iterate: the equivalence principle likens standing on the ground in inhomogeneous space to accelerating through homogeneous space. In both situations you feel an upward force on your feet. But the two situations are not the same. The surface of the Earth is not accelerating outwards in all directions. It's staying put. I can't put it any simpler than that.
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    Quote Originally Posted by Farsight View Post
    Don Koks shares my understanding of some matters, as does Ned Wright: light curves because the speed of light varies with position. That's what Einstein said.
    Book-thumping again. Book thumping instead of working out the math.

    Light curves because it travels through curved space-time. That's what one finds from the equations of motion: light travels on null geodesics. It may be that in some cases, it's convenient to calculate such geodesics by treating space-time as having some refractive index, but that's a result of transforming the geodesic-motion equation.

    The wave nature of matter is why we always measure the local speed of light to be the same,
    Nonsense. From relativity, it's because of the geometry of space-time and light traveling on null geodesics.

    and why matter falls down.
    That's from following geodesics in general. Geodesics are generalizations of straight lines to curved spaces like space-time.

    The electron falls down because of it's dynamical Dirac bispinor.
    That has NOTHING to do with it.

    And most of all, try to understand why an electron falls down.
    I do. It's from following a geodesic in curved space-time.
    Try explaining it to your grandmother.
    What's the point of trying to do that?
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    Quote Originally Posted by Farsight View Post
    I'm sorry KJW, but that's Humpty Dumpty logic. I can only re-iterate: the equivalence principle likens standing on the ground in inhomogeneous space to accelerating through homogeneous space. In both situations you feel an upward force on your feet. But the two situations are not the same. The surface of the Earth is not accelerating outwards in all directions. It's staying put. I can't put it any simpler than that.
    You could put it simpler: you could actually show us that "inhomogeneous space" can explain the "force" on a person who is standing on the surface of a planet.
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    I did that in the OP. Light bends in inhomogeneous space because "the speed of light varies with position". And the wave nature of matter is not in doubt. See Gravitational time dilation on Wikipedia and note this: electromagnetic radiation and matter may be equally affected, since they are made of the same essence. You know about pair production and spin and magnetic moment, so just think of the electron as light going round and round, then simplify it to a square path, and the horizontals bend. Hence the electron falls down. Hence the deflection of light is twice the deflection of matter. It's just so simple. It's kid's stuff. There is no mystery.

    By the way, for antimatter just draw the light going round the other way. It still falls down. Despite all the mystic hype you hear about does antimatter fall up? That's trash. Energy gravitates, regardless of the configuration / disposition / form it takes.
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW
    The definition of acceleration that you are using does not come from general relativity. Therefore, you are not entitled to say that the falling observer's frame is not more correct.
    You are declaring the falling observer's frame to be a preferred frame I reject that.
    That's fine, but then you have to use the general relativistic definition of acceleration, and that says the person standing on the ground is accelerating.

    Why do you think there are no preferred frames in general relativity?


    Quote Originally Posted by Farsight View Post
    The surface of the Earth is not accelerating outwards in all directions. It's staying put. I can't put it any simpler than that.
    This statement demonstrates a lack of understanding of general relativity. For example, in the formula:



    the term can be zero, yet the acceleration be non-zero due to the term. Thus, the non-expansion of the earth's surface does not imply that the surface of the earth is not accelerating.
    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
    I did that in the OP.
    There is nothing in the OP that allows us to use the idea of "inhomogeneous space" to calculate the force of a person stranding on a planet. Until you produce this, you have dogmatic metaphysics, not physics.
    It's just so simple. It's kid's stuff. There is no mystery.
    It is "kid's stuff" in the sense that it is a fantasy about physics without the content that adults need to consider it physics.
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    Quote Originally Posted by KJW View Post
    That's fine, but then you have to use the general relativistic definition of acceleration, and that says the person standing on the ground is accelerating.
    Well he isn't accelerating. It's like he's accelerating, but he isn't actually accelerating. Your definition is misleading. Where did you get it from? If I'm accelerating through space my time dilation with respect to you increases. Is your time dilation increasing while you're standing on the ground. No. Is the Earth exploding because its surface is accelerating outwards in all directions? While its centre is not? No.

    Quote Originally Posted by KJW
    Why do you think there are no preferred frames in general relativity?
    To make it general! Hence it is wrong to assert that the falling observer's frame is more correct, isn't it?

    Quote Originally Posted by KJW
    This statement demonstrates a lack of understanding of general relativity. For example, in the formula:



    the term can be zero, yet the acceleration be non-zero due to the term. Thus, the non-expansion of the earth's surface does not imply that the surface of the earth is not accelerating.
    Look KJW, you've been mistaught this. Go and look at The Foundation of the General Theory of Relativity. Search on accelerat. There's nine matches. But what it says doesn't match your assertion. See where Einstein says this?

    This conception is feasible, because to us the experience of the existence of a field of force (namely the gravitation field) has shown that it possesses the remarkable property of imparting the same acceleration to all bodies."

    He's talking about falling bodies. Not bodies on the ground. And see lower down where he says this:

    we can "create" a gravitational field by a simple variation of the co-ordinate system

    The word "create" is in quotes. Einstein knew full well that accelerating through space is not actually the same as a real gravitational field. You've been taught by somebody who was not in line with Einstein. There's been some re-interpretation going on.
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    Quote Originally Posted by Farsight View Post
    Look KJW, you've been mistaught this. Go and look at The Foundation of the General Theory of Relativity. Search on accelerat. There's nine matches. But what it says doesn't match your assertion. See where Einstein says this?

    This conception is feasible, because to us the experience of the existence of a field of force (namely the gravitation field) has shown that it possesses the remarkable property of imparting the same acceleration to all bodies."

    He's talking about falling bodies. Not bodies on the ground. And see lower down where he says this:

    we can "create" a gravitational field by a simple variation of the co-ordinate system

    The word "create" is in quotes. Einstein knew full well that accelerating through space is not actually the same as a real gravitational field. You've been taught by somebody who was not in line with Einstein. There's been some re-interpretation going on.
    Actually, Einstein is not talking about bodies that are falling, just bodies that are at rest in two different Galilean reference frames. Einstein says that the acceleration that exists from merely considering a new reference frame is such that, as far as the physics is concerned, "In the space-time region considered there is a gravitation-field which generates the accelerated motion relative to K'." [emphasis added]

    Einstein says that there is a gravitation-field. Why don't you believe him?
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    That's fine, but then you have to use the general relativistic definition of acceleration, and that says the person standing on the ground is accelerating.
    Well he isn't accelerating. It's like he's accelerating, but he isn't actually accelerating.
    Specifically, what does "like acceleration but not acceleration" mean?


    Quote Originally Posted by Farsight View Post
    Your definition is misleading. Where did you get it from?
    Textbooks on Tensor Calculus.


    Quote Originally Posted by Farsight View Post
    If I'm accelerating through space my time dilation with respect to you increases. Is your time dilation increasing while you're standing on the ground. No. Is the Earth exploding because its surface is accelerating outwards in all directions? While its centre is not? No.


    Sometimes, it's better to just let the mathematics do the talking.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW
    Why do you think there are no preferred frames in general relativity?
    To make it general! Hence it is wrong to assert that the falling observer's frame is more correct, isn't it?
    I did originally put the word "correct" in quotes. Strictly speaking, I just chose the local frame for which the connection is zero so that the definition of acceleration that you applied would be correct.


    One thing that I've experienced is that different authors of texts on GR use different notational conventions so that one needs to be very careful in applying texts from different authors.
    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
    Specifically, what does "like acceleration but not acceleration" mean?
    You feel a force but you don't move, your velocity doesn't change.

    Quote Originally Posted by KJW
    Textbooks on Tensor Calculus.
    Then your textbooks are wrong. Textbooks are never wholly correct. If they were, science would not progress.

    Quote Originally Posted by KJW


    Sometimes, it's better to just let the mathematics do the talking.
    No, it never is. You have to understand the physics. Mathematics is a vital tool for physics, but it's not what physics is. Sometimes it gets in the way of understanding the physics. Is your time dilation increasing while you're standing on the ground? No. Is the Earth exploding because its surface is accelerating outwards in all directions? No. So isn't really an acceleration. So you can hopefully appreciate it's the result of being in inhomogeneous space. It feels like accelerating through homogeneous space, but it isn't the same thing.

    Quote Originally Posted by KJW
    I did originally put the word "correct" in quotes. Strictly speaking, I just chose the local frame for which the connection is zero so that the definition of acceleration that you applied would be correct.
    OK.

    Quote Originally Posted by KJW
    One thing that I've experienced is that different authors of texts on GR use different notational conventions so that one needs to be very careful in applying texts from different authors.
    Fair enough. That's maybe a sign of the "mission creep" that has resulted in modern GR being different to the original.
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    Quote Originally Posted by Farsight View Post
    You feel a force but you don't move, your velocity doesn't change.
    Like when you're on an elevator? Or in a spaceship in orbit?
    No, it never is. You have to understand the physics. Mathematics is a vital tool for physics, but it's not what physics is. Sometimes it gets in the way of understanding the physics. Is your time dilation increasing while you're standing on the ground? No. Is the Earth exploding because its surface is accelerating outwards in all directions? No. So isn't really an acceleration. So you can hopefully appreciate it's the result of being in inhomogeneous space. It feels like accelerating through homogeneous space, but it isn't the same thing.
    Perhaps you can present us with some mathematical details so that we can transition from our flawed understanding to your own understanding of the hidden mysteries of Einstein.
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    (variations in notation...)
    Quote Originally Posted by Farsight View Post
    That's maybe a sign of the "mission creep" that has resulted in modern GR being different to the original.
    What's so special about the original? Was it some revealed truth with later versions being corruptions of it? That's the sort of argument a theologian would make, not a scientist.

    As to notation, Newtonian physics is nowadays never presented in the fashion that Sir Isaac Newton had presented it, as far as I know. Instead, it's presented in algebraic fashion with lots of vectors, and it's usually presented with Leibniz's notation for calculus operations, with Newton's notation only for some time derivatives.
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    Look KJW, you've been mistaught this.
    No he hasn't. It is just the basic definition of the covariant derivative of a 4-vector. There is nothing to be "mistaught" here, it's basic calculus.

    Then your textbooks are wrong.
    So all textbooks that teach multivariable calculus are wrong ? Because that is all there is to this - a linear combination of terms involving derivatives of the metric. The covariant derivative - which is what the expression signifies - is an elementary operation, and one of the most basic concepts in multivariable calculus. If you reject even this, then there is really no common basis on which to continue these discussions. One has to find a lowest common denominator somewhere.
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    That's maybe a sign of the "mission creep" that has resulted in modern GR being different to the original.
    There is no difference, except in matters of mathematical notation.
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW View Post
    Specifically, what does "like acceleration but not acceleration" mean?
    You feel a force but you don't move, your velocity doesn't change.
    You experience a net force, yet you don't accelerate? That conflicts with Newton's first and second laws of motion! Your velocity does change relative to your previous velocity. Release an object and it will continue to free-fall at the velocity that it was when it was released. Your velocity then changes relative to this free-falling object.


    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW
    Textbooks on Tensor Calculus.
    Then your textbooks are wrong.
    This carries with it the presumption that I blindly accept what the textbooks say. Not true. I often carry out my own derivations of the mathematical formulae that I see in textbooks. You wouldn't say the acceleration formula I presented was wrong if you actually understood what it is saying.
    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
    This carries with it the presumption that I blindly accept what the textbooks say. Not true. I often carry out my own derivations of the mathematical formulae that I see in textbooks.
    Admirable. That's the trademark of a serious student in any subject, i.e. not taking what the text says like it was a bible but doing the derivations yourself. Very impressive KJW!
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    Quote Originally Posted by lpetrich View Post
    What's so special about the original? Was it some revealed truth with later versions being corruptions of it?
    Einstein said the speed of light varies, but later versions say the speed of light is constant. So yes, there's been some corruption.

    Quote Originally Posted by lpetrich
    That's the sort of argument a theologian would make, not a scientist.
    Not so. The speed of light varies. We have the patent evidence for it. The theologian dismisses Einstein and the evidence and claims that his textbook is the bible.

    Quote Originally Posted by lpetrich
    As to notation, Newtonian physics is nowadays never presented in the fashion that Sir Isaac Newton had presented it, as far as I know. Instead, it's presented in algebraic fashion with lots of vectors, and it's usually presented with Leibniz's notation for calculus operations, with Newton's notation only for some time derivatives.
    Noted. But note that 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?" It's very similar to what Einstein said, and Ned Wright, see above.

    Sorry, I have to go.
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    Quote Originally Posted by Markus Hanke View Post
    There is no difference, except in matters of mathematical notation.
    There's significant differences, see [physics/0204044] Einstein's gravitational field where you can read this:

    "The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with".

    Also see History of general relativity - Wikipedia, the free encyclopedia where you can read this:

    "Kip Thorne identifies the "golden age of general relativity" as the period roughly from 1960 to 1975 during which the study of general relativity,[19] which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics. During this period, many of the concepts and terms which continue to inspire the imagination of gravitation researchers and the general public were introduced, including black holes and 'gravitational singularity'. At the same time, in a closely related development, the study of physical cosmology entered the mainstream and the Big Bang became well established. Areas of research included:

    The role of curvature in general relativity;
    The theoretical importance of black holes;
    The importance of geometrical machinery and levels of mathematical structure, especially local versus global spacetime structure..."
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    "The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with".
    I am not sure what the author of that paper is trying to achieve, but gravity is obviously not curvature of space-time but geodesic deviation. They are not the same thing, and this hasn't changed since Einstein's time. Granted, people tend to be sloppy and treat these terms as freely interchangeable, but anyone who knows even some basic differential geometry understands the distinction. The theory of GR is the exact same one in content, only the mathematical notation has changed slightly since Einstein.

    especially local versus global spacetime structure...
    Hint, hint...
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    The theologian dismisses Einstein and the evidence and claims that his textbook is the bible.
    You are doing this very deed - you are stuck on Einstein's words as if it was the bible, and dismiss everything and everyone else who came after and furthered and deepened our understanding of the foundations that underlie GR. Theologian indeed !
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    Quote Originally Posted by Farsight View Post
    Einstein said the speed of light varies, but later versions say the speed of light is constant. So yes, there's been some corruption.
    All this quoting Einstein as if his words are gospel fails to acknowledge one very important fact: We've learnt a lot of things since those words. In other words, modern day physicists are in a far better position to understand relativity than Einstein was in his day.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    All this quoting Einstein as if his words are gospel fails to acknowledge one very important fact: We've learnt a lot of things since those words. In other words, modern day physicists are in a far better position to understand relativity than Einstein was in his day.
    Absolutely. There is no doubt in my mind that Einstein was a brilliant physicist, but I often think that given the limitations in knowledge during his lifetime he had little understanding of the true scope of the model he had created. For example, was he aware that GR can be understood as a gauge theory based on the gauge group Diff(M), being the group of all diffeomorphisms on M ? I think not. Was he aware that his field equations arise naturally from associating the Cartan moment of rotation in an elementary volume of space with its energy-momentum content ? I think not. And so on. As a result of 100 years of study and investigation we now know a whole lot more about what GR actually means and how it fits into the bigger picture than Einstein or any of his contemporaries did. This is not because Einstein was too dumb to understand it, it's just that the knowledge about the bigger picture available at the time was clearly limited.

    Farsight chooses to ignore everything that came after Einstein, treating him and his words as the ultimate authority. While this is his personal choice which he is entitled to, contemporary physics and mathematics have clearly moved on and come a long way since 1916; this is the very essence of physics as a discipline - to advance rather than to stand still.
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    Quote Originally Posted by Markus hanke
    Farsight chooses to ignore everything that came after Einstein, treating him and his words as the ultimate authority. While this is his personal choice which he is entitled to, contemporary physics and mathematics have clearly moved on and come a long way since 1916; this is the very essence of physics as a discipline - to advance rather than to stand still.
    I think that you are too charitable with Duffield, it is not that physics has changed that much from what Einstein actually wrote, it is that Duffield perverts what Einstein actually wrote through his selective, dishonest, cherrypicking quotes out of context droning.
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    Quote Originally Posted by Farsight View Post
    Quote Originally Posted by KJW


    Sometimes, it's better to just let the mathematics do the talking.
    No, it never is. You have to understand the physics. Mathematics is a vital tool for physics, but it's not what physics is. Sometimes it gets in the way of understanding the physics.
    You say this as an attempt to justify not doing any mathematics, don't you? But mathematics is the language of physics. Physical reality is far too complicated to be described by any language other than mathematics. This means that without mathematics, one can't really understand physics beyond a fairly simple level.

    When one appreciates the relationship between mathematics and physics, one can begin to appreciate why physical reality is the way it is.


    Quote Originally Posted by Farsight View Post
    Is your time dilation increasing while you're standing on the ground? No. Is the Earth exploding because its surface is accelerating outwards in all directions? No. So isn't really an acceleration. So you can hopefully appreciate it's the result of being in inhomogeneous space. It feels like accelerating through homogeneous space, but it isn't the same thing.
    This is an example of how a lack of understanding of the mathematics of spacetime curvature can prevent an understanding of the physics.
    Beer w/Straw, lpetrich and x0x like 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 KJW View Post
    All this quoting Einstein as if his words are gospel fails to acknowledge one very important fact: We've learnt a lot of things since those words. In other words, modern day physicists are in a far better position to understand relativity than Einstein was in his day.
    And there's the rub: they don't. They think the speed of light is absolutely constant, they're forever confusing space and spacetime, and they think your pencil falls down because spacetime is curved in the room you're in.


    Quote Originally Posted by Markus Hanke
    Absolutely. There is no doubt in my mind that Einstein was a brilliant physicist, but I often think that given the limitations in knowledge during his lifetime he had little understanding of the true scope of the model he had created. For example, was he aware that GR can be understood as a gauge theory based on the gauge group Diff(M), being the group of all diffeomorphisms on M? I think not. Was he aware that his field equations arise naturally from associating the Cartan moment of rotation in an elementary volume of space with its energy-momentum content? I think not. And so on.
    Only nobody talks about GR as a gauge theory, or about the Cartan moment.

    Quote Originally Posted by Markus Hanke
    As a result of 100 years of study and investigation we now know a whole lot more about what GR actually means and how it fits into the bigger picture than Einstein or any of his contemporaries did.
    You might think you know better than Einstein, but you don't.

    Quote Originally Posted by Markus Hanke
    Farsight chooses to ignore everything that came after Einstein, treating him and his words as the ultimate authority. While this is his personal choice...
    I'm simply not doing this. You are. You've ignored what Ned Wright said and what Don Koks said in favour of some other ultimate authority such as Wheeler. You aren't moving on.

    Quote Originally Posted by Markus Hanke
    I am not sure what the author of that paper is trying to achieve
    He's telling you about the way the GR interpretation has changed since Einstein's day.

    Quote Originally Posted by Markus Hanke
    The theory of GR is the exact same one in content, only the mathematical notation has changed slightly since Einstein.
    Read the paper to appreciate how the interpretation has changed.
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    Quote Originally Posted by KJW View Post
    You say this as an attempt to justify not doing any mathematics, don't you?
    No.

    Quote Originally Posted by KJW
    But mathematics is the language of physics. Physical reality is far too complicated to be described by any language other than mathematics. This means that without mathematics, one can't really understand physics beyond a fairly simple level.
    Not so. Einstein said light curves because the speed of light varies with position. That's easy to understand. And the patent scientific evidence backs him up.

    Quote Originally Posted by KJW
    When one appreciates the relationship between mathematics and physics, one can begin to appreciate why physical reality is the way it is.
    I don't think that's true, KJW. To appreciate the physical reality you have to analyse the terms in the mathematics, things like e and m and c. You have to appreciate what they mean. You can't get that from the mathematics itself, because it tells you how they relate to each other.
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    Quote Originally Posted by Farsight View Post
    And there's the rub: they don't. They think the speed of light is absolutely constant, they're forever confusing space and spacetime, and they think your pencil falls down because spacetime is curved in the room you're in.
    Since you can't understand enough math to follow contemporary physicists, how can you accurately judge them?

    You might think you know better than Einstein, but you don't.
    Do you also follow Einstein in your behavior to your wife? Einstein was horrible to women. Did you abandon your first wife? The holy Einstein made mistakes, so clearly there are areas where people know better than Einstein. Einstein made mistakes in physics, too, as one can discover in the correspondence between Einstein and others.

    One has to work through physics, not simply dogmatically accept it.

    The one way to salvage Farsight Physics as something other than fantasy is to present some examples of how it could actually be used.
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    Quote Originally Posted by PhysBang View Post
    Since you can't understand enough math to follow contemporary physicists, how can you accurately judge them?
    I can understand enough math to follow them, and I can accurately judge them when they say things like "light moves through the curved spacetime around the Earth".

    Quote Originally Posted by PhysBang
    Do you also follow Einstein in your behavior to your wife? Einstein was horrible to women. Did you abandon your first wife?...
    Oh really, this is beyond the pale.
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    Quote Originally Posted by Farsight View Post
    And there's the rub: they don't. They think the speed of light is absolutely constant, they're forever confusing space and spacetime, and they think your pencil falls down because spacetime is curved in the room you're in.
    Farsight, your arguments here are mainly based on your idiosyncratic interpretation of the Einsteinian Scriptures, rather than any discussion of the content of theories independent of their inventors.
    Only nobody talks about GR as a gauge theory, or about the Cartan moment.
    I did some searches for "general relativity as a gauge theory" and I found several hits. Like:

    Phys. Rev. D 28, 286 (1983) - General relativity as a gauge theory of the Poincar\'e group, the symmetric momentum tensor of both matter and gravity, and gauge-fixing conditions
    Reformulation of general relativity as a gauge theory

    The Poincaré group is Euc(3,1), the group of symmetries of flat space-time.

    You might think you know better than Einstein, but you don't.
    Says who? That's treating Einstein as a Prophet of Revealed Truth.
    You've ignored what Ned Wright said and what Don Koks said in favour of some other ultimate authority such as Wheeler. You aren't moving on.
    Scriptural exegesis, with Wright and Koks orthodox and Wheeler heretical.

    Quote Originally Posted by Farsight View Post
    Einstein said light curves because the speed of light varies with position.
    No, he stated that it's because it follows geodesics in curved space-time. Scripture reference: The Meaning of Relativity, p. 46, eq. 90.
    And the patent scientific evidence backs him up.
    Where is the evidence against trajectories departing from geodesics only because of nongravitational forces?
    I don't think that's true, KJW. To appreciate the physical reality you have to analyse the terms in the mathematics, things like e and m and c. You have to appreciate what they mean. You can't get that from the mathematics itself, because it tells you how they relate to each other.
    That's using nonmathematical language instead of mathematical language, and nonmathematical language has the same problems of definition.
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    Quote Originally Posted by Farsight View Post
    Oh really, this is beyond the pale.
    Yet another question you dodge. However, the point of asking the question was to point out that Einstein was not perfect. You seem to pick and choose his statements based on whether they agree with your fantasy. I have asked you to provide scientific reasoning and you refuse. If you want to do science, then please use your interpretation to describe a physical system.
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    You've ignored what Ned Wright said and what Don Koks said in favour of some other ultimate authority such as Wheeler.
    No, I'm ignoring it in favour of my own understanding, which I have developed through the study of a multitude of sources. I am using the standard textbooks to underline and back-up the points I am trying to make. It just so happens that my understanding is largely in line with most textbooks on the subject matter.

    Read the paper to appreciate how the interpretation has changed.
    If that is what the paper tries to say, then I disagree with it. My argument is that there simply is no interpretive layer to GR at all. So what "interpretation" has changed since Einstein ?
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    The speed of light varying with position, and the inhomogeneous space where a gravitational field is. But you will reject that, you will dismiss what Einstein said, and you will ignore what Kevin Brown said:

    "Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse. In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in spacetime..."

    You will also ignore Don Koks and Ned Wright and Pete Brown, you will duck patent issues such as why the light doesn't get out, you will permit appalling ad-hominem abuse, you will claim that I'm advancing a personal theory and endorse the stigma of "personal theories and alternative hypotheses". And now you're claiming there simply is no interpretive layer to GR at all.

    Markus, I though we were having a sincere discussion. Clearly we are not. So my part in this discussion is over.
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    Quote Originally Posted by Duffield
    The speed of light varying with position, and the inhomogeneous space where a gravitational field is. But you will reject that, you will dismiss what Einstein said, and you will ignore what Kevin Brown said:

    "Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse. In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in spacetime..."

    You will also ignore Don Koks and Ned Wright
    None of them says that "speed of light varies with position".

    and Pete Brown
    Your buddy, Pete Brown, is not a physicist (despite his claims), he's just a sore ass crank. Not in the same class as you but a crank nevertheless. You are in a class all by yourself, John.
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    Quote Originally Posted by Farsight View Post
    The speed of light varying with position, and the inhomogeneous space where a gravitational field is. But you will reject that, you will dismiss what Einstein said,
    Why don't you quit whining and just show us an example where your interpretation is at work? You are the "physics expert" that we should "trust" more than any book or authority, so pick your favorite example and walk us through it.

    You will also ignore Don Koks and Ned Wright
    Ned Wright clearly does not agree with you, since he writes about the gravitational effects of homogeneous models, something that you claim does not exist! That would be a great example for you to do: show us step-by-step how to work out the gravitation of a homogeneous model. Then show us the mistakes made by every working cosmologist.

    and Pete Brown, you will duck patent issues such as why the light doesn't get out, you will permit appalling ad-hominem abuse, you will claim that I'm advancing a personal theory and endorse the stigma of "personal theories and alternative hypotheses". And now you're claiming there simply is no interpretive layer to GR at all.
    You claim that you are offering a personal theory: you claim that you understand this but no working physicist does. That is what makes this a personal theory. That you can't defend your theory is your problem. That you whine about it is a personal failing. That you attack others and dodge questions rather than work through a simple example is just how you attempt to argue.

    Markus, I though we were having a sincere discussion. Clearly we are not. So my part in this discussion is over.
    More whining, crying and going home. A great example to point to whenever you pop up on the internet, claiming to be a physics expert.
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    Quote Originally Posted by Farsight View Post
    ... you will dismiss what Einstein said, and you will ignore what Kevin Brown said ...

    You will also ignore Don Koks and Ned Wright and Pete Brown, ...
    Argument by book-thumping is very worthy of "Personal Theories and Alternative Hypothesis".

    you will duck patent issues such as why the light doesn't get out,
    That's not a problem for mainstream GR.
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    Markus, I though we were having a sincere discussion.
    If you want to have a sincere discussion you need to stop rejecting the basic mathematics of GR, and allow yourself to be lead through the relevant arguments and deductions step-by-step. You would find that Schwarzschild observers are by definition far-away stationary observers who are just that - far away from the black hole and the events that happen there. They do not physically measure anything except what happens in their own rest frames; they don't physically measure what happens locally in a remote frame close to the black hole ( because they aren't there ! ), they only calculate and deduce, based on their own local ( i.e. far-away and stationary ) notions of time and space. Since time and space and purely local, you cannot apply these far-away notions to other frames and expect to get something that is physically meaningful. Local time and local space at a far-away Schwarzschild observer's frame of reference are not the same as local time and local space in the frame of a freely falling observer close to the black hole, for example. If you do the relevant GR calculations for the in-falling ( as opposed to the far-away ) observer, you find a proper - this means physically measured - recorded in-fall time between radius (1) and radius (2) of



    irrespective of where these radii are. And this is all that is of physical relevance - what an instrument that is locally present physically records, not what an idealised far-away stationary reference observer might deduce based on his on time and space concepts. And here is were all the philosophising and interpreting stops, because GR is about actual, physical, real-world measurements performed with clocks and rulers and accelerometers at different local places. Your Schwarzschild observers don't measure a reduced speed of light near the black hole, because they are not there. I might as well turn this around on you and claim that because an observer at rest at the event horizon who chooses to use Schwarzschild coordinates determines that the lifespan of the universe is zero - hence the universe can't actually exist. Does this sound physically meaningful to you ? Well, that is pretty much exactly what you are saying to us. You either completely fail to understand this, or choose to reject/ignore it for your own reasons; in either case, this is why none of these discussions move forward. And since they don't move forward, I chose to stop participating, because to be perfectly honest with you going over the same old chestnuts again and again ad infinitum is of no interest to me whatsoever. I don't know why you keep doing this, for years on end, without ever moving an inch forward. It reminds me an awful lot of the Orange Order in Belfast, who march every 12th July to commemorate a battle that took place close to 300 years ago, claiming that they are the only ones who advocate the "right" politics in Northern Ireland, and that everyone else are wrong and fascists and terrorists. They are stuck in history just as you appear to be stuck on Einstein's words, but not the meaning of his model.

    you will claim that I'm advancing a personal theory and endorse the stigma of "personal theories and alternative hypotheses"
    I don't see how this is in any way different from you claiming that your understanding is superior to everyone else's - even though you can't even do the simplest of GR calculations, and know very little about differential geometry -, and that every textbook and mainstream physicist and mathematician over the past 100 years got it wrong. It is not possible to have a meaningful discussion on that basis - there simply is not enough common ground here, because regardless of what I say and how I support it, you will reject it because neither I nor the authors of established textbooks are Prof Albert Einstein. This feels like trying to argue against a religion to me, which is something I never do for precisely this reason. For example, instead of trying to interpret speeds and what different observers see, I would quite simply go ahead like so :

    1. An accelerometer in free fall measures exactly zero proper acceleration
    2. Write down (1) mathematically - the covariant derivative of proper velocity with respect to proper time vanishes. This is the geodesic equation.
    3. Solve the geodesic equation to explicitly obtain the world line of the free fall object in analytical form - no speeds etc involved
    4. Now check whether or not these world lines extend smoothly and continuously across the event horizon or not. This immediately answers the original question, because it turns out that there is no geodesic incompleteness at the horizon.

    The problem now is that the answer is not the one you advocate or like to hear, even though it is based on physically measurable quantities, so you will immediately say that these are just "mathematical abstractions" that have nothing to do with what Einstein "said". You say they are no world lines, because your eyes cannot see them. Based on this, no discussion can place.

    So my part in this discussion is over.
    Noted. I will leave the threads open and unlocked anyway, just in case.
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    No, he stated that it's because it follows geodesics in curved space-time. Scripture reference: The Meaning of Relativity, p. 46, eq. 90.
    Well spotted. Here is the link to Einstein's book, which is now public domain on Project Gutenberg :

    http://www.gutenberg.org/files/36276/36276-pdf.pdf

    The relevant discussion in Einstein's very own words, along with the maths, is found on page 84.
    In fact the entire book is an excellent beginner's overview and commentary by the man himself on his theory - going forward we should probably all quote from this text, at least that way there is no argument as to "what Einstein said". And surprise surprise, a quick search confirms that there is no mention anywhere at all in this text of "variable speeds of light" - so much for the "meaning of relativity" in Einstein's own words !
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