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Some troubling assumptions of SR
On Sat, 10 Feb 2007 20:52:38 -0000, "George Dishman"
wrote: "Lester Zick" wrote in message .. . On Sat, 10 Feb 2007 12:05:22 -0000, "George Dishman" wrote: ... The same is true in Newtonian physics, the kinetic energy of an object is zero in its rest frame and the value diffes from frame to frame regardless of what theory you use. Nonsense, George. There is only one frame of reference in Newtonian physics, ... You really need to find out what a frame is, Lester. I may not know what a frame is, George, but I certainly recognize a frame up when I see it. ~v~~ |
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Some troubling assumptions of SR
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Some troubling assumptions of SR
Dirk Van de moortel wrote: If you don't understand the definition of energy, surely you can't possibly understand conservation of energy. Dirk, Can you provide a definition of energy? When I have replied to the question "What is energy?" asked by others, I have said that energy is something one learns about through experience. Since energy is part of everything that happens, people naturally acquire a great deal of experience with it. But still we need to define the term in some way so that we know we're talking about the same thing when we use the term. The standard description of energy that I quote when I answer the question is that "Energy is the ability to do work". (I'll go on to describe what work is, if need be.) But that description seems to fall short of a definition. Granted, all definitions one can find in a dictionary are ultimately circular, because in reality all understanding is based on experience. But is it possible to do better? Can you define "energy"? -- Jeff, in Minneapolis |
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Some troubling assumptions of SR
"Lester Zick" wrote in message ... On Sat, 10 Feb 2007 20:52:38 -0000, "George Dishman" wrote: "Lester Zick" wrote in message . .. On Sat, 10 Feb 2007 12:05:22 -0000, "George Dishman" wrote: ... The same is true in Newtonian physics, the kinetic energy of an object is zero in its rest frame and the value diffes from frame to frame regardless of what theory you use. Nonsense, George. There is only one frame of reference in Newtonian physics, ... You really need to find out what a frame is, Lester. I may not know what a frame is, .. Perhaps. First I should apologise for my terse response but when you say "Nonsense" to something that is perfectly true, it isn't helping Jim to learn these basics. Consider two objects A and B moving apart with no forces acting on either. That is they are moving under their own inertia. - A B - As Daryl said, frames are subtly distinct from coordinate systems but we can make an arbitrary choice of using rectilinear coordinates with the object at the origin (rather than say polar) and use that as an example. Suppose we measure distances from A. We could set up a grid of lines 1m apart with A at the origin: -1 0 1 2 3 4 5 6 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | You can define the location of B using those coordinates and then taking the time derivative of those gives you the velocity of B "in the rest frame of A". Call that V. You can do the same the other way round, fix the origin as object B: -5 -4 -3 -2 -1 0 1 2 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | Now B's velocity is obviously zero by definition and we expect the velocity of A to be -V in the frame of B. That is true in both classical theory and SR. Going back to some comments in earlier threads, note that both frames extend to infinity in all directions hence overlap everywhere, and the origin of B's frame is moving at velocity V in A's coordinates. Notice that I have chosen to defined both grids as being equally spaced with 1m separation. Of course we are really talking about measurements using the metre as a basic unit but either way, distances in the x and y directions are using equal units so the frames are "isometric" as I think you are using the term. Again, that is true in both classical theory and SR. Where the theories differ is the equations used to work out the coordinates of an object, or more accurately an event, in one frame given the coordinates of the same event in the other frame. That's where the Galilean and Lorentz transforms come in. George |
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Some troubling assumptions of SR
On Sun, 11 Feb 2007 13:02:55 -0000, "George Dishman"
wrote: "Lester Zick" wrote in message .. . On Sat, 10 Feb 2007 20:52:38 -0000, "George Dishman" wrote: "Lester Zick" wrote in message ... On Sat, 10 Feb 2007 12:05:22 -0000, "George Dishman" wrote: ... The same is true in Newtonian physics, the kinetic energy of an object is zero in its rest frame and the value diffes from frame to frame regardless of what theory you use. Nonsense, George. There is only one frame of reference in Newtonian physics, ... You really need to find out what a frame is, Lester. I may not know what a frame is, .. Perhaps. First I should apologise for my terse response but when you say "Nonsense" to something that is perfectly true, it isn't helping Jim to learn these basics. Consider two objects A and B moving apart with no forces acting on either. That is they are moving under their own inertia. - A B - As Daryl said, frames are subtly distinct from coordinate systems but we can make an arbitrary choice of using rectilinear coordinates with the object at the origin (rather than say polar) and use that as an example. Suppose we measure distances from A. We could set up a grid of lines 1m apart with A at the origin: -1 0 1 2 3 4 5 6 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | You can define the location of B using those coordinates and then taking the time derivative of those gives you the velocity of B "in the rest frame of A". Call that V. You can do the same the other way round, fix the origin as object B: -5 -4 -3 -2 -1 0 1 2 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | Now B's velocity is obviously zero by definition and we expect the velocity of A to be -V in the frame of B. That is true in both classical theory and SR. Going back to some comments in earlier threads, note that both frames extend to infinity in all directions hence overlap everywhere, and the origin of B's frame is moving at velocity V in A's coordinates. Notice that I have chosen to defined both grids as being equally spaced with 1m separation. Of course we are really talking about measurements using the metre as a basic unit but either way, distances in the x and y directions are using equal units so the frames are "isometric" as I think you are using the term. Again, that is true in both classical theory and SR. Where the theories differ is the equations used to work out the coordinates of an object, or more accurately an event, in one frame given the coordinates of the same event in the other frame. That's where the Galilean and Lorentz transforms come in. George, what makes you think you can lay out an isometric coordinate system and then just say the equations used to work with coordinates are different in different systems when the very basis of equations is the metric system used and the whole point of anisometry in SR is that coordinate systems or spatial metrics are velocity dependent and not isometric or MM should work? All you've shown is a Euclidean-Galilean-Cartesian-Newtonian frame of reference for both A and B that applies isometrically throughout space and I agree.What you haven't shown however is Einstein's SR anisometry which describes the variable spatial metric needed to make a constant relative isotropic c both for A and B when their velocities differ. And if A and B traverse space at different v's and light for both A and B is assumed to traverse space independently of A and B then those velocity dependent second order anisometric spatial metrics in SR conflict. There simply is no way around it that I can see. And if I say it rather abruptly I apologize but we've been over and over the point and you just refuse to take it. So if Jim or whoever asked the question is going to learn what's right instead of what's wrong he might just as well start right here. ~v~~ |
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Some troubling assumptions of SR
Lester Zick says...
(Daryl McCullough) wrote: Nonsense, George. There is only one frame of reference in Newtonian physics, a universal isometric Euclidean-Galilean-Cartesian-Newtonian frame of reference whose origin can change but whose metric properties remain constant unlike second order velocitiy dependent anisometric properties of reference frames in SR. No, there are infinitely many frames of reference in Newtonian physics. What in the world are you talking about, Lester? Newtonian physics certainly has a notion of different frames of reference. That's what the Galilean transformations are about: x' = x - vt Velocity, momentum, kinetic energy are all frame-dependent quantities in Newtonian physics. The Newtonian notion of "frame of reference" is pretty much the same as in Special Relativity. Of course it is. That's exactly why Newtonian frames of reference are isometric and SR frames of reference are anisometric. You don't know what you are talking about, Lester. In both Newtonian physics and SR, a frame of reference is a particular way of choosing a 3D spatial slice for each moment of time. Those 3D slices are isotropic in both Newtonian frames of reference and SR frames of reference. I have no idea what you mean by "isometric" and "anisometric". You seem very confused. -- Daryl McCullough Ithaca, NY |
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Some troubling assumptions of SR
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Some troubling assumptions of SR
"Lester Zick" wrote in message ... On Sun, 11 Feb 2007 13:02:55 -0000, "George Dishman" wrote: "Lester Zick" wrote in message . .. On Sat, 10 Feb 2007 20:52:38 -0000, "George Dishman" wrote: "Lester Zick" wrote in message m... On Sat, 10 Feb 2007 12:05:22 -0000, "George Dishman" wrote: ... The same is true in Newtonian physics, the kinetic energy of an object is zero in its rest frame and the value diffes from frame to frame regardless of what theory you use. Nonsense, George. There is only one frame of reference in Newtonian physics, ... You really need to find out what a frame is, Lester. I may not know what a frame is, .. Perhaps. First I should apologise for my terse response but when you say "Nonsense" to something that is perfectly true, it isn't helping Jim to learn these basics. Consider two objects A and B moving apart with no forces acting on either. That is they are moving under their own inertia. - A B - As Daryl said, frames are subtly distinct from coordinate systems but we can make an arbitrary choice of using rectilinear coordinates with the object at the origin (rather than say polar) and use that as an example. Suppose we measure distances from A. We could set up a grid of lines 1m apart with A at the origin: -1 0 1 2 3 4 5 6 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | You can define the location of B using those coordinates and then taking the time derivative of those gives you the velocity of B "in the rest frame of A". Call that V. You can do the same the other way round, fix the origin as object B: -5 -4 -3 -2 -1 0 1 2 | | | | | | | | 2 -+--+--+--+--+--+--+--+- | | | | | | | | 1 -+--+--+--+--+--+--+--+- | | | | | | | | 0 -+--A--+--+--+--B--+--+- | | | | | | | | -1 -+--+--+--+--+--+--+--+- | | | | | | | | Now B's velocity is obviously zero by definition and we expect the velocity of A to be -V in the frame of B. That is true in both classical theory and SR. Going back to some comments in earlier threads, note that both frames extend to infinity in all directions hence overlap everywhere, and the origin of B's frame is moving at velocity V in A's coordinates. Notice that I have chosen to defined both grids as being equally spaced with 1m separation. Of course we are really talking about measurements using the metre as a basic unit but either way, distances in the x and y directions are using equal units so the frames are "isometric" as I think you are using the term. Again, that is true in both classical theory and SR. Where the theories differ is the equations used to work out the coordinates of an object, or more accurately an event, in one frame given the coordinates of the same event in the other frame. That's where the Galilean and Lorentz transforms come in. George, what makes you think you can lay out an isometric coordinate system and then just say the equations used to work with coordinates are different in different systems .. I can say it because those are the facts Lester, you seem to have some unusual misconceptions about SR. .. when the very basis of equations is the metric system used and the whole point of anisometry in SR is that coordinate systems or spatial metrics are velocity dependent and not isometric or MM should work? The MMx does work lester. It is not the coordinate systems themselves that change but the relationships between them. Take two points P and Q a distance D apart both at rest in frame "A". Let a photon move from P to Q in time t=D/c. Now translate the event coordinates of emission at P and reception at Q into frame "B" and calculate the speed. If you use the Galilean Transforms, the answer is c-V but if you use the Lorentz Transforms the answer is c. If you lay out an MMx in the "A" frame with a null result and then transform the coordinates of the events to the "B" frame using the Lorentz Transforms, you will find the result is also a null, just as is found in real life. All you've shown is a Euclidean-Galilean-Cartesian-Newtonian frame of reference for both A and B that applies isometrically throughout space and I agree. 1) The spatial part is Euclidean. 2) I choose Cartesian for simplicity but I could equally well have used Polar coordinates, and as Daryl says the coordinate system is not fundamental to the definition anyway. 3) It is not specified whether it is Galilean or Lorentzian, the frames are the same in both. If you translate between the frame using the Galilean Transforms, you get the Newtonian view and if you translate with the Lorentz Transforms you get SR. What you haven't shown however is Einstein's SR anisometry That's because there is no "anisometry" in SR, that is your misconception. Try the test I suggested above, work out the event coordinates of an MMX and apply the Lorentz Transforms and you will find it works just fine. which describes the variable spatial metric needed to make a constant relative isotropic c both for A and B when their velocities differ. And if A and B traverse space at different v's and light for both A and B is assumed to traverse space independently of A and B then those velocity dependent second order anisometric spatial metrics in SR conflict. There simply is no way around it that I can see. And if I say it rather abruptly I apologize but we've been over and over the point and you just refuse to take it. I too will be blunt then, the reason nobody is taking your point is because your understanding of SR is flawed and the point is simply wrong. Frames in SR are exactly the same as those in Newtonian physics, it is the Transforms that convert event coordinates between frames that differ. So if Jim or whoever asked the question is going to learn what's right instead of what's wrong he might just as well start right here. Indeed, he can learn that your statement: Nonsense, George. There is only one frame of reference in Newtonian physics, ... was wrong. You can now see that we have laid out two different frames regardless of whether we are discussing Newtonian physics or SR. At least that is one point that has been cleared up. George |
#30
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Some troubling assumptions of SR
Lester Zick says...
Einstein's postulate of an isotropically constant relative c requires a variably dependent spatial geometry. No, it doesn't. There is no special mystery about this. It's in the source document. In order to comply with FLT and his postulate of an isotropically constant relative c, spatial geometry in the direction of v must be contracted by a second order function of v. You are confused. Time dilation and length contraction are effects involving transformations between two different inertial coordinate systems. Look at the analogous transformation in Euclidean coordinates. You have one coordinate system with coordinates x and y. In another coordinate system rotated relative to the first, the coordinates are x' and y' related to x and y through x' = x cos(theta) + y sin(theta) y' = y cos(theta) - x sin(theta) To see the analogy with the Lorentz transformations more clearly, let's introduce a parameter m = tan(theta). This is the "slope" of the x' axis measured relative to the x axis. In terms of m, we have x' = 1/square-root(1+m^2) (x + m y) y' = 1/square-root(1+m^2) (y - m x) Would you say that in the rotated coordinate system, that the x' axis is "contracted" by an amount related to the slope m? No, not at all. Rotating a coordinate system by a slope m doesn't cause it to contract any more than moving it at speed v does in Special Relativity. You seem very confused. Perhaps, just not as confused as yourself, Daryl. I'm confused about a good many things, but Special Relativity is not one of them. On this particular subject, you don't know what you are talking about and I do. I'm sure there is a topic where you know what you are talking about, but physics apparently is not one of them. -- Daryl McCullough Ithaca, NY |
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