Preferred Frame Theory indistinguishable from SR
in [Relativity]
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From: Daryl McCullough on 7 Jul 2010 07:46 harald says... > >On Jul 6, 5:18=A0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >> harald says... >> >> >The twin scenario was presented by Langevin in 1911 to show that >> >physical acceleration is "absolute", even more so with SRT than with >> >Newton's mechanics. >> >> What does that mean? As I said, proper acceleration (as measured by >> an accelerometer) is absolute, but coordinate acceleration is certainly >> not. > >It means that you agree on that point with Langevin. Well, it's hard for me to believe that Einstein was unaware of the fact that an accelerometer can measure accelerations. >> Here's an analogy: A flat Euclidean plane has no notion of a preferred >> direction. Any direction is as good as any other. But it certainly has >> a notion of a *change* of direction. If you draw a path on the Euclidean >> plane, then you can unambiguously determine whether the line is >> straight or curved, because a straight line connecting two points is >> shorter than any curved line connecting the same two points. If you >> measure the lengths of two curves, you can determine which one is >> straight. > >Sorry but I can't resist pointing out the error of the above: a >straight trajectory relatively to an Euclidean plane is *only* >measured to be "straight" if that plane is part of what Einstein >called the "privileged" group of inertial "spaces". I think you are confused about this point. Euclidean space has an associated metric, which determines the lengths of paths. A straight line is defined relative to that metric as the path that minimizes the length between two points. It has nothing to do with any "privileged space". Having said that, we can define a special group of coordinate systems for the Euclidean plane---the Cartesian coordinate systems, via the requirement: A line is straight <=> It can be parametrized so that (d/ds)^2 x = (d/ds)^2 y = 0. Being a straight line is independent of coordinate system. The associated coordinate acceleration being zero is dependent on a choice of a special coordinate system. >> >"The laws of physics must be of such a nature that they apply to >> >systems of reference in any kind of motion". >> >As a result, physical acceleration is, according to Einstein's GRT, >> >*relative* - which is just the contrary of what Langevin argued based >> >on his "twins" example of SRT. >> >> As I said, proper acceleration is definitely *not* relative, but >> coordinate acceleration trivially *is*. But proper acceleration is >> measuring acceleration relative to *freefall*. > >Then we both disagree with Einstein; That's ridiculous. Einstein certainly knew that an accelerated observer feels "inertial forces", and an unaccelerated observer does not. Whatever was meant by his generalized principle of relativity, he certainly did *not* mean that what is now known as proper acceleration is undetectable. The modern way of looking at it is that "inertial forces" are felt whenever the observer is accelerating *relative* to freefall. Einstein originally thought of the equivalence principle differently: He thought that an object accelerating in a gravitational field felt two different kinds of forces: (1) inertial forces due to acceleration, and (2) gravitational forces. These two forces canceled in the case of freefall. >and this was the central point of the twin's paradox, >as criticism against Einstein's theory. I don't think you are correct. The twin paradox is not a serious criticism against anything that Einstein believed. >According to his theory, we are entitled to say that such an object >is *not* (properly) accelerating but that instead a "real" >gravitational field is induced through the universe which accelerates >all the *other* objects. I think you are confusing the physical content of Einstein's theory with the way he chose to describe it. Saying that fictitious forces due to acceleration are equivalent to gravitational forces doesn't mean that they are both real, it means that they are both *fictitious*. The modern view is that gravitational forces *are* inertial forces due to acceleration relative to freefall. Einstein specifically declined, in the dialog you pointed to, to make the distinction between "real" and "fictitious". He wrote: "In the first place I must point out that the distinction real - unreal is hardly helpful. In relation to K' the gravitational field "exists" in the same sense as any other physical entity that can only be defined with reference to a coordinate system, even though it is not present in relation to the system K." What I interpreted him to be saying is that the fictitious gravitational fields due to acceleration are real in the sense that they enter into the equations of motion in the accelerated coordinate system in exactly the same way that "real" gravitational forces do. The modern preference is to say that *neither* is real---the only real effects are ones that can be expressed in a coordinate-free manner. >> >It should not be surprising that this was not only very confusing for >> >bystanders (who already hardly understood the difference between the >> >two theories), but that it even looked like a contradiction >> >> I would like to hear any coherent explanation of why it looks like >> a contradiction. > >You spotted it yourself here above; but evidently, you refuse to >believe it I don't think you have correctly characterized what Einstein believed. He certainly did not believe that what is now called proper acceleration is undetectable. >just as you refuse to believe your own eyes when you >replace Einstein's "real" by "pseudo", assuming that it was just a >glitch. It wasn't. A lot of the confusion in physics discussions are because people are caught up in interpreting *words*, as if we are analyzing some holy text. I don't *care* what words Einstein, or anyone else, uses. His theories have physical content that are independent of the words used to describe them. Einstein certainly struggled over how best to convey his theories to the layman, and I can't say that he necessarily succeeded very well. >> The bare statement "The laws of physics must be of >> such a nature that they apply to systems of reference in any kind of >> motion" is not a contradiction---on the contrary, it is nearly a >> tautology. You can always write the laws of physics so that you >> can use an arbitrary coordinate system. > >If you think that a postulate of physics is a tautology, then probably >you misinterpret its meaning. Einstein didn't *realize* it was a tautology. He thought that the requirement that a physical theory be written in a way that had the same form in all coordinate systems would uniquely pin down the theory, or at least eliminate some candidate theories. He was wrong about that; the requirement of general covariance doesn't actually eliminate any candidate theories, since they can always be rewritten so as to be generally covariant. However, the principle of general covariance *does* serve as a heuristic in developing theories, if one attempts to come up with theories that are *simple* when written in a coordinate-independent way. General Relativity *is* simple for a theory of gravity when written in a coordinate-independent way, while Newtonian gravity is not. Newtonian gravity looks simple in inertial coordinates, but not in more generalized coordinate systems. >> To derive a paradox from the twin thought experiment, you >> need to reason something like this: >> >> 1. There exists two coordinate systems, C1 and C2, such that >> the path of the traveling twin, as described in C1, is the >> same as the path of the stay-at-home twin, as described in C2. >> >> 2. Therefore, the predicted age of the traveling twin, computed >> using C1, must be the same as the predicted age of the stay-at-home >> twin, computed using C2. > >No, you are thinking "inside the box" of SRT while this has nothing to >do with such an SRT problem. It is strongly related to your own >objection. I have read many of your posts, and I have *yet* to see you explain in what sense you think that the twin paradox is a consistency problem for any position that Einstein is likely to have believed. He certainly did *not* believe that (proper) acceleration is undetectable, so your interpretation of what he meant by the generalized principle of relativity is almost certainly wrong. If Einstein really believed what you seem to think he believed, then he certainly made a huge conceptual blunder. The dialog that Einstein makes it clear that he was aware of the differences between the two twins. The one twin's description of the journey has no "gravitational fields", while the other twin's description *does* have such fields. Clearly, their situations are not the same, and clearly Einstein understood the differences. His dialog, far from showing that his generalized principle of relativity is contradictory, shows that both twins compute the same answer for the question: How old is each twin when they get back together? The dialog as presented is a demonstration of the *consistency* of Einstein's theory, it is not a demonstration of inconsistency. I think you are very confused. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 7 Jul 2010 08:14 harald says... >Newtons laws are not magical words without cause; instead they are >based on Newton's absolute space concept. The contribution that Newton made to science was in developing his laws of motion and gravity. His beliefs about absolute space are irrelevant to the application of his physics. There is no reason to believe that Newton had any greater insight about the ultimate nature of reality than any other philosopher. In practice, with Newton or Einstein or Poincare or whoever, we keep the physics and toss the metaphysics. >> You don't need a REASON why something at rest in some inertial frame of >> reference will stay at rest, and you certainly don't need an ether to >> predict it. > >I can't wait to hear your explanation why a ball that you roll on a >merry-go-round moves in a trajectory relative to the platform that is >not straight. What causes it? The earth perhaps, or the stars? And how >can they act on the ball, with nothing between them? Or perhaps you >meant: it's *just because*? What is *your* explanation for why objects in motion continue in motion in a straight line unless acted upon by an external force? What is the cause of that behavior? You want to postulate an aether, go ahead. Then how does aether cause objects to move in straight lines? You want to postulate absolute space, go ahead. How does absolute space cause objects to move in straight lines? Ultimately, explanations for phenomena are always in terms of more basic, more fundamental phenomena. We can explain why a spinning top doesn't fall over in terms of Newton's laws of motion, but those laws of motion are not themselves explained. Either the search for causes ends at some point, with fundamental phenomena that are just postulated to do whatever they do without any underlying cause, or the search for causes goes on forever, in which causes have causes which have causes, etc. In both cases, we never have a causal explanation for everything. Anyway, there is no difference in causal explanation between the claim in GR that in the absence of forces, point masses move along geodesics and the Newtonian claim that in the absence of forces, point masses travel in straight lines at constant velocity. The two claims are *identical* in form. In both cases, "straight" or "geodesic" is relative to the manifold, either Galilean spacetime or Einstein's spacetime. To postulate the existence of a material substance (the aether) that fills the manifold accomplishes *nothing* of explanatory value, unless you also propose dynamics for this aether that allows us to probe it. -- Daryl McCullough Ithaca, NY
From: harald on 7 Jul 2010 09:45 On Jul 7, 1:46 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > harald says... > > > > >On Jul 6, 5:18=A0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > >> harald says... > > >> >The twin scenario was presented by Langevin in 1911 to show that > >> >physical acceleration is "absolute", even more so with SRT than with > >> >Newton's mechanics. > > >> What does that mean? As I said, proper acceleration (as measured by > >> an accelerometer) is absolute, but coordinate acceleration is certainly > >> not. > > >It means that you agree on that point with Langevin. > > Well, it's hard for me to believe that Einstein was unaware of the > fact that an accelerometer can measure accelerations. Einstein was as aware as most physicists that an accelerometer does not distinguish between an acceleration and a gravitational field; however, he pushed that idea to the extreme. > >> Here's an analogy: A flat Euclidean plane has no notion of a preferred > >> direction. Any direction is as good as any other. But it certainly has > >> a notion of a *change* of direction. If you draw a path on the Euclidean > >> plane, then you can unambiguously determine whether the line is > >> straight or curved, because a straight line connecting two points is > >> shorter than any curved line connecting the same two points. If you > >> measure the lengths of two curves, you can determine which one is > >> straight. > > >Sorry but I can't resist pointing out the error of the above: a > >straight trajectory relatively to an Euclidean plane is *only* > >measured to be "straight" if that plane is part of what Einstein > >called the "privileged" group of inertial "spaces". > > I think you are confused about this point. Euclidean space has > an associated metric, which determines the lengths of paths. > A straight line is defined relative to that metric as the path > that minimizes the length between two points. It has nothing to > do with any "privileged space". I agree that a straight line relative to Euclidean space can be clearly defined. Perhaps I misunderstood that you meant with straight "path" a straight trajectory as defined in Newtonian mechanics and SRT. If you did not mean that, I don't know what you tried to say. > Having said that, we can define a special group of coordinate > systems for the Euclidean plane---the Cartesian coordinate systems, > via the requirement: > > A line is straight > <=> > It can be parametrized so that (d/ds)^2 x = (d/ds)^2 y = 0. > > Being a straight line is independent of coordinate system. With that claim I wonder if I truly misunderstood you; for in Newtonian mechanics as well as SRT, a path is very much dependent of the kind of coordinate system that you use. > The associated coordinate acceleration being zero is dependent > on a choice of a special coordinate system. Yes. But what was your point? > >> >"The laws of physics must be of such a nature that they apply to > >> >systems of reference in any kind of motion". > >> >As a result, physical acceleration is, according to Einstein's GRT, > >> >*relative* - which is just the contrary of what Langevin argued based > >> >on his "twins" example of SRT. > > >> As I said, proper acceleration is definitely *not* relative, but > >> coordinate acceleration trivially *is*. But proper acceleration is > >> measuring acceleration relative to *freefall*. > > >Then we both disagree with Einstein; > > That's ridiculous. Einstein certainly knew that an accelerated > observer feels "inertial forces", and an unaccelerated observer > does not. Sure he did. :-) > Whatever was meant by his generalized principle of relativity, You mean that you really did not know, and that you still don't - even after reading all his explanations?! > he certainly did *not* mean that what is now known > as proper acceleration is undetectable. Indeed. Perhaps it helps to say it in other words than he did: he meant *indistinguishable* from gravitation. > The modern way of looking at it is that "inertial forces" are > felt whenever the observer is accelerating *relative* to freefall. > Einstein originally thought of the equivalence principle differently: > He thought that an object accelerating in a gravitational field felt > two different kinds of forces: (1) inertial forces due to acceleration, > and (2) gravitational forces. These two forces canceled in the case > of freefall. ??? I strongly doubt that. Reference please! > >and this was the central point of the twin's paradox, > >as criticism against Einstein's theory. > > I don't think you are correct. The twin paradox is not a serious > criticism against anything that Einstein believed. So far it is not clear to you what the twin paradox criticized, and still you claim that it wasn't serious criticism against anything that Einstein believed. > >According to his theory, we are entitled to say that such an object > >is *not* (properly) accelerating but that instead a "real" > >gravitational field is induced through the universe which accelerates > >all the *other* objects. > > I think you are confusing the physical content of Einstein's theory > with the way he chose to describe it. The purpose with which you and I try to describe things here is to make the physical content of what think clear to the other. Do you seriously believe that Einstein tried to do the opposite, to hide the meaning of his words? > Saying that fictitious forces > due to acceleration are equivalent to gravitational forces doesn't > mean that they are both real, it means that they are both *fictitious*. Yup. > The modern view is that gravitational forces *are* inertial forces > due to acceleration relative to freefall. > > Einstein specifically declined, in the dialog you pointed to, to make > the distinction between "real" and "fictitious". He wrote: > > "In the first place I must point out that the distinction real - unreal is > hardly helpful. In relation to K' the gravitational field "exists" in the same > sense as any other physical entity that can only be defined with reference to a > coordinate system, even though it is not present in relation to the system K." > > What I interpreted him to be saying is that the fictitious gravitational > fields due to acceleration are real in the sense that they enter into > the equations of motion in the accelerated coordinate system in exactly > the same way that "real" gravitational forces do. The modern preference > is to say that *neither* is real---the only real effects are ones that > can be expressed in a coordinate-free manner. Good, we are making progress. :-) Einstein held that, as he put it, acceleration is "relative": according to his theory we may just as well claim that the traveler is *not* physically accelerated, contrary to Langevin's and your claim. He thought to solve the problem by saying that at the turnaround (according to the stay-at-home), the traveler may consider himself as remaining in place against an induced gravitational field that appears. > >> >It should not be surprising that this was not only very confusing for > >> >bystanders (who already hardly understood the difference between the > >> >two theories), but that it even looked like a contradiction > > >> I would like to hear any coherent explanation of why it looks like > >> a contradiction. > > >You spotted it yourself here above; but evidently, you refuse to > >believe it > > I don't think you have correctly characterized what Einstein > believed. He certainly did not believe that what is now called > proper acceleration is undetectable. He did not believe that no effect is detected, nor did he or I suggest that. > >just as you refuse to believe your own eyes when you > >replace Einstein's "real" by "pseudo", assuming that it was just a > >glitch. It wasn't. > > A lot of the confusion in physics discussions are because people are > caught up in interpreting *words*, as if we are analyzing some holy > text. I don't *care* what words Einstein, or anyone else, uses. In that case we have nothing to discuss, nor can you really discuss the clock paradox: it is foremost concerned with physical concepts that had been expressed with words as well as with equations. > His theories have physical content that are independent of the words used > to describe them. Without definitions of the variables and their fields of application, there is just mathematics without physical meaning. > Einstein certainly struggled over how best to convey his theories > to the layman, and I can't say that he necessarily succeeded very > well. His papers such as this one were conveyed to scientists - only they read physics journals. His popular 1920 book however was directed at laymen, and I now think that he did a reasonable job there (I changed my mind on that). > >> The bare statement "The laws of physics must be of > >> such a nature that they apply to systems of reference in any kind of > >> motion" is not a contradiction---on the contrary, it is nearly a > >> tautology. You can always write the laws of physics so that you > >> can use an arbitrary coordinate system. > > >If you think that a postulate of physics is a tautology, then probably > >you misinterpret its meaning. > > Einstein didn't *realize* it was a tautology. He thought that the > requirement that a physical theory be written in a way that had the > same form in all coordinate systems would uniquely pin down the theory, > or at least eliminate some candidate theories. There is also the key thought "simplest form" which is not written there but implied: it is included in his special relativity definition, of which the GPoR is an extension. Anyway, a theory is that what its author says it is. Otherwise for example, I could claim that Ken Seto's Mechanics is right, and that he doesn't know his theory well enough yet, but we will do that for him! > He was wrong about that; > the requirement of general covariance doesn't actually eliminate any > candidate theories, since they can always be rewritten so as to be > generally covariant. > > However, the principle of general covariance *does* serve as a heuristic > in developing theories, if one attempts to come up with theories that are > *simple* when written in a coordinate-independent way. General Relativity > *is* simple for a theory of gravity when written in a coordinate-independent > way, while Newtonian gravity is not. Newtonian gravity looks simple in > inertial coordinates, but not in more generalized coordinate systems. Good! > >> To derive a paradox from the twin thought experiment, you > >> need to reason something like this: > > >> 1. There exists two coordinate systems, C1 and C2, such that > >> the path of the traveling twin, as described in C1, is the > >> same as the path of the stay-at-home twin, as described in C2. > > >> 2. Therefore, the predicted age of the traveling twin, computed > >> using C1, must be the same as the predicted age of the stay-at-home > >> twin, computed using C2. > > >No, you are thinking "inside the box" of SRT while this has nothing to > >do with such an SRT problem. It is strongly related to your own > >objection. > > I have read many of your posts, and I have *yet* to see you explain > in what sense you think that the twin paradox is a consistency problem > for any position that Einstein is likely to have believed. Einstein explains the cause of the distrust or criticism clearly enough; nothing that I add can make clearer what the issue was. Now, he believed (or pretended) to have solved the paradox to satisfaction (which doesn't UN-make it a paradox, as you seem to think). However, his solution was never published in another physics journal. Dingle rejected it, but didn't manage to clearly express why. The physics FAQ rejects it, but without presenting strong arguments. Nevertheless his solution is (was) known to be wrong, as I discussed here: http://groups.google.com/group/sci.physics.foundations/msg/68cd1c181f8191d2 [..] > The dialog that Einstein makes it clear that he was aware of the differences > between the two twins. The one twin's description of the journey has no > "gravitational fields", while the other twin's description *does* have > such fields. Clearly, their situations are not the same, and clearly > Einstein understood the differences. Yes - at first sight he really "solved the paradox". :-) > His dialog, far from showing that > his generalized principle of relativity is contradictory, shows that both > twins compute the same answer for the question: How old is each twin when > they get back together? > > The dialog as presented is a demonstration of the *consistency* of > Einstein's theory, it is not a demonstration of inconsistency. That was its purpose... > I think you are very confused. I think that you forgot to check the meaning of "paradox". Harald
From: Tom Roberts on 7 Jul 2010 10:05 Daryl McCullough wrote: > harald says... >> On Jul 6, 5:18=A0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >>> Here's an analogy: A flat Euclidean plane has no notion of a preferred >>> direction. Any direction is as good as any other. But it certainly has >>> a notion of a *change* of direction. If you draw a path on the Euclidean >>> plane, then you can unambiguously determine whether the line is >>> straight or curved, because a straight line connecting two points is >>> shorter than any curved line connecting the same two points. If you >>> measure the lengths of two curves, you can determine which one is >>> straight. >> Sorry but I can't resist pointing out the error of the above: a >> straight trajectory relatively to an Euclidean plane is *only* >> measured to be "straight" if that plane is part of what Einstein >> called the "privileged" group of inertial "spaces". > > I think you are confused about this point. Euclidean space has > an associated metric, which determines the lengths of paths. > A straight line is defined relative to that metric as the path > that minimizes the length between two points. It has nothing to > do with any "privileged space". harald is more confused than that. He did not realize that you were discussing "a flat Euclidean plane", and he thought you were still discussing relativity, despite your clear and unambiguous statement of this fact. Like so many around here, harald needs to learn how to read more accurately. > Having said that, we can define a special group of coordinate > systems for the Euclidean plane---the Cartesian coordinate systems, Right. They are the ANALOGY of the inertial frames in relativity. But they don't form a group, they form a set or a class. "Group" is a technical word with a different meaning than you intended. The transforms between pairs of such coordinates form a group. Tom Roberts
From: Daryl McCullough on 7 Jul 2010 12:02
harald says... > >On Jul 7, 1:46=A0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >> harald says... >> >> >> >> >On Jul 6, 5:18=3DA0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrot= >e: >> >> harald says... >> >> >> >The twin scenario was presented by Langevin in 1911 to show that >> >> >physical acceleration is "absolute", even more so with SRT than with >> >> >Newton's mechanics. >> >> >> What does that mean? As I said, proper acceleration (as measured by >> >> an accelerometer) is absolute, but coordinate acceleration is >> >> certainly not. >> >> >It means that you agree on that point with Langevin. >> >> Well, it's hard for me to believe that Einstein was unaware of the >> fact that an accelerometer can measure accelerations. > >Einstein was as aware as most physicists that an accelerometer does >not distinguish between an acceleration and a gravitational field; >however, he pushed that idea to the extreme. Then I'm *not* disagreeing with Einstein. As I said, *proper* acceleration (acceleration relative to freefall) is certainly detectable, and Einstein agrees with that. >> >> Here's an analogy: A flat Euclidean plane has no notion of a preferred >> >> direction. Any direction is as good as any other. But it certainly has >> >> a notion of a *change* of direction. If you draw a path on the Euclide= >an >> >> plane, then you can unambiguously determine whether the line is >> >> straight or curved, because a straight line connecting two points is >> >> shorter than any curved line connecting the same two points. If you >> >> measure the lengths of two curves, you can determine which one is >> >> straight. >> >> >Sorry but I can't resist pointing out the error of the above: a >> >straight trajectory relatively to an Euclidean plane is *only* >> >measured to be "straight" if that plane is part of what Einstein >> >called the "privileged" group of inertial "spaces". >> >> I think you are confused about this point. Euclidean space has >> an associated metric, which determines the lengths of paths. >> A straight line is defined relative to that metric as the path >> that minimizes the length between two points. It has nothing to >> do with any "privileged space". > >I agree that a straight line relative to Euclidean space can be >clearly defined. Perhaps I misunderstood that you meant with straight >"path" a straight trajectory as defined in Newtonian mechanics and >SRT. If you did not mean that, I don't know what you tried to say. If you a space of points S, then a path is a 1-D subset of S that can be described as the image of a function from the reals (or an interval of reals) to S. So the position of an object as a function of time defines a path through Euclidean space, but a curve drawn on a piece of paper also is a path. >> Having said that, we can define a special group of coordinate >> systems for the Euclidean plane---the Cartesian coordinate systems, >> via the requirement: >> >> A line is straight >> <=> >> It can be parametrized so that (d/ds)^2 x = (d/ds)^2 y =3D 0. >> >> Being a straight line is independent of coordinate system. > >With that claim I wonder if I truly misunderstood you; for in >Newtonian mechanics as well as SRT, a path is very much dependent of >the kind of coordinate system that you use. That's not true. The path exists independent of the coordinates used to define it. If I have a road stretching across the surface of the Earth, that road defines a path (well, in the limit as the width of the road goes to zero, anyway). You don't need coordinates to give a path, and you don't need coordinates in order to say that a road is straight. Of course, you *can* describe a path with coordinates. You can describe a road by giving two functions lat(s) and long(s), which specifies the latitude and longitude as a function of the distance s along the road. >> The associated coordinate acceleration being zero is dependent >> on a choice of a special coordinate system. > >Yes. But what was your point? That the notion of "straight" versus "nonstraight" is *not* dependent on a coordinate system. Whether a path is straight (for Euclidean geometry) or inertial (for relativity) is an intrinsic property of the path, and a path doesn't change from straight to nonstraight when you change coordinate systems. As I said, there is a special set of coordinate systems (Cartesian coordinate systems, in the case of Euclidean geometry, inertial coordinate systems, in the case of relativity) such that straight paths or inertial paths are particular simple: In such a coordinate system, an inertial path can be written as: x(t) = x_0 + v_x t y(t) = y_0 + v_y t z(t) = z_0 + v_z t where x_0, y_0, z_0, v_x, v_y, and v_z are constants. Straight paths can *only* be written that way if you are using a Cartesian inertial coordinate system. >> >> >"The laws of physics must be of such a nature that they apply to >> >> >systems of reference in any kind of motion". >> >> >As a result, physical acceleration is, according to Einstein's GRT, >> >> >*relative* - which is just the contrary of what Langevin argued based >> >> >on his "twins" example of SRT. >> >> >> As I said, proper acceleration is definitely *not* relative, but >> >> coordinate acceleration trivially *is*. But proper acceleration is >> >> measuring acceleration relative to *freefall*. >> >> >Then we both disagree with Einstein; >> >> That's ridiculous. Einstein certainly knew that an accelerated >> observer feels "inertial forces", and an unaccelerated observer >> does not. > >Sure he did. :-) You agreed that he did, above. >> Whatever was meant by his generalized principle of relativity, > >You mean that you really did not know, and that you still don't - even >after reading all his explanations?! Well, it seems to me that you don't understand what Einstein meant. >> he certainly did *not* mean that what is now known >> as proper acceleration is undetectable. > >Indeed. Perhaps it helps to say it in other words than he did: he >meant *indistinguishable* from gravitation. When I say "proper acceleration", I mean acceleration *relative* to freefall. So that already takes into account gravity. In General Relativity, there *is* no "force of gravity". There are only inertial forces which appear whenever an observer is accelerating relative to freefall. That doesn't mean that gravitation is undetectable, just that a gravitational *force* is undetectable. Gravitation in GR is manifested through curvature, through the fact that the local standard for freefall (inertial motion) changes from location to location. Unlike Newtonian physics or Special Relativity, there is no longer a global notion of an inertial frame. >> The modern way of looking at it is that "inertial forces" are >> felt whenever the observer is accelerating *relative* to freefall. >> Einstein originally thought of the equivalence principle differently: >> He thought that an object accelerating in a gravitational field felt >> two different kinds of forces: (1) inertial forces due to acceleration, >> and (2) gravitational forces. These two forces canceled in the case >> of freefall. > >??? I strongly doubt that. Reference please! I cannot find an online reference, but it occurs in a discussion by Einstein of his "elevator" thought experiment. >> >According to his theory, we are entitled to say that such an object >> >is *not* (properly) accelerating but that instead a "real" >> >gravitational field is induced through the universe which accelerates >> >all the *other* objects. >> >> I think you are confusing the physical content of Einstein's theory >> with the way he chose to describe it. > >The purpose with which you and I try to describe things here is to >make the physical content of what think clear to the other. Do you >seriously believe that Einstein tried to do the opposite, to hide the >meaning of his words? No, what I'm saying is that in your case, Einstein failed to communicate (to you) what he meant. >Good, we are making progress. :-) >Einstein held that, as he put it, acceleration is "relative": >according to his theory we may just as well claim that the traveler is >*not* physically accelerated, contrary to Langevin's and your claim. No, you are confused. As I have said, there are two different notions of "acceleration": (1) proper acceleration (acceleration relative to the local standard for freefall) and (2) coordinate acceleration (acceleration relative to whatever coordinate system you are using). Einstein and I are in complete agreement that for the traveling twin, proper acceleration is nonzero, while coordinate acceleration is zero (using the appropriate noninertial coordinate system). So where is the disagreement? There is none. >He thought to solve the problem by saying that at the turnaround >(according to the stay-at-home), the traveler may consider himself as >remaining in place against an induced gravitational field that >appears. And certainly he may, in the sense that he may choose a coordinate system in which he is always at rest. The notion of being at rest is relative to a coordinate system in relativity. >> A lot of the confusion in physics discussions are because people are >> caught up in interpreting *words*, as if we are analyzing some holy >> text. I don't *care* what words Einstein, or anyone else, uses. > >In that case we have nothing to discuss, Are you saying that you had no point other than complaining about Einstein's way of describing his theory? >nor can you really discuss the clock paradox: I can discuss it perfectly well, from the point of view of physics. >it is foremost concerned with physical concepts that had been >expressed with words as well as with equations. >> His theories have physical content that are independent of the words used >> to describe them. > >Without definitions of the variables and their fields of application, >there is just mathematics without physical meaning. The physical meaning of the theory is defined by its predictions for *actual* experiments. General Relativity describes what happens when you take clocks and move them about, move them up and down in a gravitational field. It describes how mass affects gravitational fields, and how (indirectly) it affects the behavior of clocks. It describes how electromagnetic waves change frequency as they pass near massive bodies. It describes how massive bodies orbit one another. What other physical meaning could you possibly ask for???? If you are asking, not about General Relativity, but the General Principle of Relativity: that isn't a theory of physics, it is a heuristic, or a philosophical position, or metaphysics. It has no physical meaning, except to the extent that it guides us in coming up with better theories of physics. >> >> The bare statement "The laws of physics must be of >> >> such a nature that they apply to systems of reference in any kind of >> >> motion" is not a contradiction---on the contrary, it is nearly a >> >> tautology. You can always write the laws of physics so that you >> >> can use an arbitrary coordinate system. >> >> >If you think that a postulate of physics is a tautology, then probably >> >you misinterpret its meaning. >> >> Einstein didn't *realize* it was a tautology. He thought that the >> requirement that a physical theory be written in a way that had the >> same form in all coordinate systems would uniquely pin down the theory, >> or at least eliminate some candidate theories. > >There is also the key thought "simplest form" which is not written >there but implied: it is included in his special relativity >definition, of which the GPoR is an extension. > >Anyway, a theory is that what its author says it is. We disagree about this. The author is *irrelevant* except for historical purposes. The theory of relativity, or Newtonian mechanics, or electromagnetism, have all developed considerably since they were first invented by Einstein, Newton or Maxwell. What the original authors believed is interesting from a historical point of view, and for its insight into how great minds work, but has no significance in understanding modern theories. >Otherwise for example, I could claim that Ken Seto's Mechanics is right, >and that he doesn't know his theory well enough yet, but we will do >that for him! I couldn't care less what you call a theory, as long as you make it clear what theory you are talking about. Special Relativity and General Relativity are well-developed theories today. Any physicist knows what they are, and what their content is. That content is *not* determined by what Einstein believed in 1905 or 1916. >> I have read many of your posts, and I have *yet* to see you explain >> in what sense you think that the twin paradox is a consistency problem >> for any position that Einstein is likely to have believed. > >Einstein explains the cause of the distrust or criticism clearly >enough; nothing that I add can make clearer what the issue was. He makes it clear that there *is* no consistency problem. -- Daryl McCullough Ithaca, NY |