Is Length Contraction in SR physical??
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From: Paul Stowe on 11 Feb 2010 02:04 On Feb 10, 11:36 am, Ste <ste_ro...(a)hotmail.com> wrote: {Snip...} > The question therefore remains, how can the speed of propagation > possibly be measured to be constant in all frames. The answer to your question is actually simple and 'intuitive' if you think about what must happen in a medium. The propagation of any type of disturbance travels by 'conduction' from one entity to the next. This is set by the mean speed and spacing. If the medium is 'incompressible' the entities are all touching (spacing is zero) and the entities 'infinitely hard' In that case, the speed of propagation is infinite, and no delta 'pressures' are possible 'within the medium. OTOH, in any compressible medium there is spacing, and the entities have momentum and energy. This results a distinctive independent set speed by which any disturbances (like wave propagation) will occur. This is designated as c for ANY! medium Now it should be obvious that in the case of a medium it is this process that always dominates... The speed of sources must, by that constraint, alter there emission/field profiles to conform to this limitation. So now, start with a source of a omni-directional wave generator 'at rest' with respect to the medium. The resulting waves propagate outward 'at c' in all directions, resulting in a perfectly spherical field form. Next, give this source some speed v, obviously c hasn't changed so, in the direction of motion the source is displacing forward at v so each wave front must be separating 'from the source' at c - v. In the perpendicular (transverse) direction the wave fronts are still separating from the source at c. Thus, for the hemisphere in front of the moving source the wave field form is no longer spherical, but flatten into an ellipsoid. Now what happens to the back half??? Intuitively you would think that the wave front would be separating 'from the source' at c + v. However, remember that a wave is an oscillation (a back & forth motion) so, one cycle is c - v and c + v.. It turn, the cycle must remain in- phase with the rest of the field (it's one contiguous field). Thus the actual distance of the wave form must contracted by Sqrt(1 - [v/c]^2) on the axis of motion. The end result, the field flattens (distorts) into an ellipsoid who's radius is defined as a function v multiplied by the cosine of angle (w) relative to the axis of motion. R(w) = R[Sqrt(1 - [vCos w/c]^2)] Now, look at a situation where we have two interacting fields in equilibrium. If at rest the centerline distances are, say, x. Then, if both are in uniform motion each field so x -> x' = xSqrt(1 [v/c]^2). Now, consider the QM interpretation of matter. If matter consists of waves it makes no difference what particular type, all wave must behave this way. Now, let's thake the classic MMX and evaluate it in the context of a QM wavicle system. The time it take a photon to to complete a complete transit is L/c and, because the system is moving, in axis perpendicular axis L = 2d/Sqrt(1 - [v/c]^2)... Along the axis of motion the matter contracts and d -> d' = dSqrt(1 - [v/c]^2). The round trip time is L = 2d'/(1 - [v/c]^2) = 2d/Sqrt(1 - [v/c]^2). The result is obvious, the reason is likewise obvious. Last I checked any number divided by itself is unity, thus, Sqrt(1 - [v/c]^2) / Sqrt(1 - [v/c]^2) = 1 making all inertial measurements of wave speed invariant. But!, there are real physical consequences. These are, real field distortions, and a measureable alteration of rate in physical processes. However, since all physical processes are affected equally it is also clear that the actual perception/observations/measurements in moving systems are all equally affected, making the perception in all such systems appear the same. However, it is physically noticable by relative motion. Paul Stowe
From: Ste on 11 Feb 2010 02:08 On 11 Feb, 02:07, PD <thedraperfam...(a)gmail.com> wrote: > > > I definitely can't make this aether theory work. For what I lack in > > mathematical skill, I've made up for with programming skill, and it is > > clear that propagation speed cannot be constant with reference to an > > absolute frame - its effects would be immediately obvious. > > > The question therefore remains, how can the speed of propagation > > possibly be measured to be constant in all frames. > > Indeed, as this appears to be wholly unintuitive. We'll get to how > this can be. > > What we will now do is imagine that at some point after the observers > on trains A and B made their observations, they compared notes. > Although it might have seemed surprising to both of them that they did > not agree whether the original strikes were simultaneous or not, a > moment's thought by both of them makes them feel better. > A's conclusion that the strikes were simultaneous is sound and > consistent with the laws of physics (as we will show), but it also > makes sense to him WHY those same laws of physics would have produced > the observation that B made. > Likewise, B's conclusion that the strikes were NOT simultaneous and > consistent with the laws of physics, but it also makes sense to him > WHY those same laws of physics would have produced the observation > that A made. > > We'll go through that in a bit. > > But first it's helpful to recap, A and B both agree that not only are > their own observations consistent with the laws of physics, but EACH > OTHER'S observations are also consistent with the laws of physics. And > that's really all we can hope for. > > Sadly, this does not answer the question whether the original strikes > really were simultaneous or not. And in fact, because there is no > physical priority given to either reference frame, the conclusion must > be that they are both right -- or better said, that the answer is > different, depending on the reference frame. Indeed. It is easy to reconcile the notion of perspective with the laws of physics. But the question still remains of how to reconcile this with material reality.
From: Inertial on 11 Feb 2010 02:16 "Paul Stowe" <theaetherist(a)gmail.com> wrote in message news:0db4a675-2ae3-4b9d-af25-9b5f4fac9d55(a)a16g2000pre.googlegroups.com... > On Feb 10, 11:36 am, Ste <ste_ro...(a)hotmail.com> wrote: > > {Snip...} > >> The question therefore remains, how can the speed of propagation >> possibly be measured to be constant in all frames. > > The answer to your question is actually simple and 'intuitive' if you > think > about what must happen in a medium. The propagation of any type of > disturbance travels by 'conduction' from one entity to the next. This > is > set by the mean speed and spacing. If the medium is 'incompressible' > the > entities are all touching (spacing is zero) and the entities > 'infinitely > hard' In that case, the speed of propagation is infinite, and no > delta > 'pressures' are possible 'within the medium. OTOH, in any > compressible > medium there is spacing, and the entities have momentum and energy. > This > results a distinctive independent set speed by which any disturbances > (like wave propagation) will occur. This is designated as c for ANY! > medium > > Now it should be obvious that in the case of a medium it is this > process > that always dominates... The speed of sources must, by that > constraint, > alter there emission/field profiles to conform to this limitation. > > So now, start with a source of a omni-directional wave generator 'at > rest' > with respect to the medium. The resulting waves propagate outward 'at > c' > in all directions, resulting in a perfectly spherical field form. > Next, > give this source some speed v, obviously c hasn't changed so, in the > direction of motion the source is displacing forward at v so each > wave > front must be separating 'from the source' at c - v. In the > perpendicular > (transverse) direction the wave fronts are still separating from the > source at c. Thus, for the hemisphere in front of the moving source > the > wave field form is no longer spherical, but flatten into an > ellipsoid. > Now what happens to the back half??? The opposite > Intuitively you would think > that > the wave front would be separating 'from the source' at c + v. It does > However, remember that a wave is an oscillation (a back & forth > motion) so, Not for light. It is side-to-side > one cycle is c - v and c + v. Nonsense [snip rest]
From: Ste on 11 Feb 2010 02:34 On 11 Feb, 01:57, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 10, 8:20 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Feb 10, 8:05 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Feb 10, 12:21 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > On 9 Feb, 21:02, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Feb 9, 12:26 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > > Two trains are on adjacent tracks, going in opposite directions, > > > > > > > though I say that only to deliberately reinforce an ambiguity here. It > > > > > > > doesn't matter whether the trains are going at different speeds, and > > > > > > > in fact it isn't even important if one of the trains is stopped, or in > > > > > > > fact whether they are going in the same direction but one faster than > > > > > > > the other. All that matters is that there is a relative velocity > > > > > > > between them. > > > > > > > > Two lightning strikes occur, drawn to the trains because of the > > > > > > > friction of the air between the trains. In fact, one lightning strike > > > > > > > leaves a scorch mark (a 1 cm spot, if you want to be precise) on > > > > > > > *both* trains as it hits. The other strike leaves a scorch mark > > > > > > > somewhere else on *both* trains. > > > > > > > > The question now is, were the strikes simultaneous or not? > > > > > > > > There is an observer on train A, and an observer on train B, and they > > > > > > > are both looking out the window when the strikes occur. > > > > > > > > They make the following observations: > > > > > > > 1. The observer on train A sees the two lightning flashes > > > > > > > simultaneously. > > > > > > > 2. The observer on train B sees the flash from the front of his train > > > > > > > before he sees the flash from the rear of his train. > > > > > > > > Now, it is not yet possible to determine whether the strikes were > > > > > > > simultaneous originally. We have more work to do. But I want to see if > > > > > > > you have a picture in your head of what has transpired. > > > > > > > I have a basic picture, yes. > > > > > > OK, then. > > > > > Let's now follow up these two observations above and couple them with > > > > > more observations. > > > > > 3. After the strikes, the observer on train A runs a tape measure from > > > > > his location to the scorch mark of one strike and makes note of the > > > > > number. Then he runs a tape measure from his location to the scorch > > > > > mark of the other strike and makes note of the number. These numbers > > > > > are equal. Note the scorch marks are on his train, but that's an > > > > > undeniable marker of where the event WAS when the signal propagation > > > > > began. > > > > > Not really. If his train is moving, then the scorch marks will have > > > > actually moved from the location of the event. > > > > With respect to what is the train moving? In this reference frame, the > > > train is not moving at all, though the other one is. I remind you that > > > it is not stated, nor is it clear, whether both trains are moving or > > > only one is. Nor does it matter, because even if the train is moving > > > relative to the track doesn't guarantee that the train is moving in > > > any absolute sense. For example, if the track itself were moving (say > > > because the surface of the earth is moving) and the train is moving in > > > the opposite direction, one could easily visualize that the train is > > > not moving at all, even if the train is moving relative to the track. > > > > This is a crucial point about reference frames. We are making > > > statements about observations made IN THIS REFERENCE FRAME, and in > > > this reference frame, the train is not moving, the scorch marks are > > > not moving, and we can measure the speed of light in this reference > > > frame. > > > > > > 4. After the strikes, the observer on train B runs a tape measure from > > > > > his location to the scorch mark of one strike and makes note of the > > > > > number. Then he runs a tape measure from his location to the scorch > > > > > mark of the other strike and makes note of the number. These numbers > > > > > are equal. Note the scorch marks are on his train, but that's an > > > > > undeniable marker of where the event WAS when the signal propagation > > > > > began. > > > > > I'm not sure I agree with this. > > > > It is exactly the symmetric situation with train A. Since the strikes > > > left marks on both trains, there is no reason to rule it out here if > > > it was permissible on A. > > > > > > 5. The observer on A runs some experiments to measure the speed of > > > > > light and the isotropy of the speed of light (that it is the same in > > > > > either direction), and finds that the signal speed is the same. (Note > > > > > this isotropy would NOT hold if the signal were sound, for example.) > > > > > And *how* does he measure this? > > > > A variety of ways. You could, for example, follow the procedures used > > > by experimenters as documented in the papers referenced on the first > > > Google search return on "experimental basis for relativity". > > > > > > 6. The observer on B runs some experiments to measure the speed of > > > > > light and the isotropy of the speed of light (that it is the same in > > > > > either direction), and finds that the signal speed is the same. (Note > > > > > this isotropy would NOT hold if the signal were sound, for example.) > > > > > > Given these *observations* 1, 3, and 5, what would the observer on > > > > > train A conclude about the simultaneity of the original strikes? > > > > > I must admit I don't have a clear enough picture of what is happening. > > > > This gedanken seems to presuppose the very thing in question, that is, > > > > relativity. > > > > No, it doesn't presuppose anything other than what is *actually > > > observed* in experiment. I cannot underscore this enough. For example, > > > the claims that both (5) and (6) are both true may seem > > > counterintuitive. How can both trains measure the speed of light to be > > > the same from both directions, if the trains are moving relative to > > > each other? Certainly an aether-based theory would not hold this is > > > true. Does this mean we are *assuming* relativity is true so that > > > these statements are both true? No. Statements (5) and (6) are the > > > results of *experimental observation*. Nature really does behave this > > > way, even if we find it counterintuitive. > > > > > Let's refine it a bit by stipulating that the Earth is stationary, the > > > > track is stationary, and the clouds are stationary, > > > > On what basis would you make such an arbitrary stipulation, when you > > > KNOW that this is not the case? > > > You may be tempted to say, "Because we have to have an absolute > > > reference for stationary *someplace*, and we might as well make it > > > Earth because we live here." A moment's thought will tell you this is > > > foolish. Physical laws don't care where we live. Then, in the search > > > for finding an absolute reference for rest, you may eventually ask > > > yourself why such an absolute reference would be needed at all, > > > especially if there is nothing you can clearly identify that would fit > > > the bill... > > > > > and we'll also > > > > stipulate that the lightning strike happens in an instant (even though > > > > it doesn't), and marks all locations at that instant. > > > > > Now, where are the trains on the tracks when the lightning strikes, > > > > and are they moving? > > > > You see? You are trying to establish an absolute reference frame, even > > > if it means doing so completely arbitrarily, JUST SO you can say > > > whether the trains are absolutely moving or not. > > > As a side note, let me just offer the word of encouragement that you > > are asking all the right questions and wrestling with all the right > > issues. In other words, this is what students do when they actually > > learn something. You are on your way to really understanding what > > relativity is saying, and also on your way to learning how to check > > whether the claims that are made do in fact match experimental > > observation. > > > But as a cautionary note, let me also remind you that we are ONLY > > trying to put together an understanding of where the frame-dependence > > of simultaneity comes from, which is only one small stepping stone in > > the exploration of special relativity, which in turn is itself a small > > stepping stone in the exploration of general relativity. As you can > > see, this takes work, and extended thinking, and asking lots of > > serious questions. This is why many of the basic ideas in physics > > cannot be explained compellingly in a few sentences to interested and > > intelligent hobbyists. Physics students would be expected to discuss > > this in class for about an hour, then think about it and work through > > issues for about four or five hours outside of class (with other > > students or with the teacher for some of that), before moving on to > > the next stepping stone. > > I hope you're not losing interest in this exercise. I would hope that > you would find the articulation of where some of the ideas of > relativity come from to be both valuable and intriguing. > Are you not finding the instruction helpful? I haven't lost interest, but I must admit I still haven't really got a clear picture of where the trains are or how they are moving. If indeed it is unspecified whether they are moving relative to the track or the clouds, then we may as well just do away with tracks and lightning, and just talk about two trains that are moving relative to each other, suspended in the air against a blank background. The involvement of tracks and clouds just complicates the matter.
From: Ste on 11 Feb 2010 03:27
On 11 Feb, 07:04, Paul Stowe <theaether...(a)gmail.com> wrote: > On Feb 10, 11:36 am, Ste <ste_ro...(a)hotmail.com> wrote: > > {Snip...} > > > The question therefore remains, how can the speed of propagation > > possibly be measured to be constant in all frames. > > The answer to your question is actually simple and 'intuitive' if you > think > about what must happen in a medium. The propagation of any type of > disturbance travels by 'conduction' from one entity to the next. This > is > set by the mean speed and spacing. If the medium is 'incompressible' > the > entities are all touching (spacing is zero) and the entities > 'infinitely > hard' In that case, the speed of propagation is infinite, and no > delta > 'pressures' are possible 'within the medium. OTOH, in any > compressible > medium there is spacing, and the entities have momentum and energy. > This > results a distinctive independent set speed by which any disturbances > (like wave propagation) will occur. This is designated as c for ANY! > medium > > Now it should be obvious that in the case of a medium it is this > process > that always dominates... The speed of sources must, by that > constraint, > alter there emission/field profiles to conform to this limitation. > > So now, start with a source of a omni-directional wave generator 'at > rest' > with respect to the medium. The resulting waves propagate outward 'at > c' > in all directions, resulting in a perfectly spherical field form. > Next, > give this source some speed v, obviously c hasn't changed so, in the > direction of motion the source is displacing forward at v so each > wave > front must be separating 'from the source' at c - v. In the > perpendicular > (transverse) direction the wave fronts are still separating from the > source at c. Thus, for the hemisphere in front of the moving source > the > wave field form is no longer spherical, but flatten into an > ellipsoid. > Now what happens to the back half??? Intuitively you would think > that > the wave front would be separating 'from the source' at c + v. > > However, remember that a wave is an oscillation (a back & forth > motion) so, > one cycle is c - v and c + v.. It turn, the cycle must remain in- > phase > with the rest of the field (it's one contiguous field). Thus the > actual > distance of the wave form must contracted by Sqrt(1 - [v/c]^2) on the > axis > of motion. The end result, the field flattens (distorts) into an > ellipsoid who's radius is defined as a function v multiplied by the > cosine > of angle (w) relative to the axis of motion. > > R(w) = R[Sqrt(1 - [vCos w/c]^2)] > > Now, look at a situation where we have two interacting fields in > equilibrium. > If at rest the centerline distances are, say, x. Then, if both are > in > uniform motion each field so x -> x' = xSqrt(1 [v/c]^2). Now, > consider > the QM interpretation of matter. If matter consists of waves it makes > no difference what particular type, all wave must behave this way. > > Now, let's thake the classic MMX and evaluate it in the context of a > QM > wavicle system. The time it take a photon to to complete a complete > transit is L/c and, because the system is moving, in axis > perpendicular > axis L = 2d/Sqrt(1 - [v/c]^2)... Along the axis of motion the matter > contracts and d -> d' = dSqrt(1 - [v/c]^2). The round trip time is > L = 2d'/(1 - [v/c]^2) = 2d/Sqrt(1 - [v/c]^2). > > The result is obvious, the reason is likewise obvious. > > Last I checked any number divided by itself is unity, thus, > > Sqrt(1 - [v/c]^2) / Sqrt(1 - [v/c]^2) = 1 > > making all inertial measurements of wave speed invariant. But!, there > are real physical consequences. These are, real field distortions, > and > a measureable alteration of rate in physical processes. However, > since > all physical processes are affected equally it is also clear that the > actual perception/observations/measurements in moving systems are all > equally affected, making the perception in all such systems appear > the > same. However, it is physically noticable by relative motion. > > Paul Stowe I'm afraid I didn't quite recognise this explanation as "intuitive". |