Is Length Contraction in SR physical??
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From: PD on 10 Feb 2010 21:07 On Feb 10, 1:36 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 10 Feb, 14:20, 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. > > Indeed. Btw, it's time for that embarassing climbdown on my part, that > I referred to previously. I don't think there's anything to be embarrassed about. Aether theory was a viable candidate for a number of years, supported by reputable people like Lorentz and Ritz. > > 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. PD
From: Tom Roberts on 10 Feb 2010 22:10 Edward Green wrote: > On Feb 1, 6:42 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> When someone asks "Is length contraction in SR >> physical?", they invariably don't have a definite meaning of "physical" in mind >> (if they did, they could answer the question themselves). Generally, they would >> consider a "physical length contraction" to mean that the object ITSELF gets >> physically shorter. This is manifestly not so in SR.<...> > > You perhaps unintentionally ran a circle there; disambiguating > "physical" by an emphatic phrase containing "physical". Trivially fixed: omit the last "physical". It's not needed. > A rod doesn't, > as we well know, get "physically shorter" by any measure we take in > the rest frame of the rod purely. Nor does the rod get "physically shorter" by any measure we take in any other frame, either. Making a measurement of its length does NOT affect the length of the rod itself, regardless of how the measurement is made. > It does in other frames of > reference. You mean, of course, "it does get physically shorter in other frames of reference". But to say that, you need to define what you mean by "get physically shorter". YOU have not addressed the linguistic issue (though you apparently think you have). And I point out that the word "get" implies something other than what you mean. In this usage it means a changing, and its presence thus implies that your "it" refers to THE ROD ITSELF and not to the measurement in "other frames". Note I had to put that sentence back together because you elided an important portion (which is common in English conversation, but is INADEQUATE in discussions like this where precision is necessary). Your verbal shortcut made you inadvertently say something I don't think you intended to say. It is remarkable how difficult it is to discuss this carefully and precisely. Common English idioms and conventions all too often get in the way.... And the problems often center around the shortest and most common words (e.g. "get", or as Bill Clinton learned, "is"). > That behavior is real enough to break strings, as Bell > noted in his famous thought problem. WHAT behavior? Surely not the supposed process of a measurement "making the rod be shorter". But yes, there are physical consequences of perspective -- ladders do or don't fit through narrow doorways, and strings between accelerating rockets do break. But rotating the ladder does NOT change the length of the ladder ITSELF, it only changes the ladder's length PROJECTED onto the doorway. Accelerating the rockets does not change the string ITSELF, it only changes the distance between rockets PROJECTED onto their instantaneously co-moving inertial frame. Measuring the rod's length in a frame relative to which it is moving affects the measured length (the rod's intrinsic length PROJECTED onto the measurement frame), but not the length of the rod ITSELF (meaning its INTRINSIC length, which can be measured only in its rest frame [#]). [#] because that's what these words mean. > If it someday turned out that Lorentz symmetry were subtly broken, we > might change our tune here. Nope. Not a chance. Geometric projection will still work the same way even if Lorentz symmetry is broken [@]. At most, breaking the symmetry will introduce additional modes of variation between frames, making some quantities that were thought to be invariant not actually be invariant. [@] In some sense "Euclidean symmetry" is already broken by SR (moving rods have different lengths than resting rods, though this is strictly speaking not part of Euclidean invariance). That hasn't changed how geometrical projection works. Tom Roberts
From: Inertial on 10 Feb 2010 22:32 "Tom Roberts" <tjroberts137(a)sbcglobal.net> wrote in message news:kvSdnQR4g8u56O7W4p2dnAA(a)giganews.com... > Nor does the rod get "physically shorter" by any measure we take in any > other frame, either. Making a measurement of its length does NOT affect > the length of the rod itself, regardless of how the measurement is made. Just using 'length' is also a linguistic problem (similar to that of using 'physical'). Does it mean 'proper length' / 'intrinsic length' / 'rest length' ... or does it mean the 'measured length' (ie the distance between the coordinates of two points at a given time in a given inertial frame) (or is there a better term for that 'length' that I can't think of atm :)) ??? If we refer to its 'length' 'in some inertial frame', then that would seem to imply one means the 'measured length', because the 'proper' / 'intrinsic' / 'rest' length does not depend on the frame of reference/ So when we say 'the length of the rod is shorter in the frame of the barn', that would seem to imply that length as measured in that frame, and not the rest length. Though a tilted ladder doesn't get 'physically shorter' it is also not as 'tall' (it has a lower 'height'). Can one say it is 'physically' not as tall? A 6 foot ladder lying on the ground is still a 6 foot ladder, but it is no longer 6 foot tall. It all comes down to the ambiguities of the English language (and I suspect the same or similar ambiguities in other spoken languages). That being one of the reasons why relationships and statements in physics are often made using the less ambiguous language of mathematics. Now. . the question is .. does Ken understand the linguistic issues here ... and is he of the opinion that the measured length of a rod (((ie the distance between its endpoints at a given time in a given frame of reference))) is predicted to be shorter in a frame in which it is is motion in a direction parallel to the line between those endpoints (eg in the pole and barn paradox). Ie if it was possible to devise an experiment where one could accurately (enough) measure that length, would that measurement be shorter than the proper/intrinsic/rest length of the rod?
From: Ste on 11 Feb 2010 01:46 On 10 Feb, 23:27, mpalenik <markpale...(a)gmail.com> wrote: > On Feb 10, 2:36 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > On 10 Feb, 14:20, 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. > > > Indeed. Btw, it's time for that embarassing climbdown on my part, that > > I referred to previously. > > > 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. > > Since you can write computer programs, you can try doing this: > > Remember the pictures I had you draw? Do something similar. Define > two axes, t (1,0) and x (0,1). > > Now, define another axis, t' and make it point in any direction you > want as long is it is less than a 45 degree angle from t. > > In Minkowski spacetime,the dot product of two vectors (V1 and V2) is > defined as > V1*V2 = V1.x*V2.x - V2.t*V2.t > > Remember, the length of a vector (squared) is just V*V, which in this > case gives us V.x^2 - V.t^2 > Also, remember that two vectors are orthogonal when their dot product > is zero, so: > V1*V2 = V1.x*V2.x - V2.t*V2.t = 0 > > With that said, let's say that t' represents the motion of an observer > through spacetime. Have your program find a vector called x' that is > perpendicular to t' (using the rule x'*t' = 0). This represents space > for the moving observer. > > Now, have the program normalize the two vectors (make their lengths > equal to one)--remember to use our new distance formula when you > normalize them. > > 45 degree motion through spacetime represents something traveling at > the speed of light. > Create another vector called c and set it equal to (1,1) (45 > degrees). Say this represents a photon traveling through spacetime. > > Now, project that vector onto x' and t' -- that is, find out how you > would write that in terms of x' and t'. You're essentially solving > the equation > > a*x' + b*t' = c > > The vector (a,b) will give you the motion of the photon in the x' and > t' coordinates. Try changing your t' to something else (less than 45 > degrees). > > If you've don't this correctly, no matter what you set your t' to, > you'll see that the light ray is traveling at a 45 degree angle in the > x',t' coordinate system. Surely you jest Mark! To write such a program, it would require me to understand these mathematical concepts in the first place.
From: Ste on 11 Feb 2010 01:59
On 11 Feb, 01:36, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 10, 1:36 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > The question therefore remains, how can the speed of propagation > > possibly be measured to be constant in all frames. > > Yes, indeed, and we'll get there eventually, if you like. For now, we > were just trying to figure out where this little observational fact > gives rise to frame-dependent simultaneity. Indeed. What I will say is that it appears the only remaining explanation is to make reference to the circumstances of the source *and* recipient in explaining the speed of light, but that would require a radically new way of looking at things. |