Is Length Contraction in SR physical??
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From: Sam Wormley on 5 Feb 2010 23:54 On 2/5/10 9:38 PM, Ste wrote: > > Indeed. But understanding the physical nature of these theories is > necessary for scientific advance. I mean, you can teach any fool to > follow rules that are already laid down. But the people who are coming > up with the rules need to have genuine understanding. You mean, like, Euclid?
From: Ste on 6 Feb 2010 00:02 On 6 Feb, 04:30, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: > "Ste" <ste_ro...(a)hotmail.com> wrote in message > > > Indeed. But understanding the physical nature of these theories is > > necessary for scientific advance. I mean, you can teach any fool to > > follow rules that are already laid down. But the people who are coming > > up with the rules need to have genuine understanding. > > Ohh, you mean insight into what is "really" happening. That is exactly what > Minkowski did when he pointed out that the time and space transformations of > Einstein were exactly the same as a rotation in spacetime of an invariant > vector, and that explained other stuff like Energy and Momentum. > > It also provided the basis for the General Theory of Relativity, which uses > this concept as a base. It provides a link between the two theories which > does not rely on the mathemetics just happening to work out the same for > treating SR as a special case of GR. > > If you want "genuine understanding" of SR, Minkowski space-time is the > second thing you should learn, right after Einstein's algebraic approach > based on his two axioms. I *do* have a genuine understanding already. Remember, Einstein understood his theory *before* he came up with the equations to describe it mathematically! > > I know, because Einstein, as best I can tell, thought like me, > > physically, and politically. > > You are nothing like Einstein as regards to physics. I wasn't pretending to be to physics what Einstein was. I'm saying all accounts show that he thought like me in many ways. > You are more like some crank who has been "studying physics all day and > night for a month" from popular accounts of the subject, trying to argue > with people who have been studying it for 40 years. I know, my audacity is limitless!
From: mpalenik on 6 Feb 2010 03:10 On Feb 5, 11:15 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 6 Feb, 02:36, mpalenik <markpale...(a)gmail.com> wrote: > > > On Feb 5, 9:04 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > Your conclusion "no" is in conflict with experimental measurement. > > > > When intuition conflicts with experimental measurement, then it is > > > > intuition that must give way. > > > > I checked Paul before I gave this answer. Length contraction has never > > > been experimentally tested. So my intuition does *not* conflict with > > > experimental evidence. > > > Length contraction must follow for logical consitancy based on other > > measurements. > > "Logical consistency" is a far cry from "experimental evidence". If you don't think the universe has to be logically consistant, then the entire framework of physics, and science in general, falls apart. > > > If the speed of light is constant in every reference > > frame, > > And it is my contention that it isn't relatively constant, but merely > *appears* to be so. It is my contention that the speed of light is > constant only with reference to an absolute frame, and that the time > dilation effects are due to classical-mechanical effects on the > velocity of photons. This isn't consistant with what is observed. First of all: Time dilation isn't measured on photons. I don't even know how you could claim to do that (other than, in a sense, by measuring red shifts, which has been done, but that's not generally what people mean when they say time dilation has been measured). It has been measured with actual clocks, which, after moving, can be shown to register less time having passed, once they are returned to rest, in a manner consistant with relativity. It has been measured through the half life of high energy particles, which changes in a way consistant with relativity. Second of all: The speed of light has been measured in multiple different ways, from observing the moons of jupiter to bouncing light beams back and forth along mountain tops, to interferometry, to frequency and wavelength measurements. In all cases, it comes out the same. Third of all: There are many other observations, such as particle energies, which obey relativistic physics and are inconsistant with Newtonian mechanics. > > > length contraction must necesessarily follow, as we've > > described it to you. That's how the original derivation of all of > > special relativity worked. You apply logic to the two postulates of > > relativity and see what it necessitates for consistancy. If the speed > > of light is constant, E=mc^2 logically follows (or rather, E^2 = > > p^2c^2 + m^2c^4), as does length contraction, time dilation, and the > > differences is simultanaity. Can you admit this is the case? So > > while length contraction may not have been experimentally measured > > directly, what has been measured? > > But what if, for argument's sake, the speed of light is constant *only > relative to an absolute frame*? First of all, this is demonstrably false based on measurements. Second of all, even if you choose not to believe those measurements, it would still negate the relation E^2 = p^2c^2 + m^2c^4. That expression is a direct consequence of the consistancy of the speed of light in every frame. Without it, you return to the Newtonian expression E = 1/2mv^2.
From: Ste on 6 Feb 2010 03:43 On 6 Feb, 07:59, mpalenik <markpale...(a)gmail.com> wrote: > On Feb 5, 11:57 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > I saw where you mentioned it, but I didn't see the post - I'm too > > weighed down responding to posts directed at me, to read those > > directed at others! > > > If you post it again however, I'll give it a look over. > > Here's a copy of what I posted before: > > No. I think you're confusing "geometric projection" with something > like "optical illusion". It is not an optical illusion in either > frame but it is a geometric projection in both. It depends what you mean by "optical illusion". SR is fundamentally about describing the behaviour of EMR. "Optical illusions" are manipulations of EMR that make the physical characteristics appear to be something that they are not. In that sense, SR is sometimes about "optical illusions", but I'm not sure I'd use that descriptor generally. > When we measure distance, we're measuring the distance something > takes > up in 3 dimensional space. If we rotate something in four dimensions > and then slide it forward along its time axis, it actually takes up > less of our 3 dimensional space, although it takes up the same amount > of space as before along its own spacial axis. I understand the > wording is a bit confusing there, but you can visualize it like this: > > This will actually produce the opposite result of relativity--length > expansion in both frames (instead of length contraction in both > frames). This is because orthogonality works differently in > Minkowski > space than it does in the euclidean space that we're used to. It is > mathematically well defined, and I could explain to you how to draw > it > physically, but for now I think it would just confuse you. So, if we > can start out with this, and you understand this, then I can explain > to you how to modify it to work in Minkowski spacetime. Does that > sound ok so far? > > Get a piece of paper, draw a horizontal axis labeled x and a vertical > axis labeled t. These represent space and time axis. An object "at > rest" will move straight forward through t. Let's call the origin, > where the 2 lines intersec t=0, or "the present". > > Now, lets draw the world line of a moving object. This line should > be > at an angle with respect to the t axis. Label this line t'. The > angle with the t axis should be less than 45 degrees because a 45 > degree angle represents something moving at the speed of light (equal > distances through time and space). Draw the line through the origin. > Extend it in both directions (into the past and future). This > represents an object that starts out in the past moving at some speed > and continues moving horizontally as time goes on. With me so far? After a careful re-reading and a second try. ;) > Now lets take a look at the "present", the origin. This is where all > 3 lines intersect. > > At the origin, draw another line that is perpendicular to t'. Label > it x'. This represents "space" as seen by the moving observer. The > moving observer sees his own world line as "time" and this > perpendicular axis as "space". > > Now, pick two points along the x' axis. This represents the ladder. > Extend some dotted lines from them in the direction of t' (forward > and > backward). This represents the two ends of the ladder as they move. > > Look at the points where they intersect the original x axis. You'll > notice you had to extend one point "forward" along t' and point > "backward" along t'. This represents the fact that one end of the > ladder is from the "future" of the t' frame, and the other end is > from > the "past". Also notice that the length of the ladder appears > *greater* in the x frame than the x' frame. Yes, with a bit of jiggerypokery, I think I have drawn it correctly, and indeed, it does become shorter in the x' orientation as against the x axis. > Two quick comments, though -- which end of the ladder is in the > future > and which is in the past is the *opposite* of how it would be in > Minkowski spacetime. Also, in this diagram, you will see length > *expansions*, whereas in Minkowski spacetime, you get length > *contractions*. > > Please try to actually draw this out. If you get confused, let me > know. Once you completely understand this, we can move on to modify > it to work in Minkowski spacetime. I'd be interested to learn more about that. But I will say is that I'm quite sure that this is not inconsistent with my views. It is true that, according to SR, the *apparent length* at any one *instant* is shorter. But that is *not* a shortening of the physical length. SR describes what you *observe*, not what is physically happening. Perhaps if I give you a physical analogy it will help. Imagine looking at something like a large cinema screen from one side, and at an angle of 45 degrees from your perspective. Let us also imagine that this screen generates a very short "light-pulse" simultaneously across its entire surface (and if it needs further definition, I mean simultaneous according to an observer who is stood in the middle of the screen equidistant from each edge - to this equidistant observer, both left and right edges of the screen are lit simultaneously). This light pulse is so short that it has already turned off again before the light has travelled more than an infinitesimal distance from the screen. From your perspective then, this light pulse, when it occurs, does not at any one time take up the full width of the visible screen. What it actually does is appears to "enter" from the edge of the screen closest to you, grows to a certain width, moves across the screen, and then "exits" the screen at the other edge. That means the *visible* width of this light pulse is always *less* than the total width of the screen (even though, by definition, the *whole* screen lit up at once). Now clearly, from your perspective, the "width" of this light pulse was reduced and "rotated into the 4th dimension". But that is an "optical illusion", as it were. It is *not* physical reality. If you want, because you understand more about the maths of this than I do (you can be Feynman to my Einstein), try recreating this cinema- screen analogy mathematically, and see if the predictions concur with what I've just described.
From: mpalenik on 6 Feb 2010 04:23
On Feb 6, 3:43 am, Ste <ste_ro...(a)hotmail.com> wrote: > On 6 Feb, 07:59, mpalenik <markpale...(a)gmail.com> wrote: > > > On Feb 5, 11:57 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > I saw where you mentioned it, but I didn't see the post - I'm too > > > weighed down responding to posts directed at me, to read those > > > directed at others! > > > > If you post it again however, I'll give it a look over. > > > Here's a copy of what I posted before: > > > No. I think you're confusing "geometric projection" with something > > like "optical illusion". It is not an optical illusion in either > > frame but it is a geometric projection in both. > > It depends what you mean by "optical illusion". SR is fundamentally > about describing the behaviour of EMR. "Optical illusions" are > manipulations of EMR that make the physical characteristics appear to > be something that they are not. In that sense, SR is sometimes about > "optical illusions", but I'm not sure I'd use that descriptor > generally. > > > > > > > When we measure distance, we're measuring the distance something > > takes > > up in 3 dimensional space. If we rotate something in four dimensions > > and then slide it forward along its time axis, it actually takes up > > less of our 3 dimensional space, although it takes up the same amount > > of space as before along its own spacial axis. I understand the > > wording is a bit confusing there, but you can visualize it like this: > > > This will actually produce the opposite result of relativity--length > > expansion in both frames (instead of length contraction in both > > frames). This is because orthogonality works differently in > > Minkowski > > space than it does in the euclidean space that we're used to. It is > > mathematically well defined, and I could explain to you how to draw > > it > > physically, but for now I think it would just confuse you. So, if we > > can start out with this, and you understand this, then I can explain > > to you how to modify it to work in Minkowski spacetime. Does that > > sound ok so far? > > > Get a piece of paper, draw a horizontal axis labeled x and a vertical > > axis labeled t. These represent space and time axis. An object "at > > rest" will move straight forward through t. Let's call the origin, > > where the 2 lines intersec t=0, or "the present". > > > Now, lets draw the world line of a moving object. This line should > > be > > at an angle with respect to the t axis. Label this line t'. The > > angle with the t axis should be less than 45 degrees because a 45 > > degree angle represents something moving at the speed of light (equal > > distances through time and space). Draw the line through the origin. > > Extend it in both directions (into the past and future). This > > represents an object that starts out in the past moving at some speed > > and continues moving horizontally as time goes on. With me so far? > > After a careful re-reading and a second try. ;) > > > > > > > Now lets take a look at the "present", the origin. This is where all > > 3 lines intersect. > > > At the origin, draw another line that is perpendicular to t'. Label > > it x'. This represents "space" as seen by the moving observer. The > > moving observer sees his own world line as "time" and this > > perpendicular axis as "space". > > > Now, pick two points along the x' axis. This represents the ladder. > > Extend some dotted lines from them in the direction of t' (forward > > and > > backward). This represents the two ends of the ladder as they move. > > > Look at the points where they intersect the original x axis. You'll > > notice you had to extend one point "forward" along t' and point > > "backward" along t'. This represents the fact that one end of the > > ladder is from the "future" of the t' frame, and the other end is > > from > > the "past". Also notice that the length of the ladder appears > > *greater* in the x frame than the x' frame. > > Yes, with a bit of jiggerypokery, I think I have drawn it correctly, > and indeed, it does become shorter in the x' orientation as against > the x axis. Just to be sure we're on the same page, you should have something like this (I added the circle, which represents the proper length of the ladder): http://s424.photobucket.com/albums/pp327/mpalenik/?action=view¤t=non-minkowski.gif Keep in mind this is in *non-Minkowski* spacetime, which means it will produce the oppose results that relativity produces (length expansions instead of contractions, reversed breaking of simultanaity). The dashed lines represent the motion of the ends of the ladder. The solid line labeled t' represents the motion of the center of the ladder. The moving (ladder's) frame of reference is represented by x' (the ladder's spacial axis) and t' (the ladder's time axis). If we want to find the location of any point, we can use either x and t or x' and t'. Both are equally valid. However, distances measured along the x axis will not agree with distances measured along the x' axis and times measured along the t axis will not agree with times measured along the t' axis. > > > Two quick comments, though -- which end of the ladder is in the > > future > > and which is in the past is the *opposite* of how it would be in > > Minkowski spacetime. Also, in this diagram, you will see length > > *expansions*, whereas in Minkowski spacetime, you get length > > *contractions*. > > > Please try to actually draw this out. If you get confused, let me > > know. Once you completely understand this, we can move on to modify > > it to work in Minkowski spacetime. > > I'd be interested to learn more about that. We have to get things to make sense to you in this first framework before doing that. It's not required but understanding Minkowski spacetime is another layer on top of what's required to understand this picture, so I think it's best to understand this picture first. > > But I will say is that I'm quite sure that this is not inconsistent > with my views. It is true that, according to SR, the *apparent length* > at any one *instant* is shorter. But that is *not* a shortening of the > physical length. SR describes what you *observe*, not what is > physically happening. The proper length of the ladder is unchanged in relativity but the amount of space the ladder takes up changes because the ladder gets rotated in time, almost exactly like in the picture I've shown you. It's exactly like the rotation analogy with fitting the ladder into a shorter barn by rotating it that many of us here have been trying to describe to you. An important point, however, is that neither one of the sets of axes (either x,t or x',t') is inherantly better than the other. Neither set is more correct than the other. |