Is Length Contraction in SR physical??
in [Relativity]
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From: PD on 9 Feb 2010 12:46 On Feb 9, 12:03 am, Ste <ste_ro...(a)hotmail.com> wrote: > On 8 Feb, 16:47, PD <thedraperfam...(a)gmail.com> wrote: > > > On Feb 8, 7:29 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > Minkowski spacetime is a *mathematical* explanation, not a physical > > > one. > > > What is interesting about this remark is that you consider physics to > > be the study of the material world, and by "material" you mean to > > include matter, the space in which matter resides, and all other > > manner of things in the universe. Thus the nature of space appears to > > be in the bailiwick of the physical explanations provided by physics, > > and yet somehow the structure of that space is not physical but > > mathematical to you. > > > Does this not seem oxymoronic to you? > > No, because as I've said Minkowski space is a mathematical > quantification of reality. In truth, there is no "x-axis" in physical > reality - it's a framework we impose arbitrarily to enable > mathematical analysis. The structure of Minkowski space is independent of coordinates. In fact, it would be useful exercise for you to see how special and general relativity can be described mathematically without any choice of axes whatsoever. Misner, Thorne, and Wheeler wrote a book with that approach, specifically with that intent. > That's not to disparage the role of maths, but > what I'm saying is that ultimately the mathematical explanation has to > appeal to physical reality. As it does. > > It is fairly easy to demonstrate the tenets of Euclidean space. If you > give someone a supply of rulers, and tell them to describe a place by > using the numbers on the rulers, then it becomes fairly obvious that > you need rulers in 3 axes. No it doesn't. It needs three rulers along the space that we are *familiar with* on the spatial scales that we are *familiar* with, which means laying rulers down that are longer than, say, a few nanometers and shorter than, say, a few hundred kiloparsecs. This is the point. If the universe were shaped like a thread, then we would say that there is only one ruler needed, because there is only one dimension to follow, forward and back. But to a mite, that thread becomes a cylinder, and that second dimension -- going AROUND the cylinder -- earns its own ruler, even if it ends up being a closed path around the cylinder. What is obvious on one size scale is not so obvious on another size scale, you see. > You can then relate the physical proof to > the mathematical proof, by explaining that "axes" are a framework of > rulers laid down arbitrarily. Which has certain assumptions -- for example, that if you lay two straight lines that are both perpendicular to a third line (one definition of "parallel"), then the two lines will never intersect. This seems so eminently reasonable that Euclid made it a postulate. It also turns out to be not true in our universe. > > And then, building on that, it becomes obvious that for *prediction*, > you need another dimension, that describes not just where, but *when*, > and this has its physical analogy not in the ruler, but in the clock, > and it becomes possible to describe where something will be not just > by reference to numbers on a ruler, *but when a certain number is > visible on the clock* (or the sundial, or whatever). > > So you get to 4 dimensions merely by appealing to everyday concepts > that even children are familiar with. I get that. And so your complaint is that it hasn't been presented to you in a way that makes such simple sense thus far. And in response, I'll remind you that I've suggested accessible readings that do exactly this.
From: PD on 9 Feb 2010 12:54 On Feb 9, 12:19 am, Ste <ste_ro...(a)hotmail.com> wrote: > On 8 Feb, 16:57, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Feb 8, 8:10 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > The geometry of the universe is the explanation, just like how the > > > > geometry for the universe is the explanation for why a ladder gets > > > > shorter in the x direction if you rotate it. There's nothing more to > > > > it than that. If you think there's more to a ladder getting shorter > > > > when you rotate it, I'd love to hear your *physical* explanation for > > > > why a ladder gets shorter when you rotate it. > > > > Indeed. The physical explanation for "why a ladder gets shorter when > > > you rotate it spatially" is that it apparently *doesn't* get shorter. > > > Experience suggests that the ladder remains the same physical length > > > no matter what orientation it takes in space. > > > No, it DOES get shorter. Remember there are at least two lengths > > involved here, both of which are physical. One is the distance between > > the endpoints of the ladder in the plane of the doorway. That is > > clearly a physical distance and one that we would ascribe to a length, > > because it is the distance between two endpoints. The fact that this > > changes with ladder orientation does not change that fact. > > > What you are saying is that intuition tells you that there is > > *another* length which does not change with ladder orientation, and > > that is certainly correct. The mistake you make is saying that it is > > THIS quantity that is called length and the other is not a length, > > because it does not meet your invariance criterion. Sorry, but that is > > an artificial criterion with no physical basis other than your own > > preference. > > On the contrary, my description of length has a physical basis - not > least because the word "length", if unqualified, strongly implies a > description about the object itself. Whether that association is warranted or not. :>) You see, one of the things one has to establish is whether a property is associable with the object itself, rather than just asserting that it IS so, or even appealing to some desire that it SHOULD BE so. We could return to kinetic energy as an illustrative example, if you like. Or if you like, we can talk about the fact that a 2-photon system can have a mass of 0.924 GeV, where the mass of each photon is nowhere near 0.462 GeV. > Your description is a geometric > one. The difference is that my description involves describing non- > geometric properties of the object. Really? What are its NONgeometric properties? Define the length of an object without reference to geometry. > Yours is about describing its > relationship with other objects - and indeed, a relationship takes > two, and the geometric relationship between two objects can take place > without any physical change in the properties of the object itself. That's correct. There are some properties of objects that change without there being any physical interaction with the object at all. And in fact, this is highlighted by the fact that the SAME property of the SAME object can have two different values at the SAME time, when viewed by two different observers --- which makes it abundantly clear that the difference in valued cannot have occurred as the result of some interaction with the object. Note that it is an *assumption* that a physical property of an object has a single, unique, true value unless the object is impinged upon by some physical interaction which changes that property. This assumption turns out to be not particularly sustainable in a model that provides predictive and measurable consequences. > It > would be baffling for someone to say that you could change the length > of the ladder by rotating the house, and yet geometrically this is > perfectly valid - but note that we're still able to create physical > analogies for these mathematical concepts. > > > Now, in the case of relatively moving frames, what is established > > through experimental evidence (some of it not as direct as you'd like) > > is that the quantity that we at one time THOUGHT was invariant (that > > is, the thing we write sometimes as X^2 + Y^2 + Z^2) turns out to be > > not invariant. This doesn't make it not a length. It is certainly what > > we have always attributed to a length, regardless of the fact that it > > turns out to be not invariant. What is also true is that there is a > > space-time quantity (the thing we'd write sometimes as X^2+Y^2+Z^2-(T/ > > c)^2) that *is* invariant, but that's not really what we'd call a > > length anymore because of the time admixture. > > I'm curious, what is this "spacetime quantity"? Is it something like > "total volume"? It is commonly called "interval", and no it is not volume. Volume would be the *product* of dimensions, not a sum.
From: Ste on 9 Feb 2010 13:26 On 9 Feb, 17:12, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 8, 11:19 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 8 Feb, 16:20, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Feb 6, 11:33 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > On 7 Feb, 03:54, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Feb 6, 8:52 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > > The only thing that is required is to note at the detector X or the > > > > > > > detector Y whether the signals from the events arrive at the same time > > > > > > > or at different times. This is a point decision. It is a yes or no > > > > > > > question. "Signal from A just arrived at X. Did signal from B arrive > > > > > > > at X at the same time? Yes or no." > > > > > > > If detection is instantaneous (i.e. if a photon is absorbed > > > > > > instantaneously), then it is possible for A and B to be simultaneous > > > > > > according to both X and Y. However, if detection is not instantaneous, > > > > > > then it is *not* possible. > > > > > > I didn't say "according to both X and Y". What I said in fact was the > > > > > opposite. Please reread. > > > > > What I did say is that X is *right* in concluding that A and B are > > > > > simultaneous, based on the procedure we established as reliable. > > > > > But the procedure isn't reliable! I've said that repeatedly. > > > > It isn't reliable for what? > > > For driving a consensus between X and Y? Is that a necessary > > > requirement? Why? > > > Let's revisit the procedure. > > > If you were going to try to determine whether two events are > > > simultaneous, according to a *particular* observer, then our suggested > > > procedure is as follows: > > > 1. Position a detector midway between the two events, where "midway" > > > can be established at any time by directly measuring the length > > > between the marks left by the events and the mark at the location of > > > the detector. Let's amend this to say that this can be repeated on two > > > occasions to determine that the "midway" condition has not changed. > > > 2. Have the events send a signal known to travel with equal speeds > > > toward the detector. The equality of the speeds can be established at > > > any time by reproducing the signal and directly measuring the distance > > > covered by the signal per unit time. > > > (Note that (1) and (2) unambiguously determine that the propagation > > > delay is the same from both events.) > > > 3. Determine whether the signals from the events arrive at the > > > detector at the same time or at different times. If the signals arrive > > > at the same time, then from that information the correct conclusion is > > > that the original events were simultaneous. If the signals arrive at > > > different times, then from that information the correct conclusion is > > > that the original events were not simultaneous. > > > This works only if neither detector is moving. > > Moving relative to what? Notice that I said that the "midway" > determination can be done at ANY TIME, and in fact repeated as > necessary. Does this establish what you need? > > > > > > You agreed earlier that this procedure should be sufficient for > > > determining the simultaneity of spatially separated events, according > > > to a particular observer. > > > > Now you seem not so sure. What's the source of your sudden > > > reservation? What procedure would you otherwise propose for > > > determining the simultaneity of two spatially separated events? > > > The source of my reservation is that equidistance cannot be > > maintained, nor symmetry maintained, over the detection *interval*, if > > the two detectors are moving relative to each other. > > Perhaps it would be best if we moved to an example. I'm going to use a > modified version of Einstein's codification of these experiments. > > 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.
From: Ste on 9 Feb 2010 13:35 On 9 Feb, 17:46, PD <thedraperfam...(a)gmail.com> wrote: > > > It is fairly easy to demonstrate the tenets of Euclidean space. If you > > give someone a supply of rulers, and tell them to describe a place by > > using the numbers on the rulers, then it becomes fairly obvious that > > you need rulers in 3 axes. > > No it doesn't. It needs three rulers along the space that we are > *familiar with* on the spatial scales that we are *familiar* with, > which means laying rulers down that are longer than, say, a few > nanometers and shorter than, say, a few hundred kiloparsecs. > > This is the point. If the universe were shaped like a thread, then we > would say that there is only one ruler needed, because there is only > one dimension to follow, forward and back. No we wouldn't, because there is no such thing as a one-dimensional thread - at least, not in our experience. Anything that is within our physical experience has 3 spatial dimensions. > But to a mite, that thread > becomes a cylinder, and that second dimension -- going AROUND the > cylinder -- earns its own ruler, even if it ends up being a closed > path around the cylinder. What is obvious on one size scale is not so > obvious on another size scale, you see. This seems to be just a statement that the universe "works in a different way" at some scale, whereas I reject that view. If we are free to simply define arbitrarily the areas where the universe "works in a different way", then I dare say any explanation will do - and if I remember correctly, that is precisely the problem with string theory, that it is unfalsifiable because it has so many degrees of freedom, which are inconceivable except in mathematical terms.
From: mpalenik on 9 Feb 2010 14:54
On Feb 9, 1:35 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 9 Feb, 17:46, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > It is fairly easy to demonstrate the tenets of Euclidean space. If you > > > give someone a supply of rulers, and tell them to describe a place by > > > using the numbers on the rulers, then it becomes fairly obvious that > > > you need rulers in 3 axes. > > > No it doesn't. It needs three rulers along the space that we are > > *familiar with* on the spatial scales that we are *familiar* with, > > which means laying rulers down that are longer than, say, a few > > nanometers and shorter than, say, a few hundred kiloparsecs. > > > This is the point. If the universe were shaped like a thread, then we > > would say that there is only one ruler needed, because there is only > > one dimension to follow, forward and back. > > No we wouldn't, because there is no such thing as a one-dimensional > thread - at least, not in our experience. Anything that is within our > physical experience has 3 spatial dimensions. > > > But to a mite, that thread > > becomes a cylinder, and that second dimension -- going AROUND the > > cylinder -- earns its own ruler, even if it ends up being a closed > > path around the cylinder. What is obvious on one size scale is not so > > obvious on another size scale, you see. > > This seems to be just a statement that the universe "works in a > different way" at some scale, whereas I reject that view. If we are > free to simply define arbitrarily the areas where the universe "works > in a different way", then I dare say any explanation will do - and if > I remember correctly, that is precisely the problem with string > theory, that it is unfalsifiable because it has so many degrees of > freedom, which are inconceivable except in mathematical terms. You're not free to say that the world works in a different way at an arbitrary scale. Your misinterpreting the meaning of what he's saying. Here's another example that you might find more relatable-if you look at your TV set from a distance, it appears to be able to produce a perfectly smooth image. The farther you get from the TV, the smoother the image appears. However, if you get close up, you can see that you don't actually have a smooth image but a series of discreet pixels that flicker on and off. If you describe the motion of a ball across the TV screen, you could approximate it as continuous motion or you could describe it exactly by the describing the flickering of pixels. If you want to look at the whole TV screen, the classical motion approximation works pretty well. But if you want to look at, say, 4 pixels in the upper right hand corner of the screen, the classical motion approximation is useless. |