Is Length Contraction in SR physical??
in [Relativity]
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From: Ste on 9 Feb 2010 01:19 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. Your description is a geometric one. The difference is that my description involves describing non- geometric properties of the object. 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. 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"?
From: mpalenik on 9 Feb 2010 01:34 On Feb 9, 1:19 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. Your description is a geometric > one. The difference is that my description involves describing non- > geometric properties of the object. 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. 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. This is more or less what relativity is saying. The length of the ladder doesn't change when it's moving, simply the amount of "space" that it takes up. The the reason that it takes up less "space" is because the definition of "space" is different in the moving frame than in the rest frame, as per the picture I drew. Length, by the way, is a geometric property of an object. When we speak of rotations, it is not the geometry of the object that changes. And indeed SR does not say that the geometry of the object changes. It is only the coordinate dependant description of the object's geometry that changes. > > > 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"?- Hide quoted text - It's more analogous to length than to volume. Geometrically speaking, we can define length squared as X*X, where X is a vector that starts at one end of the object and ends at the other end. So, for example L^2 for the vector (1,0,0) is (1,0,0)*(1,0,0) = 1^2 + 0^2 + 0^2 = 1. It just so happens that the way we take dot products is different in Minkowski spacetime than in normal spacetime, as defined by the metric tensor of Minkowski spacetime.
From: Ste on 9 Feb 2010 01:37 On 8 Feb, 17:01, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 6, 11:48 pm, Ste <ste_ro...(a)hotmail.com> wrote: > > > Ah, but the difference is I *will* discuss my views, I'll discuss them > > on each and every occasion someone expresses a legitimate interest in > > discussing them, and I'll generally continue to discuss them until > > either one of us changes our views, or until the other person gets > > tired. > > But you've already established that it won't be you that might change > your views. It's unlikely I'll change my axiomatic beliefs, but I'll certainly hold my hands up and shut my mouth if it turned out that what I'm saying is simply illogical. > As for your insistence that you should be able to expect an education > suitable for the "ordinary man" at the hand of physicists on a > newsgroup, in order for you to change your views, then I think on that > too you will guarantee your own failure. That's not what I said Paul. I said the essence of these theories should be such that an ordinary man can understand it. I mean, I don't pretend to be able to plot a trajectory through the solar system, but I understand the basic concepts, and indeed have done so since I was a child.
From: mpalenik on 9 Feb 2010 01:40 On Feb 9, 1:34 am, mpalenik <markpale...(a)gmail.com> wrote: > On Feb 9, 1:19 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. Your description is a geometric > > one. The difference is that my description involves describing non- > > geometric properties of the object. 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. 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. > > This is more or less what relativity is saying. The length of the > ladder doesn't change when it's moving, simply the amount of "space" > that it takes up. The the reason that it takes up less "space" is > because the definition of "space" is different in the moving frame > than in the rest frame, as per the picture I drew. > > Length, by the way, is a geometric property of an object. When we > speak of rotations, it is not the geometry of the object that > changes. And indeed SR does not say that the geometry of the object > changes. It is only the coordinate dependant description of the > object's geometry that changes. > To clarify, we don't need coordinates to do geometry. We can do coordinate independant geometry, which is described by distances between points and the angles between vectors (not to be confused with polar or spherical coordinates, which is still a coordinate dependant description). For example, we can say that we have a vector sitting at (0,0,0) that points in the direction (1,0,0), defining a point at (1,0,0) and another vector sitting at (0,0,0) that points in the direction (0,0,0) pointing to the point at (0,1,0). Or equivilantly, in a non-coordinate dependant description, we can say "we have two vectors that are perpendicular to each other that define points at a distance of sqrt(2) from each other". Note that general relativity can be described in both coordinate dependant and coordinate independant language. It is only the coordinate dependant description of an object that changes when one object is moving with respect to another, however, the measurements that we make are dependent on our coordinate system. Again, this is what I was trying to demonstrate in the diagrams we were working with earlier.
From: Ste on 9 Feb 2010 01:46
On 8 Feb, 20:21, PD <thedraperfam...(a)gmail.com> wrote: > On Feb 8, 3:57 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > Indeed, I have no information about how the decay products are > > measured in these accelerators nor access to the raw data set, and I'm > > not willing to take the word of scientific authority in which I have > > utterly no faith, particularly because so many supposed experts appear > > to have no insight whatsoever into the physical nature of their > > mathematical models, and even more shockingly the request for a > > physical explanation often produces the reply "what do you mean by > > physical", as though it needed to be defined! > > Well, here we run into the small conundrum: > S: "I don't see why I should believe this theory without a physical > model that makes sense to me." > P: "Well, you see, physicists choose which model to believe based on > which of the models matches the largest set of experimental data." > S: "But I don't believe the experimental data either, because I do not > trust that they haven't been skewed by physicists." And indeed, I don't believe mere *assertions* that the experimental data supports a theory that is contrary to my axioms. > P: "What would it take for you to believe the experimental data?" > S: "It would require physicists to explain the data with a model that > makes sense to me." > > Self-fulfilling prophecy, you see. Indeed, but I'd already identified that the problem is axiomatic. Without putting too fine a point on it, I require a physical, mechanical explanation, and you're right that I would not consider something an explanation unless it meets those requirements. That said, this goes back to what I said at the start, and indeed what Einstein said, which is that it is the theory that determines what you can observe, because it is the theory that determines what is evidence and how it should be interpreted. If it is your argument that the physical world cannot be understood except in your terms, then my argument is that you haven't tried hard enough to understand it in any other terms, and indeed you haven't. |