Is Length Contraction in SR physical??
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From: mpalenik on 4 Feb 2010 11:54 On Feb 4, 10:04 am, kenseto <kens...(a)erinet.com> wrote: > On Feb 3, 8:12 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Feb 3, 3:58 pm, kenseto <kens...(a)erinet.com> wrote: > > > > On Feb 3, 3:36 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Feb 3, 12:19 pm, kenseto <kens...(a)erinet.com> wrote: > > > > > > On Feb 3, 12:11 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Feb 3, 10:04 am, kenseto <kens...(a)erinet.com> wrote: > > > > > > > > On Feb 3, 4:41 am, artful <artful...(a)hotmail.com> wrote: > > > > > > > > > On Feb 3, 4:18 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > > > > > > Uncle Ben wrote: > > > > > > > > > > On Feb 1, 11:36 pm, Tom Roberts <tjroberts...(a)sbcglobal..net> wrote: > > > > > > > > > >> [...] > > > > > > > > > > > Tom Robrts takes the conservative position on what is "physical." > > > > > > > > > > Hmmm. I tried not to make any statement about what is or is not "physical", > > > > > > > > > because that word is too ambiguous. > > > > > > > > > > To me it is irrelevant whether one considers this or that quantity to be > > > > > > > > > "physical". What is important is whether or not a given quantity can be an > > > > > > > > > appropriate model for some physical phenomenon. For that, it's QUITE CLEAR that > > > > > > > > > no coordinate-dependent quantity can be a valid model of any physical > > > > > > > > > phenomenon, as arbitrary human choices cannot possibly affect physical > > > > > > > > > phenomena. Nor can the perspective from which one looks at an object affect the > > > > > > > > > object itself. Coordinates are, of course, arbitrary human choices that define > > > > > > > > > the perspective one uses to look at and describe objects and situations. > > > > > > > > > > > To > > > > > > > > > > be consistent, he would have to deny physicality to kinetic energy and > > > > > > > > > > to the magnetic field of a moving charge. Or even motion itself. > > > > > > > > > > I deny that any of those can be valid models for physical phenomena. I make no > > > > > > > > > statement about their "physicality" -- arguments over word meanings are > > > > > > > > > uninteresting (but inappropriate word meanings must be dealt with before the > > > > > > > > > real discussion can even begin). > > > > > > > > > > In every case I know of, if you analyze the physical situation sufficiently > > > > > > > > > well, you will find an appropriate quantity that is a valid model for the > > > > > > > > > physical phenomena in question. For instance, when considering a collision > > > > > > > > > between two particles, don't use kinetic energy, use the Mandelstamm s (total > > > > > > > > > energy squared in their center-of-momentum frame); instead of magnetic field, > > > > > > > > > use the Maxwell 2-form; instead of motion, use the particles' individual > > > > > > > > > trajectories. Tensor and geometric analysis provide methods to analyze all > > > > > > > > > situations of interest in a coordinate-free manner. This is one of the major > > > > > > > > > lessons of GR (but it took about a half-century to sink in). > > > > > > > > > > > Or do > > > > > > > > > > I not understand? > > > > > > > > > > The issue is more subtle than you seem to think. It is not merely about the > > > > > > > > > meanings of words, or about what is or is not "physical", it is about what types > > > > > > > > > of quantities can be used to model physical phenomena. > > > > > > > > > > Tom Roberts > > > > > > > > > At first reading you seem to be equating 'physical' with 'frame > > > > > > > > invariant'. ie. Only things that are not dependent on the observer > > > > > > > > are physical. > > > > > > > > > But am I right in my assessment that you are really saying that it is > > > > > > > > only nature / reality itself that is physical. The measurements and > > > > > > > > calculations we make are parts of our models of reality .. and so are > > > > > > > > never really 'physical' themselves. The best models (and > > > > > > > > measurements) for reality are those that are not observer dependent, > > > > > > > > because physical reality is not observer dependent (ignoring some > > > > > > > > interpretations of QM :)). > > > > > > > > > In the case of length contraction, what we define as length (roughly > > > > > > > > speaking: the spatial distance between two simultaneous events in a > > > > > > > > given time) is contracted .. even though the proper interval is > > > > > > > > invariant. In both cases they are valid (but different) measurements > > > > > > > > of the same pair of events. > > > > > > > > > Ken's claim that contraction not being 'physical' means a pole doesn't > > > > > > > > physically fit between the barn doors at the same time in the barn > > > > > > > > frame of reference (in the well-known 'paradox'). I guess the issue > > > > > > > > there is really whether 'between the barn doors at the same time in > > > > > > > > the barn frame of reference' itself is physical .. as it is observer / > > > > > > > > frame dependent. > > > > > > > > No it was specified that, in the barn frame, the barn doors close > > > > > > > simultaneously for a very brief period while the pole is completely > > > > > > > inside the barn. This requires real physical contraction and not > > > > > > > observer dependent. > > > > > > > No, it doesn't. You obviously don't understand the pole and barn > > > > > > puzzle at all. > > > > > > No it is you who don't understand the pole and the barn paradox. > > > > > Ken, look again. It is stated explicitly in the pole and barn paradox > > > > that in the pole frame, the pole is LONGER than the barn. This means > > > > the physical shortening of the rod obviously is not frame-independent. > > > > If it required the rod to be physically shorter to all observers, then > > > > it would be claimed to be shorter than the barn in the pole frame, > > > > too. Since this is not claimed, then it is not required to be observer > > > > independent. > > > > You get a clue....in the barn frame you claimed that the doors are > > > closed simultaneously while the pole is completely inside the barn. > > > In the barn frame, yes. Only in the barn frame. > > No....once it is physically contracted it is contracted to all > observers. > > > > > > This means that the pole is physically shortened and physically > > > shortened pole is not observer dependent. > > > No it certainly does not mean that. > > Sure it means that. > > > Because if it did mean that, then > > the pole would also have to be shorter than the barn in the pole > > frame. > > The point is: the pole is not physically contracted in the barn frame > or the pole frame. In the barn frame the geometric porjection of the > pole unto the barn frame is contracted and this projected length is > able to fit into the barn with both doors close simultaneously. This is correct so far. > In the > pole frame the geometric projection of the length of the barn is > expanded and this expanded length is able to encase the pole > completely with both doors close simultaneously. This is incorrect. In the pole frame, the length of the barn is *also* contracted but the closing of the doors is no longer simultaneous. *Time* as well as distance gets "geometrically projected" in the pole frame. In the barn frame, closing the doors simultaneously just long enough for the man with the pole to run from one end of the barn to the other corresponds to the front door being open, while the back door is closed just long enough for the man with the pole to run to it, then the back door opening and the front door closing after the back end of the pole enters the barn. There is a four dimensional projection going on--you can't project a vector onto another in a way that makes it appear bigger, only smaller--for example: Say you have two vectors that are parallel to each other. The projection of vector 2 onto vector 1 has the same magnitude as vector 2. Now, say you rotate them at 90 degrees to each other. The projection of vector 2 onto vector 1 has a length of zero. So the projection of vector 2 onto vector 1 will always have a length between 0 and the length of vector 2. The same is true the other way around. The projection of vector 1 onto vector 2 doesn't get *bigger* as the angle between the vectors increases. It *also* gets smaller. This projection ranges in length between 0 and the length of vector 1. In relativity, the same type of thing is going on, except instead of rotating solely in space, the "rotation" is taking place in space AND time, and so, the projection must take into account both space and time.
From: "Juan R." González-Álvarez on 4 Feb 2010 13:56 Tom Roberts wrote on Wed, 03 Feb 2010 19:52:10 -0600: (...) > "Proper length" is not the same as "length", because a) it is > intrinsic to the object, It is not. > and b) it is invariant. Only under certain approximations (i.e. under certain *specific* class of transformations). -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/en/publicationzone/canonicalsciencetoday/canonicalsciencetoday.html
From: mpalenik on 4 Feb 2010 14:03 On Feb 4, 1:56 pm, "Juan R." González-Álvarez <nowh...(a)canonicalscience.com> wrote: > Tom Roberts wrote on Wed, 03 Feb 2010 19:52:10 -0600: > > (...) > > > "Proper length" is not the same as "length", because a) it is > > intrinsic to the object, > > It is not. > > > and b) it is invariant. > > Only under certain approximations (i.e. under certain *specific* > class of transformations). > Yes, proper length is only invariant under transforms in the Lorentz group. However, to show that proper length is not invariant, you'll have to come up with a scenario where an object undergoes a transformation not in the Lorentz group (which includes translations, rotations in space, velocity boosts, parity reversal, and time reversal).
From: PD on 4 Feb 2010 14:14 On Feb 4, 9:57 am, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > artful wrote: > > I would still say that a pole fitting between barn doors at a given > > time in the barn frame is still a valid description of what happens > > physically. In that sense length contraction is 'physical'. > > As I have said before, you are free to use words however you want. But don't > expect others to understand what you mean without explanation. Most people, when > they hear "the contraction of the pole is physical" immediately think that the > pole itself has been squished; we both know that is wrong, but many of your > readers don't. > > I prefer to use words in ways that foster communication rather than hinder it. > While that is difficult at best, at least I try to avoid phrases that are known > to confuse people. > > > I know that the label 'physical' is used differently by different > > people (leading to confusion) .. I wonder what you would think of my > > notion of 'physical in frame of reference' : a well-defined > > measurement (OF something physical) that is invariant for all > > observers at rest WITHIN the inertial frame of reference. > > As a frame of reference is a purely abstract concept, adding the adjective > "physical" to it is both inconsistent and incredibly confusing. I doubt that > anybody would know what you mean without extensive explanation. > > > I don't know if there is a term for something being 'frame dependent > > but not observer invariant within the frame'. > > I think "fictitious" covers it well. As in "centrifugal and Coriolis forces" are > fictitious. Given the confusion that surrounds them (especially among people who > never took Physics 101), I'm surprised you want to extend it to other situations.... > > What's wrong with simply stating the truth: "length contraction" is purely > geometrical in the 4-D spacetime of relativity. As is common, geometrical > relationships can have physical consequences (e.g. the ladder does or does not > fit through the doorway). Physics can never be separated from geometry. > > Tom Roberts I laud the sentiments in this post, really I do. The last paragraph is where we run into trouble with the very same people you are trying to avoid confusing. These people believe that the study of physics *should* be about things physical and should avoid making physical arguments based on mathematics only. You and I know that geometric structure *is* essential to the conceptual foundation of certain fundamental physical laws, and it's not just "cogs and levers" of material things -- but I think we need to be explicit about that. When one says that length contraction is not physical in the sense that the amateur reader might understand that term, this gives the impression that there is a theory used in physics that isn't about physics at all but about mathematics, which is not true, either. PD
From: PD on 4 Feb 2010 14:14
On Feb 4, 10:23 am, glird <gl...(a)aol.com> wrote: > On Feb 4, 10:57 am, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > > > > > What's wrong with simply stating the truth: "length contraction" is >purely geometrical in the 4-D spacetime of relativity. > > What's wrong is that length contraction may be something real, but the > 4-d spacetime of relativity is a purely geometrical figment of the > imagination. > > glird Tom, this is a case in point. |