Is Length Contraction in SR physical??
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From: Tom Roberts on 3 Feb 2010 11:50 jem wrote: > Tom Roberts wrote: >> PD wrote: >>> I >>> find frame-dependent quantities like kinetic energy and magnetic field >>> to be arguably physical, even if frame-dependent and coordinate- >>> dependent. >> >> And I argue that you are mistaken -- you confuse such >> coordinate-dependent quantities with the more fundamental, underlying >> quantities that are invariants: >> kinetic energy => s >> magnetic field => Maxwell 2-form >> ... etc. > > Who's confused? You insultingly tell an expert (PD) that only invariant > quantities can be considered physical, then turn around and concede to a > kook (Ste) that it doesn't matter to Physics what's considered physical. It all depends on what you are trying to do. If you just want to apply labels like "physical", then how you do that is up to you -- no method of applying labels has any significance (except in the usage of such labels). But if you want to construct models of natural phenomena, in a process we call science, then the choices of quantities used to form the model are important. Some quantities, such as coordinate-dependent ones, simply cannot be used in a valid model because they have aspects that are inconsistent with the world we inhabit. > Would you agree that a mathematical theory is not a physical theory, and > that a scientific theory is a physical theory? If so, can you describe > the essential difference(s) between the two? Does your description > mention invariance? Science in general, and physics in particular, is the process of constructing models of the world we inhabit, and testing those models experimentally. With the improved understanding we have gained over the past few centuries, all models of modern physics are necessarily mathematical. That is, they present relationships in mathematical formulas, and prescribe a correspondence between symbols in those formulas and phenomena (or measurements) in the real world. Any model that uses coordinate-dependent quantities in its equations [#] will not correspond accurately to phenomena, because the arbitrary human choices involved in constructing coordinates do not affect the phenomena being modeled. So the quantities involved in valid models will all be invariant under coordinate changes. [#] unless they happen to be coordinate-dependent representations of coordinate-INdependent quantities; replace the former by the latter. Tom Roberts
From: rotchm on 3 Feb 2010 12:01 > > WE USE CIRCULAR DEFINITIONS > > No .. we don't. We use a standard universal constant speed (c) and a > standard time and define length from that. That is no more circular > than having a standard length and standard time and have a value for c > from that. Actually, its we use a standard for time. The standard for distance (length) uses the standard for time and the *integer* 299792458. These two standards, with the (operational) definition for speed, makes the speed of light to be 299792458 (constant). Bollean logic: If [ A and B] then C, that is not the same as If [ C and A] then B.
From: PD on 3 Feb 2010 12:09 On Feb 2, 11:39 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > PD wrote: > > I > > find frame-dependent quantities like kinetic energy and magnetic field > > to be arguably physical, even if frame-dependent and coordinate- > > dependent. > > And I argue that you are mistaken -- you confuse such coordinate-dependent > quantities with the more fundamental, underlying quantities that are invariants: > kinetic energy => s > magnetic field => Maxwell 2-form > ... etc. Well, I don't confuse them. I just think both categories (the "more fundamental" and the coordinate-dependent) are both classifiable as physical. > > Tom Roberts
From: PD on 3 Feb 2010 12:11 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. > > Ken Seto > > > > > Obviously there is *some* 'physical' relationship between the barn > > doors and pole that means an observer in that frame would measure the > > pole as being within the barn. How would you best describe that > > relationship? Is talking about 'between the barn doors at the same > > time in the barn frame of reference' something valid and meaningful to > > say?- Hide quoted text - > > > - Show quoted text -
From: PD on 3 Feb 2010 12:13
On Feb 2, 5:59 pm, waldofj <wald...(a)verizon.net> wrote: > > Words used in physics have more precise meanings than the ones found > > in the dictionary. If you want to communicate with physicists about > > physics, then it is extremely important to DROP the meanings of words > > as listed in the dictionary and LEARN the meanings of those same words > > as they are used by physicists. > > AH, h2so4 professor. Don't synthesize anything I wouldn't synthesize. > Oh, and the reciprocal of pi to your good wife. Exactly! |