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|    sci.physics.research    |    Current physics research. (Moderated)    |    17,516 messages    |
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|    Message 15,585 of 17,516    |
|    Roland Franzius to All    |
|    Re: How to measure a Lorentz contraction    |
|    05 Mar 17 02:55:53    |
      From: roland.franzius@uos.de              Am 03.03.2017 um 10:04 schrieb John Heath:       > I like it. Simple and do-able. Should       > be able to swing a 3 foot wire at 3 or       > 4 Hz by hand with the hand end of the       > wire clamped to a scope. I have spectrum       > lab audio analyzer software on a lap top       > for VLF whistlers , moving sky charges.       > With this most of what is needed is already       > in place. As you have already done this I       > can proceed with confidence. One concern.       > Standing in the middle of no where spinning       > a 3 foot wire while looking at a lap top could       > draw unwanted attention. I am tested for       > a better WIFI connection officer , that's       > my story and I am sticking to it.       >       > As to your dislike of the Lorentz contraction       > interpretation of magnetism you are not alone.       > I can say from my shoes it grows on you       > over time. How often is there an opportunity       > to toss a fundamental force in nature such       > as magnetism straight into the trash bin?       > One less to worry about.       >                     Don't, because there are genuine electric and magnetic fields.              The two quadratic forms E^2-B^2 and E.B are invariant with respect to       Lorenz transformations. E.B=0 and |E|=|B| is mainly radiation.              So there are static fields with |E|>|B| which are predominantly electric       fields because you can find a system of reference with B'=0 and E' =       E/sqrt(1-(v/c)^2).       This system can be thought to be the rest system where you see charges       at rest producing their common Coulomb field.              And there are predominantly magnetic fields |B|>|E| where you can find a       system reference with E'= 0 and B' = B/sqrt(1-(v/c)^2)              Taken cum grano salis of course, because E,B are components of a rank 2       tensor field, transforming with the product of two Lorentz tranformation       matrices.              An example of pure magnetic field with E=0 everywhere is the cylindrical=              magnetic field B_phi =1/r around a finite conducting wire with with two       equal constant currents: one of the negative charges to the left and       positive charges to the right of identical current and charge density.              So as an experiment, move at constant speed with your synchronized       clocks/meterstick/ampere-meter/volt-meter equipment along a wire with       the half velocity v/2 of the electron current.              Now you have two equal currents of negative electrons and positive ions       with equal but opposite velocities +-v/2.              The wire is assumed somehow to be electrical neutral in the rest system       of the ions.              Of course, there will be a small longitudinal electrical field E_z to       drive the electric current against the resistivity and to supply by ExB       the dissipation energy current density from the field outside into the       wire.              E_z and dissipation can be made very small or even zero for a       superconductor. So we can neglect the dissipation problem in a first       approximation.              Now you have by the Lorenz formula               B'_phi = B_phi /Sqrt(1-(v/2c)^2)              and              E'_r = v/(2c) x B_phi / Sqrt(1-(v/2c)^2)              which means that in this system the current is larger and the wire is       not neutral but - as an ideal conductor - carries some surface charge       density D_r that, by definition, is the value of D_r at the surface.              How does this happen?              Lorentz contraction contracts the longitudinal measured distance of the       ions from rest at v=0 to v/2 using the simultaneity of the moving       clocks. By the same argument the distance of electrons is enlarged       because their velocity is reduced from v to v/2. So the net charge       density varies linearly with v.              This fundamental effect arises at velocities as small as the current       velocity of electrons of order 10^-11 lightseconds/second for a current       of 1 A at a density of some 10^27 m^-3.              The gigantic particle density of charges moving freely in metallic       conductors makes these macroscopic effects easily detectable and       measureable with high precision. This simple fact enabled Gau=DF, Faraday       Maxwell and Einstein to find the laws of electrodynamics.       These laws, applied by the gauge of the 4-momentum, imply Lorentz       invariance of all physical laws.              --              Roland Franzius              --- SoupGate-Win32 v1.05        * Origin: you cannot sedate... all the things you hate (1:229/2)    |
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