From: tjroberts137@sbcglobal.net   
      
   On 10/1/17 10/1/17   12:07 PM, Nicolaas Vroom wrote:   
   > On Monday, 25 September 2017 01:59:52 UTC+2, Tom Roberts  wrote:   
   >> On 9/24/17 9/24/17   3:56 PM, Phillip Helbig (undress to reply) wrote:   
   >>> [...] Length contraction here is obviously an illusion.   
   >>   
   >> Not so. An "illusion" could not have physical consequences, but   
   >> "length contraction" does. For instance (1) the magnetic forces from   
   >> current-carrying wires, (2) the correspondence between fixed-target and   
   >> intersecting-beam cross-sections, and (3) the frequency/wavelength of   
   >> free-electron lasers.   
   >   
   > Is there "length contraction" involved in these 3 examples?   
   > If yes then please explain one.   
      
   (1) For a wire carrying a current involving moving electrons, in the rest frame   
   of the wire it remains electrically neutral (the power supply generating the   
   current ensures this is so). So a nearby charged particle at rest in that frame   
   experiences no EM force from the wire and its current. But a charged particle   
   moving parallel to the wire at the same speed as the electrons sees the ions of   
   the wire (i.e. the atomic nuclei) as "length contracted", and the electrons as   
   not, so in its frame there is a net positive charge on the wire, and it feels   
   an   
   EM force. In the wire rest frame we call this "magnetic force", while in the   
   moving frame it is "electrostatic force". This is much more general that my   
   simple description, and when worked out numerically it is correct; I believe   
   that Perkins's book on E&M goes into this in detail.   
      
   (2) scattering an unpolarized particle beam from an unpolarized target is   
   cylindrically symmetric, and we measure the differential cross-section as a   
   function of polar angle. For a fixed-target experiment the target is at rest in   
   the lab; for a colliding-beam experiment the center-of-mass is at rest in the   
   lab. To reconcile these two measurements at a given center-of-mass energy, one   
   must invoke "length contraction".   
      
   (3) a free-electron laser consists of an energetic electron beam traveling   
   through a magnetic field that alternates transverse directions in space,   
   typically every 10-20 cm over a length of several meters (the magnets are at   
   rest in the lab). As the beam is "wiggled" by the magnetic field, it oscillates   
   with the frequency it sees the field alternate -- this generates radiation of   
   that frequency, and for quantum reasons this can be a laser. In the lab this   
   radiation is measured, and to account for the observed frequency, that 10-20 cm   
   alternation must be reduced by the "length contraction" formula in the beam   
   rest   
   frame.   
      
   Tom Roberts   
      
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