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  1. L

    Invariance of the speed of light

    OK, that was trivial...I knew it must be easy…if one arranges things the right way. I too was using the pythagorean theorem in order to get rid of some terms. But at the same time I was computing the difference u^2_x+u^2_y-c^2 to get 0…and yeah…somehow fell asleep. Many thanks, George.
  2. L

    Invariance of the speed of light

    Oh yes, that sounds much more promising! I'll try this now…thanks in advance! :-)
  3. L

    Invariance of the speed of light

    If you mean using the angles in u_x=u \cos \theta,\, u_y=u \sin \theta, \, u'_x=u' \cos \theta',\, u'_y=u' \sin \theta' …does it really help? I tried to plug them in, too…but same thing…the computation gets lengthier and seems to be getting nowhere. There is actually no more on that page, except...
  4. L

    Invariance of the speed of light

    Hello! Consider the law of addition of velocities for a particle moving in the x-y plane: u_x=\frac{u'_x+v}{1+u'_xv/c^2},\, u_y=\frac{u'_y}{\gamma(1+u'_xv/c^2)} In the book by Szekeres on mathematical physics on p.238 it is said that if u'=c, then it follows from the above formulae that...
  5. L

    The Structure of Galilean Space

    I think I got now what the message is. The message is simply that the spatial distance is not a well-defined function on non-simultaneous events, i.e. not independent under the Galilean transforms, for that is what we wish it to be -- the (classical) frame reference change must preserve...
  6. L

    The Structure of Galilean Space

    At this stage I actually meant nothing, except that I agreed that what Bill said was in fact exactly what Szekeres said by example, and I pointed to my previous post.
  7. L

    The Structure of Galilean Space

    Yes, as a matter of fact I recognized the example in his formulation. But the problem is that I saw a slightly different thing in it.
  8. L

    The Structure of Galilean Space

    OK. Now I think that I somehow didn't get the point. I thought the point is that two non-simultaneous events can be brought by a suitable choice of Galiliean frame to simultaneity, i.e. simply by time shift (adding a constant), so that their distance becomes purely spatial distance. You...
  9. L

    The Structure of Galilean Space

    A Galilean transformation is defined as a transformation that preserves the structure of Galilean space, namely: 1. time intervals; 2. spatial distances between any two simultaneous events; 3. rectilinear motions. Can anyone give a short argument for the fact that only measuring the...
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