I agreed the rod was shortened in terms of simultaneous measurements of both ends in the observer's rest frame, so presumably you are just talking about visual appearance here? Keep in mind that what you see visually at any given moment is a sum of events on the surface of your past light cone at that moment, events which can have occurred at different moments in your rest frame. In the case of a rod moving towards you, the light you are seeing from the back end must have been emitted at an earlier time (when the back end was further away) then the light you are seeing from the front end, assuming we measure the time both ends emitted those photons in your own rest frame.
A little numerical example: suppose the rod has a rest length of 10 light-seconds, but it is moving along your x-axis at 0.6c in your frame so it has a contracted length of 8 light-seconds in your frame. And suppose at a time coordinate of t=0 seconds, the back end of the rod was at x=100 light-seconds while the front was at x=92 light-seconds. At that moment, the back end emitted a photon which reached your position at the origin 100 seconds later, at t=100 seconds. Meanwhile at t=20 seconds, since the front of the rod is moving towards you at 0.6c it will have reached a position of x = 92 - 0.6*20 = 80 light-seconds. At that moment the front end emits a photon which naturally takes 80 seconds to reach you, so it also reaches your eyes at t=100 seconds. Thus at t=100 seconds you are seeing an image of the back end of the rod aligned with the x=100 light-seconds mark on your ruler, and an image of the front end aligned with the x=80 light-seconds mark on your ruler, meaning that visually the rod appears to be 20 light-seconds long, which is elongated compared to its rest length of 10 light-seconds. On Sat, Sep 7, 2024 at 10:50 PM Alan Grayson <[email protected]> wrote: > AFAICT, the approaching rod is shortened. Possibly I don't understand your > argument, but it directly contradicts my understanding of SR. AG > > On Saturday, September 7, 2024 at 7:46:16 PM UTC-6 Jesse Mazer wrote: > >> Again, are you talking about visual contraction, or contraction in terms >> of simultaneous measurements of both ends in your reference frame? If the >> former the approaching rod appears elongated rather than contracted (it >> says so on the Terrell rotation page), if the latter then the rod is >> contracted by the gamma factor regardless of whether it's moving towards >> you or away from you (assuming that either way its velocity vector is >> parallel to the line between the two ends). >> >> On Sat, Sep 7, 2024 at 6:41 PM Alan Grayson <[email protected]> wrote: >> >>> It's the *approaching *rod that is contracted, say the distance to the >>> Andromeda galaxy as the observer is approaching it. But what if the >>> observer is receding from Andromeda? How is the problem modeled in this >>> situation, where the observer doesn't see the ends of some rod? Your second >>> link might have the solution. AG >>> >>> On Saturday, September 7, 2024 at 4:18:24 PM UTC-6 Jesse Mazer wrote: >>> >>>> Answer depends on whether you are talking about how the rod looks >>>> visually to them (in which case a receding rod appears contracted but an >>>> approaching rod appears elongated, see >>>> https://en.wikipedia.org/wiki/Terrell_rotation ) or if you are talking >>>> about how they assign coordinates to the rod in their own rest frame, using >>>> a system of rulers and clocks which are at rest and synchronized relative >>>> to themselves (like in the illustration at >>>> https://faraday.physics.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring >>>> with synchronization based on the procedure described at >>>> https://en.wikipedia.org/wiki/Einstein_synchronisation ), which was >>>> what Einstein was concerned with in his original SR paper. In terms of the >>>> latter, if they measure the back end and front end of the moving rod >>>> simultaneously using their own clocks and rulers, they will always find the >>>> distance to be shrunk by the gamma factor regardless of whether it's moving >>>> towards or away from them. >>>> >>>> On Sat, Sep 7, 2024 at 3:25 AM Alan Grayson <[email protected]> >>>> wrote: >>>> >>>>> For an observer moving toward a rod of some fixed length in a rest >>>>> frame, the rod shrinks, but what happens when the observer is moving >>>>> *away* from the rod, given that the gamma factor remains unchanged? >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "Everything List" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/everything-list/02981fe3-8c92-41e4-aa3c-98b57be89e54n%40googlegroups.com >>>>> <https://groups.google.com/d/msgid/everything-list/02981fe3-8c92-41e4-aa3c-98b57be89e54n%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>> . >>>>> >>>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> >> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/9b485ffe-d1d6-4338-8775-5db979608277n%40googlegroups.com >>> <https://groups.google.com/d/msgid/everything-list/9b485ffe-d1d6-4338-8775-5db979608277n%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/42f90ed5-15e9-43ba-a9e4-151d8b2f3ad9n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/42f90ed5-15e9-43ba-a9e4-151d8b2f3ad9n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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