> Your simulation may be more or less correct, but it doesn't help much in
> one's understanding it correctly, it even may induce erroneous
> First, it should be made clear in which direction the moving observer is
> supposed to move. My first impression was that he should move vertically
> which didn't make sense.
In my simulation:
- observer B moves (instantaneously) to the right, i.e. towards body C
- observer A is stationary with respect to body C
- Observers A and B, at time t=0 of both, share the same space and the same time
- The time of C in the reference of A is different from the time of C in the reference of B.
> Furthermore, it doesn't help to superpose both 'circles' in a same
> graph, which suggests a same reference frame, where in fact different
> reference frames are superposed. Now it gives the impression that "there
> are two circles in space", one for each observer.
> The fact is that there is only one object, but that both observers "fill
> in" the space towards it, and the time values, differently! In order to
> respect the singleness of the object, your method is not a very proper
> one. There are better alternatives. One is, to make two graphs, each
> with its reference frame. Another one, to display only one object, say
> in the rest system, and superpose the different reference frame of the
> moving observer upon that, showing the length contraction, and possibly,
> time dilation effects.
> Lastly, this is not what the observers are going to *see*! Einstein's
> Lorentz equations don't describe objects *as seen*, they describe
> *measured*, backcalculated, positions of simultaneity. What the
> observers are going to see, is what the light photons are telling them,
> as they arrive at each observer, come from the different parts of the
> distant object. In other words, they include Doppler distortions!
Ok, let's talk about what happens when photons of light arrive on the
photographic film (the observer) and form the image.
Are Einstein's Lorentz equations able to predict whether the body C will
appear perfectly spherical or whether it will be squashed in the
direction of motion?
[[Mod. note -- Yes.
As wugi noted, (1) and (2) below are very different questions, with
very different answers:
(1) What are the coordinate positions of the objects measured (i.e.,
"backcalculated", as wugi quite correctly terms it) in different
(inertial) reference frames, as determined by the Lorenz transformation?
(2) What image(s) would taken by a (ideal) camera located at a certain
point given (1) together with differential light-travel-time effects
(i.e., the Lampa-Penrose-Terrell effect, often just called the Terrell
effect or Terrell rotation)?
(1) is what's usually meant when we ask what an observer "measures" in
special relativity. (2) is what you (Luigi) have now asked about.
for a nice introduction to (2). Reference 4 in that Wikipedia article
(written by Victor Weisskopf!) is a very clear exposition of the effect,
explicitly working out the Terrell rotation for a moving cube and then
generalizing it to an arbitrary-shaped body. The original 1960 paper is
(still) behind a paywall :(, but as of a few minutes ago google scholar
finds a free copy.