*Post by Luigi Fortunati**Post by wugi**Post by Luigi Fortunati*https://www.geogebra.org/m/dzuyjaz6

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

understanding.

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.

- 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.

*Post by wugi*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

(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.

See

https://en.wikipedia.org/wiki/Terrell_rotation

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.

-- jt]]

Thank you. About Terrell rotation, if I remember correctly it would seem

to alledge that length contraction is part of the "seeing" effects, in

that the object, together with its backside becoming visible, would seem

rotated, and total length "seen" would be preserved. This is messing up

what I call "Lorentz" data (measuring, backcalculating: length

contraction) with "Einstein" data (*seeing, watching* , the back side

becoming visible).

But it is partly true. From my webside which I mentioned in another

reply, let's see some examples here.

How would a frontline that's approaching an observer at relativistic

speed be perceived? Here:

Loading Image...(fat dot = observer, dotted line = actual 'true' position, rightmost

curve = as seen 'now', others = previous positions.)

Same case, after having past by the observer:

Loading Image...(doppler 'blue shift' at approach, 'red shift' at regression)

A series of frontlines combined into a "squadron" of squares:

Loading Image...(dots = actual position of the squad)

Notice the following "seeing/watching" effects:

At approach, a "length dilation" is seen, not a contraction!

At regression, an extra length contraction is seen.

This is due to the fact that light needs the longest time to reach the

observer from the farmost parts of the moving object.

The squares appear more or less distorted, according to position and

distance from observer. This is analogous to, and more general than,

what Terrell rotation tries to tell us.

But observe this! ->

The true *Lorentz length contraction can be seen*, but only

perpendicular to the motion, and far enough away: in our picture, along

the vertical through the observer point, at the far distances up and

down (compare with dot positions).

I'd promised some other links to the effects of 'seeing' relativistic

motion. Here are some:

https://www.physicsforums.com/threads/terrell-revisited-the-invisibility-of-the-lorentz-contraction.520875/page-4

(with nice animations by J. Doolin)

https://www.tempolimit-lichtgeschwindigkeit.de/ueberblick/1

(with links to more videos)

https://www.spacetimetravel.org/tompkins/tompkins.pdf

(with other cases)

https://timms.uni-tuebingen.de/tp/UT_20040806_001_sommeruni2004_0001

(a lecture with animation videos of previous cases)

--

guido wugi