I'm going to be comparing two animations of special relativity from spacetimetravel.org. The first is a 2-dimensional simulation of lines moving toward and away from the observer.
The second will be a three-dimensional simulation of dice moving toward the observer.
Now, both of these animations show a set of oncoming objects as they travel along at relativistic speeds. The rods over on the right are receding or approching at 70% of the speed of light, whereas the dice over on the left are approaching at 90% of the speed of light.
Now, my eye seems to detect the motion of the line on the right as entirely straight-line motion, whereas on the left, mye eye detects the motion of the edges of the dice as a rotationg motion.When I play the straight-line motion, the oncoming lines seem to be stretched by the same amount as the distance between them.
Another phenomenon that I'm seeing in the dice is that while the distance between individual dice seems to be stretched, the actual dice themselved don't appear to be stretched.
The other is that the original organization of the dice had around two or three dice spaces between them, so it shouldn't be a surprise that they are further apart than the lines in the diagram on the right.
Now, how can I say for sure that the oncoming lines are stretched by the same amount as the distance between them? Let's pause these videos at an opportune time.
One thing I can say for sure about the blue lines on the right. They definitely appear to maintain linearity.. They are lined up with the checker grid in the picture, and stay lined up with the checker-grid in the picture.
On the other hand, my eye tells me that the edges of the dice are not lined up properly. But is that real, or optical illusion?
What I'm testing is the edges on the bottom side and top side of the one-face of the die. To see if they are actually aligned, even though it looks like they are not.
So I have two observations to make here. One is that it does indeed appear that the top and bottom sides of the 1-face actually do appear to keep to the straight line paths.
One other point I probably ought to make is that this checkerboard pattern shouldn't quite remain straight as it passes underfoot.
I decided to look up panoramic views in the google to see if I couldn't make this point clearly. Here's a panoramic view of a fence near St. Bartholomae, I found on wikimedia commons.
You can see that this fence seems to be angled upwards to the right, then it is flat in the middle, then it goes downward on the top. Even though that is a straight fence, it does not appear from the perspective of my eye to be a straight line.
If I could do a similar panoramic view with the die face, I should expect when the 1-face becomes perpendicular to the observer, If the angles from the observer were equal. Then this would be the Lorentz-Contracted length of the 1-face.
We need some additional structure in the dice video to represent some additional structure that is conveyed by the
Additional structure of straight power lines, or a straight fence would provide the extra detail to the environment to see the Lorentz Contraction at the point of the dice-face's nearest approach to the observer.
Let's look at one other detail, by pausing these two videos at an appropriate time.
What I want to see is the apparent elongation of the parallel lines. Here, comparing the back-to-front length of the oncoming dash to the back-to-front length of the stationary dash.
In the dice video, these two lines (planes) simply don't feel parallel,
Okay. I really can't tell at all, but what I would want is to have the same kind of stationary structure in the background in the dice-video so we can easily tell what path the edges of the 1-face are taking.
I think if you brought the 1-face around until top and bottom edge of the 1-face of the die were parallel, and the velocity vector was perpendicular to our point-of-view vector, you could measure Lorentz Contraction across the face of the die.
But you'd need that stationary structure in place--a fence, or power-lines to help identify the more familiar panoramic distortions that are easy to recognize, but maybe a bit hard to account for.
http://www.spacetimetravel.org/bewegung/bewegung3.html
http://www.spacetimetravel.org/tompkins/tompkins.html
http://commons.wikimedia.org/wiki/File:St_Bartholomae_panoramic_view.jpg