# Terrell-Penrose Effect

1. Jun 19, 2006

### clj4

Hi,

I have found this website that shows some fantastic animations of objects flying by an observer at near c speeds:

The reference image for the wheel located in the observer's frame doesn't look quite right, I haven't done the calculations, it might be just my misconception as to how it should look, Enjoy!

2. Jun 21, 2006

### meemoe_uk

The first bit I don't understand is...
The spokes on the stationary but spinning ( green wheel ) are affected by space-contraction, but the rims aren't. Shouldn't the rims and therefore the whole wheel contort into maybe an ellipse?
Looks wrong to me.

3. Jun 21, 2006

### clj4

In my mind that is not the problem. After all , the wheel located in the observer frame should not get distorted at all. Only the wheel whose center is in frames in relative motion should appear distorted. What bothers me is that, in one animation, the spokes of the wheel located in the obsever frame appear distorted while i the other animations they are not. I do not think that they should appear distorted at all.

4. Jun 22, 2006

### meemoe_uk

Yes, but it's spinning! It's subcomponents AREN'T in the observers frame. Thus the spokes should contract, which they do. But not the rims? Why not?
It quite a central question to SR. If, in the observers frame, a wheel spins, by space contraction, maybe the whole wheel should shrink!

5. Jun 22, 2006

### pervect

Staff Emeritus
Don't forget that the simulations include light travel time as well as the Lorentz contraction.

6. Jun 22, 2006

### Hans de Vries

I think its OK after looking at it for a while. The movies indeed take also
light travel time into account as well as non-simultaneity and Lorentz
contraction. To see the effects without travel time look at this angular
momentum 8 wavefunction which I did and compare it to the 8 spokes
of the wheels:

http://chip-architect.com/physics/spin_8_from_near_c.jpg

The left image is stationary with respect to the observer while the
right one is moving horizontal at 0.8 c. The "spokes" show a similar
effect as in the blue wheel in movie 2.

This effect where there are more spokes at one side of the wheel
as on the other is the entirely the result of non-simultaneity.
The effect is seen in the moving blue wheel in the second movie
which is correctly Lorentz contacted in the direction of motion.

The second movie is the one which is least distorted by the light
travel times since it looks at the scene straight from the front

Now concentrate at the green wheel which rotates but doesn't
move. Looking from the front, (movie 2) It is not so much dis-
torted since the light travel times from the right and left side
of the wheel aren't that much different.

That's very different in movies 1 and 3 were we look at the scene
from the left and the right. The different travel times from the
left side and right side of the green wheel to the observer gives
exactly the same effect as non-simultaneity.

Note that in movie 1 the green wheel has more spokes at the bottom
while in movie 3 it has more spikes at the top. This is just like it
should be!

Looking at the blue wheel in movie 1 we see that the effects of
non-simultaneity and different travel times tend to cancel each other
while the effects add up in movie 3. This again is like it should be.

Note that there is a little bit of top-bottum distortion in all movies
because the camera is located a bit higher as the centers of the wheels.
This again is caused by the difference in light travel times.

This is why the blue wheel is tilded over a bit in all movies. It takes
more time for the light to travel from the bottom of the wheel: You
see the bottom of the wheel in an older position than the top-part
of the wheel.

Regards, Hans

Last edited: Jun 22, 2006
7. Jun 22, 2006

### pervect

Staff Emeritus
I haven't studied these particular animations much, but Terrell rotation is a subject with quite a bit of literature on it, including a sci.physics.faq entry.

One of the more notable links on the topic is Searle's visualizations, which I have edited to put first for their "gee-whiz" value, on the idea that if anyone clicks on a link, it'll probably be the first link.

http://www.anu.edu.au/Physics/Searle/

Other notable links on Terrell rotation include the sci.physics.faq entry

http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html

(be warned CH's appendix gets to be technical for "overview" purposes).

And some past discussion on PF, which includes a link to Searle's visualizations mentioned earlier

https://www.physicsforums.com/archive/index.php/t-19860.html

(I'm pretty sure I recall other discussions here on PF on the topic as well).

Last edited: Jun 22, 2006