# Penrose-Terrell rotation

1. Apr 13, 2004

### arildno

I have a couple of questions concerning P-T rotation.
1. From what I've seen, the basic message seems to be that the Fitz-Gerald contraction cannot be directly observed in practice, i.e. in the "world picture"
Is this correct?
2. Any good book treating this topic?

2. Apr 13, 2004

### turin

Can you please explain what is the P-T rotation, or at least where you saw it? I think I've heard of it, but I can't remember if what I'm thinking about was called P-T rotation or something else.

3. Apr 14, 2004

### arildno

This is something I found in the Appendix of McComb, "Dynamics and Relativity",
(Oxf. U. Pr., 1999);
the original articles are:
Penrose, R. (Proc. Camb. Phil. Soc. 55, 137-139 (1958))
Terrell, J. (Phys. Rev. 116, 1041-1045 (1959))

According to McComb, (if I have understood him..), a "world picture" is formed by light signals recieved simultaneously.
(For example, the light signals hitting a photographic plate at the same time will be the information used to construct a photograph (2-D picture of the world))

Since the speed of light is finite, light signals emitted simultaneously in a moving object's rest frame, will not, in general, be recieved simultaneously.
(Light signals from the furthest parts of the object will come later than the signals from the closest parts of the body (measured from the observer)).

Hence, the object formed on basis of recieved light signals (i.e. the photograph) will consist of information sent out from at a variety of times and positions, it is not an exact representation of the object as it exists in the observer's frame of reference (or in its own rest frame).

Apparently, Terrell showed that this distortion exactly cancels out the length contraction predicted by special relativity; that is, the Fitz-Gerald contraction can never be seen or photographed directly.
(Rather fascinating, or what?)

This is at least how I understand it; I'd like to be corrected if I'm wrong.

4. Apr 14, 2004

### turin

arildno,
That is what I thought you were talking about. I never investigated this to personally determine the result for myself, but this phenomenon is accepted, or at least, I have seen it mentioned in various sources. There is a literal rotation of the image, and that's why it's called a rotation. There is no photographed contraction. If I'm not mistaken, though, there is another distortion of the image. From your description, it sounds like you have the same level of understanding that I do of the phenomenon, so affirmation is the only help I can give you.

5. Apr 15, 2004

### arildno

Great!
I have a classical (fluid) mechanics background, so whenever I venture into the realms of relativity, a dizziness falls upon me..

I have one particular question that bugs me about P-T rotation:
I assumed that P-T rotation occurs for luminous bodies, i.e light signals sent out simultaneously in the object's rest frame will not arrive simultaneously to the photographing device.

However, I'm not sure..
If the region in the observer's frame occupied by the object sends out light signals simultaneously (with respect to obs. frame of ref.), that set of light signals will not arrive sim. to the phot. dev. either (due to differences in distances and the finite speed of light)

I guess the solution is to identify the set of (light signal) events which will happen to strike the photographing at the same time in the device's rest frame, but I don't know...

6. Apr 15, 2004

### turin

I think I understand your uneasiness, and so I think that your self-resolution is appropriate. This is not flash photography. You are assuming that the object is constantly illuminated. Consider at least two (related) problems this phenomenon presents for flash photography. Let's assume that the shutter is extremely fast, so fast, that you can approximate it as instantaneous. This will require that every point on the film was exposed simultaneously in the camera's rest frame. Now, consider the need for a flash to illuminate the subject.

Problem #1: How long the shutter waits to operate should depend on the distance to the object.

Problem #2: A maximum of only one instant of reflected light will pass through the shutter, however a range of time is needed to capture the reflected light from the object if it has point that are at different distances from the camera.

In other words, flash photography cannot capture a faithful image of an object moving at relativistic speeds. The object must be illuminated independent of the photography process, and the illumination must be constant and steady for the duration.

7. May 10, 2004

### RMDumse

For a while, I had a web link where someone had put up an image of Terrell's original paper. Too bad it was taken down, although it probably was a copyright infringement on Phys. Rev.

Anyway, while popularly often presented in the 1960's - 80's mention of Penrose-Terrell rotation has been largely abandoned as a topic of discussion because it is an "optical effect" and lead to some false considerations of the phenomina being a real rotation.

Basically, the effect can be described like this. Take a book, and place it in front of you with the cover in normal orientation so you can see the title. Now imagine this book passing you at very high relativistic speed. From right to left, or along the x axis for simplicity (but in the negative direction). What would you "see" of the cover? It would appear relativistically foreshortened. The foreshortening happens only in the direction of motion. The book would appear very short, but of normal height.

Now think of the back edge of the book, the exposed pages ends. Imagine what happens to a light emitted from the edge of from the edge last page in the book at the back cover. It will take time to propogate the distance from the back cover to the front cover. When it gets to where the front cover was, the front cover will not longer be there, but a distance further along the x axis. How far? Well, if the book is travelling (almost) the speed of light, and the light coming from the back page is travelling at the speed of light, the edge of the last page appears behind the cover by the width of the book.

Now the same is true for each page edge. It also appears to be behind the cover by the distance back from the cover. So the first page appears (to your eye) to be right being the very foreshortened cover, and the next page just behind that, and so on, until the last page edge appears just before the back cover.

So if you can imagine that, you can imagine what a highly relativistic book passing you would look like. Even though it's cover were toward you, what you'd see was an image that looked like the back of the book was turned toward you. In short, the book would "look" rotated.

Does that help?

8. May 11, 2004

### arildno

Yes it does, thank you!

My own interest in this topic was actually aroused in the fact that P-T rotation "flies in the face" of a popularized view going like this:
"Imagine that the speed of light was much smaller than it is"
The (popular) view then continues and states that we would "see" Fitz-Gerald contractions all around us (which we wouldn't, due to P-T rotations).

9. May 11, 2004

### robphy

Last edited by a moderator: May 1, 2017
10. Jan 21, 2010

### yuiop

That is not entirely true either. A cylindrical rod with a length much longer than its circular cross section and moving parallel to its long axis, would look (to an eye or camera) length contracted as it passed nearby you.

11. Jan 22, 2010

### clem

I don't know how you came across such an old thread, but I have to reply.
The rod will look length contracted in the same way a rod (having only one dimension) would look length contracted if it were rotated in space.