# Visual Effects of Special Relativity

1. Nov 7, 2015

### vJames

Hi all,

I've got a high school special relativity physics test coming up in a week and thought I should post here instead of under homework/coursework as I don't really have any set questions that I'm asking.

My problem is that I can explain the visual effects we learnt but not with enough depth and understanding that I think I will need for the test.

We looked at 4 visual effects mainly, these being: angular compression with the headlight effect, the Doppler effect and Terrell Rotation.

It's likely we will be required to identify and comment on photos from movies/animations etc. that illustrate different optical effects of special relativity.

Does anyone have any good sites or possibly their own explanation that can assist me with my understanding?

I'll try to give my explanation/interpretation of the visual effects and I would appreciate any feedback on mistakes or gaps in my knowledge.

My explanations-
Terrell Rotation:
At any given moment, all light being received by the observer has reached the observer at the same time. In order for all light from different sources to arrive at the same time and Einstein's second postulate of special relativity to hold true, the light would have left different sources at different times. Therefore, light from a source at a greater distance would have subsequently left the source earlier to arrive at the same time as light leaving a source at a shorter distance.

Objects that are viewed on an angle from an observer travelling at relativistic speeds appear to rotate as a time lag exists between light leaving the further points of the object and when light leaves the closer points of the object. As the object moves or is perceived to move at a relativistic speed, the light sources do not line up with the true shape of the object. This results in a rotated visual distortion of passing objects to the observer.

Doppler Effect:
The Doppler effect explains shifts in the observed wavelengths of light seen by an observer travelling at relativistic speeds. As an observer approaches a light source, the observed wavelength of light will be compressed and they will see the oncoming light with a higher frequency, causing a blue-shift towards the shorter wavelength side of the spectrum. Light from receding sources will undergo rarefaction as the waves are being emitted in the opposite direction of motion. To an observer, a red-shift is seen as the wavelength of light increases and the frequency decreases.

A side note: If the Doppler effect is an optical effect, am I correct in saying that a blue-shift does not mean that you are seeing more energetic light, but just a visual effect of light that appears to be at a higher frequency? In other words, does it mean that blue-shift light has more energy?

Angular Compression (This confuses me.)
I've seen the diagrams of angular compression and a few visual animations but unfortunately our teacher didn't cover the cause of it very clearly. I've heard the aberration of rain comparison but I just can't understand how rain that appears angled to an observer in motion is comparable to an observer at relativistic speeds that can see light from almost 360 degrees around him in his center field of vision.

I'm sorry if I've rambled on, but I've needed a bit of space to try and lay out my thoughts and think about what I know and don't know.

Thanks.

2. Nov 7, 2015

### m4r35n357

Try playing around with this or this. They won't necessarily help you directly to explain, but they will at least give you some good visuals to base your explanations on. While I'm here, I might as well plug my own rough videos on the subject . . . ;)

3. Nov 7, 2015

### bcrowell

Staff Emeritus
If your perceptions are correct, then your teacher's choice of topics to emphasize seems bizarre to me.

4. Nov 7, 2015

### m4r35n357

On reflection, the material seems very advanced for "high school" level.

5. Nov 7, 2015

### bcrowell

Staff Emeritus
If I had to guess, I would say that the teacher is doing what I do in my college freshman physics surveys. I introduce this material briefly, for fun, by showing one of the ANU animations, and I also use it for conceptual purposes. Conceptually:

- Many students believe that length contraction describes what we would actually see.

- Many students don't really absorb the fact that we can only gather information through signals that travel at a maximum speed of c.

If my guess is right, then the OP is misunderstanding the educational goals.

6. Nov 7, 2015

### m4r35n357

I agree on both points and your conclusion, but I think you and the teacher are right to do so. I find it increasingly frustrating that many introductory, popular, and even undergrad presentations use the word "see" in this wrong sense.

7. Nov 7, 2015

### Janus

Staff Emeritus
Here's a couple of animations that help to illustrate Doppler effect:
First a source at rest with respect the observers:

The light waves expand outward evenly from the source and each observer receives them at the same rate they are sent.

Now with the source moving with respect to the observers.

Each light wave still expands outward evenly from the point at which it was emitted, but now the source does not emit every wave from the same spot relative to the observers. With each successive wave he emits, he is closer to the blue observer and further from the Red. Thus the blue observer receives waves faster and the red slower. ( if we viewed this as if the observers were moving and the source stationary, the light waves would expand out as circles while the Blue observer moves towards the source and runs into them faster then the Red observer moving away.)
The blue shifted light would be more energetic as measured by the observer. Look at it this way. Assume the source sends a 2 sec pulse of light with an energy of X. The observer receives that pulse at twice the frequency, but that also means he receives it for half as long. For him to receive the same total energy as was sent, he has to measure the light as being twice as energetic. ( A Doppler shifted photon has just as much energy as a non-shifted photon of the same frequency.)
Rain falling straight down appears to be coming from an angle in front of you. But what if the rain was already coming in at a angle from in front before you started to drive. Would it not appear to come from even a sharper angle when you start driving?. What if the rain was at an angle from behind? Could you not now, by driving at the right speed have it appear to come straight down from your perspective, or at a shallower angle or even from ahead of you? But if the rain was coming from directly ahead, it doesn't change its angle of apparent direction. Each ray of light coming at you from different directions is going to have its apparent direction changed by your relative motion with respect to the source by different degrees, with the result that the light rays seem to crowd together in the direction of your relative motion.

Last edited by a moderator: May 5, 2017
8. Nov 7, 2015

9. Nov 7, 2015

### vJames

Thanks for the responses.

I think I understand what you guys are saying, but let me explain. It's my final term of high school in Australia and our final results that we receive upon exiting high-school are almost entirely decided and only drastic changes will effect our result. Our term is almost half the length that it normally is, our tests cover less content and they run for less time. In my opinion, our Head of Physics decided upon Special Relativity to give us all a taste of something completely different, interesting and exciting. It is quite a difficult topic and there are some students who are interested in physics who will not cope well with the test. It's a topic that we can't have practical lessons in understanding and ultimately, our knowledge is only in the most basic form of understanding.

Our topic is Special Relativity but besides the visual effects, we've looked at Einstein's Postulates, simultaneity, time dilation, length dilation and relativistic mass.

So if you're driving a car while it's raining, as your speed increases, you interpret vertical falling raindrops to be falling at an angle from the direction of your motion. I will try to apply that to a light source that is to the right of the car, rather than rain falling from above. If I drive a car with a regular speed of 60km/h past a stationary light on my right, the light will pass through my vision as it normally would. Travelling at relativistic speeds, I would look right out of the window and I would see a light blur past from left to right, but as my speed increases, it will appear that the source of the light is coming from the left when I look out the window, or in other words, the front. Likewise with a light source that I might see out of the passenger window behind me, it would appear that the light source is not at a 130 degree angle but rather at a 80 degree angle. All angles compress.

I've been using this site and it's slowly helping me to understand:
https://www.fourmilab.ch/cship/aberration.html

10. Nov 7, 2015

### mathman

One important misconception - Doppler shift occurs at any speed. It doesn't have to be at relativistic speed. Things moving toward us will be bluer and away will be redder - speed determines the magnitude of the shift.