What would an object moving at 99.99% the speed of light see when looking at a stationary object?

I am currently in high school and we were just learning about the speed of light. I am fascinated by it but this question was bugging me for a while now. The system is as follows:

A stationary observer
A massless object moving close to the speed of light(or at the speed of light, whatever serves the explanation better) away from the observer.

What does the observer see and what does the object see when looking at the observer? Does the object "see" a static image of the observer as it is moving at the same speed as light that was reflected from the observer?

I can't really wrap my head around this

• From the point of view of the observer, the object is travelling at 99.99% the speed of light so it would swish past really fast. The length of that object along the direction of motion would be squeezed down by a factor of 70%. Apr 28, 2023 at 13:04
• @Prahar $\gamma\approx 70$. "Squeezed down by a factor of 70%" is confusing.
– JEB
Apr 28, 2023 at 14:48
• "Relativistic visualization", related: physics.stackexchange.com/q/43695/226902 physics.stackexchange.com/q/749130/226902 and links here physics.stackexchange.com/q/700355/226902 May 2, 2023 at 12:00
• The question is likely to be answered with opinions: e.g., one could discuss purely relativistic aspects of this problem, but one could also discuss how human eyes or equipment perceive an object flashing in front of them for about a nanosecond. May 2, 2023 at 12:00
• There should be no such "opinions"; what you see is determined only by light hitting the retina. May 2, 2023 at 12:12

A small correction: massless objects have to travel at the speed of light. Massive objects can't move at the speed of light. So let's consider two massive observers, moving at a speed of say 99% the speed of light.

As a second note, the situation is completely symmetric with respect to the two observers (considering they are both massive). So the effects that I describe below appear the same for both observers. Consider two observers Alice and Bob. If Alice, from here perspective, sees Bob's clock ticking slower, then Bob will see Alice's clock ticking slower from his perspective.

There are four interesting effects that happen because of special relativity

1. Length contraction
2. Terrel rotation
3. Doppler shift
4. Time dilation

Length Contraction

Length contraction means that objects that are moving close to the speed of light in a certain frame will be shorter in the direction of movement. As an example of how 'real' this effect is, consider the ladder paradox (or barn-pole paradox). Imagine a barn with width $$L$$ which has two doors, one in the front and one in the back. A ladder moving close the speed of light is moving towards the barn, whose doors are open. The length of the ladder is chosen such that at rest it wouldn't fit in the barn, but when it is moving close to the speed it will fit in the barn. Right when the ladder is inside the barn, the two doors are briefly closed and then opened again. Because the ladder is length contracted this is perfectly possible. The paradox arises when we switch to the frame of the ladder. In the frame of the ladder, the ladder is no longer length contracted so it has its original size. Even worse, the barn is now length contracted and so it is smaller! If the doors close, will the ladder fit inside? The answer is yes, it turns out that in the ladders frame the doors close at different times and so the ladder will fit inside. For more details see the wiki link I provided.

Terrel Rotation

Terrel rotation is a purely visual effect. It means that objects viewed from the side appear rotated. This effect occurs because light from the left of the object reaches your eyes earlier, just like light from the front of the object compared to the back. What you see when you are right in front of the object is a combination of light from the left of the object and from the (now contracted) front of the object, which appears as a rotation to you. Straight lines also appear curved, which is again purely visual.

Image credit: By Stigmatella aurantiaca - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=58075763

Doppler Shift

Doppler shift means that object moving towards you appear blue-shifted, while objects moving away from you appear red-shifted. This is similar to how the pitch of an ambulance changes as it moves towards/away from you, but now for photons.

Time Dilation

Time dilation means that the clocks of objects which are moving fast in your reference frame appear to slow down. Like length contraction, this is a very real effect. As an example of this consider muons generated in cosmic rays (1). When cosmic rays hit the upper atmosphere of earth, they sometimes generate muons, which are particles similar to electrons. They have a very short lifetime: they have a half-life of about 2 microseconds. When we don't take relativity into account, we would basically no muons to ever hit earth. But, because from our perspective the clocks of muons are slowed (about 7 times!), more muons reach the earths surface than we would initially expect. In fact, this agrees with what we see.

(1) Relativistic Effect of Cosmogenic Muons Efrain Covarrubias, B.S. Candidate, Department of Physics, California State University Stanislaus, 1 University Circle, Turlock, CA 95382

• Wow, that is fascinating. Just did a little research into Length Contraction and found out it was not just an optical illusion but a real physical effect which is even more fascinating! Apr 28, 2023 at 19:08
• Terrell "rotation" is just another piece of woolly reasoning that makes learning relativity so hard. Nothing rotates, you really are seeing (sic) the back of the object because you have gone past it, and aberration of light places its image in front of you. May 2, 2023 at 12:15
• I would also question the conceptual and physical validity of a "view" which has you varying your relative speed (from 0 to c) whilst holding separation constant! May 2, 2023 at 15:40

When there is motion, we have found no way of determining which part of the system is moving and which is not. On this basis, we postulate that all motion is relative.

Then, in this case, you cannot say "one thing is stationary, the other is moving". The observer sees an object moving at 99.99% of the speed of light relative to their "frame".

• What about the object moving away from the observer. I am more interested in that part. Would the object "see" the same image always as it travels at the same speed as light, would it see nothing or something completely different ? Apr 28, 2023 at 12:44
• The object sees the observer as moving away. The observer sees the object as moving away. There's no difference. Apr 28, 2023 at 12:52
• @darko6977 there are no frames moving at c, so the question is ill posed
– JEB
Apr 30, 2023 at 20:16

If the object reaches the %99.9 of the speed of light then it would see the observer as almost frozen. It is like the observer's time flows really slower than the object's time. However, it is completely relative to the reference point since it is the object in this scenario. Einstein's relative time theory starts from this point. At both sides the other side is moving away at %99.9 of the speed of light.