Hi all, I have two questions about light in Special Relativity. (I'm going to pad these questions out with a few statements about my understanding of length contraction and time dilation, so you can see how I currently think about it and clear up any misconceptions if I've got the basic idea wrong. Sorry if that makes them a bit lengthy! I've put the questions themselves in bold if you want to skip to them).
- Due to length contraction, the length of a moving object shrinks in the direction of motion as measured by observers outside its reference frame. (The moving object experiences the contraction happening to everyone else - the distance it travels). At the speed of light, length contraction reduces all distances in the direction of motion to zero, so a beam of light would experience the Universe traveling past it at c as a flat sheet, with all distances in the direction of motion contracted to zero.
But what about the light from our frame of reference? It's moving at c relative to us - relative to all of us. This implies to me that an electromagnetic wave (or anything else like a gravitational wave) moving at c should be contracted to zero length in the direction of motion from our perspective. So how can light have a measurable wavelength? Shouldn't length contraction reduce its wavelength to zero for all observers?
Is the answer because the Lorentz transformation equation contracts rest lengths, and there's no such thing as a light wave at rest, so the concept of "rest length" doesn't apply?
- Due to time dilation, time slows down for a moving object - again, from the object's perspective, it's the rest of the world which slows down. If an object's moving at the speed of light, time dilation causes time to stop.
From our perspective, a beam of light takes 4.3 years of time to cover the 4.3 light years of distance from Alpha Centauri to Earth. Time on board the light beam itself comes to a halt, and as mentioned in question 1 the light (should?) shrink to zero length.
From the light's frame of reference, it's the rest of the world whizzing past it at c, and time should stop for everyone else. So the distance in the direction of motion is zero and the journey takes no time at all. As mentioned in question 1, the entire Universe appears to the light as a flat sheet, contracted to zero length along the direction of motion, so it takes no time at all to travel from Alpha Centauri to Earth. That makes sense.
But what happens when you look at light from a source reflected in a mirror? Light travels from the source to the mirror, then changes direction and bounces off into our eyes. That's not a problem from our point of view with light traveling through space and taking time to do so. But from the light's point of view, the distance between the source and mirror is zero in the direction of motion and takes no time at all, and then it reflects and changes direction, causing all distances to be shortened to zero from its perspective in a different direction. And then? How can "and then" or "change direction" make any sense for an entity that doesn't experience the passage of time? How can we talk about light changing direction (or changing anything, e.g. wavelength) if it doesn't experience time?
It can't make the journey from the source to the mirror and from the mirror to our eyes in one timeless moment, because it's traveling in two different directions before and after it reflects, and therefore the Universe should be flattened from the light's perspective in two different directions too. So it has to make two different journeys before and after reflection - "before" and "after" implying the passage of time. How does that work?