SR Light Wavelength & Direction: Questions Explained

[Amaterasu21]

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).

1. 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?
2. 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?

Hope you guys can clear this up for me! (Not sure if the "intermediate" prefix is right btw, this seems like a fairly basic question which I considered tagging with "beginner" but I've never heard of Special Relativity being covered in high schools before... maybe this is a beginning first year undergrad question?)

 

[PeroK]

The fundamental issue is that SR and, in particular, the equations for length contraction and time dilation are not defined for light (or anything traveling at or beyond the speed of light). These phenomena apply to sub-light velocities only.

The examples of "all lengths being 0 at the speed of light" or "time stopping at the speed of light" are invalid extrapolations of the equations. These are rife in popular science books and videos but are not found in undergraduate textbooks on SR.

 

[Ibix]

Just to add to what @PeroK said, the length contraction and time dilation formulae relate the lengths of rulers and tick rates of clocks in an inertial frame in which they are moving to their lengths and rates in the inertial frame where they are at rest. But a rest frame for light is a contraction in terms: light travels at c in all inertial frames. It cannot travel at c and zero at the same time. So attempting to apply time dilation and length contraction formulae to light is nonsensical, which is why the resulting deductions are also nonsensical.

 

[Amaterasu21]

Ah, thanks for clarifying. That makes more sense now! I have read textbooks on special relativity where "lengths become zero and time stops for light" wasn't mentioned, but I've popular books too where it was hinted at, and this video which explicitly states it:

It's a shame because that channel's usually very good for a popular physics channel, going into a lot more mathematical details (exploring tensors and Einstein's field equations in General Relativity for example, or going into the details of Schrodinger's equation in quantum mechanics) than popular science videos usually do. But they have been wrong when it comes to relativity before, especially in their explanation of the twin paradox. Thanks!

 

[sweet springs]

You seem to have cleared the case. Here is just my personal post script.
Your question stimulate me to think that lights have no rest frame so no "home" where they hold their own characteristics. For example the same light is infrared for one IFR but gammma ray for anothere IFR. I know but still feel it wonder that photon show its nature i.e. wavelength and freauency that are measured in space and time, to each IFR.

A group of lights or photons have their rest frame except the case that they are all moving in the same direction. A special IFR called center of mass system can be chosen to describe the character or mass of the group.

 

[Mister T]

Ah, thanks for clarifying. That makes more sense now! I have read textbooks on special relativity where "lengths become zero and time stops for light" wasn't mentioned, but I've popular books too where it was hinted at, and this video which explicitly states it:

The claim made in the video that light's point of view is equivalent to other points of view is simply not valid, and it's definitely not part of Einstein's theory. His theory is about time dilation and length contraction, and it's founded on a principle that very much distinguishes between the speed of light and other speeds, they are about as far from equivalent to each other as I can imagine. So, the video uses length contraction and time dilation to disprove the foundation upon which length contraction and time dilation are founded.

As soon as you utter the phrase "from light's point of view" you have created a contradiction.

For example, in the video they say it takes no time for light to move from A to B because the distance from A to B is zero, and that light's point of view is equivalent to Sarah's. If that's true then from light's point of view Sarah moves at speed $c$. But they point out (correctly) in the video that nothing with mass can travel at speed $c$. Sarah may be trim, but her mass is not zero.

 

[PeterDonis]

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.

No, it wouldn't. The length contraction formula is undefined for $v = c$; that means there is no such thing as what "a beam of light would experience" as you are trying to use that concept here. The concept doesn't make sense.

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.

Same answer as above.

Others have already weighed in on similar lines to the above, but it's worth pointing out that we already have a FAQ on this as well:

https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/