What would happen if you were to look in a mirror while you traveling at the speed of light? Would it be dark because the light can’t reach the mirror from your face? The answer might surprise you.
Speed of light
I’ve written about the speed of light before. In that post I explained the speed of light is both a constant a barrier. Nothing can travel faster than light, because of the Lorentz contraction. At the basis of this law of physics is the concept that the speed of light is constant, regardless of the frame of reference. This has some interesting consequences.
In this case, ‘frame of reference’ means ‘regardless of how fast the observer is traveling’. In other words, if you are standing still, light will move at 299,792,458 meters per second. If you are in a plane, flying at 600 kilometers per hour, light would still move at 299,792,458 meters per second. Even if you were in a super-powered rocket going 100,000,000 meters per second, light would still travel at 299,792,458 meters per second for you.
Okay, back to the mirror. If I were to travel at the speed of light, you might assume that the light from my face would never reach the mirror. The same way two cars won’t pass each other if they travel at the same speed. So the mirror would be black, right?
But no, the speed of light is constant, regardless of your frame of reference. This means that even if you were to travel at the speed of light, the light would still travel away from you, bounce of the mirror, and show you your reflection.
But wait… what if I was standing still, and was watching somebody going the speed of light and watching a mirror? For me standing still, the light would move at the speed of light, just like the person I’m watching. So from my frame of reference, standing still, the light would never reach the mirror. And that is in fact the case!
How the heck could that both be true? How could light both reach the mirror and not reach the mirror? Is physics broken? Are we talking Shrödinger’s mirror?
Enter time dilation
No, physics is not broken, it’s just pretty hard to wrap your head around. For high-speed objects, time contracts. The consequence of the speed of light being constant, regardless of frame of reference, is that time dilates according to the Lorentz equation.
In other words: when I move at great speeds, for an observer times seems to move slower.
Before I get back to the mirror example, let’s look at it at going 0.866 times the speed of light. Traveling at .866 times c (the speed of light). The Lorentz equation would then yield ~2 ( 1 divided by the square root of 1 minus a 0,866 times the speed of light squared, divided by light speed squared, which not coincidentally yields 2).
What does that mean? Well, if you were moving at .866 times the speed of light, you would see light move to the mirror and back at the regular speed of light. However, to an observer, you would be moving at half your normal speed, in slow motion. And that neatly solves the problem: to the observer light would still move at light speed, but because of the time dilation, the light would seem to travel to the mirror and back in twice the time.
You can extend this to the full light speed example. To you traveling at light speed, light would seems to move to the mirror and back at light speed. To the observer, you would actually be frozen: the closer you got to light speed, the slower time would go. And of course, actually going the speed of light is impossible: the Lorentz equation becomes 1/0.
The differently aged twins
A perhaps more practical example of this, is if you imagine twins. One twin stays put, and another twin travels around at .866 times the speed of light for a year. From the above equation we know they only seem to move at half speed from the observer.
So, to the twin staying put, the other twin has traveled two years, while from that other’s perspective they have only aged one year. They are no longer the same age. This sounds insane, but has been tested with atomic clocks traveling at high speeds.
Einstein’s theory of relativity has some weird implications, but before you start looking for this cure to aging: the fastest we’ve managed to make something travel consistently is Voyager I at 17,000 m/s, which is 0.005% of light speed. That’s not going to make a dent in your aging.
Still, good to know about this.