What's so weird about lightspeed, anyway?

Posted on Thu 16 January 2020 in Ramblings

Have you ever experienced that thing where you're in your car, stopped at a traffic light - you suddenly get the sensation that you're rolling backward, so you slam on your brake... but you already had your brake on, and you weren't moving! It was the car beside you rolling forward, but your brain misinterpreted it as your own - backwards - motion.

So, another mental image: imagine that you find yourself suddenly transported to a quiet, peaceful mountaintop. There's a monastery here, and Monks are quietly meditating. There is no sound, no wind, just silence and calm. You would probably say you're standing perfectly still.

Now, remembering that perception of stillness, think about the example in this tweet:

Take a kid & explain to him the true fact that the Sun is so far away that it would take a car going 100 mph a 100 years non-stop to get there. And then tell him to picture that same distance BEYOND the Sun! And then tell him that he and you were at that very spot 6 months ago.

-- @KevinPaulGregg

... your peaceful mountaintop really wasn't that still at all. In fact, it was hurtling through the galaxy at ... (cough) ... an astronomical rate. And on top of that, it's spinning wildly: at the equator, the earth's surface is moving at almost 1700km/h.

This speaks to the very basis of an important question: What is speed?

Over 400 years ago, Galileo Galilei's Principle of Relativity (not to be confused with Einstein's Theory of Relativity) emphasised that the concept of speed requires a frame of reference. That is, speed is always relative to something else. If you're driving at 100km/h, that speed is relative to the road under your tyres - but compared to a motorbike passing you at 120km/hr, you're moving backwards. Or ... from a different perspective, you're sitting still, and the motorbike is only travelling at 20km/hr. And no matter how fast you're driving, your steering wheel isn't really moving relative to you.

OK I think I've explained that point to death now. Speed is always measured between two points in space. But here's the interesting bit.

Maxwell's Equations, published in the 1860's, can be used to calculate the speed of light - exactly 299,793,458 metres per second in a vacuum. But there's something missing: that all-important frame of reference; the OTHER point in space to measure the speed against. What's going on there? Lots of theories and experiments were floated to figure out where this missing factor was, but everything was shown to be incorrect... that is, until Einstein looked at the problem.

Einstein - in typical Einstein fashion - simply looked and said, "if the speed of light doesn't have a frame of reference, that must mean that the speed of light is the same in any frame of reference". That is, if you shine a torch forward, the light is travelling away from you at 300,000km/s. If you keep the torch on and hop into a speeding car, the light is still travelling away from you at 300,000km/s. If you turn around and point the torch out the rear window, the light is travelling away from you at 300,000km/s... and towards someone else, still at 300,000km/s. So what's happened to the speed of your car??

Okay, so the speed of light is weird. But the weirdest part is what happens when you look at what that means. Let's go back to my earlier question -- what is speed? In one way, this is easy: speed is simply the distance travelled over a certain duration. But take a closer look at what those words mean: distance refers to space; duration refers to time. So, speed is the rate of movement through spacetime. Fine, semantics, whatever.

But these semantics matter. Because what we're seeing here isn't just light being weird: now we're actually seeing space and time moving weirdly - dancing around themselves in a big conspiracy to force the speed of light to be 300,000km/s, no matter what your frame of reference is.

It's time to wrap up this episode - mostly because I've reached the limits of my knowledge. Earlier in this article, I asked "what's happened to the speed of your car" and, frankly, I have no idea. When it comes to the warping of spacetime I get really confused. If you're travelling in a train at 200,000km/s, and point a powerful laser in the direction of travel, that laser's light is going 300,000km/s relative to you. But ... then we get silly business, like Lorentz contraction squishing the length in the direction of travel, time dilation starts messing with things, and we get space bending. So to the outside observer, the laser is going ... 300,000km/s. ¯\_(ツ)_/¯

"People assume that time is a strict progression of cause to effect, but actually — from a non-linear, non-subjective viewpoint — it's more like a big ball of wibbly-wobbly... timey-wimey... stuff."

-- The Tenth Doctor, Doctor Who, "Blink"