Relativity

Image credit to NASA

I thought I’d just blather away today about something that I think a lot of people find fun and interesting. I’ll talk a little about physics, but I promise, no equations, and we aren’t sitting down in the classroom right now.

I think that just about everyone has some idea who Albert Einstein is, and I think most people are familiar with relativity in some way. The concepts of relativity are really fun to just kind of navel gaze about.

Einstein put forth two main concepts of relativity. The first was special relativity, and the second was general relativity. Special relativity gets its name from dealing with more specific situations (moving at constant velocity). General relativity gets its name from being the overarching theory of relativity, the one that fully encompases our knowledge of relativity in the Universe.

The first really interesting thing about relativity is that there is a speed limit on the universe. We generally call it the “speed of light”, but it doesn’t actually have anything to do with light. The speed of light is actually only the speed that light travels when it moves through completely empty space. When light moves through stuff, it slows down. Even when it moves through air. There are, in fact, some interesting effects that happen when particles move faster than light can move through some material. Yes, that actually happens.

What we call the speed of light is actually the speed limit of the Universe. Nothing is allowed to travel faster than this speed. It just happens that when light is completely unimpeded it travels at the speed limit. There are no speeding tickets in the Universe, you simply cannot exceed this speed under any circumstance, it is impossible. The question then is, why does the Universe have a speed limit? The answer (skipping all of the math) is that it turns out that a finite amount of space is equal to a finite amount of time, and the conversion factor is the “speed of light”. That’s it. The basic property that space and time can be exchanged with this conversion factor creates a speed limit for the Universe. So this basic property rules over all known existence with an iron fist.

That concept brings up one of the really big and interesting ideas behind relativity. I casually said that an amount of time could be equal to an amount of space, given our conversion factor. What the hell? This is one of the ways that relativistic mechanics really starts to separate itself from our everyday lives. In normal, everyday circumstances (Newtonian mechanics), we think of time as this clock that’s ticking away on the side while everything is happening in space. I sit on the sidewalk while you drive by, and time is happily ticking away on one side, tracking the order of events. Time isn’t happily ticking away by itself though, and you aren’t moving through space in your car. You’re moving through spacetime, and even though I’m sitting on the sidewalk (will someone get me a chair?), I’m also moving through spacetime. Space and time are both part of one thing, we call it spacetime because physicists love names that are way too obvious and on-the-nose. Spacetime is one four-dimensional thing. To me, this continues to be wondrous. We are moving through four dimensions, not the three we normally think of.

In our everyday lives, we can safely approximate time as sitting on the side, ticking away the same for everyone, because we are moving slowly relative to each other. However, when we start to move fast, our reference frame really starts to matter. Reference frame is just a coordinate system in which we (or the thing we’re considering) isn’t moving. So when you’re in a car driving straight down the road, your reference frame would be one fixed to the car. You and everything in the car are not moving in that coordinate system, but that coordinate system is moving through spacetime.

The fact that we are moving through spacetime has some really interesting knock-on effects. The first of which is time dilation. It turns out that, because space and time are one four-dimensional thing, when you move really fast time slows down. So if you and I synchronize our watches, and then I travel near the speed of light for a while, when we compare watches again mine would be behind yours. Similarly, if I’m moving at a speed near the speed of light, the length in the direction I’m moving is contracted. So if I was running by you at a relativistic speed with a 20 foot ladder pointing in the direction I’m running, you might only see a 15 foot ladder.

Now, in both cases, while I’m moving at the speed of light everything looks normal to me. To me, my watch isn’t moving relative to the rest of me, so it is ticking away at normal speed. Likewise, the ladder, since it isn’t moving relative to me, is 20 feet long. That can be a little wild to think about, but the really mind bending thing to think about is that it doesn’t only seem like the ladder is shorter to you, or my watch is ticking slower. It actually is. The ladder is actually, really shorter for you than for me. And my watch actually, really is ticking slower than yours. This means that, for example, if I was running the ladder into a 15 foot long barn, we would disagree about whether I got the back end of the ladder inside the barn before I blasted the front end of the ladder out the back of the barn. It means that simultaneity, something that we take completely for granted, depends on the reference frame you’re in. Things only happen at the “same time” in one reference frame. The real mind-fuck of it all is that this is real, it doesn’t just seem like simultaneity is thrown off, it actually is. Simultaneity, in the absolute sense that we normally think about it, does not exist. I actually do ram the ladder through the back of the barn before it fits all the way in, and you actually do see me get the whole ladder in the barn for that brief moment. The idea that something as basic as simultaneity isn’t actually the way the Universe is really operating never ceases to amaze me.

There’s one more mind-blowing relativistic idea that I want to bring up, and that’s gravity. On Earth, we think of gravity as this kind of magic force between two objects (the Earth and us) that pulls the two objects together. In reality, general relativity shows us that gravity is actually the curvature of spacetime. Spacetime isn’t flat, it’s curved, and the paths that things follow are just the shortest paths in this curved spacetime. Gravity is nothing more than everything continuing to do what it always does when you leave it alone, travel the shortest path through spacetime.

The idea that gravity is actually just the shape of spacetime is interesting in its own right, but there was something even better in there. We know that gravity exists around objects, to be specific, mass causes the bending of spacetime. I move toward the Earth because the large mass of the Earth is bending spacetime. My mass also bends spacetime, just far less than the Earth’s, because I have so much less of it. This little piece has a huge implication though.

We think of things existing in the Universe, and spacetime being the place where they happen. We think of all the stuff in the Universe as the players on a football field, and spacetime as the field where they’re playing the game. In reality, mass bends spacetime, and then curved spacetime affects the way things move. The implication is that spacetime isn’t just the place where the events of the Universe are taking place, it’s part of the game. The field is out there tackling players.

This concept is absolutely amazing to me. There is nothing that is just the place where things happen, everything is part of the game. The entire Universe is taking part in what is happening, right down to the playing field. Obviously we aren’t affected by basically all of the Universe, but in our little local area every single part of existence is part of the game.

So that’s it. I just thought it would be fun to bring up a couple of the ways that relativity is a complete mind-fuck. It’s so different from the way that we see the world, but it’s the real way. As of now, it has as much evidence supporting it as probably any scientific theory out there. Relativity is a scientific fact. The way we see it is just the low-speed, low-mass approximation of the way things actually are. I hope you find it as fun to think about as I do, or at least fun enough.