Tuesday, June 8, 2010

An adventure through the space between my ears - Part I: Relatively Special

Image: The Crab Nebula, the result of a supernova noted by Earth-bound chroniclers in 1054AD At its centre, a neutron star. NASA Image of the Day.

A note to begin:
I’ve been thinking about time, as a relative concept. I want to talk about that, but first you’ll need to know a little of Einstein’s Special Theory of Relativity. Like all things I do, I’ll try to make this extremely pleasurable.

If you’ve never sat down to think about this – first of all, good for you. You’ve probably had a much more physically eventful life than I, and probably a life filled with fewer headaches and less confusion.

But this is about me.

Special Relativity can be... complicated. It is a ‘theory of measurement for an inertial frame of reference, which states that a relative inertial frame of reference will uniformly accommodate all laws of physics; and adds that the speed of light is constant and independent of the velocity of an observer in any inertial frame.’

And if you immediately understood that, you’re very smart. Good for you.

For the rest of us, it doesn’t actually have to be as difficult as that sounded. I don’t know why, but scientists and science enthusiasts seem to insist on using their own slang and discipline-specific terms to make it difficult for the rest of us to keep up. This makes them tossers.

Before we go any further, I should put a small disclaimer here: I have no formal qualifications in physics; I have no degrees in cosmology or any fancy letters after my name. I am simply a person who is passionate about this world; hungry to know how it works and why it works and how it came to be.

I am, you might say, ‘well read’. Cosmology for me is more than a hobby, but less than something I do to make a living. Of course, most professional cosmologists would probably say the same; it’s not necessarily a lucrative, jet-setting career.

While the science and history I will use are so-called ‘text book’, I will occasionally make intuitive leaps as to how someone – say, Einstein - would come up with a concept, or why. Remember, this is a trip through the space in my head.

Lastly: I think, to really understand this world, you need more than just mathematical formulae to say ‘because it’s true’. I think we have an obligation to deeply examine a discovery for ourselves in order to see its beauty; to understand why it is so important and what it really means. That’s what I’m doing here.

This is how my brain works. I am aware it can be a unique, often unconventional place, so hold on tight - it’ll be an awesome ride.

An adventure through the space between my ears:
Relatively Special

Our universe didn’t always look the way it does now. It was once very different; governed by different rules. This strange new cosmos we live in was re-imagined; our journey paved by mistakes and often futile beliefs - but, like so many things humans do, it was made possible through wild leaps of faith and a beautiful, unquenchable passion.

The journey began in the 1600s. Then, our knowledge of the universe was based on what is called a Euclidean model. In this model, our universe was made of simple geometry - three dimensions of space, length, width and depth, and in it, time was constant. Time could be measured uniformly at any point and it would be the same for all observers.

Space itself was filled with a substance called aether. Aether was the stuff of absolute stillness and universal time; it was the birthplace of light and the keeper of mystical forces. At home, on our tiny blue marble, we moved through the aether like a submarine at sea.

To understand how and why Einstein’s Special Relativity changed the world, we first need to look in on a fellow named Galileo.

The year is 1632. This is the year Galileo created the principle of relativity.

That’s right - relativity wasn’t a new concept when Einstein presented his theory. That bright spark had started nearly 300 years earlier. Galileo’s principle of relativity states: There is no ‘internal observation’ an observer can use to distinguish between a system that is moving in a straight line at constant speed and one that is at rest. Therefore, any two systems moving without acceleration are equivalent, and unaccelerated motion is relative.

If you’re already lost – that’s okay. So was I. And so were the luddites of the 16th Century. At the time, they were still struggling to believe the Earth spun on its axis, because surely we’d all fall down due to its spinny-roundedness. They were also arguing that if the Earth was speeding to the east and someone threw a ball straight up in the air, they would have to lean slightly west to catch it again, because Earth would move in the interim.

It’s sweet, really – this misguided simplicity of logic. You have to appreciate it, much as you appreciate puppies. But Galileo was left with the task of explaining ‘inertial frames of reference’ and ‘relative motion’ - to puppies. Understandably, his explanation makes more sense to me than any other - I embrace my clumsy, inquisitive puppy nature. Also, Galileo’s example has a ship and some butterflies and those things are pretty.

Here’s how he did it:
Imagine you’re in a ship at a dock. You are below deck and there are no windows. You have a ball, some butterflies and a bowl of fish. The fish are swimming in their bowl in all directions, the butterflies are flapping around aimlessly the way butterflies do and you are throwing your ball into the air and catching it.

It’s just you and your animal friends.

The ship starts moving.

At first you might sense you are moving because there is an initial feeling of acceleration, but soon your speed becomes constant and you feel nothing. This is called ‘uniform motion’ – travelling at a constant speed in a straight line, so that you can’t tell if you are moving or perfectly still.

Congratulations! You are in an inertial frame of reference. Here - have a treat.

This is what Galileo meant when he said there was no ‘internal observation’ someone could use to distinguish between a system in uniform motion and one at rest. When you are in uniform motion, there are no ‘fictitious forces’, such as acceleration, to tell you if you’re moving. And without a window, you have no way to judge your motion relative to the world.

As for your animal friends; the fish are still swimming in all directions in their bowl and the butterflies are still flapping aimlessly around the room as they please. The movement of the ship is having no affect on them, or on the ball you throw into the air because the laws of physics hold true in an inertial frame of reference.

Pretty cool, huh? (Admittedly, my cool threshold is lower than most.)

Now that you know what an inertial frame of reference is, we should talk about relativity. To prove inertial frames of reference were relative, Galileo used a series of equations called Galilean Transformations. Since I prefer puppies to math, I’m not going to put those here, but I will say the principle of relativity has a lot to do with velocity.

To understand, you’ll have to get back in your ship. I’m going to take a seat on the shore.

... So here we are; me with my legs dangled over a pier and you in your ship. The sun is warm and I am juggling, because it’s nice weather and secretly I am circus folk. Back in your ship, travelling in uniform motion, you are appreciating the butterflies.

Suddenly, a window appears in your bow and through it, you see the shore, moving west at 10km/h.

It’s possible you find this idea counterintuitive. Obviously you know the shore can’t move, but remember, you are in an inertial frame of reference, which is as good as standing still. If you are not moving, it must be my pier that is moving. If it’s easier, your ship cannot intuit the shore doesn’t move because it’s not as clever as you, so imagine that you are the ship - the important part here is relative velocities.

In a Galilean transformation, everything needs to be relative, including velocity. In this scenario, you are travelling east at 10km/h from my frame of reference; I am travelling west at 10km/h from yours. With Galilean transformations, these velocities are perfectly relatable.

This is when it is important to remember that the principle of relativity is about more than pretty butterflies and puppies not falling over. It has to do with the hows and whys of the universe. Relativity was a way for Galileo to reconcile physical laws on a cosmic scale. Your ship is analogous of Earth, and the pier I am sitting on is the absolute space of the aether.

Keeping that in mind, there’s one last thing you need to know about Galilean relativity, and this is the part that would later cause big problems for Einstein.

The wondrous world of velocity addition.

Let’s say I’m standing on the pier, and I shoot a canon over the water, and in that canon is your ship - and yes, I do realise that would be the most awesome weapon ever. Your ship is now flying through the air at 30km/h. From your ship, you shoot a canon and a projectile flies out at 30km/h.

(At this point, I know you’re wondering what your projectile is, and I’m going to leave it to your imagination. I’m pro-midgets, but would urge against the butterflies.)

In the world of Galilean relativity, your projectile is travelling at 60km/h, relative to me. That’s my speed (0km/h) plus your speed (30km/h) plus its speed (30km/h). This may not seem all that important right now, but when we get to special relativity and velocities approaching the speed of light, it will be.

For now, just enjoy the idea of shooting ships from canons, and the fact that you (hopefully) understand the principle of relativity. Doesn’t it make you feel tingly? Don’t you want to tell all your friends?

No? Just me then?


It’s time for us to ride this crazy flying ship 250 years into the future. That’s where we’ll find what would become the beginning of the end for Galilean relativity.

See you in 1885...

Part II: The Aether Is Magic


  1. You continue to be one of my favorite writers.
    As I glared back at the people who stared at me for laughing loudly while reading this during my commute, I realized that I was seriously regretting not having this around fifteen years ago when I was trying to learn physics. I fervently hope that you continue writing this and then promptly ship it out to every book agent and publisher you can find.

  2. Love this! Believe it or not, special relativity is a favorite topic of conversation for my sister and me. I can't wait to read more!

    I'll say it again... You are beyond talented, girl!