Relativity 101

What is Special Relativity?

Ah, one of the great achievements of Albert Einstein. Special Relativity tells us what happens when things travel near the speed of light. At such high speeds, our classic, Newtonian instincts no longer work. Normally, it turns out, this doesn't matter to us. The speed of light is immense (~300 million meters per second... or 671 million miles per hour). We don't travel that fast. This means two things: (1) it took a long time for us to figure out that we needed Special Relativity. And (2) our intuition really stinks at helping us understand it. This simulation aims to help with the latter issue.

Special Relativity is based on two ideas:

The laws of physics are the same in all Reference Frames. The speed of light through empty space is c=300,000,000 m/s.

That's it! How hard could it be?

What are the limits of this simulation?

This simulation is no mere toy, nor is it an "artist's rendition" (not that either of those are bad things). This is an accurate and mathematically based depiction of the world at high velocities. Its basis? The equations of Special Relativity (Lorentz Transformations). Space is changed correctly. Time is changed correctly. And in certain cases, color is changed correctly, too. (Mostly, the color is left untouched, just to keep the game from inducing unneeded nausea.) Also, the simulation accurately depicts what you would See when traveling near the speed of light. Due to the fact it takes light some amount of time to reach your eye, it ends up that the world seems to bend and warp. Strange, but very true.

There are, of course, some approximations in the simulation. For instance, when things, such as trap doors, appear/disappear, they do so at once (even though in reality the far corners would be at slightly different times). This helps keep the calculations more manageable, while not changing the physics much.

Also, the light spectrum has been altered slightly. When it comes to changing colors, if you were to really move like Velocity Raptor, you'd experience how small the visible range of colors is. Red-shift would quickly take objects into the infrared part of the spectrum, and similarly for blue-shift. In order to keep the color-changing blocks generally visible, the doppler shift has been minimized slightly.

And, finally, as in all of science, I reserve the right to be completely wrong. If you find something that isn't right (beyond any necessary simplifications), I'll be delighted to find out - and of course will fix it.

Can you go faster than light?

No. Even in a speedy jet, you'd be lucky to travel just 1/1,000,000 (one one-millionth) the speed of light. Not even close.

But aside from that, there is a more fundamental principle afoot. Nothing that has mass can accelerate up to (or past) the speed of light. The closer to the speed of light an object moves, the harder it is to accelerate it. It is as if it has more inertia (aka more mass). The end result is that the speed of light is an impassable barrier.

In this game, Velocity Raptor runs with a constant force from her feet. But as she comes close to the speed of light, she accelerates less and less, just as mentioned above. Even she, in this strange Lair, has no chance of reaching the speed of light.

Why is there Length Contraction?

The first effect of Special Relativity you come across in this game is Length Contraction. When you move fast, objects you go by seem (aka are measured to be) shorter than otherwise.

In special relativity, Space and Time are no longer separate entities. They mix together into Spacetime. This mixing is described in the Lorentz Transformations. Length Contraction comes right out of these transformations. Objects only contract along the axis of relative motion. So if a train is running past you (sitting at the station) the length of the train would seem to shrink. However, its height and depth would remain unchanged. The faster an object moves, the more it contracts. As an object approaches the speed of light, it shrinks down without limit.

Of course, the object doesn't really change size (at least as far as it is concerned). To the passengers on the train, everything seems normal. However, they are surprised at the very thin person standing in the very thin station. Since you are moving with respect to them, you seem to them to be shrunk. This is what is referred to as 'relativity.' Basically, the effect is the same for each of you: the moving entity is contracted.

More about Lorentz Transformations

More about Length Contraction

What's up with the colors changing?

This is called the Doppler Effect. You are likely familiar with this effect for sound. An ambulance coming towards you has a different pitch (frequency) than when it drives away from you. This is because the sound waves are bunched together as it comes towards you (thus reaching you more frequently).

A similar (though more complex) effect occurs for light. If an object is moving towards you, the peaks of the waves of light hit your eyes more frequently. A higher frequency means the color appears bluer. When it moves away, the frequency is lower, and it appears redder.

You can also think of this in terms of length instead of time (frequency). Wavelengths are not some invariable entity. Rather, based on you motion, the lengths can change. To understand why you get both red and blue-shift, then, you will need to keep "Seen" relativity in mind...

More about the Doppler Shift

What are those doors you call 'garages'?

These represent the Garage Paradox. Imagine running with a 7-foot ladder into a 5-foot-long garage. This garage has one door leading in, and one leading out. You have two friends standing at these doors to help you out with this experiment. The front door is open for you. The back door is closed. The moment your ladder reaches the back door, though, your friend will open it up. At that same instant, your other friend closes the front door. So in that moment, your ladder would have to fit inside the garage. That seems impossible.

It seems even more impossible considering relativity. You're running with the ladder, so the garage seems length contracted. It seems even shorter than 5-feet! That can't be good. But it turns out, if you are moving fast enough, you will be just fine.

There are a couple ways to resolve this problem. The easiest is to keep relativity in mind. Namely, while the garage appears shorter to you, YOU appear shorter to the garage. Your friends wouldn't be surprised if, say, a 4-foot ladder fit inside.

(The further point to understand is that TIME, just like length, changes. People moving differently will not agree on whether or not something happened "Instantly". To your friends, the doors open and closed instantly. However, to you, that doesn't seem to be the case. Thus, if both doors stay open for a while, you shouldn't be surprised that you could run through with a ladder.)

More about the Garage Paradox

I'm really confused by time...

I'm glad you're being honest. Though length contracting is odd, it is nothing compared to relativity's effects on time. There are two important effects:

1. Time Dilation: a moving clock seems to run slow. Think back to those train-passengers zooming past you. If you could look in and see their watches, the seconds would seem to tick slowly. Of course, if they could see your watch, it would seem to tick slowly to them. Who is right? Both of you, of course. Special Relativity is truly wacky.

2. The absence of "Simultaneous." Two observers might not agree on whether two events happen at the same time. Back to the train example: two lights flash on the ends of the train. Imagine they seem to flash at the same time for the passenger. To you on the platform, however, they will not appear to flash simultaneously. There will be some delay. This effect comes straight from the Lorentz Transformations. The flashing light that is moving towards you seems to blink before the one that is moving away from you.

More about Time Dilation

More about Time Shift

What's the deal with the Fire Blocks?

The fire blocks are based on the Twin Paradox. To activate a fire block, you tap it. From that event, you have 12 seconds (by your watch) where you can melt snow. The fire block has 15 seconds (by its watch) until it turns into snow. In the normal world of Newton, this would mean the fire block is safe, unable to be melted by you. But in relativity, that is not the case.

If you run away from the block, then back towards it, you'll find that your clocks have advanced different amounts of time. Basically, when you get back, you'll be surprised that the fire block has gotten older faster than you'd expect. The reason for this comes from the second 'time effect' listed above.

Imagine a level filled with clocks (one does exist in the game). As your raptor runs across the room, the previously synchronized clocks no longer match. The ones you're running towards are advanced in time, and the ones you're running away from lag behind. The further away from you they are, the more strongly they are affected. Depending on where a stationary observer might be, their clock will not line up with yours. The key to understanding the fire blocks is that you are always running towards the more advanced clocks (since these are precisely the ones in front of you). So you are, in a way, running into the future of the room.

This means when you get back to the fire block, a few extra seconds have gone by for it, and you may well melt it.

The classic Twin Paradox involved two twins starting on earth. One zooms away and back near the speed of light. Who is older when they get back? It is a confusing topic (perhaps the strangest in Special Relativity), and there are many explanations of the results out there. (I will say that much of the confusion comes from acknowledging only Time Dilation, and not the second time effect). From the description of the past few paragraphs, though, and from playing the game, I hope things may be a bit clearer.

More about the Twin Paradox

Wait... "Seen" relativity? What does that mean?

Up until this point, the effects have been that of measured relativity. For instance, if you really measured a meter stick, you'd find it length contracted as it zoomed past you. But if we think about what we'd really see with our eyes, it gets even weirder.

The part that we've mainly left out is that light takes a finite amount of time to reach our eyes. It doesn't get to them instantly. This means we only ever see objects in the past. This is true in the real world (and very important when we're looking at distant galaxies many light-years away). And it is particularly striking in this game, where even the object across the room is a few seconds old.

This is all fine and well: when you see distant objects, you're seeing them from the past. But when you combine that with things moving, it gets strange. As you experience in the game, the world warps and bends. The basic principle can be described thusly:

Imagine a vertical flagpole zooming towards Velocity Raptor. At the moment it reaches her, the base of the flag pole is a very short distance from her eyes. This means she is seeing it without much time delay... her eyes agree that it is right near her face. If she looks up to the top of the flag pole, however, it is much further away. Thus, she sees it pretty far in the past. Well, where was it in the past? A few seconds ago the whole flagpole was further from Velocity Raptor. So she'd see the top of the flag pole shifted away from her (and not directly above the base of the flagpole). This shifting effect happens across the whole length of the pole. The result is that it curves.

The math of this effect does get very involved (especially when you bring in Length Contraction as well). But with this game, you simply get to experience Seen relativity.

More about the Curvature

What happens when I toggle from 'panning' to 'center'?

There's a bit of confusion about this feature in the game, and rightfully so! As it appears on the screen, in one of the two views (the 'center'-ed one), your raptor is always in the middle of the screen. The room moves relative to her. You are seeing the room from the raptor's reference frame (as if you were moving along with her). The room shrinks, the raptor doesn't.

So what happens when your press 'panning'? Does that put you in the room's reference frame (as if you were standing still)? No. In this game, you are ALWAYS observing the world as if you were the raptor.

What 'panning' does is not shift the reference frame, but rather it is a simple attempt to make the game easier to play. With it activated, the game tries to center the level on the screen, so the player can see all of it. As you'll notice, with the game centered on the raptor, you can often not see the far end of a level. But of course, as a player, you want to see the whole level and plan out your strategy. Thus, 'panning' artificially keeps as much of the level on the screen as possible.

Though it would be neat, the game does not allow you to sit still and watch the raptor move. I'd love to add a feature like that when I have time. Of course, according to relativity, in that case you would see the raptor shrink and/or bend, and you'd see her clock tick differently.

The reason I don't let you toggle between reference frames (aside from the extra effort it would take) is that it would interfere with some of the gameplay. For instance, if you are standing still, the doppler blocks would never change color. And in the 'seen' view, what you see would depend on where you were in the room. The effects, after all, rely on the fact that light takes time to reach your eyes. To figure it out, we need to know where your eyes are! It was for those reasons that I left reference frame switching out of the game.

More about Reference Frames

Where is "E=mc2"? I thought that was THE equation, but you haven't mentioned it.

Ah, yes, perhaps the most famous equation out there. This simulation deals with Relativity's effects on space and time. E=mc2, on the other hand, deals with the inherent rest-energy of matter. It as much as anything would belong in a game about Special Relativity. However, energy is not something I deal with directly in this simulation. It is not terribly tangible, compared with, say, clocks ticking.

If you want to learn more about that equation and the math behind it, I encourage you to check out further resources.

Don't Velociraptors have feathers?

From what we've seen in the fossil record, it seems that they did! But this is a Velocity Raptor. Not a velociraptor.

How hard was this to code?

Very.

When will you make a game that does full-on General Relativity?

I hope that this game can bring the wonder of Special Relativity to a larger audience. Sometimes, it is nice to step away from the math of a subject, and use some experience to build up instinct. With this game, I wanted to make that possible for Special Relativity.

But I don't plan to stop there. There are many other topics that could use a fun game. The best way for you to help out: an encouraging email. Those always boost my efficiency.