Read more about the project here.

-Andy

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Does that just show up as a black box for you? Well, you’ll find the original here.

*-Andy*

—–

*TestTubeGames and the CaSTL Center are happy to announce a release date for Bond Breaker, a puzzle game based on real nano-scale science — coming to web and mobile on August 28th.*

At the Center for Chemistry at the Space Time Limit (CaSTL) at UC Irvine, scientists are able to break apart individual molecules in incredible ways. In fact, their research is so mind-blowing, they wanted the world to see it. Their first plan: let everyone rush into the lab, with their grubby little fingers, and proceed to break all of their multimillion dollar equipment. After talking with their insurance agent, they reconsidered, and decided to make a game.

Thus **Bond Breaker** was born! Now the game is nearly complete, and will be coming to iPhone, Android, and the web on August 28th. In this science puzzle game, you get to enter CaSTL’s laboratories in the smallest way possible – as a single proton. You don’t even have an atom to call your own. Learn what it takes to be a proton, experience subatomic forces, and with luck and determination, grow into an atom. Collide atoms together into molecules, or break them apart again using lasers, tunneling microscopes, and heat.

The game is being developed by TestTubeGames, a studio that doesn’t take science lightly. When you make molecular bonds (or break them apart), you’ll encounter real forces and real physics. You won’t just be learning how to beat challenging puzzles, you’ll truly be gaining a new understanding of the atomic world. This isn’t just simple stuff, either! While the game assumes no prior knowledge, by the end, you’ll have an understanding of:

• Atomic Energy Levels

• Light Absorption with Lasers

• Muons, and their crazy effect on atoms

• Morse Potentials

• Up-to-date research, straight from the labs and into your hands

You can find the Bond Breaker press kit, with more information and screenshots here: http://www.testtubegames.com/press/sheet.php?p=bond_breaker

Stay tuned for more developments, or get in touch with andy@testtubegames.com with any questions or to request an advanced copy.

]]>This is a game that I’ve been working on with the **CaSTL** research group at UC Irvine — which stands for Chemistry at the Space Time Limit, so you know it’ll be good. And to boot, the game is packed with Real Physics*. They do research with lasers and tunneling microscopes, grabbing single molecules, and breaking apart and breaking single bonds. So like doing Chemistry… but instead of using a beaker, you grab an individual molecule and bend it to your will.

The game itself is based on the forces you’d experience at the atomic scale. It’s a puzzle game where you, as a proton, are moving around the nano-world. Atoms drift into one another, and if they get close enough, they’ll form molecules. You can excite the electrons, create ions, fuse into helium, fire lasers, and more.

There’s a whole bunch of physics going on, as you can tell from the list of levels:

The game itself will be coming out on web/iOS/Android for **absolutely free**, and soon, at that. We’ve got it slated for release in late August, though stay tuned for the details. Wanna know more? Join the conversation (or even help by playtesting the game) here.

*-Andy*

**The Baseline****: 1/r^2**

Ah yes, Newtonian gravity. The perfect place to start. This is gravity as we know it in our universe (ignoring pesky things like general relativity for the moment). With the “one-over-r-squared” law, gravity decreases inversely as the square of the distance between the two objects.

That’s a mouthful, but really it’s quite simple: If we get twice as far away from the center of the earth, it’ll pull on us with one quarter of the force it does now. If we triple the distance, gravity will pull just one-ninth as hard.

And with this wonderful, happy force law, we get orbits that look like this:

(As usual, all the gifs you’ll see today are taken right from the Gravity Simulator. Feel free to play around, yourself!)

**Experiment 1: 1/r^2.1**

In the Gravity Simulator, we can do something you can’t do in the real world: we can change the force of gravity and see what happens! So let’s increase that exponent over ‘r’. So now the force goes as “one-over-r-to-the-2.1.” Doesn’t quite roll off the tongue as easy, eh?

Well, let’s see what happens:

Huh, the orbits no longer match up. That’s called precession — basically the planet is *nearly* making an ellipse as it goes around the star, but not quite. The path keeps twisting around and around. Turns out 1/r^2 is special — very few force laws will make orbits that don’t precess.

Why does making it 2.1 instead of 2 change things? Well, ‘r’ is raised to a slightly higher power, which means as two planets get further away, the force of gravity **drops off faster** than it would in our world. And as they get closer, the force of gravity **increases faster**, too!

So when the planet comes in close, gravity pulls on it stronger (than in our universe at least), deflecting its path even more, which gives it a tighter curve. That tighter curve when it’s close to the star means that the planet swings around faster than we’d expect. So by the time it comes back out to its furthest distance again, it’s gone **more** than 360 degrees. Matches with what we see above. (Go, science!)

**Experiment 2: 1/r^3**

Let’s keep going! Let’s raise ‘r’ to an even higher power! We should expect even stronger precession, right? Well, let’s see:

Huh, now we’re getting something different. When an object gets close, gravity starts pulling so strongly that the planet just spirals inward until it collides. And if the object is too far away, it spirals **outward**… and since gravity gets a lot weaker the further out you go, it keeps spiraling out more and more, never to return.

**Experiment 3: 1/r^10**

What if we went really crazy with this? (*I always go really crazy with this.*) Let’s try a force law that decreases extremely fast. 1/r^10!!!! (Excitement, there, not factorials) Now if two objects get twice as far apart, the force between them is about 1000 times smaller! That makes for this weird world:

Objects really don’t notice each other in that weird universe, they mostly travel in straight lines… at least until they get juuuust close enough to the star. And once they do, they’re pulled quickly and without remorse into a collision. Boy, I’m glad we don’t live there! You can imagine how hard it would be to create galaxies in that universe, let along solar systems with stable orbits.

Tune in next week when we take things the other way… what happens for 1/r^1.9? Or 1/r? In the meantime, play around with your own force laws in the Simulator!

*-Andy*

**Black Holes**

How hard could it be to add in black holes, right?

We all know that black holes are extremely massive, extremely dense objects. (Mostly.) Get close enough to them, and gravity pulls so strong, that not even light can escape. Whoa! So we just need to make a big star in the Gravity Simulator — and we get a black hole!

Well, no. You’ll never get a black hole if you’re dealing with boring, old Newtonian gravity, though. In the old simulator, say, you could make a star bigger and bigger and bigger, and all you’d get is a bigger star. Any astroid or planet or star can escape its pull, so long as it’s moving fast enough.

**Event Horizon**

Around black holes, there’s a line of no return called the Event Horizon. If you’re outside of this boundary — you could escape the black hole. But the moment you cross it, you’re sunk. You’ll get swept ever further into the black hole.

This happens because General Relativity contains our old friend Special Relativity. And, if you’ll recall, a key part of Special Relativity is that nothing can travel faster than light. The speed of light is the speed limit for everything. The Event Horizon represents the line near enough to the black hole where, if you wanted to escape, you’d have to travel at light speed. Fall in a bit closer, and gravity gets a bit stronger, and you’d need to go even faster than light to escape. No can do. You’re stuck.

In the pictures above, I draw where the Event Horizon would be on each the star. The smaller the star is, the weaker the gravity it, and the closer you’d have to get to reach the Horizon. In fact, most of the time, you’d actually have to go deep inside the star to find this line. Which means, it isn’t *really* an Event Horizon. The calculations I used to draw these assumed that all the mass of the star is **inside** the Horizon. As you can see above, that’s not the case. The stars aren’t dense enough, which means: no Event Horizon and no black hole.

But if we get enough mass in place, the Horizon grows big enough that it swallows up the whole star — and we finally get our black holes! Now let’s have some fun with them!

Black Holes have tons of neat properties, which you’ll all be able to check out in the next update to the Gravity Simulator. Stay tuned for more General Relativistic fun!

*-Andy*

**RELATIVITY IN THE GRAVITY SIMULATOR.**

At least, *mostly* relativity. You see, we’d talked about adding in Black Holes… which would be awesome. But not just *nom*nom*nom* generic sci-fi ‘sucks-stuff-in’ Black Holes. This is TestTubeGames, after all. So I wanted to *at least* get stuff approximately right. Maybe so ‘orbits’ become something like this:

A while back, in an earlier chat in the forums, we found a General Relativistic formula for the attraction between two objects. Seems reasonable that we could plug in that force law (after all, we’ve got change-able force laws already). It won’t be precisely right (there won’t be gravity waves…), but it’ll get us close.

Simple, then, slap on a GR Force Law and call it a day! Well, nope. Because Black Holes have this neat feature where once something gets too close — ~~inside the event horizon ~~ — it’ll *never* come back out. Mwahahaha.

Never, that is, unless it travels faster than light. Which, in the real world (as far as we know) nothing does. But in the Gravity Simulator, you can launch stuff at any speed! Black Holes would lose all meaning, objects could escape at will. They’d become just ‘really strong stars’ instead of ‘points of no return.’ Boo, hiss.

That means I need to add **more** relativity in the sim, to make objects obey the speed limit of light. Now when something accelerates, it can get close to, but never reach the speed of light. And, lo and behold, we get neat orbits like this:

Great. Can we just paint that star black and stop there?

**NO!**

Because once you have objects traveling near the speed of light, well, then E=mc^2 becomes important. Namely, mass is energy, energy is mass. So what? So EVERYTHING. Imagine two stars colliding. They rush inwards to meet one another, then *boom* they combine to form a single, stationary star.

The total energy has to remain the same, which means that Kinetic Energy had to go somewhere. In our sim, there’s only one place that energy can go: into rest mass. Just as two subatomic particles can combine to form something massive (wee protons crashing into each other to make the Higgs boson, anyone?), two stars can combine to make one *huge* star.

What other parts of relativity will come into play down the line? Well, the Schwartzschild radius is important. And relativistically slowed clocks are awesomely fun…

Where does this all end? With a bang? With a whimper? Will the simulation collapse into a singularity under all the weight of the new code? Stay tuned to find out!

*-Andy*

*No.*

Antimatter, in spite of its ‘anti’ name, still has a positive mass. An electron and an antielectron (positron) have opposite charge, but they have the same mass. Charge flips to negative, mass stays the same.

If antimatter is out of the picture — what in the world *does* have negative mass? Well, nothing really that we know of. It would take a very strange, exotic form of matter to have negative mass. The closest we come is with the complex Casimir Effect. But let’s imagine that a chunk of negative mass does exist. What do we know about it?

First off, negative masses would have… negative energies. When an object is moving, it has a kinetic energy equal to 1/2*m*v^2. If the mass is negative, the kinetic energy is negative. Even when you look at E = mc^2, the rest energy of matter, you’d find that the negative mass would lead to negative energy here, too!

Strange stuff. The faster it goes, the less energy it has. The more you have of it, the less energy you’ve got.

**Gravity Time!**

What would a negative mass mean for gravity? Well, we can check this out in the Gravity Simulator. Two planets with positive mass will, of course, attract.

This is because the force between them is:

Where m and M represent their masses. Positive masses mean a positive force, which in this case means the objects pull towards each other.

What about negative masses? Suppose we had two planets with negative mass.

Looking at the equation above, if we change m to -m and M to -M… the equation doesn’t change at all! (Negative*Negative = Positive!) So they should attract as before, right?

There’s an extra bit of the puzzle we’ve left out. The force hasn’t changed, but the acceleration has. To figure out how something will move, we use F=ma. The force is equal to the mass times acceleration. Even if the force hasn’t changed in our example… if the sign of the mass has flipped, the sign of the acceleration has to flip. So instead of the pulling force making the planets accelerate together… they accelerate apart.

With all that in mind, the final puzzle is: what happens when you have a positive mass and a negative mass. Will they attract? Will they repel?

The test is easy to do (Note, you can do all these tests and MORE in the Gravity Simulator):

…whoa. Why did that happen?As a final note, it would seem that having two planets suddenly zoom off the screen, ever faster, would violate Conservation of Momentum, or Conservation of Energy. But in fact, it doesn’t. As the positive mass gains positive kinetic energy, the negative mass gains **negative **kinetic energy. They cancel out.

Same with the momentum. Both planets may start moving in the same direction in that gif above, but the planet with *negative* mass has its momentum moving to the *right*. (Momentum = m*v, so flipping the sign of the mass flips the direction of the momentum). So even with strange negative masses around, conservation laws stay intact.

Will we ever really encounter a chunk of negative mass? Who can say. But at least we can make some good predictions about how we’d expect it to behave.

*-Andy*

I’ve talked about something similar before with the Electric Shocktopus, but this topic warrants **more**. And it needs some swanky gifs from the new Gravity Simulator.

**3D**

Let’s start off simple. The world we live in, for all practical purposes, is in three spatial dimensions. You can go up-down, left-right, or forward-backward. And in this world, Newton’s Law of Universal Gravitation tells us that two objects with mass will attract each other, according to:

If you only care about the distance, the force goes as 1/R^2, which is why we call this an inverse-squared law. Double the distance between the earth and the sun, and gravity will pull them together with 1/4 the strength. Inverse square laws are beautiful, because they lead to cool things like closed and stable orbits.

All GREAT things for life!

Unfortunately, Newton’s Law of Gravity can’t help us when we’re in a world with a different number of dimensions. The law only works in 3D.

**Gauss’s Law**

Instead, our starting point instead is Gauss’s Law. Take a point mass, make an imaginary spherical surface around it. Imagine that instead of gravity, the point mass is just shooting out 100 bullets in random directions.

How many bullets pass through the sphere around the point mass? No matter how big or small you make your sphere, the answer will always be 100. That’s the core of Gauss’s Law. The number of bullets passing through a sphere doesn’t depend on its radius. When we’re talking about gravity, the bullets represent the Flux, which is simply the strength of gravity times the area of your sphere.

So then:

If the total flux is always the same, that means the Force of Gravity is proportional to 1/(Total Area of a Sphere). In 3D, a sphere has a surface area of 4PI*R^2. So the Force goes as the inverse of that, or 1/R^2.

**2D**

Suppose we were like the Flatlanders, and lived on a 2D plane. We could move forward-backward and left-right, but not up-down. How would that change gravity?

Well, Gauss’s Law still holds. But this time our ‘sphere’ that we draw around the point mass is actually just a circle. (Remember, we can’t leave our 2D surface!) The ‘surface area’ of the circle is just its circumference: 2PI*R. Which means that the Force of Gravity goes as 1/R. And we get orbits that look like this:

**4D**

What if there were an extra dimension? Suppose we lived in a world where we could move up-down, left-right, forward-backward, and… and… uh… 4Up-4Down. We don’t have a word for those last two of course, since we never move through a fourth spatial dimension. But nonetheless, we are armed with all the information we need to figure out how gravity would look.

This time the ‘sphere’ we make around a point charge is in 4D, which is hard to draw, but we can figure out what it must be like with a simple pattern. In 2D, the ‘surface’ of a sphere is a line. In 3D, the ‘surface’ of a sphere is an area. So in 4D the ‘surface’ of a sphere should be a volume. Its units should be length cubed. No surprise, then, that the surface ‘area’ of the 4D sphere is 2*PI^2*R^3. Which means that the Force of Gravity must go as 1/R^3. So we get orbits like this:

**Beyond**

You’ve now got everything you need to ponder the force of gravity in any number of dimensions. And with the Gravity Simulator, you can check out what any of these worlds might look like. Try to make a 5D solar system, I challenge you!

This was just a quick introduction to some interesting topics — so if you wanna know more, there are plenty of resources out there you can use.

*-Andy*

**The Latest Additions:**

- -Set the orbit trails to the length you want, they aren’t always infinite, now
- -Snap the planets to the grid, for some easy symmetry
- -You can now fling the ‘fixed’ stars… they still won’t be affected by gravity
- -Edit planets on the move — change their mass, speed, position…
- -Set the density of an object to whatever you like
- -Pick whatever force law you like. The force goes as tan(r)? Sure! Or maybe r^ln(pi*r)? Uh, that’s fine too!
- A bunch more… naturally. Check out the forums to learn more!

Also, keep your eyes peeled for some YouTube videos of the simulator in action. But hey, why not just go grab the simulator, yourself? Get playing today!

*-Andy*