Wednesday, January 29, 2014

Speculating on Blindsprings

I recently stumbled on to a web comic called Blindsprings, after seeing a banner ad for it.  Let me take this time to recommend it to you.

Blindsprings is a comic that just went online back in October.  If you go to the website, you can see that not much has happened yet.  As such, it's hard to gauge just what the story is or where it's going.  So far though, surmising from the information available, I think this has the potential to be something really, truly great.  What is also exciting is being able to see the story develop from the beginning.

Plus, the artwork is beautiful.

this was the ad for it
Here's a non-spoilery description blurb of it:

The main heroine is a young girl named Tamaura.  She lives alone in the forest, where she attends to animals and plants trees and performs many other tasks for a shady group known as "the spirits".  It's a simple, idyllic kind of life.  One day she meets a young man named Harris, who has heard a fable of her and came to investigate the truth of it.  The two become friends, and after spending time with her, Harris decides to go off to a place called Kirkhall to study what is called Academic Magic.

The setting is not the standard "medieval" fantasy kind of setting, but something more like early Enlightenment era.  Really, not much of it has been revealed yet, so that's mostly a surmisation.  We are not even finished with the prologue.

Go read it.

After you've read it, come back here and let's talk about it.  There's not much of it (so far), so should be easy.

There are SPOILERS below.

Sunday, January 26, 2014

What is Spin? A Concrete Explanation.

To say that a particle has "spin 1/2" is to say that it must be rotated through 720 degrees before it can return to its original configuration.  This is not something normally witnessed in the world of classical mechanics, and so this aspect of quantum mechanics is often piled up with unhelpful metaphors and mysticism.

I wrote a post previously trying to point out that quantum mechanical spin is just a degree of freedom.  Spin tells you the components of a particle in a combination of two wave states with the same energy.  You can make pseudospins and isospins with any two such states, no matter what they are.  When you rotate the system, the components get mixed up -- just like angular momentum states.  You have to rotate the system by 720 degrees before the components get mixed up enough to be un-mixed up (i.e. back to there they were).  That's all it is.

What gives spin states this weird property is that the space of rotation is three dimensional, but the spin "vector" is only two-dimensional.  Rotations of typical vectors with three components (even if one of those components is zero) work just the way you'd think they should.  But, it's not completely surprising that 2D objects in 3D space don't rotate like 3D objects in 3D space.

To illustrate where spin comes from, and how it contrasts to orbital angular momentum, consider the case of rotation in 2 dimensions.  The best way to talk about rotations is to start at the unit circle.

Thursday, January 23, 2014

Everything Cool is Impossible

Physics has known for a long time how to build a time machine.  The possibility in a real spacetime geometry was first noted by Van Stockum, but this possibility was only really first analyzed by Frank Tipler in the 70's.  All you need is a massive rotating cylinder.  And also it has to be infinitely long.

This illustrates how frame dragging
can lead to time travel 
Since then, at least a dozen other possibilities have been proposed for time travel to the past, and physicists have proven that these spacetime geometries result in what are called "Closed Timelike Curves" (CTCs), which are trajectories a massive object could follow to go back in to its own past.  We know that they would work within the theory of General Relativity.  But, they're all impossible.  They either require the universe to be rotating (it isn't), they require infinitely large systems (we can't make them), they require negative-mass matter (no such matter exists), or they require you perform your time travel within the interior event horizon of a Kerr black hole (which is fine, but then you can't leave).

This situation is worse than merely having a concept of physics that excludes time travel, or that merely says that time travel is impossible.  For if time travel was excluded by theory, then we could always say the theory was incomplete.  What we have instead is a system that fully allows time travel possibilities without prejudice, as long as we're able to break some other law of physics to get there.  It's not just the stubborn "no" of a parental figure; it's like having your parents describe step-by-step exactly what you can do to eat chocolate cake for breakfast, and one of those steps is "eat infinite broccoli".

Physics also knows how to effect FTL travel.  The speed of light puts a prohibitive barrier on
our ability to explore the stars, but a number of work-arounds have been proposed.  Technically, relativity only prohibits local FTL movement, but says nothing of global FTL travel.  So if you can distort space and time in just the right way, you can move however fast you want.  One of the more frequently explored proposals is wormhole travel.    Wormholes produce a kind of "short cut" in spacetime, and it is actually a Federal Law that when you want to discuss how wormholes work you must draw two dots on a sheet of paper, "A" and "B", draw the straight line connecting them, then fold your paper so "A" and "B" touch and jab a pencil through it.  While going along the line you draw may take billions of years, going through the wormhole may take minutes.
My lawyers also recommend I show you this diagram

Sadly, you can't make a wormhole.  And even if you made a wormhole, the throat collapses when you try to travel inside of it, so you can't even use the wormhole for travel anyway.

Another proposal is the Alcubierre warpdrive.  This contracts spacetime in the front and expands it in the back, producing what some call a "wave" of spacetime contraction that "tips over" the light cones inside the warp bubble.  Locally, you're moving slower than light, but globally you may be moving, in theory anyway, as fast as you want.

But you can't make the Alcubierre warp drive either.  If you took the mass of the universe and made it negative, the Alcubierre warp drive requires ten times that number in negative-mass matter to move a standard-sized spaceship.   To clarify, we haven't even found one single particle of negative-mass matter.

Science knows how to make a Bag of Holding, and can even make a Bag of Holding that slows down time (see chapter 3 here).  You can store a lifetime supply of hot pies and ice cream in the same box, and whenever you take them out the pie is still oven-fresh and the ice cream still ice cold, and so even twenty years later you can serve yourself delicious pie a la mode.  But, like so many awesome things, it requires either negative mass or impossible mater distributions and can't be made.

I just made a post about how the Bag of Holding (aka, Van den Broeck Bubble) can be exploited to, potentially, travel to parallel worlds (if any even exist).  This one is a lot more speculative, requiring ideas way beyond established science, but is at least partially based in what we already know about general relativity and curved-space geometry.  It isn't really scientific, but if we wanted to know if there were other universes, this has potential to actually find them.  But it also requires not only negative mass, but infinitely much of it.  So we won't ever be able to try.

Pictured: A guy wearing a green screen.
Not Pictured: An invisibility cloak 
Science has pretty recently discovered (less than ten years ago) how to make a literal cloak of invisibility.  It involves bending light in just the right way.  We know what that just-the-right-way way is, and we even know how to make materials that bend light in just that way.  Sadly, it only works for a single frequency (i.e. color) of light at a time.  There's no way to be completely invisible, because there don't exist materials with  the right optical properties naturally.  So you can be green-invisible, but you'll still be perfectly visible in red and blue.  I guess you'll just look slightly more purple?

I recently calculated (as part of my research) how to make a slightly different kind of cloak, namely a shadow cloak.  Also something you'd read about in fantasy books, the shadow cloak works on the same spacetime distortion principle as for a black hole, but now modified to work with optical materials (so not requiring it be made of actual black holes).  A perfect realization  would allow light to enter, but trap it there.  If you were wearing it, you would appear to be not just covered in a black garment, but actually swathed in shadows.  (Look at a black object, then look at an unlit hole; there's a big visual difference)  You'd also probably heat up a lot (since all the energy is trapped), which would make this kind of material perfect for solar panels, increasing their efficiency probably to near 100%.  But you can't make the shadow cloak, because it requires material parameters that are both infinite and negatively infinite.  Like with the invisibility cloak, you can only realize this (if at all) for a single color of light at a time.  Which vastly diminishes its coolness.

You can probably see where my knowledge tends to specialize, but physics knows a lot more cool things in the quantum domain, such as teleportation devices and solutions to the P=NP problem.  All of which, we know how it would work, and only minor technicalities render it impossible.  Things like wavefunction collapse, quantum decoherence, and the no-cloning theorem.

Any time there's something cool in physics, there's something else that renders it impossible.

Again, this isn't the situation of wanting to do something incredible and merely lacking a theoretical model to describe it.  Our formulations of physics account for it exactly.

It's just that all the cool stuff is impossible.

More and more, it just seems like the Universe comes equipped with fail-safes against our ever doing the cool things of science fiction.

Wednesday, January 22, 2014

What Do Wizards Even Do?

The Malfoys are very rich.  The Weasleys are very poor.  However, they are not nearly as poor as the inbred and horrible Gaunts.


This is again part of the same basic problem with the series: Rowling never bothered to figure out her universe from the perspective of the characters who live in it.

How do wizards generate wealth?

As revealed in the books, there are really only so many things a wizard or witch can do professionally.  You can make wands.  You can make magical pranks.  You can manufacture magical candy.  You can sell books or robes.  You can teach at Hogwarts (and there's only a dozen positions there).  You can work for a news publication.  Or you can work for the Ministry of Magic.  That is the entire wizarding economy.

For instance, when the students begin taking their OWLS and deciding their classes for future employment, almost every single job opportunity considered is at the Ministry of Magic.  Harry becomes an auror, but what else was he going to become?  An accountant?

Tuesday, January 14, 2014

Sailing Away to Narnia

I stumbled upon an article a few months ago that I've been meaning to blog for a while and never got around to.

The original article is by Chris van den Broeck, and deals with the subject of warp drives.

Yes, warp drives.  The Alcubierre warp drive engine is a device that stretches the spacetime around a spaceship, forming what is known in scientific literature as the "warp bubble" (really, that's what we call it).  Within the warp bubble, the ship is moving at "normal speeds", but outside of the bubble, the ship is moving faster than the speed of light.  The geometry for this is known and well understood, and the means of producing it are also fully understood.

You're probably wondering, if we know how to make a warp drive, why we haven't actually... you know... made a warp drive.  And that's a wonderful question.  We haven't made a warp drive because it requires a lot of stuff that probably doesn't exist, namely negative energy mass.  It requires a whole lot of it.  Like, ten times the positive mass of the entire universe in negative mass.

Van den Broeck proposed an idea to get around this, one elegant in both its simplicity and apparent absurdity.

Here's what you do: Take a bag.  Distort space, so that the inside of the bag is bigger than the outside of the bag.  The inside is big enough to hold a spaceship, and the outside if around the Planck length.  Now stick your spaceship inside of the bag, and then put a warp bubble around the bag.   It requires a lot less negative energy.  Voila!  Crisis averted.
Schematic from original article.
Region II is the bag.
Region I is where the ship is.
Region IV is the warp bubble
Now, warp drives are cool of themselves, but what I really want to talk about is the device that distorts space so the inside of the bag is bigger than the outside of the bag.  This is sometimes called a "van den Brocek bubble", or, somewhat more appropriately, a Bag of Holding.

We've gone from warp drives to the bag of holding, and we're not even done yet.  We're going all the way to Narnia.