## 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.

Why?

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.

## Saturday, December 28, 2013

### Please Stop Ruining the Hobbit

I just saw the second movie in the Hobbit "trilogy".

The movie itself is a series of pointless sword fighting and action scenes with a cast of a dozen or so flat characters whose stories go nowhere.  I guess if you like Michael Bay movies, go see the Hobbit; you'll love it.

There is precisely one interesting character in the movie, and that is Tauriel.  This is a Peter Jackson original character.  And I'm saying a lot here when I say that Bilbo, Gandalf, and Smaug, the three characters who near single-handedly enchanted my childhood, do not come across as as interesting as some random elf lady practically from legolas by laura, thrown in to appease focus groups.

I've determined that the only way to make sense of the movies is to perceive them as fan fiction.  Extremely expensive, high budget fan fiction.  Peter Jackson is telling his own made-up story using the characters and elements of Middle Earth, and it just happens to vaguely correspond somewhat to the series of events in the Hobbit.  And it's great if Peter Jackson wants to write fan fiction and spend billions turning it in to a movie, but I'm sorry to say that Peter Jackson isn't as good of an author or story teller as J.R.R. Tolkien.

So why is the cinema making the movie about Peter Jackson's fan fiction, and not about Tolkien's story, the one that sold all the millions of copies and inspired all the millions of authors?

## Saturday, December 21, 2013

### The Cross-Section of Angels

Solidity is an illusion.

You may or may not already know this.  Matter is mostly empty space: when you smack your hand against a table, what prohibits the further movement of your hand is the interaction of electrons, protons, and neutrons.  At base, everything is likely a point particle, and all appearance of volume is caused by energetic excitations.

When you fire one point particle at another point particle, from a strictly geometric standpoint, the probability of collision is 0%.  Nothing should ever hit anything else.  And yet, two electrons launched at one another will "bounce"; the reason there being the electromagnetic repulsion.  To account for this discrepancy between the expected geometric probability of scattering and the empirical measured scattering caused by the interaction, physicists who study such collisions use a quantity called a scattering cross-section.  A scattering cross section is, more formally, a fictitious area describing the strength of interaction between two particles.  This is given as a ratio: number of scattered particles divided by total incoming particles.

This ratio can be measured empirically in the lab by mere bean counting, but it can also be derived theoretically from considerations of the interaction potential.  This is how we know the majority of what we know about anything on scales smaller than molecular.  The existence of the nucleus within the atom, for instance (as opposed to Thompson' plum-pudding model) was discovered through a scattering experiment.  We only know about quarks and the strong interaction through scattering.  The recently discovered Higgs particle is also a result of scattering experiments.  In all of these cases, just bouncing particles off of something and measuring the exact way that the particles bounce is enough to tell us what a thing is made of, how it is shaped, and -- more importantly -- the kinds of interactions that it undergoes.

Visible light is not normally useful to this purpose at subatomic lengths, but actually normal vision is an example of a kind of scattering experiment.  Light from a bulb bounces off of an object and to your eye: you in a sense "measure" the angular deflection and intensity of this incoming light, and can thus determine the size, shape, and color of the object in question.

All of the things that you can see scatter light because all of the things that you can see are made of charged particles.  Charged particles participate in the electromagnetic interaction, as does light, which means that normal matter is able to scatter light (as opposed to, say, dark matter).  Were it not for the interaction (or coupling) between light and matter, then the electromagnetic cross-section of matter would be zero; light would see every surface as having zero area and therefore not bounce off of it.

To make this point more clearly, consider the neutrino.  Neutrinos are not known to participate in any interaction besides the weak interaction.  Therefore, neutrinos can fly right through the planet without slowing down.  They're not flying through it like bullets, boring tiny holes; they're just flying through it.  The solid matter of the earth is, to them, intangible and ethereal.  They don not undergo the electromagnetic interaction, and so do not "see" the earth there.

I say all of this as introduction.  What I really want to discuss are angels.  In particular, how do we see them?

## Friday, December 13, 2013

### Christmas: the Meta-Holiday

I would like to introduce a word to the language: meta-holiday.  A meta-holiday is a holiday that celebrates the fact of its celebration.

Initially, holidays are celebrated because of actual reasons.  Purim celebrates the deliverance of the Jews from the plotted genocide of Haman.  Passover celebrates the deliverance of the Jews from slavery in Egypt.  Yom Kippur celebrates redemption and atonement.  To stop picking on the Jews, Easter celebrates the Resurrection of Jesus.  The Feast of the Immaculate Conception celebrates the Catholic belief in beginning of the life of Mary without Original Sin.

Actual things.

But after a while, people stop caring about the reasons for the celebration.  But not only do they keep celebrating, but the particulars of the celebration become the reasons for the celebration.  Thanksgiving is celebrated because turkey and pie.  Halloween is celebrated because candy and costumes.  St. Patricks Day is celebrated because green beer and clovers.  Talk Like a Pirate Day is celebrated because talk like a pirate.

The worst of these is Christmas.

Christmas is the celebration of the celebration of Christmas.