## Powers of 10: the next generation

If you teach astronomy, you probably know Powers of 10, an old film by Charles and Ray Eames to illustrate vast range of length scales in the Universe.  (To see it on the official web site, you seem to have to register, but youtube has it too.)  Well, the American Museum of Natural History has created a new video along the same lines.

Powers of 10 from AMNH

It’s got a few big advantages over the old Powers of 10: it goes out to 100 times larger scales than the Eameses’ film, and it’s based on real data even out to very large scales, which of course wasn’t possible when Powers of 10 was made.

The new film only goes up in scale from the Earth, unlike Powers of 10, which also went down to the subatomic realm.  Whether that’s an advantage or a disadvantage is up to you.

Powers of 10 explicitly showed the length scale at all times: on the right is a running counter showing how many meters we’re looking at, and on the left is the same thing in other units.  Also, every factor of 10 is indicated by an outlined box.  The new video indicates the occasional milestone in length scale, but it doesn’t do it consistently throughout.  I think that’s a pretty big pedagogical disadvantage of the new film.  It’d be nice if someone added a counter like that to the film.  But it’s still pretty cool.

## How 3D movies really work

In a comment on my earlier post about 3D movies, Phillip Helbig writes

In the latest Physik Journal (magazine of the German Physical Society), there was a two-page article on 3-D techniques. You mentioned three: colour, linear polarisation and the quarter-wave-plate model (your hypothesis was correct; that's how it works). The last is definitely the best of these three, but shares this problem with linear polarisation: the reflected image has to be polarised, so the screen has to be mirror-like, not just a white screen.

It’s nice to know that that’s what’s really going on!

Phillip goes on to say

There are two other techniques. One projects frames at twice the normal rate, altenately for each eye, and the glasses contain infrared-controlled LCD shutters which alternate at the appropriate rate. Probably the best system, but the glasses are more expensive.

I actually used a system that worked on this principle, way back in the 1980s, when I had a summer job working in Don Wiley‘s lab at Harvard.  It was a special computer with a huge monitor that rapidly switched between two images, along with a pair of glasses that plugged into the computer and alternately switched from opaque to transparent so that each eye was presented with one of the images.  This must have been a special-purpose, very expensive system back then.  I don’t remember how fast the switching was;  I’m sure it wasn’t fast enough to show movies and have it look good.  The lab used it to visualize big biological macromolecules.

Phillip again:

Another one is quite interesting: for one eye, use three primary colours, and for the other eye, use three OTHER primary colours. The filter for each eye only lets through the primary colours intended for that eye. (For a given perceived colour, there are many ways of mixing it out of narrow-band "primary" colours".

I’ve never heard of this.  What a cool idea.  The next time I teach our mathematical methods class, I’ll use it as an example of vector spaces and projection operators:

The spectrum of a light source is a vector in an infinite-dimensional vector space, but we only see color in a three-dimensional space.  Your visual system is in effect projecting from the big space down to the small space, so of course there are many different spectral shapes that are perceived as the same color.  The filters in front of each eye are additional projection operators.  By a clever choice of those operators, you can use different parts of the original, big vector space for each eye, and still present the entire three-dimensional space to each eye.

I bet you can mock up a not-very-many-dimensional model of how all this works.

## Never believe an experiment until it has been confirmed by a theory

Supposedly Sir Arthur Eddington said this, and supposedly he was at least partially joking.  I like to think he was only half joking, though, because there’s a pretty big nugget of truth in this supposedly backwards statement.  It’s really just an obnoxious way of stating another favorite adage of scientists: Extraordinary claims require extraordinary evidence.

If someone tells you the result of an experiment, and that result fits nicely in with a previously-established theoretical framework, you should be more inclined to believe it than you would be for a claim that does not fit into such a framework.  In so doing, you’re just being a good Bayesian reasoner, taking into account both your prior knowledge and the information contained in the new experiment.

Take, for instance, the idea that cell phones cause cancer.  Maine is considering a law requiring warning labels to this effect.  The epidemiological evidence is, to say the least, mixed.  I find the “don’t believe an experiment until it’s confirmed by a theory” maxim to be a pretty convincing argument against the idea tha there’s any risk: as far as I know, no one has proposed a plausible mechanism by which the microwave radiation emitted by cell phones could cause cancer.  As Bob Park has been pointing out in his What’s New column for quite a while now,

Cancer agents break chemical bonds, creating mutant strands of DNA. Microwave photons cannot break chemical bonds.

I’m terribly ignorant about biology, so maybe this argument is all wrong, but it sounds convincing to me.

## 3D

I went and saw Avatar in 3D last night.  Everybody told me it was visually amazing but the story was lame.  The first part is definitely true, but (probably in part because my expectations had been lowered so much) I was actually pleased by the story.  It’s totally formulaic, but I’m not sure that’s such a bad thing.  There are lots of things worse than a well-executed formula.

But that’s not what I want to talk about.  Naturally, after the movie was over, I had to try to reverse-engineer how the 3D glasses work.

To get 3D, you have to present slightly different images to the two eyes.  In the old days, the glasses had color filters on them, and the two images were presented on the screen in different colors. That has the significant disadvantage that you can’t use color to convey other information (i.e., color!).  So in modern 3D, the different images for your two eyes are projected onto the screen using two different polarizations.

The simplest way to do this would be to use horizontal and vertical linear polarizations.

[(Information for people who don’t know / don’t remember optics.  If you do know, then skip everything in brackets.) Light is a wave of electric  and magnetic fields.  The fields have to be perpendicular to the direction the light is traveling, but subject to that constraint they can be oriented in different ways.  Linearly polarized light just means light where the electric field is wiggling back and forth in a particular plane.]

The simple procedure would be to stick a filter in front of your left eye that only lets through horizontal polarization, and one in front of your right eye that only lets through vertical polarization.  Then project the two images onto the screen with the appropriately matched polarizations, and you’ve got it.

That’s not how it’s done, though.  One reason is that if you tilted your head, the polarizers wouldn’t be aligned right.  In fact, if you tilted your head 90 degrees, the image intended for each eye would reach the other one, which would have the disconcerting effect of flipping the image, so that stuff that was supposed to look close to you looked far away, and vice versa.  Even if you tilt your head less than 90 degrees, you’d get an unacceptable distortion.  This doesn’t happen — I tried it.

The solution to the head-tilting problem  is to use circular polarization rather than linear polarization.

[With circularly polarized light, the electric field rotates as the light propagates, so that the tip of the electric field vector traces out a spiral pattern.  In other words, it rapidly switches between horizontal and vertical as the light moves along.  There are two kinds of circular polarization, left and right, corresponding to clockwise and counterclockwise spirals.]

The images for your two eyes are actually projected on the screen in left and right circular polarizations.  Since a clockwise spiral is still clockwise no matter how you tilt your head, this solves the head-tilting problem.

So you might imagine that the 3D glasses just consist of a filter for each eye, one that lets through left circularly polarized light and one that lets through right circularly polarized light.  I think that is the general idea, but the details are a bit more complicated.  One way to see this is to take two sets of glasses and hold them up so that light passes through the left lens of one pair, followed by the right lens of the other.  (They’re not really lenses, of course; I’m just using “lens” to mean one of the two things in a pair of glasses.) In the simple picture I just described, you might expect to see no light at all get through: the first lens would block all of one polarization, and the second would block the other.

[If you’re just looking at a natural light source, it’s probably unpolarized, meaning that the electric field points every which way.  But even unpolarized light can be thought of as a combination of left and right circular polarizations, so the first lens would knock out half the light, and the second would knock out the other half.]

But that’s not what happens. Quite a bit of light gets through in this experiment.  Moreover, if you rotate one lens with respect to the other, the light that gets through changes from gray to yellow.  What’s up with that?

A couple of clues: First, the fact that the image changes as you rotate the lenses suggests that linear polarization is involved after all.  Second, there’s a fact you can dredge up if you’ve studied optics: it’s not easy to make a filter that passes one circular polarization and not the other.  What you can make is something called a quarter wave plate, which magically converts circular polarization into linear polarization and vice versa.  For instance, you can make a quarter wave plate that turns left circular polarization into horizontal linear polarization and right circular polarization into vertical linear polarization.

So now we can make a guess: each lens consists of two parts: a quarter wave plate to turn circular into linear, followed by a polarizing filter that just lets through one linear polarization.  The two lenses either have different linear polarizers at the back end (one horizontal and one vertical), or different quarter wave plates at the front (one that turns L/R into H/V, and one that turns L/R into V/H).  Either way should work.

Here’s one test of this theory.  Take two sets of glasses, and hold them up to a white light source, so that the light passes through one lens in the usual way, and then through another lens in the reverse direction.  According to the hypothesis, the light coming out of the first lens should be linearly polarized, and when it hits the second lens it should hit a second linear polarizer.  That polarizer will let light through if it’s lined up the same way as the first one, but block it if the two are perpendicular.  Sure enough, that’s what happens. When you rotate one lens with respect to the other, the amount of light that gets through changes, dropping to essentially zero when the rotation is 90 degrees.  This is true whether you’re using the left or right lens in each case.

So the answer’s got to be version 2 of the hypothesis: both lenses have the same kind of linear polarizer at the back end (let’s say vertical), but they have two different quarter wave plates at the front end: one converts left circular polarization to vertical and one converts right circular polarization to vertical.

You can try a bunch of other similar tests, flipping the orientations of the two lenses various ways.  I think they’re all consistent with this theory, with the exception of one thing: sometimes, as noted above, the way the light gets through depends on color.  The most dramatic example is if you send white light through, say, the left-eye lens backwards, and then through the right-eye lens forward.  The result is a nice, rich purple.  What’s up with that?

According to the theory I sketched, the experiment I’m describing consists of sending the light through four elements: a linear polarizer and quarter-wave plate for the first lens, and then a quarter-wave plate and a linear polarizer for the second lens:

LP1  QWP1  QWP2  LP2

The two quarter wave plates next to each other form something called (not surprisingly) a half wave plate.  A half wave plate rotates linear polarizations by 90 degrees — that is, turns horizontal into vertical and vice versa.  In that case, we’d expect this sequence to let through no light at all: the first linear polarizer lets through only (say) vertical, then the HWP turns it to horizontal, and the second linear polarizer blocks horizontal.  So we should see black, not purple.

I think the explanation is that a quarter wave plate (or a half wave plate) can only be designed to work perfectly at one wavelength [i.e., one color].  The glasses are probably designed to behave correctly in the middle part of the visible spectrum, which means they’ll be imperfect at the two ends.  So this particular combination of lenses would do a good job at blocking out light in the middle of the spectrum (yellow, green) but not so good at  blocking out light at the edges (red and violet).  That seems consistent with what I observe.

I guess this must mean that the 3D effect is only perfect for light in the middle of the spectrum, and for other colors some of the image meant for one eye actually reaches the other.  Presumably this imperfection isn’t very noticeable “in the wild.”

One experiment I wish I’d tried during te movie: put the glasses on upside down, so that the image meant for the left eye goes to the right eye and vice versa.  This should have two effects:

1. Make you look even goofier than the other people in the room wearing 3D glasses.
2. Show you the picture inverted in depth (close stuff looks far and far stuff looks close).

If you try this during a 3D movie, let me know if it works (particularly #2 — I’m pretty confident about #1).