3D Movies and Quantum Mechanics

As 3D media becomes more popular, it’s interesting look at the technology which allows light to be targeted to the left and right eyes separately.  If you saw Avatar in the theaters you donned glasses which have polarized lenses.  We can call the filter over the left eye “L-polarized” and the right filter “R-polarized”.  The movie projector emits unpolarized light, but that light can be passed through a polarization filter which is synchronized to each frame of the movie.  Frames meant for the left-eye are L-polarized so that they match the left-eye of the glasses, while frames meant for the right-eye are R-polarized.  In the RealD technology, the filter switches between L and R polarization 240 times per second, allowing 120 Hz frame rate for each eye.

Something interesting about polarization is that it works even with a single photon.  If you send an unpolarized photon through a L-polarization filter there is a 50% chance it will be blocked and a 50% chance it will pass through.  If you then this L-polarized light through another L-polarization filter it will pass through 100% of the time, but with an R-polarization filter it will pass through 0% of the time.  This is a purely quantum mechanical (QM) effect that cannot be explained through classic means.

A basic rule of QM is that if you want to observe the state of a system, you must make an observation by operating on the system.  In this case our observable is the polarity of the photon and our operator is the polarization filter.

Incredibly, QM says that the eigenvalues of a quantum operator are the observables, where the states of the quantum system are the eigenvectors!  If we can remember our eigenvectors and eignvalues from linear algebra we have the following:

where, is the operator, is the eigenvector and is the eigenvalue.

Now for our observables to be real our eigenvalue solutions to this equation must be real, since QM tells us they are equivalent. (We assume our observables are real because we can only measure real values in nature, not imaginary one.)  In linear algebra, to assure that we have real eigenvalue solutions, the operator should be a Hermitian matrix.  This is a square matrix where the entries on opposite sides of the main diaganol are complex conjugates of each other.

Here is a table which sums up the relations in this equation:

Symbol	Math	QM	3D Movies
	Hermitian matrix	quantum operator	L or R polarization filter
	eigenvector	quantum state	L or R polarized light
	eigenvalue	observable	L or R measurement

What’s bizarre is that when unpolarized light passes through the filter, it must “decohere” into the eigenvectors of L or R polarized light so that we get a real observable. The process of decoherence is one of the great mysteries of QM: particles only exist as probabilities until they are measured, at that point, Nature appears to “reset” them into a well-defined state.

Universal Instruments

I’ve written before about how great Netflix streaming movies are.  The library isn’t spectacular; however, if you’re into documentaries, you can instantly watch a huge selection.  I love docs, and over the past couple weeks I’ve seen a few specifically about artists: Rivers and Tides, Scratch, B-Boy Planet, and Touch the Sound.

Scratch is about turntabalism, a musical form where the instruments are record players.  While these turntables produce highly unique sounds, they also are capable of mimicking any other instrument depending on the given input (i.e. record).  This will instantly remind any computer scientist of universal Turing machines, which are capable of mimicking any other Turing machine.  (Turing Machines, first defined by Alan Turing, are the basis of all computation including human intelligence (more about this in future posts)).

A musical instrument which can mimic any other might be called a “universal instrument.”  It seems there are 2 categories of universal machines: audio players which can play an arbitrary input (e.g. record players, cd players, mp3 players), and instruments which can change their tones in real-time (e.g. tone generators, synthesizers, computers).  Any device which can output arbitrary sine waves in unison can re-create any other instrument due to Fourier decomposition.

Some might debate whether a cd player is really an instrument, but it becomes clear when you realize a musician can manipulate the output through even rudimentary controls (e.g. seeking, volume).   A more realistic debate is whether such a player is really a universal instrument, if all of the information is only in the input string.  Interestingly, this parallels a similar debate about a disputed univeral Turing machine! Stephen Wolfram offered $25,000 for a proof that this machine was in fact universal.  It only has 2 states and 3 symbols and is the simplest possible universal machine, although some have debated whether the universality is only a result of a specific input, which actually encodes the universality, and not the machine itself.

Video Feeds

These days, paying for cable TV makes less and less sense.  My roommate got an HDTV.  i hooked up this ghetto antenna (basically a short wire), and we picked up 6 HD ATSC channels!  Sure it helps to live close to an ATSC antenna.  You can check antennas near you on AntennaWeb.  Unfortunately we cannot get NBC HD over ATSC, but that’s ok because the best show on NBC is Sunday Night Football, but nbc has an incredible online SNF feed where you can choose various camera angles!

Also, if you have a Netflix membership, you can watch thousands of movies instantly online.  Only problem is you need to use IE because of Microsoft DRM.  Although DRM is extremely annoying, it allows providers to stream copy-protected material, so that definitely makes it worth it.

Another great online source of video is Hulu.  They have the entire series of Arrested Development which I highly recommend.

So where is this all leading?  Well cable companies seem to be in trouble, since they no longer have a monopoly on video distribution.  All that matters now is who is who can provide the best IP connection.