Posts Tagged ‘Avatar’

3D Movies and Quantum Mechanics

February 3, 2010

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:

H\, \psi = \lambda\, \psi

where, H is the operator, \psi is the eigenvector and \lambda 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
H Hermitian matrix quantum operator L or R polarization filter
\psi eigenvector quantum state L or R polarized light
\lambda 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.