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.

Life’s Handedness

Origin of life research is a facinating subject, but one of its most baffling findings is that all life that we know of on this planet has a certain chemical “handedness” or chirality.  Well there is some new research that shows why evolution might prefer a certain handedness: certain reactions are more effecient depending on the handedness of the chemicals.

UPDATE: An insightful comment brought up the fact that chirality is an important subject in physics as well.  It turns out this is a useful concept throughout the sciences (maybe because of its relationship to symmetry.)   Here’s some more detailed information I found online, as we go from concrete to abstract:

Biology – Amino Acids are the building blocks of proteins (a subject which I want to blog about another time) which are essential to life.  There are left-handed and right-handed versions of them, designated L and D respecitively.   In chemistry, there is in general no preference between the two, and most reactions will result in equal numbers of each (called racemic).  However, in nature generally only L-amino acids are found in proteins.  Why this “homochirality” occurs is under much debate, but the above (and simlar) research may point in some promising directions.

Chemistry – Chiral molecules are those for which the atomic pattern differs from its mirror image.  The differences can be described by the following:

1. Configuration (R/S) – The relative position of the atoms in a molecule as it relates to their atomic numbers.
2. Configuration (D/L) – The relative position of the atoms as it relates to the molecule glyceraldehyde.
3. Optical Activity (+/-) – How a solution of the molecule rotates polarized light.

Physics – According to wikipedia: “The chirality of a particle is more abstract. It is determined by whether the particle transforms in a right or left-handed representation of the Poincaré group.”  Unfortunately I do not understand the slightest about this group (a 10-dimensional lie group which represents the isometries of Minkowski spacetime), so it will have to wait for its own blog posting after some research.  Anyway, what is so interesting about chirality in physics, and what our insightful commenter alluded to, is that the weak interaction (one of the 4 fundamental forces of nature) only acts on left-handed fermions!  Remember that fermions have half-integer spin and make-up all matter due to their adherence to the Paui Exclusion Principle,  Nature is sometimes not as symmetrical as we would like her to be.

Mathematics – Again from wikipedia: “A figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. (In Euclidean geometry any isometry can be written as with an orthogonal matrix A and a vector b. The determinant of A is either 1 or -1 then. If it is -1 the isometry is orientation-reversing, otherwise it is orientation-preserving.)”

Hello World!

I’m putting together a blog of things I find interesting.  Hopefully I will update it at least once a day, since I’ve always felt that is the sign of a good blog.

What a better topic to start with than the exciting results from the CDF experiment at Fermilab running on a particle super-collider called the Tevatron in Illinois.  All high-energy physics experiments have confirmed the Standard Model (SM), which was discovered in the 60s,  but some new results from CDF do not fit into this model!  There could be many reasons for this, but it could be the signature of an unexpected particle!  Considering that the SM has been perfect for the past 40 years, it seems quite likely that there is a more mundane explanation for the results (e.g. unexpected background noise), but that will not keep the physicists from theorizing about new potential particles.

Here is a basic explanation of the results:CDF Ghost Muons

Here is more detail from one of the experimenters: CDF publishes multi-muons!!!!

And here is the actual paper: Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV

Another interesting phenomena is not only the physics involved, but also the physicists themselves and their communication.  Many world-class physicists regularly post comments on other physics blog.  (Is there another academic subject which has this same level of open communication??)  And when physicists communicate sometimes there is fireworks.  In the case about the CDF, one physicist accused another of getting leaked results of the CDF experiment and used it his paper which happens to coincide with the unexpected CDF results.

The author of the paper stated: “I can tell you officially we had no word on this [the CDF reuslts]. This blog is, in fact, the first I’d heard of it”.

To which a CDF experimenter replies: “That is pretty hard to digest. Lepton jets with lifetimes. Come on. I think you owe it to the physics community to let us know where the leak came from.”

Which then received a several paragraph diatribe scorning the skeptics and the blogging community: “I find your cynicism remarkable . . . at least most of us don’t think of physics as a soap opera rife with rumor and innuendo, or spend the precious time we have cynically tossing around completely baseless and deeply offensive accusations.”

You can read about this confrontation form one of the participants here: Nima Arkani-Hamed’s letter on multi-muons – and my reply

All very entertaining in my opinion.  Not be out down is of course the infamous Lubos Motl who is a String Theory researcher at Harvard, who compares one of the commenting physicists to “slightly retarded children”.  And accuses another of “attempting to spread rumors that Arkani-Hamed and Weiner may have heard about the upcoming experimental paper in advance.”  You can read his entertaining commentary here: CDF sees dark unified SUSY in lepton jets?