Wave or Particle?

Light is said to have the characteristics of both a wave and particle depending on its 'Mood' or quantum effect.

This is the only simple experiment that I know of.

Take three polarized sunglass lenses,hold two of them up with an inch between them,turn one until it goes dark, then take the third one and insert in between the other two and turn just it. You end up getting MORE LIGHT with three than you were getting with two.

The light is Magically changed from a wave function to a particle function. This is the Einstein Podolsky Rosen effect.






Okay, the EPR "paradox." First off, it's called a "paradox" because it patently contradicts all sorts of assumptions we make about the behaviour of objects in the classical world (see my follow up to Adrian). It is a natural feature of the quantum world, and there is (by definition) no paradox there, just stuff we classical humans can't wrap our brains around. With that out of the way ...

Before I can explain the EPR paradox, you need to understand basis states and superposition. I'm going to do that with a very cool experiment that some people will probably recognize. [I probably ought to write this as an I'ble, but I don't have the time or energy right now...]

First, a very quick introduction to quantum states and (alternative) basis states. We describe quantum mechanical states mathematically, using the notions and notations of coordinate systems. You can identify any point on the plane with (x,y) coordinates, writing r-vector = x*x-hat + y*y-hat, where "x-hat" and "y-hat" are orthogonal (perpendicular) unit (basis) vectors in each direction.

While the location of a point in space is fixed and absolute, the values of its coordinates is not. Consider navigating south of Market in San Francicso. If you have a GPS system, you can use longitude (North) and latitude (East) to identify your position. If you're old school, you can use street locations (northeast and northwest). Your actual location is unique, but the values of the coordinate numbers depend on which coordinate system (basis) you choose.

Similarly we can write (decompose) a quantum mechanical state into a sum of mutually orthogonal basis states, each with a coefficient which is a complex number (amplitude and phase). I will describe a very simple quantum system with just two basis vectors, namely linearly polarized light (for the cognoscenti, you can do exactly the same analysis using a circular polarization basis, but it would be much less accessible to the reader, so don't give me a hard time).

Light can be polarized in any direction -- up and down, side-to-side, or at any angle perpendicuar to the direction of the light beam. If you have a (cheap) pair of polarized sunglasses, take some Liquid Paper and paint a stripe on each lens, then pop them out of the frame. That stripe will define, for this experiment, the polarization direction of the lens. Actually, you're going to need two pairs of sunglasses, hacked the same way.

Take a non-coherent light source, like a nicely focused incandescent Maglite, and put one of your polarizers (lenses) in front of it with the stripe vertical. You now have a light beam which is 100% "vertically polarized." Keep it and cherish it, because shortly you're going to make it very confused.

Take a second polarizer, and put it in front of the first with the stripe horizontal. No light will come through. Since your beam is 100% vertically polarized, obviously it is 0% horizontally polarized, right? Right.

Now turn that second polarizer 45 degrees left (let's call it NW, by analogy with the streets I mentioned above). You'll see that some light (in fact, half the light) comes through. the 100% vertical polarization can be equally described as a sum of NW plus NE polarization (this is just vector arithmetic; technically V = 1/sqrt(2) NW + 1/sqrt(2) NE). By putting the NW polarizer in front of the beam, you're picking out just the NW component of that sum.

So far, all this is simple and obvious, right? Put a third polarizer in front again, this time oriented 45 degrees right, NE. It's dark, right? Obviously. NE is perpendicular to NW, and by the same argument as before nothing comes trhough.

Now for the fun part. Set up two polarizers, one N and one E (horizontal), in front of each other. This is back to the setup I described earlier. No light gets through, since the two are orthogonal.

Take a third polarizer, and put it in between the two you have set up, oriented
NE. What do you see? There's light getting through! about 25% intensity, but definitely not dark. "What the BLEEP is going on?" (no, Ramtha is not channeling the photons).

Follow the changes of basis in sequence. You start with 100% N polarization, which can be written as "1/sqrt(2)NW + 1/sqrt(2)NE". The NE polarizer picks out just the NE component at (1/sqrt(2))2 = 1/2 intensity. Now, NE can equally well be rewritten in the (N,E) basis as "1/sqrt(2)N + 1/sqrt(2)E". The next, E polarizer picks off the E component of that, again at 1/2 intensity. The net result is 1/4 the original intensity, because you've changed basis twice.

This change of basis will be an important piece of what's going on in EPR systems.