A Matter of Relativity?
Copyright 2006/2007 James A. Tabb
Part 3: Polarized Light Weirdness
Figure 7 shows calcite crystals in which the light is split into two parts, a horizontal (H) and a vertical (V) channel. If we send individual photons through, they go through only one channel or the other, never through both, and those that come out of the H channel are always horizontally polarized, those that come out of the V channel are always vertically polarized as we might expect.
Figure 7. Photon in Calcite
It is possible to orient photons to other angles at the input. One such arrangement is to adjust them polarized so that they are tilted 45degrees right or left. If we orient the input to 45 degrees, tilted right (+45), we get half of the photons coming out the H channel and half out of the V channel, one at a time, but these are always horizontal or vertical polarized, no longer polarized at +45.
Figure 8. Reversed Crystals
Now comes the weird part as shown in Figure 8. If we put a second calcite crystal in line with the first one, but reversed so that the H channel output of the first goes into the H channel of the second and the V channel output of the first goes into the V channel of the second, we expect the output to consist of one photon at a time (and it is), but since the first crystal only outputs H or V polarized photons we expect only H or V polarized photons out of the second crystal.
However, if we test the polarization of the output, we find that the photons coming out are oriented to +45. Individual photons go in at +45 at the input, become individual H or V oriented photons in the middle, but come out oriented +45 again at the output! Somehow the two channels combine as if the individual photons go through both channels at the same time, despite rigorous testing that detects only one at a time. Quantum weirdness at work.
The polarization problem, like the double slit problem, is often called a quantum measurement problem. An often-quoted theory is that the photon does go both ways, but any attempt to detect/measure one of the paths disturbs the photon such that the measurement results in a change in the path of the photon.
Relativistic Effects Again
When you apply relativistic effects to this scenario the effect is exactly the same. The calcite crystals and all the paths are initially zero length as the photon approaches them.
The crystals and the paths expand as the photon enters them until the photon spans them end-to-end of the entire experiment. The two paths are separated by zero distance and have zero length and can be treated as if they are only one path. The experiment has no depth.
Much like the case of the double slits, if the paths are complete such that the edges of the photon can “feel” itself through the crystals when it hits them, it partially separates and then melds together at the front to recombine without ever becoming two parts while maintaining its integrity, in this case +45. If the paths are not complete, it is forced to choose one path or the other. When it is able to meld around a path, the recombination restores the wave polar orientation. When it can’t, the recombination does not occur and the polar orientation is destroyed.
Once again, the effect is due to the relativistic effects of time dilation and length distortion/contraction for the photon.