Weirdness of the Universe

Greek letter psi Friday in my advanced physical chemistry lecture, we stumbled upon the bizarre reality of the universe in which we reside: collapse of the wavefunction. Before today, I was familiar with such notions, but did not know the explicit name for the phenomenon that many of the great minds of quantum mechanics and physics in the early twentieth century found unsettling. Before I get more into what collapse of the wavefunction is, I would like to say that this discussion starts to cross philosophical bounds that many people have wrestled with for some time. Many scientists find the results a bit uncomfortable (as anyone should who understands what I am about to present).

I have not read the parts of my textbook that cover this, so my explanation and word usage may not be consistent with literature. I will do my best to present the idea. First a definition. A wavefunction that is a solution to Schrödinger’s Equation contains the probability of configuration in space and time. Because the configuration of a particle in space can give us certain physical information about the particle (energy, momentum, angular momentum, et cetera), the wavefunction allows for extraction of those physical quantities. (There are some restrictions on what one can and cannot know from a wavefunction modeling a system, but I will not get into those gory details here.)

So, collapse of the wavefunction means that when a physical measurement of a system is taken, the wavefunction (being a probability of many states linearly combined to form a superposition state) collapses to the value measured physically. This may not initially strike you as bizarre or shocking simply because you do not understand the scope of this fact. Here is an interesting example of this phenomenon at work.

Figure 1 shows that a vertically-oriented polarizer (90 degrees) produces vertically polarized light when randomly-oriented incident light passes through it.

Figure 1. A vertically-oriented polarizer produces vertically-polarized light.

Figure 2 shows what happens when a second polarizer is introduced at forty-five degrees to the first. The first gives vertically-polarized light and the second, produces one-half the intensity of the light produced by the first. Why? The second polarizer is oriented to select only half of the same number of vertically-polarized photons. So far so good.

Figure 2. A linear polarizer at 45 degrees will produce one half the intensity of light when vertically polarized light passes through it.

Building on the concept presented in Figure 2, we see that two polarizers that are oriented perpendicular to one another in Figure 3 and allow no light through. These are often termed cross-polarizers.

Figure 3. Two polarizers perpendicular to one another produce no light.

Now for the weirdness of the universe that is collapse of the wavefunction. In figure 4, if we introduce a third polarizer at forty-five degrees between the two crossed polarizers, we expect that the light coming out the end to be of zero intensity. Why? The second polarizer selects half the light (3) coming out of the first (2). When this light passes through the last polarizer, we expect it to block all light given that it should block all vertically-polarized light. But, as it turns out, the light is no longer vertically polarized. Upon making the measurement of the polarization, we have caused the wavefunction that defines the orientation of the light to collapse to the measured value as it emerges from the second polarizer. So, the next polarizer selects only the horizontally-polarized light, producing half the intensity of (3). Bizarre huh?

Figure 4. We introduce a third polarizer and expect no light at the end, but this is not the true result.

For the longest time, I was perplexed about the nature of polarizers in my research. The activity of one polarizer is not that bizarre and neither is two, but when a third is introduced, these contradictory behaviors emerge that defy the logic that drive the activities of the one- and two-polarizer setups. I am still perplexed by this result, but at least I can now attribute the behavior to some phenomenon. I’ll post another example about this another day.

When I began pondering this more on Friday, I was inclined to ask what is happening physically that causes such a result. That is difficult to answer, but as it was explained to me, the act of measuring disturbs the wavefunction, altering it and causing it to take on the form that gives the value extracted. I am not sure if I have explained this well enough, but if you have questions, please post them!