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Third-Polarizing-Filter Experiment Demystified -- How It Works

(c) Copyright 2004 Darel Rex Finley. All rights reserved. This article,
with illustrations and copyright notice intact, may be freely
distributed for educational purposes.



Shine light through two polarizing filters oriented at 90deg to each
other, and no light gets through. But put a third filter inbetween
them, at 45deg to each of the existing filters, and amazingly enough --
some lights gets through!

This popular experiment is often described as "strange." It is
usually presented in the context of quantum mechanics, as an example
of the "spookiness" of quantum effects. Rarely, however, does the
presenter inform the audience that this experiment can be explained
in very simple terms of cause and effect, without reference to spooky
quantum magic or anything like that.

Let's start by going over the standard experiment:

                                [01]
                              Figure 1

In Figure 1, an unpolarized, parallel light source is fired through a
polarizing filter, and the light strongly registers in a light meter
at the other end.

                                [02]
                              Figure 2

In Figure 2, a second filter is introduced, oriented at 90deg to the
first one. Now, no light gets through.

                                [03]
                              Figure 3

In Figure 3, a third filter is placed inbetween the first two, at 45deg
to each of them. Suddenly, the light meter registers a significant
amount of light, although not as much as in Figure 1. Spooky!


Spookiness and the Word "Filter"

Why do these results seem spooky? The reason is because of the
misapplication of the word "filter." A filter is commonly understood
to mean a device that knocks some items out of a stream, while
leaving others essentially untouched. A good example of a filter is a
sieve -- it blocks objects of a particular size, while allowing
objects of other sizes to pass through.

                                [04]
                              Figure 4

Another example would be a color filter that knocks out some
frequencies of light while letting others through.

                                [05]
                              Figure 5

Understood this way, the results of the polarizer experiment are
indeed spooky. If the all-blocking equivalent of Figure 2 is
constructed using sieves or color frequency filters (see Figures 4
and 5), we are certainly confident that the addition of more filters
in the middle of the sequence will not yield different results at the
end.

But what if our so-called "filters" could not only block components
of the stream, but also change them? Then we would not be surprised
at all if the addition of new "filters" in the middle caused items to
get through to the end. If a sieve could not only block particles,
but also change their size, or if a color filter could not only block
frequencies, but shift light to a different frequency, then all bets
are off.

This, in fact, is what a polarizer does.

                                [06]
                              Figure 6

Look at Figure 6 and ask yourself this question: What percentage of
the unpolarized light is oriented to exactly 0deg or very nearly 0deg?
Almost none of it -- certainly less than 1%. So, if a polarizer simply
knocked out undesirable orientations, the strength of the remaining
light would be almost entirely gone -- it would be less than 1% as
strong as the original light source. But you know a polarizer doesn't
do that, because you can pick up an ordinary pair of polarizing
sunglasses and observe that they're not even particularly dark!
Obviously, something else must be happening.

                        polarizing sunglasses
                              Figure 7

Let's see what happens to each of the orientations represented in our
simple diagram (from Figure 6):

                                [08]
                              Figure 8

In Figure 8, we see that light already at 0deg is unchanged. We knew
that already.

                                [09]
                              Figure 9

In Figure 9, we see what happens to light oriented at 45deg -- it has
its transverse (vertical) component destroyed, and becomes oriented
to 0deg, but with a weaker magnitude. Simple geometry tells us that it
must have a magnitude about 71% of what it had before being polarized
to 0deg -- i.e., 1/sqrt(2) = .707

                                [10]
                              Figure 10

Figure 10 shows us that light that is close to 0deg loses only a little
of its magnitude when being crushed to 0deg...

                                [11]
                              Figure 11

...while Figure 11 shows us that light that is close to 90deg off of
the polarizer loses most of its magnitude when being crushed to 0deg.

                                [12]
                              Figure 12

And finally, Figure 12 illustrates light at 90deg to the filter being
crushed completely out of existence. Figure 12, in fact, illustrates
what is happening in Figure 2 when we had only two polarizers in the
path of our light source.

What is happening in Figure 3? With our new understanding of what a
polarizer does, it is easy to figure it out:

                                [13]
                              Figure 13

Figure 13 shows the middle filter taking 0deg polarized light (from the
first filter) and crushing it to a 45deg orientation. This causes the
light to drop to about 71% of its magnitude coming from the first
filter.

                                [14]
                              Figure 14

And Figure 14 shows the last filter taking the 45deg polarized light
(from the middle filter) and crushing it to a 90deg orientation. This
causes another 29% drop (0.71x) in magnitude, for an overall drop of
exactly 50% (as compared to the results of the single-filter setup in
Figure 1). These results can be verified by performing the experiment
with an actual light meter -- the meter should show about twice as
strong a reading in the Figure 1 arrangement as it does in the Figure
3 arrangement.


So there you have it! No spooky quantum properties. Nothing very
mysterious about it, in fact. A straightforward chain of cause and
effect, yielding rational, comprehensible results.


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