May 17, 2005

part 6 - measurement

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Let's look a little at the measurement problem now. Let's first start with one of the odder experiments undertaken to show quantum effects.

The area taken up by a probability wave is typically quite small. When we're talking about the odds that an electron will be here or there we're usually not talking about large macro distances. There is a fairly straightforward example of where this is not true though. Photons arriving here that come from a distant star.

Because these photons have traveled so far and we are pinpointing that photon down to a relatively small location (our eye) the sideways momentum (uncertainty principle) makes the probability wave expand to sizes we can measure with our arms. This sideways momentum is much like the effect that increases the size of the electron glow when we decrease the aperture in the previous experiment. In effect our probability function looks something like a giant flat pancake hurtling towards earth. For photons arriving from Betelgeuse we're talking about a pancake 10 feet wide.

But we don't see a big pancake. We see the observed photon, a gleam in the eye. That doesn't however mean it is impossible to measure this pancake. In fact it was done in Australia. A scientist used 2 twenty foot mirrors mounted on box cars. The mirrors reflected light from a distant star onto a photon detector. First the box cars were close together. Consider one photon. The probability function hits both mirrors, reflects back to the photon detector and interferes with itself on the way there (think about how a water wave interferes as it bounces back from a wall). The result is an interference pattern. The mirrors are then slowly separated and eventually it will be far enough apart that the proxy wave (I can't remember if I've used this term before, proxy wave is Psi) isn't large enough to hit both mirrors and the interference patterns will cease to exist. As we go forward think about this giant pancake wave as it collapses to a single photon.

Now a little more physics background again. We'll use some of this stuff throughout the remainder of the posts. Polarization is one of the simplest dynamic attributes - it can only take on 2 values. Any simpler and it would be a static attribute. A individual photon is either entirely polarized in a particular direction or entirely polarized perpendicular to that direction. This polarization direction is always perpendicular to the direction light travels. Think of a clock with a light beam coming out where the 2 hands connect. The hands point in a direction of polarization for any photon.

When you measure polarization you can only check for polarization in one of those clock directions. You either you get a 'hit' or you know it's polarized 90 degrees to the direction you tried to measure. For those of you who have done polarization work before don't confuse the effects of a light source (many photons) and what I'm saying here about individual photons. Because we can only do this in one direction we can only learn so much about the overall polarization of any photon.

Let's explain this with an experiment. I have a light source that kicks out photons one at a time and a polarization measurement device. I can set the polarizer to any direction I wish to measure with 0 degrees representing the 12 o'clock position. When I measure the polarization at 0 degrees I am measuring P(0) or if it's set to 45 degrees I'm measuring P(45).

For the photons coming into my polarization measurement device I can get a number of different outcomes for a series of photons:
  1. 100% hits - this means the light was polarized in the direction I measured
  2. 100% misses - the light was polarized perpendicular to the direction I measured
  3. 50% hits/50% misses - The light is unpolarized in that direction
  4. Anything else - the light is partially polarized in that direction
Examples of light being unpolarized in every direction are light from the sun or a lightbulb. Light that is partially polarized is light that reflects off of water or the blue light in the sky.

Consider if we measure P(0) for a wave. We get a hit or we don't. For a hit we know it's vertically polarized (V photon). If not, it's horizontally polarized (H photon). Similarly if we measure P(45) for a wave and we get a hit it's diagonally polarized (D photon). If not, it's slant polarized (S photon).

Say our experiment has a light source emitting D polarized light. P(45) = 100% or 100% of the photons record a 'hit' in our measuring device. How about P(0)? Well the D photon can really be thought of as a combination of an H photon plus a V photon. The superposition of those two proxy waves adds up to a D photon. This tell us that there is a 50% chance we'll get a hit and a 50% chance we'll get a miss. We don't know which of the 2 potential photons represented by the proxy wave will end up being recorded once the wave function collapses. Now if we inquire about how this works we get to the heart of the measurement problem. There are a number of ways to think about this:
  • Physicists can't represent what the photon is doing in classical physics. They must use quantum possibilities. The measuring device and it's result can't be represented in quantum possibilities. It must use classical certitudes. Where do we put the cut from quantum to classical?
  • Another way - Orthodox ontology says all photons in this experiment are identical. The measurement gives different answers (hits or misses). At what point do the differences arise?
  • Another way - Feynman says that a quon takes all possible paths. At what point in this experiment do the numerous paths becomes one single actual path?
  • Another way - A D-photon will take both paths (going through the H part of the polarizer or getting blocked and deflected out another path of the polarizer). At what point do the 2 paths become a single path and what happens to the path not taken?
  • Another way - When does quantum ignorance turn to classical ignorance? Before we look at the polarizer measurement device, is the recording in the device a quantum possibility or is it a classical hit or miss?
  • Another way - When does the wave function collapse? In the measurement device? In your mind? When you look at the recording on the measurement device? Somewhere else? Ask yourself what is so special about these places versus the others that the function would collapse here?

We could ignore the orthodox ontology which leads to these kinds of questions but then we have to deal with faster than light transmissions (a la the hidden variable theories) which is not at all appealing to scientists. Those who believe the ontology fall into 2 camps - Bohr/Heisenberg and von Neumann.

von Neumann was a mathematician (see Godel posts) so he approached this concept of the wave collapse very logically. Where could it collapse? In the polarizing measurement device? What's so special about that? In fact you can run an experiment where you prove this isn't the case. The device spits out the light one of two sides. If it's polarized in the direction of the device it goes one way and you measure a hit. Otherwise it goes out another way and you measure a miss. You can rejoin these two pathways with mirrors and guess what? You get an interference pattern. It's still a wave after it leaves the device. You can keep doing this again and again. von Neumann eventually decided there was only one place left where the mechanics of the wave wasn't susceptible to this problem - the consciousness of a human. Think about this. von Neumann is a mathematician. A supreme logician. And he ends up saying we create our own reality by way of our consciousness.

Now take this to the extreme. This literally means when no one is there to see and hear a tree fall in the forest, it not only doesn't make any sound, it doesn't actually fall. It is still in a wave of possibilities - fallen, not fallen, self combusted, etc. Schrodinger rebelled against this concept with the concept of the Schrodinger Cat. You put a cat in a box. Inside the box is a polarizing measurement device. If a photon goes out one way it triggers a poison to be released. If it goes out the other nothing happens. Send a photon into the box (for this to truly work the box has to be fully separated from us - no sound, no heat, no anything can get out). Is the cat alive or dead? If consciousness creates reality and we don't know what happened, Schrodinger says the cat is both alive and dead. The photon's possibility went through both ways. The wave hasn't collapsed yet. So the cat has been killed by the poison and yet has also not been killed by the poison. As someone famously said, this does not mean the cat is sick :).

Shrodinger didn't make this point to create a paradox. He made it to show how preposterous it is. But is it? Tough to say. I personally think it is preposterous but there's no real way of deciding one way or the other. Since the proxy wave's existence requires us to not measure it, then how can we learn anything more about the status of the cat? Any attempt to learn the cat's fate by definition collapse the wave function.

Bohr just avoided the whole issue in its entirety. He said the quantum world and the classical world (the only world we can experience) are just separate things that don't commingle. The quantum theory represents what is going on but has no interpretation. Don't step into explanations of the quantum world. It is unknowable. He is saying stop this line of thought because it is futile. The quantum world is utterly beyond any ability to be grasped. A hard line for a scientist to take.

Others have tried to point out that we are quantum too. There is no such thing as a polarizing measurement device. It is a host of possibilities as well. That device is quantum so there is no way to possibly measure a quantum event in a way we want to. I actually think there is some truth to this. If we and all things are made of quantumstuff then how do we do a traditional observation of an experiment? We suddenly become part of the experiment. We have a wavefunction. The device has a wavefunction. How our wavefunctions intermingle with the wavefunction we're trying to observe screws up the experiment we actually want to conduct.

How? Hard to say. It's this line of reasoning that led to the many world hypothesis. We are a multitude of possibilities since we are a waveform. Just like the quon we take all paths possible. Since we only experience one path perhaps somewhere else we are taking the other paths. It's only the magnitude of what we're talking about that makes us want to shy away from this concept. How can an infinity of universes and 'we's' exist? If you have no problem with that concept you can see how it nicely explains much of our problem. All these possibilities do exist in the classical world except in other (I hate to use this word) parallel universes. The cat is alive perhaps in ours and dead in another. There is no collapse. Just a forking of reality.

Ultimately though you can see how none of these leave you with a satisfied taste in your mouth. Nothing is clean about any of these interpretations which is why there are so many of them.

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