capybara

2008-Apr-11, 07:03 PM

On the latest Astromony Cast show, Pamela and Frasier describe the wave-particle nature of photons as having a wave-function that collapses into a single point upon detection.

I am having trouble understanding this concept. What is a wave-function, and what is meant by "collapsing." How does detection of the photon cause it to immediately act like a single particle?

Tensor

2008-Apr-11, 07:14 PM

On the latest Astromony Cast show, Pamela and Frasier describe the wave-particle nature of photons as having a wave-function that collapses into a single point upon detection.

I'm sure a few others will jump in here. Simplified....

I am having trouble understanding this concept.

You're in very good company.

What is a wave-function,

The wave function is a quantum mechanical concept. It is the probability of finding the photon in a particular location.

and what is meant by "collapsing."

If you find the photon in a particular location, then the probability of finding it anywhere else, is zero. Hence, the wave-function collapses.

How does detection of the photon cause it to immediately act like a single particle?

Well, once you find the particle, it acts like a particle. You have to realize that your experimental set up will determine what you will most likely find. If it set up to find a particle, you will more than likely find a particle (think particle detector) . If it is set up to find a wave, you will most likely measure a wave (think antenna).

Ken G

2008-Apr-11, 07:47 PM

I am having trouble understanding this concept. What is a wave-function, and what is meant by "collapsing." How does detection of the photon cause it to immediately act like a single particle?The wave function represents our information about the particle, and it involves magnitude and phase, and you can picture it as stretching through space like a water wave, because water waves also have magnitude and phase at any point, and it propagates. It is used to make statistical predictions about what will happen when we confront that particle with a measuring apparatus. The whole idea behind that confrontation is to couple the particle to external influences that involve untracked information, or "noise", and when we make our predictions, we average over that noise because we can't track it. We set up the apparatus quite intentionally to bring in noise in exactly the right way to destroy "coherences" between different "points" the particle could be, and the result of that noise is that we can't know where it will go but we can know it will go to some particular point.

To fill in some of the trickier details, it turns out the wave function can be sliced in many different ways, but one way to do it is to associate an "amplitude" to the particle arriving at various points (an amplitude is a number with magnitude and phase, where the magnitude tells us the probability of it showing up there, and the phase controls a process called "interference" between the various ways the particle could show up there). If we do that, we are treating the wave function as a "superposition" of the particle showing up at all these points.

We are free to think in terms of that superposition, we haven't really done anything yet, but where we do something is we choose a measurement apparatus (say a photographic film) that introduces noise in exactly the way that destroys the coherences that connect the different pieces of that particular type of superposition. That type of coupling is what we call a "position measurement", so a photographic film is one of the things that has the right noise attributes to generate a position measurement, and that's why we choose it.

Now comes the really tricky part. After we intentionally destroy those coherences in that particular way, expressly to obtain a position measurement, we don't know where the particle will go because we had to use noise to do it. We only get statistical tendencies, called probabilities, stemming from those magnitudes of the wave function-- we don't need to track the details of the noise, it is the details of the wave function that count. No one knows, because science can't tell us, if the noise we introduced actually caused the particle to show up where it did, or if some metaphysical "dice" get rolled, but if you don't like metaphysical baggage there would seem to be no harm in selecting the former model-- that the noise controls where the photon goes, but the wave function controls its probabilities. As we can't track the noise, we just end up with a distribution for our prediction, like a poker player just before looking at the cards. Here each "card" is "the photon showing up at a different place".

One might ask where the concept of "particle" emerges from all this, and it has to do with the limitations on what the noise can do. Some kinds of noise can make a particle show up at a point, other kinds can make it have a particular momentum, but none can make it show up at two places or have two momenta at once, so that's where the concept of "particle" comes from. Sometimes people confuse "particle" for something that follows a definite trajectory, i.e. a classical notion, so it is safer to substitute the word "quantum" for "particle".

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