Simple example of the collapse of the wavefunction?

Ulysees

I'm not sure the double-slit experiment is one such example, maybe I have not understood it yet.

This experiment shows the wave nature of light due to the wavefunctions of photons. But how does it show a particle of zero size that is not just a burst of waves?

andrewm

First, do not be quick to assume photons have zero width, because otherwise the uncertainly principle would have [tex]\Delta x = 0[/tex], which is forbidden.

The collapse of the wavefunction can be imagined by detecting the photon as it passes through one slits. With the detector off, the photon is in a superposition of paths 1 and 2 and the experimenter observes an interference pattern. With the detector on, the photon travels either path 1 or path 2,and no interference pattern is observed.

Ulysees

Ok, so here's what happens when bursts of waves come to the entrance of a naval port. Let's say the entrance is very narrow. Each burst comes in, diffuses, and ends up pretty much all over the place inside of the port. No interference pattern observed. This does not prove sea waves have a particle nature. It is just short bursts that produce no interference.

So where do I find an undisputable example of the collapse of the wavefunction?

monish

I'm quite sure the double-slit experiment with light is NOT a good example of the collapse of the wavefunction. At least it's not a simple example. The famous experiment where you observe the particle as it passes through the slits is actually a THOUGHT experiment proposed by Feynmann, and it uses electrons, not light. I don't think it's ever been done with electrons, and I don't think it really works with light because there is no way of detecting single photons as they pass through slits.

I'd really like to see what people suggest as a simple example of the "collapse of the wave function."

monish

No, it's not because the burst is short that the wave ends up all over the place. It's because you have it passing through a single slit. A burst of waves through two slits will indeed show an interference pattern.

I agree with you that I'd like to see a good example of the collapse of the wavefunction.

Ulysees

You missed the point here, that it ends up all over the place is just additional information. The point is that the lack of interference does not prove particle-ness.

Can't believe no one noticed this.

Ulysees

Sure when they're in their normal condition, the probabilistic wavy one where the uncertainty principle is defined. But when they collapse?

Do they collapse to something that has a size?

andrewm

I would just like to correct my [tex]\Delta x = 0[/tex] assertion:

In order to measure the position of a particle, one needs a probe (say a photon, if we use Compton scattering) of sufficient momentum. As the position measurement becomes more ideal (to the limit where we know exactly the particle's position and [tex]\Delta x = 0[/tex]) one needs a photon of infinite momentum.

So the ideal position measurement is not forbidden, but it is strictly theoretical, as an infinite photon momentum implies an infinite photon energy. For all experimental measurements, the wavefunction does not collapse to a perfect position eigenfunction and so the resulting wavefunction has nonzero width.

A good discussion of this subject is given in Shankar, 2e, Section 4.2 "Collapse of the State Vector".

andrewm

I am not involved in quantum optics, but I am skeptical that there is impossibility in detecting single photons as they pass through slits.

See "Heralded Generation of Ultrafast Single Photons in Pure Quantum States" by Mosley in PRL.

monish

I can't comment on your reference except to note that it is a very modern one whereas the collapse of the wave function was something that bothered people in 1927. So I think if we are looking for a simple example of the phenomenon we should be going back to the source rather than arguing after the fact.

Ulysees

So collapse is when the wavefunction becomes smaller in extent? (Due to a device that detects the entity).

I found this in wikipedia, not sure if it says anything useful about the collapse of the wavefunction:



Electrons hit a screen that detects where they hit. But first they pass through a double slit. So collapse is when they hit the screen, right? I've read somewhere a statement by R Feynman I think that no one really understands the collapse of the wavefunction. But here things look so simple, too simple to be true. Dots on the screen is where the wavefunction of each electron collapses. Is it just that?

andrewm

I think so, yes.

From my memory of Feynman's books, he may have been trying to express the fact that most physicists postulate that the wavefunction collapses after measurement. If we assume that it is true, we can derive many of the experimental predictions such as the uncertainty relation.

As for the actual clockwork that occurs when a wavefunction collapses, your guess is as good as anyone else's. I think that's what he was saying.

monish

So it has nothing to do with the double slits or the interference pattern? You could shine a weak light on a piece of photographic film and watch the dots appear one at a time, and that would be the collapse of the wave function?

andrewm

Yes, when the photographic film "measures" the position of the photon it collapses the particle's wavefunction.

There is a nice example of the "dots appearing one at a time" in the book Principles of Quantum Physics by French and Taylor. I do not have the book with me, but the figure is 2-2 (or 12-2, maybe?) showing a photograph that is "built up" over time by using a weak light source (10^5 photons or so).

pmb_phy

I disagree. It's not forbidden. It just that you'd have [tex]\Delta p_x[/tex] = infinity.

Pete

andrewm

Yes, you're right. (I realized this in post #8)

monish

The appearance of dots doesn't mean the wave function has collapsed. The molecules on the photographic film (silver nitrate??) are presumably happier after they change color, and it is perfectly reasonable to think that they only need a bit of a quiver from the light wave to induce them to change states. To show the collapse of the wave function you would need one more step: you'd need to show that once a dot has appeared somewhere, that no other dots appear elsewhere at the same time...in other words, that the same wave can't stimulate the molecular transition in two places at once.

What is the evidence to show that it works this way?