Simple example of the collapse of the wavefunction?

[Ulysees]

I wonder if you read the exchanges in this thread. It is clear the double slit experiment demonstrates the form of a wavefunction, but it is not obvious at all that it demonstrates collapse because the same fringes or lack of them could be observed with sea waves entering a naval port.

So it seems that only dots demonstrate collapse. And if they have a statistical pattern, then they demonstrate the likely presence of the same wavefunction for all particles detected.

Any thought as to what is going on at dots and they are so big? The photographs from wikipedia I posted, might be showing square pixels on the grid of some sort of camera, not round dots on a continuous medium.

 

[Ulysees]

this is the Copenhagen interpretation of quantum mechanics. It can be argued the other way - I know that Everett's many world interpretation says that observation does not cause a system to stop being a superposition of states.

Therefore dots do not appear if no one is watching?

 

[bryanosaurus]

It is clear the double slit experiment demonstrates the form of a wavefunction, but it is not obvious at all that it demonstrates collapse because the same fringes or lack of them could be observed with sea waves entering a naval port.

This is the reason why this experiment's results are so fascinating. Yes, sea waves through a naval port would give the same interference pattern. When you talk about sea waves, you are talking about pure waves propagating through a medium. The double slit experiment was done first with photons, and later electrons. Photons and Electrons, for all previous intents and purposes, behaved as particles - they should not behave in the same way a classical wave behaves - yet under certain circumstances they do. The basis of classical physics was based on waves and particles, however now in quantum mechanics we see another form of behavior, which is a particle-wave duality (a poor name, as this is not a mix of particles and waves, it's something completely different. you don't call the color purple "blue-red duality".)

When we are talking about the "Wave Function" we are talking about Schrodinger's Wave Equation, which applies to particles (photons, electrons, etc) NOT regular sea waves. Sea waves through a naval port do not have a probability function. Also, keep in mind that this wave equation applies even when a single particle is put through the the slits. It gives the probability of where the particle will land.

So it seems that only dots demonstrate collapse. And if they have a statistical pattern, then they demonstrate the likely presence of the same wavefunction for all particles detected.

If by "dots" you mean particles, then yes. What the wave function is doing is giving probabilites about a particle. Over a long amount of time, and when many particles are involved, we are going to see an interference pattern similar to regular water waves. The point is that for each particle going through the slits, we can not with 100% accuracy predict where it will strike the wall. The probability of course is given by the wave function.

Any thought as to what is going on at dots and they are so big? The photographs from wikipedia I posted, might be showing square pixels on the grid of some sort of camera, not round dots on a continuous medium.

Are you talking about why the "dots" that appear on the screen after being hit with a particle are not the size of the particle itself, and why we can see them with the naked eye? It has to be enlarged so we can see it. This is the same logic as thinking that billboards are photographs of giant 80 ft. human beings.

 

[bryanosaurus]

Therefore dots do not appear if no one is watching?

You are taking what I said out of context and failing to see the logic here. The wave function gives probability and collapses when the actual results are observed. Yes the dots would appear on the screen, but without someone looking at them the knowledge of where the particles wound up is still a variable; therefore the wave function still exists. It collapses when we observe the "dots" as you call them.

 

[Ulysees]

Did you see the photograph? Please do, otherwise you won't be able to follow the arguments about dots, which is NOT my term but it is the white dots shown on the photograph. People said photographic film produces dots too. A dot in the wikipedia photo shows that a macroscopic effect has been triggered by an electron hitting an atom and getting absorbed. But then the electron ends up orbiting atoms, therefore it still has a wavefunction.

So either we've seen a change of wavefunction, not a collapse, or a collapse is an intermediate event after traveling in space and before orbiting atoms.

So collapse only occurs in interaction with matter?

 

[bryanosaurus]

Okay so if I am correct, what you are asking now is that for the electron to be detected, it must ionize whatever material the screen is made of, and if the electron is absorbed it remains in motion so therefore should still be described by the wave equation - and if it is still being described by the wave equation, then there was no collapse.

Once the electron is absorbed, the momentum is changed and therefore so is the entire state, which would then be predicted by a different wave equation with different eigenvalues. The original wave equation (showing probability of where it would land on the screen) still collapsed.

Also, in your question, are you asking that since it seems to be a macroscopic dot in the picture that you posted, are the results of where the particle hit the film not 100% precise. To deal with a question like that you should understand that the experiment done with electrons, though in theory is similar to being done with photons, has an entirely different apparatus - it is a MUCH more complicated experiment. It wasn't until the 1960s (Claus Jonsson) that it was performed with electrons, and not until 1989 (Akira Tonomura) that it was performed with a single electron beam using an electron biprism. If you look into those experiments you will see that the detection process is far more involved than just hitting film.

I hope my posts help somehow. I originally replied based on the title of the topic, but now I see that your questions are far more involved and interesting.

 

[Ulysees]

since it seems to be a macroscopic dot in the picture that you posted, are the results of where the particle hit the film not 100% precise?

No it's not about precision, it's about the possibility that this is simply the unstable state of atoms being kicked out of balance without any collapse occurring, as others have pondered about for photographic film. An analogy would be plastic cones like the ones used in road works put on the ground upside down - their balance is then unstable and a little wind can drop some. If strong low-frequency sound waves go through a double slit before reaching the cones, cones will fall mostly at the peaks of the intereference pattern. So the existence of some fallen unstable cones does not prove any collapse of a wave. Likewise the existence of dots on photographic film might not prove the occurrence of collapse of a wavefunction but just metastable states being affected by the wavefunction globally as it was pondered upon.

Quantum mechanics should not be approached as text to be memorised. This example seems simple but it seems to me an intelligent observer is required for a collapse to occur, otherwise all possibilities exist simultaneously as a mix of wavefunctions.