Does the wave function really collapse into a state?

[Erland]

Take the famous double slit (thought) experiment. The wave function for the photon is a superposition of two orthogonal states, one for each slit passage. But it is claimed to collapse into one of these two states when the photon hits the screen beyond, and then continue in this one state.
But when the photon hits the screen, it is totally absorbed and ceases to exist. How can one then claim that its wave function collapses into a state? It does not exist anymore, in any state at all, or...?

 

[mfb]

The wave function for the photon is a superposition of two orthogonal states, one for each slit passage. But it is claimed to collapse into one of these two states when the photon hits the screen beyond, and then continue in this one state.

Where does that come from? The idea of the double-slit is the impossibility of that.

But when the photon hits the screen, it is totally absorbed and ceases to exist. How can one then claim that its wave function collapses into a state? It does not exist anymore, in any state at all

You can say the wavefunction collapsed to "how the world looks like if there was a photon in this specific state and then got absorbed".

Note that there are interpretations of quantum mechanics without collapses.

 

[atyy]

But when the photon hits the screen, it is totally absorbed and ceases to exist. How can one then claim that its wave function collapses into a state? It does not exist anymore, in any state at all, or...?

There are two ways to deal with the collapse postulate here.

(1) Recall that in the Copenhagen interpretation the wave function is not real, and is only a tool to calculate the probabilities of events. The collapse postulate only applies when successive measurements are made. When the photon is absorbed, there is (commonly) no successive measurement, and the wave function is not needed beyond the first measurement, so collapse is irrelevant.

(2) The collapse postulate as projection is too restricted, and must be generalized to allow for collapse into other states. In this more general framework, for photons one uses a second quantized description, in which the state of zero photons is a state. See http://arxiv.org/abs/1110.6815 (p13, comment R2). For the generalization of projective measurements, see http://arxiv.org/abs/0706.3526 (Eq 2 & 3).

 

[vanhees71]

Just to add to atyy's posting: If photons, i.e., the electromagnetic field, are involved you must use a "second-quatization description". There is no such thing as a wave function of a single- or many-photon system, because there is not even a position operator for photons in the usual sense. So the only consistent description of photons is Quantum Electrodynamics (QED), i.e., "second quantization" of classical electrodynamics.

The name "second quantization" is, however, a misnomer since there's only one quantization. QFT is only the most general form to formulate quantum theory. It includes the possibility of creation and destruction of quanta, i.e., situations, where you don't have a conservation law that fixes the number of quanta. The latter is, strictly speaking, only possible in non-relativistic quantum theory. In relativistic quantum theory the creation and destruction of quanta (particles or photons) are very common as soon as the necessary energy is involved in collisions of particles and/or fields.

 

[bhobba]

Take the famous double slit (thought) experiment.

You may be interested in seeing a correct analysis of the experiment:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Its a bit different from the usual textbook treatment because it uses QM to explain it, rather than use it motivate QM.

Thanks
Bill

 

[Nugatory]

I have removed an interesting but basically off-topic digression from this thread.

 

[liquidspacetime]

Q. Does the wave function really collapse into a state?
A. In terms of de Broglie's Double Solution theory the answer is no as the wavefunction is a statistical, non-physical, mathematical construct.

 

[vanhees71]

You may be interested in seeing a correct analysis of the experiment:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Its a bit different from the usual textbook treatment because it uses QM to explain it, rather than use it motivate QM.

Thanks
Bill

The text in the above link is heavily misleading. Position or momentum "eigen vectors" not representing states. They are generalized functions and live in the dual of the domain of the position and momentum operators (see you favorite Book by Ballentine). It is highly misleading to analyze any quantum situation by starting with wrong statements like this! The correct treatment must use wave packets.

This is also true for the standard treatment of scattering processes. You cannot simply use plane waves as asymptotic states to derive the formula for the cross section. The correct treatment with wave packets can be found in, e.g.,

Peskin, Schroeder, Introduction to Quantum Field Theory.

 

[bhobba]

The text in the above link is heavily misleading. Position or momentum "eigen vectors" not representing states.

It has definite issues and a guy wrote a critique of it:
http://arxiv.org/pdf/1009.2408.pdf

Its purpose however is to break down the common misconception the double slit experiment demonstrates wave-particle duality.

I think anyone advanced enough to understand its issues is advanced enough to know what a crock the wave-particle duality is.

Small steps mate, small steps :D:D:D:D:D:D.

Thanks
Bill

 

[vanhees71]

Here is a very nice study by some students, which is mathematically entirely correct (although I disagree some formulations concerning "wave-particle duality", but that are only minor obstacles in formulations):

http://www.pa.msu.edu/~duxbury/courses/phy480/SchrodingerDynamics.pdf

 

[Demystifier]

But when the photon hits the screen, it is totally absorbed and ceases to exist. How can one then claim that its wave function collapses into a state? It does not exist anymore, in any state at all, or...?

Photon does not longer exist, but the state of the quantum system (a generalized wave function, mathematically described as a wave functional) still exists. This state is a state in a Fock space, in which the number of particles may not be fixed.

 

[nikkkom]

I think the Stern–Gerlach experiment is a better one to shine some light on this issue, especially the triple-SG experiment.

In 3-SG, the middle SG apparatus clearly "does something" to the silver atoms, since it clearly affects what happens at the last SG apparatus. IOW, to me this experiment seems to be an experimental proof that collapse is real.

 

[Nugatory]

to me this experiment seems to be an experimental proof that collapse is real.

It's proof that the SG apparatus does something to the silver atoms, but it doesn't follow that that something is necessarily wave function collapse.

 

[nikkkom]

It's proof that the SG apparatus does something to the silver atoms, but it doesn't follow that that something is necessarily wave function collapse.

After first SG apparatus atoms fly away in two narrow streams, they have definite spins (up and down) along selected axis (say, x axis).

After second SG apparatus atoms fly away in two narrow streams, they have definite spins (up and down) along a different selected axis (say, y).

Naively classically thinking, I'd expect the atoms in each stream have definite spin components in both x and y axes.

But third apparatus shows that "definitedness" along x-axis was lost. The second apparatus "made spin definite along y" (thus "collapse" sounds like a fitting word) but destroyed "definitedness" along x-axis (thus, this "collapse" thing is real - it has observable consequences).

 

[Nugatory]

But third apparatus shows that "definitedness" along x-axis was lost. The second apparatus "made spin definite along y" (thus "collapse" sounds like a fitting word) but destroyed "definitedness" along x-axis (thus, this "collapse" thing is real - it has observable consequences).

You can choose to think of it that way, but there's nothing in the formalism of quantum mechanics that says that you have to - indeed, there's nothing in that formalism that even says that the wave function is real, let alone a real thing that can collapse. With QM, the only thing that you get without ambiguity is statements about the results of measurements.

There are many problems, including just about all that involve a straightforward series of observations on a single article, in which you'll get the right intuition if you think in terms of the wave function being something real and collapsible. Thus, this approach appeared early in the history of quantum mechanics and is still taught today - it's useful. But there are plenty more problems where thinking of the wave function as something real and collapsible will just get in the way.

 

[atyy]

I think the Stern–Gerlach experiment is a better one to shine some light on this issue, especially the triple-SG experiment.

In 3-SG, the middle SG apparatus clearly "does something" to the silver atoms, since it clearly affects what happens at the last SG apparatus. IOW, to me this experiment seems to be an experimental proof that collapse is real.

If there are no irreversible operations by any Stern-Gerlach apparatus, you should be able to combine all the beams back before the last apparatus and show they are still coherent, which is a prediction different from collapse in which coherence is lost.

I have not actually worked it out for 3SG (so maybe my comments don't hold for 3SG), but you can find a simpler example where the beams are recombined after a single SG in Ballentine's textbook (https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20, section 9.5). I think the single SG example is good enough, since what you seem to be saying is that even a single SG causes collapse. I don't normally recommend Ballentine, because it is such an erroneous book. Anyway, Ballentine actually uses this to say that collapse after a measurement is wrong. Ballentine is wrong, because a (strictly alone) SG apparatus implements a unitary operation. Measurement requires an irreversible macroscopic mark to be made. So while Ballentine is right that there no collapse by an SG apparatus, he is wrong about the lack of collapse after measurement because there is no measurement either.

In order to have measurement in an SG apparatus, the apparatus cannot be strictly alone. At the quantum level, one can put in a measuring ancilla, and trace out the ancilla. A more careful treatment of the SG experiment than Ballentine's erroneous discussion can be found in http://arxiv.org/abs/quant-ph/0306072 (see Figure 1, where the SG apparatus is not strictly alone, but includes a detector).

Edit: Also, just in case there is any misunderstanding: the wave function is not necessarily real, and neither is collapse. So no experiment can "prove" collapse, rather the wave function and collapse are just tools to calculate the probabilities of events. Within Copenhagen which is where collapse is usually used, the events are real, but the wave function and collapse are not necessarily real. As long as observations match the predictions, we accept the wave function and collapse as valid tools.

 

[naima]

Erland wrote that on the screen the particle was in superposition of two paths and had to choose one of them.
Of course this not correct.
In interferometers nature only offers the choice between the possible recorded ouputs of the device.
So Erland could have written that on the screen detector the particle is in a superposition of orthogonal positions (states or operators)

 

[nikkkom]

there's nothing in that formalism that even says that the wave function is real, let alone a real thing that can collapse. With QM, the only thing that you get without ambiguity is statements about the results of measurements.

I am not talking about "reality" of wavefunctions. I'm taking experimentalist view here. I'm saying that experimental fact is that 2nd (y-axis) SG apparatus affects silver atoms' x-axis spin (destroys their polarization in that axis), and it's reality. It's up to theoreticians to explain it, but they can't deny that it happens.

 

[Nugatory]

I'm saying that experimental fact is that 2nd (y-axis) SG apparatus affects silver atoms' x-axis spin (destroys their polarization in that axis)

That I won't argue with.

However that's not the claim that you made above that "this experiment seems to be an experimental proof that collapse is real". The undisputed experimental fact is that that silver atoms behave in a particular way in an S-G device. Wave function collapse is one way of explaining this fact, but it's not the only way - and you'll have to unlearn it at some point.