# Measurement collapsing wave functions [duplicate]

I'm sure variations on this come up a lot, but I was specifically interested in a response to a claim made by a particular article:

https://medium.com/@roblea_63049/the-double-slit-experiment-demystified-disproving-the-quantum-consciousness-connection-ee8384a50e2f

The article is aiming to disprove the idea that an 'observer' collapsing a wave function has anything to do with consciousness or human observers.

At one point it argues that the reason an electron in the double slit experiment has its wave function collapsed when detected before entering one slit or the other is due to the photons fired at it to detect its position having momentum and physically interacting with it. The author uses the analogy of tennis balls being fired into a dark room and using a tennis racquet to detect them - the method of detection causes a change in their behaviour.

Now in this instance that's all well and good, but firing photons is not the only means of detecting something. In the Schrödinger's cat thought experiment, for instance, a Geiger counter is used. As far as I understand it, these simply detect passively rather than firing out photons with momentum.

I know many people disagree with the wave function collapse theory and prefer decoherence (which I'm still wrapping my head around) but I'm interested to know if this is something that's explained within collapse theory or if it's something that's seen as disproving it.

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I know many people disagree with the wave function collapse theory and prefer decoherence (which I'm still wrapping my head around) but I'm interested to know if this is something that's explained within collapse theory or if it's something that's seen as disproving it.

There is no collapse theory. The theory is quantum mechanics and the attribute "collapse" is given to the wavefunction , which is a solution with boundary conditions, given by a quantum mechanical wave equation.

What is called collapse refers to the attribute of the modulus, $$Ψ^*Ψ$$ to give a real number function which is the probability of finding a particle at (x,y,z,t), or a system with a specific list of real numbers for energy momentum etc.

Now probability distributions are the same concept, from economics to throwing dice. The probability distribution for a dice is a flat histogram for the numebers from 1 to 6. So when you throw a dice and 5 comes up you have collapsed the probability distribution of the dice to 5, one count in building up the probability distribution. There is nothing more esoteric than this in the term collapse.

Take the double slit experiment one electron at a time: The wave function is a solution of "electron of fixed energy scattering off two slits a fixed distance apart and fixed width"

The top frame shows the electron footprint as a dot, that is one collapse, and then the accumulation shows the interference pattern of the $$Ψ^*Ψ$$ of the system under study.

If you introduce a detector in the system, you will change the wavefunction because it depends on the boundary conditions, and any detector introduces new bounds which may or may not destroy the phases between successive electrons. The experiment depends on having exactly the same boundary conditions.

Now the cat is another sad story sacrificed to the obsessive need to treat mathematics as reality, and not as a model that allows prediction for reality. The atoms have a probability to decay, and the Geiger counter picks an instance of that probability and the poor cat, which of course is alive until the poison is released , becomes a point in the probability distribution.

Collapse is just an interpretation of the mathematical model of quantum mechanics.

• You really like that picture :) – Aaron Stevens Nov 10 '18 at 12:41
• @AaronStevens I really like the experiment because in one simple series of photos it encapsulates the need for quantum mechanics wave function to explain experiments – anna v Nov 10 '18 at 12:47
• Thanks for the answer, are you able to explain a bit more what the boundary conditions are exactly? The dice analogy is a nice one, but to me makes it seem like the wavefunction and the collapse are theoretical - a way of talking about probability before and after the event. I'm still not sure I understand how this results in the interference pattern disappearing - what specifically is the detector doing? The article I linked seemed to be claiming it was specifically about the impact of the photons on the electron and the momentum they had - surely there are detectors that don't fire anything – Theo Johnson Nov 11 '18 at 11:19
• At the quantum level to detect something, a particle or a field, you have to interact with it. Interactions change energy and momentum . The single electron approaching the two slits has a probability of going through one or the other, and the boundary is the dimensions and distance of slits, because they define in space the possible limits of the electric fields that the atoms and molecules composing the slits spill out.All this is one quantum mechanical wave function, which complex conjugate squared gives the probability. Any detector will change the fields and a different wave function – anna v Nov 11 '18 at 12:03
• will define the new system, and which destroys the coherence of the complex wave function between successive electrons, Electrons hitting/interacting with a detector will have a different wavefunction than the ones that do not.. See this experiment phys.org/news/… . – anna v Nov 11 '18 at 12:06

At one point it argues that the reason an electron in the double slit experiment has its wave function collapsed when detected before entering one slit or the other is due to the photons fired at it to detect its position having momentum and physically interacting with it.

This can't be the reason. Imagine that I have two light sources, one at each slit. Now the amount of light-electron interaction is higher when compared to when there was only one light source. But the pattern observed at the end is the same as before! Clearly it's not the light-electron interaction (amount of) that is causing the lack of interference pattern, but something deeper. Our prediction of interference pattern is wrong because we are working with incomplete knowledge of the system and if you account for the extra knowledge of which slit the electron went through, then your predictions will match the experiment.

One can device many other mechanisms for detection. Say a loop of conductor around the slit that has an emf induced as an electron passes through it. There is no interaction in the sense of contact, but the interference pattern again disappears.

Our prediction of interference pattern is wrong because we are working with incomplete knowledge of the system and if you account for the extra knowledge of which slit the electron went through, then your predictions will match the experiment.

The issue stems from the fact that we haven't accounted for the measuring apparatus quantum mechanically. The collapse of the wavefunction only occurs when one treats the measuring apparatus classically.