# Why does the electron wave function collapse in a double slit experiment?

Did the electron wave function collapse in the double slit experiment due to being observed, OR is it that the electron wave function collapsed because the instrument used to measure it physically interacted with the electron in a way to collapse it's wave function? Keep in mind the delay choice experiment.

• There's no difference between being observed and physicall interacting with a measurement apparatus. Jan 24, 2015 at 16:58

This sounds like a homework question from a QM course which assumes (perhaps, tacitly) a particular interpretation of the QM. I personally prefer collapse-free interpretations precisely because of this problem: instantaneous collapse of the electron wave function involves unphysical infinite electric currents. As soon as a reasonable model is introduced for the measurement process, the "collapse" becomes a three-stage process:

1) The system that is being measured is entangled with the measurement apparatus.

2) The degrees of freedom of the measurement apparatus are discarded ("traced out", in the language of density matrices). At this point, the system (i.e., the electron) can no longer be described by a wave function, one does have to switch to density matrices.

3) The density matrix is updated taking into account the measurement result. If the resulting density matrix is "pure", one can switch back to the wave function description.

In this picture, there is nothing like a collapse of the wave function into another wave function. Instead, there is a collapse of the density matrix into the wave function which is about as exciting as updating probabilities via the Bayes theorem.

• It does not seem clear to me how the instantaneous collapse problem can be solved just moving from a density matrix with superposition to a single state. Here it says that quantum decoherence cannot explain the wave function collapse: en.wikipedia.org/wiki/Density_matrix#Example_applications Apr 9, 2023 at 17:16

Observing means interacting with the system using instruments and thus introducing uncertainty. But since the wave function descibres the probability distribution of the position of the electron, observing the electron and trying to determine its position will collapse this probability distribution from a superpositions of states into a single state.

To answer just the question in the title, the answer is we don't know. This is the measurement problem and we don't know why the wave function collapses at one point on the screen as opposed to another, just the probability that it will collapse at any given point.

To answer the rest of your question, it is the interaction of the wave function and the detector that causes collapse. Observation (by a person) is just the data recorded by the detector, sent down wires to a screen where it emits photons that then go to your eye so you can interpret them. E.g. there is a long chain of events from detection to your brain that still starts with the interaction of the wave function with the detector.

Wheeler's delayed choice experiment is about switching the detection screen with two telescopes at a further distance after the photon has traveled through the slits (or vice versa, switch the telescopes with the detection screen). The detection screen causes the interference pattern (e.g. the photon behaves like a wave and goes through both slits) and the telescopes detect a single photon (e.g. it behaves like a particle and goes through one slit). The thought is that how can it choose whether to go through one slit and behave like a particle or both slits and behave like a wave if you are switching the detector after it's gone through the slits?

I think this causes a lot of confusion because we picture the photon as a single particle, e.g. it travels in a straight line from A to B and is at every point in between as it travels. The reality is that we usually detect it at B and back trace it, assuming it was at each point along the way. If we put a detector half way in between we measure it there so this confirms our assumption but in reality all we've done is shortened the distance of A to B (e.g. and repeated the same experiment).

If you throw away your picture of a photon as a particle and instead consider it a wave, so now it always travels through both slits and always interferes. When the wave hits the screen it "collapses" at a single point and is detected. The question is now what causes the wave to collapse at a given point, e.g. we're back to the measurement problem, and if we imagine that with Wheeler's delayed choice experiment that the two telescopes give a collapse probability at two points (e.g. the telescopes) while the screen gives a spread out probability as given by the interference pattern and so it doesn't matter that you have switched the two different detecting devices, a wave (photon) passed through both slits every time and "collapsed" depending on what detector it hit when it got there.

Just to be clear observation is irrelevant in this experiment and the photon does not travel back in time to "decide" whether to go through one or both slits.

I think observation and measurement are the same thing. By observing, we are measuring the electron. In other words, trying to find the location of the electron is observation, which is measurement. Any observation/measurement of trying to find the location of the electron, instantly collapses the wave function and electron behaves like a particle.

In other words, wave function doesn't exist when observation comes into effect. Observation changes the quantum state.

From a density matrix point of view, it seems to me that the interaction between the electron and the apparatus causes the electron to transition from a superposition state to a single state in which the electron is "trapped" in the detector.

The double-slit results show an interference pattern cause by the photon passing through both slits at the same time, this behaviour shows a different pattern of detection that the one obtained when one slit is opened half of times and the other slit is open the other half of times.

However, the electron collapse due to interaction with an apparatus is independent of the slits. The collapse happens because the electron wave function tends to expand over a considerable region of the space and after the interaction, its position gets reduced to the detector's position, the same happens when a free electron gets trapped by a Hydrogen atom.

The reasons this happens seem to be unclear to me, but what I can see is that the electron/photon behaves as a wave until some "interaction" happens. The probability of that interaction is determined by the existing wave function. The nature of the interactions that cause the wave function collapse is unclear to me, as it is the process to transition to the new state.

• There is no difference between the electron and the photon. Both are quanta of energy. Because of relativity there are simply two different dispersion relations, one of which has a rest mass. The language we are currently using in QM is simply not useful. There is no "collapse". The free QM system is isolated whole the QM system under measurement can undergo irreversible energy transfers to external measurement systems. After a measurement there is simply less energy in the QM system than before. Whether that is less energy in form of a photon or an electron is irrelevant to the formalism. Apr 9, 2023 at 18:16