The Von Neumann interpretation of the Double Slit Experiment First, I am a philosopher not a physicist, so apologies for limits in my understanding of quantum physics. My interest is in the philosophical implications of physics.  I've just joined looking for physicists I can ask questions to, but my first question hasn't worked ... so I am going to rework it and ask it in an extremely simple way.
In the double slit experiment, if the experiment is repeated with the device measuring ‘which-way’ information switched on or off, but without the experimenter knowing when it it on or off, can we tell from the pattern on the screen when it was on and when it was off?
Thank you.
 A: In the von Neumann interpretation the wave function does not have physical existence, but is an expression of the probability of finding a particular measurement result. The collapse of the wave function refers to the change in probability when the outcome of an experiment is known (and is no different in that respect to the change of a classical probability).
An observer cannot know the probability distribution from a single measurement result. The pattern on the screen is made from many experimental results. If individual particles are sent through the slits the interference pattern builds up over time

If he is sending many particles at once through the slits, then the pattern will change depending on whether which way information is available, and therefore the observer will know whether which way information is being gathered, but he only observes the probability distribution. He does not observe the position of any individual particle, so he has not observed a collapsed state of a particle.
If he were sending individual particles through the slits, while which way information is randomly gathered, he would not be able to tell whether the information had been gathered for a particular particle (except in a rare case where one possibility has zero probability of a particle arriving at a particular point). He would only end up with a pattern over time which combined both possibilities.
A: Any setup that allows left and right to be distinguished prohibits interference. No conscious act is needed.
There is a lot of confusion about quantum mechanics as many interpretations lead to paradoxes. One interpretation that does not is the ensemble interpretation, to which I adhere since reading Leslie Ballentine's work.
A: Had to look it up

The von Neumann–Wigner interpretation, also described as "consciousness causes collapse", is an interpretation of quantum mechanics in which consciousness is postulated to be necessary for the completion of the process of quantum measurement.

Italics mine, to emphasize that the hypothesis is not accepted in mainstream physics. It is not consciousness but interactions that model the probable outcomes of experiments.
One does not need to set up double slits with observers, as there are an enormous number of data in high energy particle physics that clearly separate measurements in decohered classical space  from the basic quantum mechanical interaction.
To get an intuitive understanding, think of bubble chamber pictures:

The quantum mechanical probabilistic interaction happens at the vertices ,the film is the recording with decohered interactions of the charged particles with the hydrogen atoms of the chamber. Thousands upon thousands of pictures are recorded and stored.
The measurement of the quantum mechanical probability distribution comes from scanning and measuring in the geometry on the film, the same type of interaction, in this case the creation of an (omega-) particle, the cherry on the decouplet prediction of the quark model.
These measurements are independent of the interaction, which happened once , when the film was triggered, and there was no consciousness there, just programmed machines. The same probability distribution ( the quantum mechanical interaction)will come up again, if the films are looked over again.
At present the detectors are sophisticated electronic detectors, but the argument is the same: the data are stored by smart electronics, and the same quantum mechanical probabilities will show up every time they are examined.
No conscious observers affecting the interactions, so the hypothesis is disproved .
A: "Consciousness causes Collapse" is based on the idea that the measuring device should be described by a waveform as well as the experiment. Before measurement is done the system under examination is in a mixed state, say
   |up> + |down>
Once the measurement is done, the combined system + measuring device is in the state
   |up>|measuring device says 'up> + |down>|measuring device says 'down'>
I.e. the final waveform is also in a mixed state, and the waveform never collapses. Von Neumann conjectured that, since we only see one outcome, it therefore does collapse at some point and perhaps it is the interaction with consciousness that causes the collapse.
CCC is only one of many possible solutions to the so-called measurement problem - it cannot be proved or disproved - it is matter of interpretation.
