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In the double slit experiment attempting to measure which slit the particle passed through causes the wave function to collapse.
According to the question: What is the quantum mechanical definition of a measurement?
Until we have an accepted solution of the Measurement Problem there is no definitive definition of quantum measurement, since we don't know exactly what happens at measurement.
The many-worlds interpretation defines measurement as any physical procedure in which the observer gets entangled with a quantum system.
To me, the most obviously arising avenue of investigation would be to narrow down on precisely what does or doesn't cause the wave function to collapse.
Have physicists extensively experimented with what conditions cause it to collapse? Do you have to be taking a measurement to make it collapse or will any interaction cause it to collapse? For example, what if you measure it with an apparatus that then destroys the data gathered without allowing the data to exit a faraday cage, so that it is impossible for any information to ever be accessible to the outside universe? Then what ever the answer, one might invent even more obscure hypothetical circumstance to test...
Has this avenue been explored?