The idea of wave function collapse and measurement has caused so many unnecessary problems when it comes to Quantum Mechanics. Both of these things
are nowhere in the theory; they're just postulated because you have a wave function of a quantum system that consists of probable states the particle
can be in and once you have knowledge of the state the probabilities go away. Now you’re left with a single state. Scientists assumed there must be
collapse of the wave function caused by a measurement.
This leads us to two central problems with Quantum Mechanics. How do you explain wave function collapse and the measurement problem? The problem, no
pun intended, is that neither of these things are anywhere in the theory of Quantum Mechanics. Again, they’re just postulated in an ad hoc way to
explain features that we see in experiments on quantum systems.
There’s a simple yet elegant answer to this. It’s found in the Relational interpretation of Quantum Mechanics and the recent Wigner’s friend
Simply, no collapse or measurement occurs. Here’s an explanation from Relational Quantum Mechanics that’s just mind blowing.
All physical interactions are, at bottom, quantum interactions, and must ultimately be governed by the same rules. Thus, an interaction between two
particles does not, in RQM, differ fundamentally from an interaction between a particle and some "apparatus". There is no true wave collapse, in the
sense in which it occurs in the Copenhagen interpretation.
Because "state" is expressed in RQM as the correlation between two systems, there can be no meaning to "self-measurement". If observer O measures
system S, S's "state" is represented as a correlation between O and S. O itself cannot say anything with respect to its own "state", because its
own "state" is defined only relative to another observer, O'. If the S+O compound system does not interact with any other systems, then it will
possess a clearly defined state relative to O'. However, because O's measurement of S breaks its unitary evolution with respect to O, O will not be
able to give a full description of the S+O system (since it can only speak of the correlation between S and itself, not its own behaviour). A complete
description of the (S+O)+O' system can only be given by a further, external observer, and so forth.
Taking the model system discussed above, if O' has full information on the S+O system, it will know the Hamiltonians of both S and O, including the
interaction Hamiltonian. Thus, the system will evolve entirely unitarily (without any form of collapse) relative to O', if O measures S. The only
reason that O will perceive a "collapse" is because O has incomplete information on the system (specifically, O does not know its own Hamiltonian,
and the interaction Hamiltonian for the measurement).
What this says is that wave function collapse and what’s called self measurement doesn’t occur. What we call measurement isn’t a problem. It’s
just some observer gaining information about a quantum system. The problem occurs because people assume a measurement must cause “collapse” even
though this isn’t anywhere to be found in Quantum Mechanics or Quantum Field Theory.
So an observer gains knowledge about the quantum system and it’s wave function just expands to include the observer's obtaining knowledge. So an
observer that’s entangled with the wave function of the quantum system can’t measure interference because he or she is a part of the entire system
described by the wave function. So Schrodinger’s cat is alive and dead.
Now, an observer O’ that’s external to the S+O system in the lab in the case of Wigner’s friend, is a quantum system and Wigner can do an
interference measurement and see his friend, the system and the lab in a superposition of both states.
So the wave function never collapses. Here’s an example.
Wigner’s friend is in the lab carrying out the double slit experiment. The friend sees interference when a photon gun is shooting photons at the two
The friend puts an apparatus next to one of the slits to obtain which path information. The photon behaves like a particle now. This isn’t due to
collapse but now the wave function extends to the apparatus next to the slit. The friend gains knowledge about the system and now the wave function
extends to the friend and the lab.
No collapse or measurement to cause collapse. The friend sees a classical particle because he’s now a part of the wave function of the quantum
system and him, the apparatus and the lab in a superposition of all measurements that can occur.
Wigner outside the lab can confirm this by doing an interference measurement on the results and the system. So Wigner acts as a super observer O’
that can measure and see interference between S+O in the lab.
This has profound implications because it shows, different observers can reach different outcomes of an event. It also shows that a system whether
quantum or classical in size is never in a state of collapse. They’re always entangled with some wave function.
What does this show about parallel universes? Say Wigner’s friend is measuring the polarization of a photon. He starts with the wave function that
says photon is vertical/photon is horizontal. When he carries out a measurement he only sees a result locally from his frame of reference which is
that the photon is vertical or the photon is horizontal. Both of these states exist in superposition but each friend can only measure the state in his
or her frame of reference. Wigner outside can measure both states and see interference.
Now, Wigner finds out the results. He’s now part of the system and there’s 2 Wigner’s. One who’s in a universe where his friend measures v and
one where his friend measures h. Wigner’s Uncle can act as a super observer and measure interference between all 4 states. These 2 states,
Wigner+friend v and Wigner+friend h will eventually decohere and evolve as two separate universes.
So what we call a measurement is observer dependent and is relative to the frame of reference(lab in this case) between S and O.
So this interpretation treats collapse and measurement like Einstein treats the distinction between past, present and future. These things are both
relative to the observer’s frame of reference.