What mathematical results support the idea that the wavefunction does not evolve unitarily before the experimenter interacts with the system?

Question

Some interpretations of quantum mechanics support the conclusion that, from the perspective of an experimenter, the state of the universe evolves unitarily until the experimenter observes the outcome. e.g. if we measure the spin of a particle using an apparatus, then both MWI and Relational interpretations describe the state as:

$$|\text{experimenter} \rangle \otimes \left(|\text {apparatus measures up }\rangle \otimes |\text{up}\rangle + |\text{apparatus measures down} \rangle \otimes|\text{down}\rangle\right)$$

where the state inside the () brackets results from unitary evolution of the electron+apparatus system.

After the experimenter interacts with the system, MWI derives an "apparent collapse" which occurs as a consequence of unitary evolution of the interaction, while Relational Interpretation introduces an actual collapse relative to the experimenter.

What are the mathematical/experimental results which support that, instead of the above state, the system is in one of these two states before the experimenter interacts with it:

$$|\text{experimenter} \rangle \otimes \left(|\text {apparatus measured up}\rangle \otimes |\text{up}\rangle\right)$$

Or

$$|\text{experimenter} \rangle \otimes \left(|\text {apparatus measured down}\rangle \otimes |\text{down}\rangle\right)$$

This involves a violation of unitarity for the electron+apparatus system.

P.S. I know about the result of decoherence, but it is an interpretation-independent feature of measurements. It can be used to support both MWI as well as the above hypothesis. I am asking for some additional mathematical/ experimental results which support the above hypothesis.

Answer 1

There is (weak) experimental evidence that simple systems are already in the final measured state just before measurement in the form of "post-selected weak values". (Here's the wikipedia page on the topic, with more references therein.)

The idea here is that right before some eventual (strong) measurement, you can make an additional "weak measurement" which gives very little information, but has an even smaller effect on the wavefunction. (If you get out information of order "a" (a<<1), the calculated effect on the wavefunction is of order "a^2", so in the limit of an infinitely-weak measurement you're able to see what's really going on much more than you're affecting what's going on (or so the argument goes).

Now, what can you do with such a tiny bit of information, infected by huge amounts of noise? Well, if you only do the experiment once, not much. But if you do it over and over again (as is done in the lab), you can start averaging the results together, eventually getting a signal out of the noise. Call the average weak measurement the "weak value". At this stage, you find that what you eventually measure for the weak value (on average) is just the expectation value of the uncollapsed wavefunction.

BUT -- now that you have a set of individual measurements taken before the measurement outcome, combined with the actual measurement outcome that comes later (you write all those down as you do the experiment), you can do more analysis. Now you can "post-select" for a certain outcome, throwing out all your weak measurements that don't end up with that one measured outcome. Now, when you re-average just those weak measurements, lo and behold, you find that the post-selected weak value now matches the expectation value of the collapsed state! And this weak measurement was made before the strong measurement. So it's an experimental indication that the true state of the system was somehow already in the final collapsed state.

You couldn't see this if you didn't post-select your data, because otherwise you're averaging all of the final outcomes together, which made it originally look like the wavefunction was uncollapsed. The nice thing about post-selection is that you can start separating out different outcomes and seeing that they really do have different weak values.

This is far from an ironclad argument, since these measurements are noisy and the weak values can only be measured on average over many runs, but I think the argument is pretty good, certainly stronger than most people give it credit for.

Edit:

Just to clarify, the "match" between the post-selected weak values and the final outcome is only for the particular operator which is later (strongly) measured. The weak values of other (unmeasured) operators yield a particular blend of the final outcome along with the information from way back at the preparation, and also incorporates what has happened inbetween.

Answer 2

Spontaneous collapse theories claim that the wavefunction sometimes randomly changes to have a single state:

https://arxiv.org/abs/2310.14969

This theory, like all of the other modifications of quantum theory, is both non-local and non-Lorentz invariant and doesn't reproduce predictions of quantum field theories that are the vast bulk of actual tested predictions of quantum theory

https://arxiv.org/abs/2205.00568

Answer 3

Mathematical models are great at making predictions, but sometimes they simplify things too much and ignore important physical details. This can lead to an incomplete understanding of what is really happening physically.

If we think about experiments and particles as having real, measurable properties that exist on their own, we can see that the idea of wavefunction collapse might not be necessary. Instead, we can understand the system as having consistent physical properties without needing anything to collapse.

This is because photons, like other particles, have many properties, such as speed, direction, frequency, polarization, phase and timing. Focusing on frequency shows us that photons behave like they are oscillating. This means that the way photons oscillate adds a linear dependency that affects experimental outcomes in ways that the wavefunction alone can't explain.

When scientists measure a particle's state, they are simply seeing an energy transfer that matches one of the possible outcomes, like "up" or "down." This doesn't mean that the wavefunction collapses. Instead, the system stays in a balanced state, with particles continuing to oscillate. The idea of decoherence fits well here, as it results from these interactions. When we take a measurement, we see a specific state, which is just the result of the measurement process, rather than something like splitting into different worlds or collapsing wavefunctions. (Splitting worlds is part of the Many-Worlds Interpretation, which says that every possible outcome of a quantum measurement creates a new, parallel universe.)

To support this idea, we could do experiments to observe how photons interact under different conditions. For example, watching how photons behave in a double-slit experiment or analyzing quantum states could show that the state we observe comes from a continuous energy exchange, not an abrupt change caused by observation. The observed state comes from real, physical interactions—not from abstract collapses or imagined universe splits.