Testability of consciousness-causes-collapse interpretation The consciousness causes collapse a.k.a. Von Neumann–Wigner interpretation says that the wavefunction collapse occur only at the point when a conscious being observes the result. I myself find it totally absurd and I thought this must have already been disproven. However, Wikipedia says that

All interpretations of quantum mechanics are empirically indistinguishable, as they all predict the same outcomes to quantum mechanical experiments.

Well, I do not really get this. Suppose you have a particle in the state ${1\over\sqrt2}(|0\rangle+|1\rangle)$ and you perform a physical measurement (in the basis $(|0\rangle,|1\rangle)$) not yourself checking the outcome and then, according to the result, but completely autonomly by some machine, you prepare a second particle into the measured state. Then, if I understand the interpretation correctly, this means that you are preparing an entangled state ${1\over 2}(|00\rangle+|11\rangle)$. In contrast, if this interpretation is false, you simply get a mixed state of $|00\rangle$ and $|11\rangle$ both with probability 1/2. Well and these two are experimentally distinguishable, so where is the problem?
 A: You've essentially outlined the Wigner's friend argument.
We have three parties. An electron (E), Wigner's friend (F) and Wigner. The experiment is as follows. Wigner's friend and an electron are in a sealed room (look Schrodinger's cat's box). The electron is placed in a superposition state $\frac{1}{\sqrt{2}}(|0\rangle_E + |1\rangle_E)$. Wigner's friend observes the electron. This observation can be described by a unitary interaction $U$. Wigner now (through experimental miracles) causes the room to undergo $U^{\dagger}$. The question is what is the state of Wigner's friend and the electron after the experiment?
Suppose the initial state of Wigner's friend and the electron is $|\psi\rangle$. Under an Everettian interpretation the state at the end of the experiment is the same as the state at the beginning because $U^{\dagger}U|\psi\rangle = 1|\psi\rangle = |\psi\rangle$. But if you believe the quantum state undergoes nonlinear collapse due to an interaction between the electron and measurement device or the measurement device and a human or whatever then the state of the system after that collapse is not $|\psi\rangle$ but some other collapsed state $|\phi\rangle$. Because $U^{\dagger}$ is invertible and $|\phi\rangle \not= |\psi\rangle$ we have that $U^{\dagger}|\phi\rangle \not= |\psi\rangle$.
So depending on if you accept collapse of the wavefunction (due to any cause inside Wigner's friends lab) or not the resulting state of the system after the experiment is testably different.
Now, this experiment is literally dozens of orders of magnitude from being experimentally feasible today because it requires complete coherent control of ALL the quantum physics happening inside of Wigner's friends lab. So far we have made superpositions of particles with maybe 10s or 100s of particles. Not even close.
Nonetheless, it is true that collapse theories make testably different predictions than no-collapse theories, and macroscopic superposition experiments are quantitative tests comparing such theories.
Suppose we could do the experiment above. Suppose we see a discrepancy in the experiment when we put a human in the room compared to when we just have an electron in the room. If we're controlling for all particles it means pure unitary evolution is wrong. We could then do something like put a robot in the room and see if the collapse happens. We could then try putting an unconscious human in the room and seeing if the collapse still happens or unitary evolution prevails. That said all of this is pretty ridiculous. If collapse of the wavefunction does occur the physical cause for that collapse is going to be due to something like the rules of quantum mechanics breaking down at (1) large particle numbers (2) large spatial superpositions, and or (3) large masses or (4) something similar to the previous. No one (reputable) thinks we could unitarily de-evolve a room where Wigner's friend is a robot (or asleep) but not de-evolve a room where Wigner's friend is a human.
A: The "consciousness causes collapse" idea is utter nonsense. Suppose I perform an experiment, the result of which is recorded on a photographs plate, which I do not see. I photocopy the plate, without looking at it, and post 100 copies to 100 separate physicists who all look at their copy at the same time. Which of the 100 consciousnesses has caused the collapse?
Let us consider a more elaborate scenario. The property being measured is the spin state of an electron. The electron will trigger a left hand detector if it is spin-up or a right hand detector if it is spin down. The detectors are connected to a computer which notes which detector is triggered and prints the result in the form of a six-digit code. The encoded result is put into an envelope by a robot and posted to a physicist currently on holiday at Malibu.
While the result is en route to Malibu, individual digits of the code are sent by expert radio operators to teams of crack masons at various stone quarries around the world. The masons hastily carve their allotted digit in giant blocks of granite in front of a live crowd, the carving of the granite being beamed to a world-wide TV audience.
Some days later, the physicist in Malibu gets round to opening her mail and sees the six-digit code. She looks in her code-book and deciphers the message to reveal the result of the measurement, hers being the first conscious mind to see it. The wave function now collapses.
Up until that point, the six-digit code was simultaneously in a state off being the code for spin-up and the code for spin down. The giant blocks of carved granite were simultaneously in states of having being carved into one set of digits and having been carved into another. The massive TV audience was simultaneously in a state of having seen the granite blocks spelling out the code for spin-up and having seen the granite blocks spelling out the code for spin down. Ok, I get it- it all makes sense now.
A: There is a controversy in physics about the interpretation of quantum mechanics that isn't really about interpretation at all. If consciousness caused the state of a system to change to one of the possible states of the measured observable that would make different predictions from the theory that the wave function doesn't collapse when you observe it. I will call quantum mechanics without the collapse "unmodified quantum theory".
To understand why this is difficult to test you have to try to apply quantum mechanics consistently to all of the systems involved, including the conscious agent who observes the measurement.
Consider the state of the system $S_1$, the measurement device $M$, the conscious agent $C$ and the other system $S_2$ at the start of your experiment:
$$\tfrac{1}{\sqrt{2}}(|0\rangle_{S1}+|1\rangle_{S1})|0\rangle_{S2}|0\rangle_M|0\rangle_C.$$
So then you do the measurement and the state evolves to
$$\tfrac{1}{\sqrt{2}}\left(|0\rangle_{S1}|0\rangle_M+|1\rangle_{S1}|1\rangle_M\right)|0\rangle_{S2}|0\rangle_C.$$
Then the measurement device changes $S_2$:
$$\tfrac{1}{\sqrt{2}}\left(|0\rangle_{S1}|0\rangle_M|0\rangle_{S2}+|1\rangle_{S1}|1\rangle_M|0\rangle_{S2}\right)|0\rangle_C.$$
So you don't end up with an entangled state of $S_1$ and $S_2$ since the measurement system $M$ is also involved. This means that the entanglement between $S_1$ and $S_2$ can't be observed without involving $M$ in the experiment. In reality, a measurement device is also going to be a large object that is interacting with its environment so the problem will be even more intractable as a result of decoherence:
https://arxiv.org/abs/quant-ph/0306072v1
Various ways around this have been proposed. In Section 8 of his paper "Quantum theory as a universal physical theory" David Deutsch proposed using an AI implemented in a quantum computer to test whether consciousness causes collapse:
https://link.springer.com/article/10.1007/BF00670071
This isn't going to be experimentally feasible any time soon.
But there is a better way of thinking about this. It is possible to discard a theory even if it isn't experimentally testable because it's a bad explanation:
https://arxiv.org/abs/1508.02048
The conscious collapse theory doesn't explain what consciousness is, doesn't explain how it causes collapse and also doesn't explain what's wrong with decoherence as an explanation of us seeing only one possible outcome of an experiment. So consciousness collapse solves no problems and creates a lot of problems, which ought to be sufficient for us to discard it.
A: My below answer, except for the last paragraph, is based on Sec. 17.10 of Greiner's "Quantum Mechanics" textbook.
The three possible states of the computer are $\chi$ before registering the particle, $\chi_{1}$ if the particle is in state $Z_{1}=\left|1\right>$ and $\chi_{0}$ if the particle is in state $Z_0=\left|0\right>$.
First, we consider the case of the particle being in state $Z_1$. The wave function of the total system, consisting of a particle and a computer, is given by
$$
\psi=Z_{1} \chi .
$$
After the computer has measured the particle, the total wave function is
$$
\psi_{1}=Z_{1} \chi_{1} \,. \tag{1}
$$
Similarly, if the particle is in state $Z_0$. The wave function of the total system, consisting of a particle and a computer, is given by
$$
\psi=Z_{0} \chi . 
$$
After the computer has measured the particle, the total wave function is
$$
\psi_{0}=Z_{0} \chi_{0} \,.\tag{2}
$$
Now we look at the case of the particle being in the state.
$$
\frac{\left(Z_{1}+Z_{0}\right) }{\sqrt{2}}.
$$
The initial state of the system is then.
$$
\psi=\frac{\left(Z_{1}+Z_{0}\right) \chi}{\sqrt{2}}\, .
$$
After the measurement, the total wave function is
$$
\psi=\frac{\left(Z_{1} \chi_{1}+Z_{0} \chi_{0}\right)}{\sqrt{2}}\, 
%\label{17.25}
 \tag{3} 
.
$$
Let us consider a second measurement by a person or computer. If the system is in a pure state, the expectation value of the measurement described by the operator $\hat{Q}$ follows from (3):
$$
\langle\hat{Q}\rangle=\frac{1}{2} \int_{\tau}\left(Z_{1}^{*} \chi_{1}^{*}+Z_{0}^{*} \chi_{0}^{*}\right) \hat{Q}\left(Z_{1} \chi_{1}+Z_{0} \chi_{0}\right) \mathrm{d} \tau,
$$
where all variables necessary for the particle and measuring device specification are contained in the volume element $\mathrm{d} \tau$. Multiplication yields
$$
\begin{aligned}
\langle\hat{Q}\rangle= & \frac{1}{2} \int Z_{1}^{*} \chi_{1}^{*} \hat{Q} Z_{1} \chi_{1} \mathrm{d} \tau+\frac{1}{2} \int Z_{0}^{*} \chi_{0}^{*} \hat{Q} Z_{0} \chi_{0} \mathrm{d} \tau \\
& +\operatorname{Re}\left\{\int Z_{1}^{*} \chi_{1}^* \hat{Q} Z_{0} \chi_{0} \mathrm{d} \tau\right\} . 
\end{aligned}
\tag{4}
%\label{17.27}
$$
where we have taken into account the Hermiticity of $\hat{Q}$.
To calculate the properties of a mixed state, we have to consider that the expectation value of $\hat{Q}$ in a mixed state is equal to the average of the expectation values, which are calculated by separate measurements with the wave functions $Z_{1} \chi_{1}$ and $Z_{0} \chi_{0}$. Since the number of particles is the same in both states, it holds that
$$
\langle\hat{Q}\rangle^{\prime}=\frac{1}{2} \int Z_{+}^{*} \chi_{+}^{*} \hat{Q} Z_{+} \chi_{+} \mathrm{d} \tau+\frac{1}{2} \int Z_{-}^{*} \chi_{-}^{*} \hat{Q} Z_{-} \chi_{-} \mathrm{d} \tau .
\tag{5}
%\label{17.28}
$$
A comparison of (4) and (5) shows both expectation values to be identical if $$
Q_{10}=\int Z_{1}^{*} \chi_{1}^{*} \hat{Q} Z_{0} \chi_{0} \mathrm{d} \tau=0 . \tag{6} 
%\label{17.29}
$$
Now we want to consider the conditions under which the two states $\psi_{1}$ and $\psi_{0}$ yield a vanishing integral (6). The quantity $\left|Q_{10}\right|^{2}$ can be interpreted as being proportional to the probability of a transition between the states $Z_{1} \chi_{1}$and $Z_{0} \chi_{0}$, caused by the action of the measurement operator $\hat{Q}$. The particle can't transition between the states if $Q_{10}$ is equal to zero. This means that the particle would have irreversibly changed the state of the computer, which can be described as an indelible recording of the event. This property is typically attributed to a measuring apparatus: it records the result until an external action resets it.
The total system can be described either by a pure form (3) or a mixed form consisting of collapsed wave functions $\psi_1$ and $\psi_0$, each with a probability of $1/2$ in this case. However, it is more useful to use collapsed wave functions because they allow us to calculate the results of future particle measurements without considering the details of the first measuring apparatus. Collapse enables us to describe an isolated physical system without considering the other systems interacting with it irreversibly. However, doing so is unnecessary since using pure states yields the same results.
If a conscious observer rather than a computer makes the first measurement, then the conscious observer will be in a superposition state as described by state (3). This feature can be removed by postulating that the collapse of the wave function actually occurs when a conscious observer rather than a computer makes the measurement. However, this does not change the theory's predictions, as a conscious observer will make an indelible recording and therefore have $Q_{10}$ equal to zero. Also, there is no known mechanism that would make the wave function collapse when observed by a conscious entity rather than a computer.
A: Just a word of caution. Physics is not about "reality", whatever that means. It is about modelling and, ideally, predicting measurement outcomes (i.e. subjectively non-unitary  perceptions) by certain experimenters and observers. "Collapse" may refer to certain observers and not to others, who may detect instead superpositions of "subjectively" collapsed observers. This is indeed the key idea behind Rovelli's (and arguably others' before him) Relational Quantum Mechanics, whose ancestor is indeed  Wigner's friend.
