# Position of collapse in von-Neumann chain

I have often seen the following claim (for instance on Wikipedia: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation):

In his 1932 book The Mathematical Foundations of Quantum Mechanics, John von Neumann argued that the mathematics of quantum mechanics allows for the collapse of the wave function to be placed at any position in the causal chain from the measurement device to the "subjective perception" of the human observer.

But I simply don't understand how this can be true. To me this reads as if it would have no experimental consequence where the point of collapse (between measurement device and observer). But how can this be? For instance, for a given quantum experiment we could imagine two hypothesis:

1. It is really the measurement device that causes the collapse (due to some proprety of the way it measures), completely independent on any human observer. The human observer just plays the role of observing whatever resulting value was recorded due to the collapse.
2. The human observer plays a crucial role in causing the collapse (through consciousness or in some other way) so before the human gets involved, the measurement device has now entered into a superposition itself based on the possible states of what it measured. Only when the human observes the measurement device does the collapse take place.

To me it seems it must be possible, for any given experiment, to change the experiment to find out if one or the other case is true.

For instance, if case 2 is true, the whole experimental setup (including measurement device) retains the superposition of states until the human observes it. This should make it possible to elucidate the well-known quantum effects ("quantum weirdness") even after the measurement by the measuring device. For instance if the experiment being measured involved a binary state of potentially negative amplitudes then the measurement device would now also be in a binary state with potentially negative amplitudes. If the measurement device is made to emit, say, a photon with different polarization based on the binary value the device observed, then the device will (still assuming case 2) be emitting photons also in superposition with potentially negative amplitudes. These photons can then be used in a second experimental setup that would show the effects of destructive interference among particles (exploting the negative amplitudes). The human then observes the effect of the second experiment: If the destructive interference is seen, this confirms case 2 because it can be concluded that the measurement device did not collapse the wave-function. On the other hand, if the interference effects are not observed, it means that the measurement device itself actually did collapse the wave function even before the human looked at the measurement, thus causing the photons emitted of being in a state with only positive amplitudes (0,1) or (1,0) meaning that destructive interference was not impossible, human observer or not.

Since there are obvious experimental differences it follows that this cannot just be an interpretational isuse. What am I missing?

• Your list of options misses 3. Collapse is not a physical process but an artifact of description. Quantum mechanical formalism does not imply that collapse "occurs", it simply gives a description of how to calculate probabilities of events, which verbally involves collapse. The fact that its timing is movable suggests that there is no collapse (i.e. it can be eliminated from description but perhaps at the price of making it more cumbersome), just as in relativity the fact that absolute velocities can not be measured suggests that there is no absolute space. – Conifold Feb 24 '17 at 21:32

If you actually tried this experiment you would not observe any interference effects because the measurement device is a macroscopic system which undergoes decoherence. So according to the criterion in your question you would say the device collapses the wavefunction. Decoherence is generally how physicists think about "collapse" now.

This doesn't resolve all the differences in interpretation because we could say even after decoherence the measurement device together with the degrees of freedom in the environment are still in a coherent superposition. Also even though we can't observe interference effects due to the measurement device itself, it is still in a superposition in the sense that we still don't know which state we will actually observe. There is more discussion in the paper in the link above.

• Do we think of it as decoherence because it removes, or at least shifts the focus away from the conscious observer. I am just curious.with no particular "agenda" or favoured viewpoint :). If this is best asked aa a separate post, no problem. Or is the word collapse that is the problem, thanks – user146020 Feb 24 '17 at 20:01
• It's called decoherence because the system goes from a 'coherent' superposition of states, where the phase difference in terms might matter depending on what you measure, to an 'incoherent' superposition that can be interpreted like classical probability. An incoherent cat is either dead or alive but we don't know which. A coherent cat might be something in between that we can measure with an operator that doesn't commute with 'aliveness'. – octonion Feb 24 '17 at 20:09
• Thank you, just working my way through related material and that's a very useful summary. – user146020 Feb 24 '17 at 20:12
• Thanks but isn't this more of a practical limitation that the measurement device causes collapse? Isn't it possible to imagine a measurement device that on the one hand would not cause significant deoherence while still being able to emit, say, a photon based on what it read? Also some claim de coherence doesn't solve the measurement problem... this is what I really have trouble understanding, how much of the original measurement problem has been addressed by coherence – Morty Feb 24 '17 at 20:37
• What you are talking about in your question as a criterion for determining wavefunction collapse is exactly decoherence. No it doesn't solve measurement problem, although some people might disagree with me. Read the paper in any case, that's what it's about. – octonion Feb 24 '17 at 20:40

The following is taken from Kurt Jacobs 2014. Quantum Measurement Theory:

How do we decide when it is appropriate to pretend that a measurement has occurred, and select one of the orthogonal subspaces as the outcome? We explain this in two stages. First the following process acts like a measurement, although it cannot guarantee that the measurement will not be undone. Consider a system in the state $\lvert \psi \rangle = \Sigma_n c_n \lvert n \rangle$, and allow the system to interact with a second system so that the joint state become $$w=\Sigma_n c_n \lvert n \rangle \otimes \lvert n \rangle_{sys2}$$
If we now trace out the second system, the state of the first system become the mixture $$\rho = \Sigma_n \lvert c_n \rvert ^2\lvert n \rangle \langle n \rvert$$
The interaction between the two systems, followed by the loss of access to the second system, turns the initial superposition into a mixture. Since a mixture of states is equivalent to the situation in which the system is really in one of the possible states $\lvert n \rangle$, but we do not know which one, the interaction produces an effective collapse of the wavefunction, but without selecting one of the possible outcomes.

To be able to safely assume that a measurement has been performed, we need to be sure that it is not going to be undone. In the above scenario a second interaction could undo the correlation, and return the system to its initial superposition. It turns out that the effectively irreversible behaviour of large quantum systems provides a physical process, in fact the only known process, that allows us to safely apply a measurement and pretend that a collapse has taken place.

When a microscopic quantum system is correlated with the macroscopically distinguishable states of a macroscopic system, then because of the unavoidable interaction of the macroscopic system with the environment, we can assume that a measurement of these macroscopic states, and thus of the microscopic system, has taken place.