Copenhagen Interpretation vs Quantum Decoherence?

Question

I'm learning about Quantum Mechanics, and have a question about the Copenhagen Interpretation. It states that the act of observation collapses the wave function. It seems many people take this to mean that the system has a definite state only when observed by a conscious observer.

However, the decoherence principle states that the wave function can collapse due to interactions between the quantum system and the environment, without the need for an observer. Thus, although observation causes decoherence and collapse of the wave function (because observation requires interaction), an observer is not necessary for the wave function to collapse or for the system to have a definite state.

What confuses me is why it seems the general understanding of QM is that an observer IS required for quantum systems to have a definite state, and this is often presented as one of the central paradoxes of QM. According to the decoherence principle this is not true; while observation causes collapse, it can also happen without an observer, thus there is no paradox regarding QM requiring a conscious observer.

Answer 1

There is indeed no paradox regarding QM requiring a conscious observer. It's just that the Copenhagen interpretation is the simplest one to have as a starting point when learning QM, while understanding decoherence generally requires one to already be reasonably familiar with the theory.

I should point out, however, that decoherence is not an interpretation of QM, it is a physical phenomenon that produces measurable effects, as anyone in the field of quantum computing will certainly tell you. Decoherence itself does not solve the "measurement problem", although it helps in making the whole discussion more precise. Attempts to solve the measurement problem via decoherence alone must overcome the fact that, while decoherence tells you why the system seems to collapse to the eigenstates of the measured operator, it does not determine the probabibilities of collapsing to each one. In other words, it does not explain Born's rule. There are interesting attempts to derive Born's rule from decoherence, by means of the idea of "Envariance". I recommend watching Zurek's talk "The Quantum Theory of the Classical":

https://www.youtube.com/watch?v=7Sn63t3BeMc&

or reading his paper with the same title. There is also another very well written pedagogical paper that explains decoherence, as well as it's relation to the measurement discussion. Reading it may help in understanding what decoherence alone can and can't do with respect to this problem:

https://arxiv.org/abs/1508.04101

Answer 2

You have some misconceptions that are very common in the physics community. The state of physics education about basic quantum interpretations is just abhorrent.

First of all, there is no such thing as a universally understood Copenhagen interpretation. You can try to argue with 10 adherents of it, and get about 4 different versions.

In the version you have received, it seems to be the case that consciousness plays a rôle, and really, that is an incredibly rare version of Copenhagen. Most people would not have had that, not least because of the theological implications that seems to have, and the usual distaste of mixing that into science. It definitely does not help that those who do believe consciousness has something to do with quantum interpretations, exit Copenhagen by themselves and subscribe instead to Consciousness Collapse = von Neumann–Wigner interpretation, which is always a rare viewpoint.

It is more common that people accept that experimental equipment alone can collapse the wavefunction in Copenhagen interpretation. This is the dominant view in Copenhagen because cloud chamber tracks show lines, and this is taken as evidence that measurement equipment alone should be able to collapse the wavefunction.

If you are interested in looking at decoherence, it is quite important to realise that you should not be using Copenhagen language. In particular, you should not speak of collapse of the wavefunction. The whole point of discussing decoherence is that Copenhagen gives a physically unsatisfactory insistence on the nature of measurement, namely that we must never ask what measurement does, only assert that it collapses the quantum system's wavefunction in a non-unitary-evolution kind of way.

Instead, decoherence is attempting to make a better understanding of what quantum theory itself says that measurement should be doing. First of all, it is no longer the instantaenous random collapse that Copenhagen insists it to be, but rather you get a smooth transition from pure states that are not the eigenstates of the measurement apparatus, into entangled pure states between the object and measurement apparatus and environment. Partial trace of the environment alone is sufficient to lead to the kind of wavefunctions we actually get from the measurement postulate that we all use in quantum theory. The only thing that is missing is that decoherence does not explain Born rule.

That is, either you postulate collapse, or you postulate Born rule on top of decoherence. Try not to mix the two together.

Part of the reason why decoherence is getting more and more accepted in the community is not just that we have more and more simulation evidence that it really does make for a better explanation of the process of measurement, but also that it is much more sensible in theory and better agreement with experiment. I am referring to the theory in the sense of Wigner's Friend thought experiment, that your measurement apparatus is also a quantum system that thus can be put into quantum superposition. This is also experimentally testable—with better and better control over the noise in a big quantum system, we are getting more and more able to put larger and larger systems into quantum superpositions, and also being able to control them. So, we can put a measurement apparatus into the detected-entanglement states, and then reverse the entanglement, so that it seems as if the detection did not happen.

That is, unless you really believe consciousness is somehow special, the lack of an upper bound at which a macroscopic system ceases to exhibit quantum behaviour (by this I mean GRW style, or more widely, Objective Collapse interpretations), forces us to treat human brains, which are also made of quantum material, as potentially able to be put into quantum superpositions.

As a sidenote, after the decoherence process and the universe wavefunction is now composed of separated branches, that the density operator is now filled with Born probabilities $p_i$ in $$\rho=\sum_ip_i\left|s_i\right>\!\left<s_i\right|$$further manipulations of the system need to act relative to each branch separately. In particular, one needs to use conditional probability $P(A|B)=P(A\cup B)/P(B)$, and then the decoherence + Born rule result will be equivalent to collapse postulate. Needless to say, this is incredibly important because, obviously, the correct behaviour of quantum theory predictions must be independent of the particular interpretation chosen, in order for the interpretations to even be acceptable as a contender for correctness.

Answer 3

Your mistake is to assume that 'observation' means there must be an observer. An observation is an interaction between the quantum mechanical body being observed an a collection of other quantum mechanical particles that form the measuring apparatus- there is no need for a human being to be involved at all. In that sense, the measuring apparatus is part of the environment with which the observed body interacts, so conceptually there is no conflict between Copenhagen and decoherence interpretations. The Copenhagen interpretation effectively treats the interaction between the observed body and the measuring device as a 'black box' interaction, with an abrupt change between the before and after states of the wave functions associated with the observed body, while while decoherence interpretations are looking at how the transition from the 'before' state to the 'after' state actually comes about.

Answer 4

You are correct that decoherence provides some understanding about the measurement problem. You are also correct that you do not need in principle any consciouceness mechanism. Though there is a part that decoherence does not explain regarding the measurement problem, and this is where some people think that consciouceness plays a role.

I do a quick summary of decoherence and at the end I discuss where the consciouceness aspect could play a role according to some people.

In what follows, I assume you know what a density matrix is (but I could easily edit the answer so that such knowledge is not necessary).

The whole story behind decoherence is to consider that the quantum system $S$ you want to measure is not "alone in the universe", as there is also the measurement apparatus $A$ that will measure it (technically we also need to model the environment around the apparatus in some cases, but I won't go in this details here).

During a measurement, $S$ and $A$ will get entangled and this entanglement will enforce $S$ to become a mixed-state in some basis, i.e. quantum coherences will be killed.

I call $\{|s_l\rangle\}_l, \{|a_l \rangle\}_l$ to be orthonormal bases for $S$ and $A$.

I assume $|\psi_S\rangle = \sum_{l} s_l |s_l\rangle$ is the initial state of the system to be measured, and $|a_0\rangle$ the initial state of the apparatus. The interaction with the apparatus will transform the state of $SA$ in some state:

$$ \sum_{l} s_l |s_l\rangle \otimes |a_0 \rangle \to \sum_{l} s_l |s_l\rangle \otimes |a_l \rangle$$

Tracing out the apparatus, we realize that the system is now a (classical) mixture:

$$\rho_S = \sum_l |s_l|^2 |s_l \rangle \langle s_l |$$

What decoherence tells you is how coherences are killed by the apparatus (or environment more generally), and in which basis these coherences are killed (what are the possible classical states you will observe).

However on the conceptual level, for decoherence theory, the full state is still supposed to be entangled after this interaction. It does not tell you what "breaks" this entanglement. Related to this fact, decoherence tells you nothing about which outcome you will actually observe: there is still some probability to get one or the other. Finally, even though the evolution I described is continuous in time (unitary evolution), the moment you will observe one outcome (say $|s_k\rangle$) still needs an "instantaneous collapse" that does:

$$\sum_l |s_l|^2 |s_l \rangle \langle s_l | \to |s_k \rangle \langle s_k| $$

Hence, we see that we lack some mecanism allowing to understand the full problem. What some people believe is that this mecanism could be related to consciouceness (although it is by far not the only thing that could explain it, their opinion is very highly debatable). Such people consider that to break the entanglement or to take the specific outcome you observe, you need some consciouceness mechanism.