Decoherence & collapse of the wavefunction

[SamLuc]

From what I have gathered, whether or not decoherence has solved the measurement problem is still a matter of debate. But to those who say that it does, my question is: how does it solve it? Does it actually cause the collapse of the wavefunction?

These questions are actually pieces of a larger puzzle I am trying to put together: Has the superposition of states of quantum entities which are not being observed by a conscious mind collapsed, or not? E.g. are the photons of light from a light bulb in a superposition of states when no one is looking, or has decoherence already caused the collapse?

If anyone can help me in trying to put the pieces together I'd appreciate it!

P.S. I know that I could gather a lot of info on this topic via an engine search, but as a non-scientist I find the accompanying mathematical formulae too hard to understand. I would appreciate if people could keep explanations simple. Thanks!

 

[ZapperZ]

Originally posted by SamLuc
From what I have gathered, whether or not decoherence has solved the measurement problem is still a matter of debate. But to those who say that it does, my question is: how does it solve it? Does it actually cause the collapse of the wavefunction?

These questions are actually pieces of a larger puzzle I am trying to put together: Has the superposition of states of quantum entities which are not being observed by a conscious mind collapsed, or not? E.g. are the photons of light from a light bulb in a superposition of states when no one is looking, or has decoherence already caused the collapse?

If anyone can help me in trying to put the pieces together I'd appreciate it!

P.S. I know that I could gather a lot of info on this topic via an engine search, but as a non-scientist I find the accompanying mathematical formulae too hard to understand. I would appreciate if people could keep explanations simple. Thanks!

Decoherence doesn't actually cause a "collapse" of the wavefunction, although it can if the extra degree of interaction is an act of measurement. Decoherence is an explanation on why we don't see (or very, very seldom see) quantum effects at large scales and long lengths of time.[1] It is why we don't see the weird QM effects on our cats, for example, contrary to the poor creature in Schrödinger's experiment.

It does, however, mean that if we can preserve coherence at larger and larger scales, QM effects should be preserved, and that's what we are beginning to see in those SQUIDs experiments.

Zz.

[1] See, for example, http://www.nature.com/nsu/000120/000120-10.html

 

[vanesch]

what decoherence explains, and what not...

Decoherence is to standard quantum theory what the emergence of species is to population biology: no extra assumptions, postulates etc... are introduced, the standard theory is used fully, one just had to think of it !

What does decoherence in fact say ? It says that quantum systems that are "observed" are necessarily coupled (though an interaction term in the hamiltonian) to a *system with many degrees of freedom*, aka a macroscopic system. This system is nothing else but the observation device in the case of an explicit measurement. It can however, also be the environment in the case of a non-explicitly observed quantum system.

It is then mathematically rather simple to deduce that the global state (system + environment) quickly evolves into an entangled state that cannot be written as a product of a state of the system and a state of the environment, but rather as a sum of such terms. If one insists on a 'local system description', then the only possibility left is to consider a statistical ensemble of local states, described by a local density matrix. Moreover, one can show that this density matrix is diagonal in so-called "coherent states", which are the quantum equivalent of macroscopic states, and that the diagonal elements are nothing else but the probabilities you'd calculate naively using just the local description of the quantum system, and the "collapse technique".

However, decoherence doesn't explain collapse, or the probabilistic nature of measurements. It *uses* in fact, by introducing the density matrix, the collapse technique in a certain way.
What decoherence shows is that you almost never find systems which are coupled to the environment in "non-classical superpositions" which would correspond to non-zero non-diagonal terms in the density matrix. So decoherence explains why we don't observe a Schroedinger cat which is in a superposition of a dead and an alive cat. It doesn't explain the "collapse of the wave function" because it uses the probabilistic interpretation of the wave function by using a density matrix.

cheers,
Patrick.

 

[SamLuc]

I appreciate the replies guys, although I don't pretend to understand everything contained in them.

Decoherence doesn't actually cause a "collapse" of the wavefunction, although it can if the extra degree of interaction is an act of measurement.

It doesn't explain the "collapse of the wave function" because it uses the probabilistic interpretation of the wave function by using a density matrix.

These responses lead me to believe that the answer to my question (Has the superposition of states of quantum entities which are not being observed by a conscious mind collapsed, or not?) depends on whether or not one believes that observation by a conscious mind is the only thing that actually qualifies as a measurement. Would this belief be correct?

 

[vanesch]

These responses lead me to believe that the answer to my question (Has the superposition of states of quantum entities which are not being observed by a conscious mind collapsed, or not?)...

As I tried to point out, decoherence answers this question partially: a conscious mind, but also a macroscopic measurement apparatus, will always observe "classically-looking" results, and no "weird superpositions". What one calls "decoherence" is simply the application of orthodox quantum theory (Schroedinger evolution) to a system coupled to an "environment" (= another system with a huge number of degrees of freedom). So the part: why don't I see superpositions of cats and dogs in the street, as naive quantum theory seems to allow for ? is answered by decoherence.

What is NOT answered is whether there is an actual collapse (meaning a non-unitary change in the state of the wave function of the universe) or not. In fact, decoherence seems to indicate that to find this out is an untractable problem because of the almost immediate entanglement with the rest of the universe. Indeed, the only way to find out something about a collapse would be to work with superpositions of "classical" states and see when their interferences disappear. However, decoherence shows us that from the moment we get "macroscopic", these interferences disappear due to entanglement with the environment.
It seems that decoherence has made of the question, of whether there is a collapse or not, a non-scientific question because non-falsifiable by experiment. (but that's my own interpretation !).

cheers,
Patrick.

 

[SamLuc]

Ok. It's becoming a little clearer now; I'm beginning to get my head around what you're saying. Thanks again.