Understanding the Copenhagen Interpretation

[g.lemaitre]

This is from Wikipedia regarding the first point of the Copenhagen Interpretation:

A system is completely described by a wave function , representing the state of the system, which evolves smoothly in time, except when a measurement is made, at which point it instantaneously collapses to an eigenstate of the observable measured.

What does it mean to make a measurement? Is this something that only living beings do or can a dead particle make a measurement? Why does measurement collapse the wave function.

 

[atyy]

A measurement is something that is made by a "classical" apparatus.

In this interpretation, QM is incomplete, because the classical world is just as fundamental as the quantum world.

 

[g.lemaitre]

What about in the double-slit experiment and a detector is placed over the two slits? I think a particle is sent down from the detector which records which slit the particle went through. Isn't that a sort of measurement? Thanks for your help.

 

[the_pulp]

In my own interpretation, a measurement is to make the system interact with another system "A" (the apparatus). This interaction, in order to be a measurement has to accomplish 2 things:

1) You have to have uncertainty of the proper state, not of the system but, of the apparatus (most probably because it may have a lot of degrees of freedom -it may be composed of a lot of particles-)

2) This uncertainty has to be "arranged" in such a way that the system, after the interaction, should randomly choose one of the eigenstates of the observable (ie it should go to a state where the measurement has a precise value) and its probability distribution should depend only on the state of the system (and not of the apparatus because, otherwise, it wouldn't be a measurement, it would be a preparation device).

In my interpretation, the randomness appears not because something intrinsic in the state of the system, but because of our ignorance about the precise state of the apparatus

Ps: I haven't seen this interpretation in any other place so, it is not very popular and perhaps its not right. But, up to today, it is the most satisfying (to me) interpretation that I found.

 

[atyy]

What about in the double-slit experiment and a detector is placed over the two slits? I think a particle is sent down from the detector which records which slit the particle went through. Isn't that a sort of measurement? Thanks for your help.

I'm not sure about the exact answer, but here's the rough idea.

When an array of detectors is placed close to the two slits, then the particle's position just after it emerged from the slit is measured (ie., which slit it went through).

But when an array of detectors is placed far from the two slits (like a distant screen), then the particle's momentum just after it emerged from the slits is measured (if you repeat the experiment many times, you'll get an interference pattern, from which you can infer wavelength, which is like momentum).

 

[g.lemaitre]

This is some other guys interpretation whom I don't really trust. So if you find anything wrong with it I would appreciate it

First of all, the Copenhagen Interpretation is just that, an interpretation. There is no evidence to support any interpretation of QM. If there was, it wouldn't be an interpretation. It would be a new, distinct, scientific theory.

Second, line 5 in your quote specifically says what a measuring device is. And it says nothing about it having to involve consciousness in any way.

That said, the Copenhagen Interpretation predates our modern understanding of decoherence. We now know that the collapse of the wave-function from a coherent mixture of eigenstates to an incoherent one occurs due to interaction with complex systems. So called "measurement devices" are examples of such systems.

Now, at this point according to the standard model the system will be in a superposition of all possible outcomes. So for example in the double slit experiment, the interaction of the photon with the detector changes the wave-function of the photon from one where the two wave fronts are coherent with each other (and can therefore interfere with each other) to a superposition of incoherent wave fronts which cannot interfere with each other. Note that this is the critical point responsible for the destruction of the interference pattern in the experiment, which is why I said before that the outcome of the experiment does not depend on any conscious observer ever looking at the results. The interaction between the photon and the detector is all that is required to destroy the interference pattern.

This is as far as the standard model goes, and as far as it needs to go. One can hypothesize that at some point the wave function collapses from this superposition of incoherent states to a single state, but it is not necessary to do so. The Copenhagen Interpretation is an example of an interpretation that posits the collapse of the wave function to a single state, but there is no evidence to support the claim that this actually happens. And of course there are other interpretations where this doesn't happen. The Copenhagen Interpretation was a lot more compelling to people when the collapse of the wave function from a coherent superposition to a decoherent one was not understood, and was lumped together with the hypothetical collapse to a single state. Now that this is no longer the case, the Copenhagen Interpretation is really only compelling for those who are convinced that the wave function directly represents something real (as opposed to being a useful tool for computing probabilities), but at the same time are unwilling to accept a many-worlds type interpretation (in which the wave function does not ever collapse to a single state, and all possible outcomes of all interactions are represented in the full wave function).

So again, nothing in quantum mechanics in any way suggests that consciousness plays any role whatsoever in determining what the outcome of any experiment will be, or in causing the collapse of the wave function, or in restoring a coherent wave function in a quantum eraser type experiment. Many people like the idea that consciousness is somehow responsible for determining the outcome of seemingly random quantum events. But there is no evidence to support such an idea.

 

[bhobba]

This is some other guys interpretation whom I don't really trust. So if you find anything wrong with it I would appreciate it

Yea that looks OK.

But to elaborate a bit further. Copenhagen is generally considered to be the views of Bohr but even some of his disciples like Heisenberg or Landau had slightly different takes on it so I would not say its a well defined interpretation - but I also have to say all interpretations I am aware of have slight variations. For example my interpretation is the Minimal Statistical Interpretation (MSI) but with decoherence added.

To understand about decoherence you need to understand what a mixed state is. Imagine you are taking a measurement but the state of the system you are measuring is randomly selected by someone. The state of such a system is called mixed because its a 'statistical ensemble' of states one of which has been randomly selected and presented. Now if that ensemble are of states is the same as the states you are measuring no collapse occurs, what you measure it what is there before you measure - you don't have this observation created 'reality' - the observation reveals an objective preexisting 'reality'.

What decoherence does is transform a superposition into what is called an improper mixed state of the states of your measuring apparatus. Here proper means it is observationally and mathematically exactly the same as a mixed state - but it has not physically been prepared the same way. Because of this it does not solve the measurement problem unless you make some other assumptions. I simply assume it is the same as a proper mixed state - and low and behold - the measurement problem is solved - no observer created reality and what you measure is there before you measure it.

Interestingly I have come across a development of QM where that is part of it from the outset:
http://arxiv.org/pdf/0911.0695v1.pdf

It assumes all systems of the same information carrying capacity are equivalent. Since a mixed state and improper mixed state carry exactly the same information - vola - measurement problem solved. Indeed if you go through that paper it assumes mixed states - improper or otherwise - are all the same eg in proving state transformations are linear.

Other ways of using decoherence exist in other interpretations. Probably the modern interpretation closest to Copenhagen is Decoherent Histories - also known as Consistent Histories:
http://quantum.phys.cmu.edu/CHS/histories.html

Some call it Copenhagen updated or Copenhagen done right. I am not expert enough in Copenhagen to know if its true - but it does give precise meaning to stuff like complementarity Bohr talked about - bur perhaps not precisely.

Thanks
Bill

 

[Double-Slit]

This is from Wikipedia regarding the first point of the Copenhagen Interpretation:


What does it mean to make a measurement? Is this something that only living beings do or can a dead particle make a measurement? Why does measurement collapse the wave function.

Oh so your are trying to include consciousness in the collapse which the coppenhagen interpretation also invokes.Well think about this,Schrodinger looked at it this way,the wave form is just a probability distribution no particle is there physically only if you measure it or interact with it sufficiently to cause it to collapse to a particle.So it can be either be made by an observer or any particle which interacts with it,take for example the photoelectric effect experiment,photons knocking out electrons,where is there a measurement needed,IT'S NOT.Also at the 2 slit experiment the wave form,if not observed,is present only until it hits the screen,after that it must be a particle in order to see it,the interferce pattern is physically a collection of particles,but which originated it was a wave.If we measure it before it goes through the slit then its a wave until measured and then a particle.So the accent should be on interaction not on measurement,since the measuring apparatus is also interacting in a way with the quantum system.I know there is still a flaw that if all systems originate from a probability how it becomes actuality ever,since wave+wave stays wave only wave+particle can make particle.This is the enigma if quantum physics,we hope we can find a good explanation for this soon.We all look forward!

 

[bhobba]

Oh so your are trying to include consciousness in the collapse which the coppenhagen interpretation also invokes.

Copenhagen does not invoke consciousness causes collapse. The key issue with Copenhagen is it assumes the existence of a classical world that acts along classical lines. To Copenhagen an observation is anything that registers here in the macro world like the particle leaving a mark in a photographic plate in the double slit experiment or a particle detector clicking. Consciousnesses does not cause collapse. Since the world is all quantum exactly how does this magic classical realm emerge - that is the key issue for Copenhagen - and of recent times further research has shown the reason classical objects behave as they do is decoherence ie entanglement with environment. In fact these days measurement itself is viewed as a kind of entanglement - the classical world exists in a sense because it is constantly being measured.

If you want to see what the real situation is check out Susskinds superb lecture explaining Schrodengers cat and all that stuff:
http://www.newpackettech.com/Resources/Susskind/PHY30/LectureRv9_Video_Lec6.htm

Thanks
Bill