I Is the state observer dependent

[Jilang]

I was just reading the thread about the dead cat/live cat. Is the state of the cat dependent on the knowledge of the observer?

 

[dextercioby]

Just like in classical mechanics, states and observables are frame (thus observer) dependent in Quantum Mechanics. We connect oberservers/frames through general space-time transformations, to these transformations (which usually form a group) we assign operators which map states and observables in one frame to states and observables in another frame.

 

[Jilang]

OK, then the state has little to do with the cat per se?

 

[Sturk200]

I was just reading the thread about the dead cat/live cat. Is the state of the cat dependent on the knowledge of the observer?

You'll probably have gathered that the answer is dependent upon who you ask. My understanding is that most right thinking physicists will say it's nonsense to propose that the state of a physical system depends on whether the system has been perceived by human consciousness. The "state" of the cat in QM is a precise mathematical concept that has to do with possible measurement values. We use the state to calculate probabilities of measurements. In terms of what the cat is actually up to in there, we don't really know, which makes sense, since we haven't opened the box.

 

[atyy]

Yes, in quantum mechanics, the state of the cat is observer dependent.

If the cat has not been observed, its wave function will not have collapsed.

Thus quantum mechanics, in the orthodox interpretation, differs fundamentally from classical mechanics, because the observer plays a fundamental role. Some people don't like the term "observer", so they may prefer to use the term "classical apparatus" instead. However, the concept of an observer or classical apparatus as distinct from the quantum system is fundamental.

 

[Simon Phoenix]

Is the state of the cat dependent on the knowledge of the observer?

The states we assign in QM have to be, in some sense, dependent on the 'knowledge' of the 'observer'.

I've put those words in parentheses because I find terms like knowledge and observer to be a bit vague - but I'm certain that information, in its technical sense, is critical.

A simple example kind of illustrates this point. Let's take a quantum key distribution set-up running the BB84 protocol. In this protocol Alice prepares spin-1/2 particles, selected uniformly at random, from the eigenstates of spin-x and spin-z and sends them off to Bob (one particle per timeslot, ideally). The eavesdropper Eve needs to perform some measurement on the particles in order to have any chance of recovering the information that will ultimately be used to establish a key between Alice and Bob.

Alice, knowing the actual states she has prepared, assigns a pure state to each timeslot. Eve, however, has no idea which of the 4 possible eigenstates has actually been prepared and so for each timeslot she assigns a mixed state to the particle.

So is the particle 'in' a mixed state or a pure state? Yes it is :-)

The quantum state assigned thus has an element of 'subjectivity' that depends on the information one has access to. No experimental contradictions follow from this subjectivity. It is a common perspective that the quantum state (and the whole machinery of QM) is just some fancy maths that just models how information gets updated and has precious little to do with some quasi-classical notion of "what's really going on" - and this was mostly the subject of the fascinating and entertaining (and illuminating) thread "when does a quantum experiment begin?"

I tend to do QM calculations thinking of things actually being in some sort of state that has some kind of physical 'reality' - states get instantaneously changed ('collapsed') by projective measurements and so on, in this world view. There are a number of what I would call metaphysical problems with this (dare I say even philosophical) but ultimately you get the right answers from working in this perspective - you won't generate a prediction at odds from experiment using this view of QM (at least not yet).

My own feeling, although I can't pin this down precisely, is that there's something fundamental about the exchange and recording of information - for a quantum experiment to have actually 'finished' - and a state 'collapsed' (whatever we mean by collapse) - then some classical information has to have been generated. Some real bit has to have been recorded somewhere, be that in the environment or in some device.

So it's my view that information is critical - both in the mathematical 'state' one assigns, which depends on what prior information we have, and also in the more problematic 'collapse' part - which leads to no end of tangled discussion :-)

 

[Jilang]

Thanks Simon, it's adds an interesting dimension, with one man's knowledge being another's ignorance. Perhaps it could be phrased similar to relativity:the laws of physics being the same in all states of ignorance. As you mentioned, I do wonder if it all comes down to information. Entropy must enter into it too somehow, since the reversibility of quantum processes requires that any reduction is entropy is small and given the link between entropy and information.