# Are quantum states relative?

1. Apr 18, 2015

### underworld

Here is a thought experiment. Imagine Schrodinger's cat... in the traditional model, there is a single observer outside the box, and the observer creates an entanglement with the catbox device which reveals the quantum superposition of the enclosed cat. The cat is said to be in a superposition of both alive and dead.

My question is.... is that superposition absolute? or only relative to the observer?

What if the box were instead a room. And in the room was another "local" observer of the cat? To the observer outside the room, both the cat and the local observer are in a superposition of alive and dead. However, the local observer would necessarily be either alive or dead only. Thus, the local observer would not see the cat as a superposition of both alive and dead, but as a definite state of one or the other. Supposing the local observer is alive along with the cat, the local observer would say the cat is alive, while the external observer would say that both the cat and the local observer are in a superposition of both alive and dead.

I believe this suggests that the observed quantum states are not absolute, but instead, relative to the observer.

2. Apr 18, 2015

### Staff: Mentor

You have misunderstood the point of Schrodinger's thought experiment. There has never been any serious doubt that the cat is always either alive or dead (although we may not know which it is) with no funny 50% alive/50% dead states.

Schrodinger proposed the thought experiment to point out a problem with the 1920's vintage understanding of quantum mechanics - the formalism as it was then understood suggested that the cat could be in one of these funny states even though no one believed that it could be.

The resolution came with the discovery of quantum decoherence some decades later. The half-dead/half-alive state very rapidly evolves into a state in which the cat is either alive or dead - we may not know which, but it is one or the other as surely as a tossed coin is heads or tails but not some funny mixture of the two.

3. Apr 18, 2015

### underworld

My understanding is that only some schools of thought subscribe to the perspective you describe, while others subscribe to the idea that macro scale objects can be quantum entangled in the way I described. This is correlated to the idea that an electron either does or does not really have a location and velocity. If it does have a real location and velocity, as you described, then quantum mechanics is less a theory about physical reality, and more a theory about information. I would call this the "black box" problem in that quantum mechanics can never say what is really going on in the black box, it can only describe what goes in and what comes out. Everything inside the box is hidden. Everything QM describes is information, not physical reality. For example, in the experiment above, the local observer can determine if the cat is alive or dead, but the external observer cannot. Both have information about the state of the system and the state of the cat, but the external observer can only measure the probability of alive vs dead, while the internal observer can measure the absolute state as either alive or dead. The information about the cat is incomplete to the external observer, so he must rely on probabilities if he wants to describe what is happening inside the box.

If, however, an electron really doesn't have a particular location, and is instead "smeared" or otherwise superposed, then QM may be describing what really is happening, and it may allow for entanglement of macro objects. And if that is correct, then I believe the thought experiment above is valid. In that case, the external observer measures the probability that the cat is alive or dead, while the internal observer exists in both states in parallel or otherwise superimposed - perhaps something like the many worlds interpretation. The internal observer would not be aware of his superposition, however, and he would have an absolute perspective on the state of the cat. I imagine it something like 2 parallel internal observers and cats. In the first, they are both absolutely alive, in the second they are both absolutely dead. But outside the box, the external observer cannot know which pair is inside. And perhaps, in fact, both are equally probable to be inside, and equally "smeared" into that location. The external observer opening the box causes an intersection of the external observer's reality with the internal probabilities, allowing only one of the internal realities to mesh.

4. Apr 18, 2015

### Staff: Mentor

I have an interest in QM interpretations and have come across quite few. The only one I am aware of along those lines is conciousness causes collapse which is very very fringe these days. It came about, without going into the details, from a misunderstanding the great mathematician and polymath Von Neumann had in his fully quantum analysis of the measurement process found in his classic Mathematical Foundations Of QM. If you know that book I can explain the issue - but the details aren't that important. What's more important is, despite Von Neumann's reputation, it was too weird and even then, and didn't garner much support. Unfortunately Von Neumann died young and didn't live to see how his misunderstanding was resolved. One supporter though was the great mathematical physicist, Wigner, who, when he came across some early work on decoherence by Zurek saw the error and did a complete 180% turn and advocated objective collapse theories. I personally don't go that far - but it can be said these days conciousness causes collapse is very fringe.

Ok lets look at what our modern understanding of what you wrote says. The observation does not occur when the box is opened or with the external observer. The observation happens at the particle detector. Here the detector and the emitted particles become entangled (its a phenomena of spontaneous emission which really requires Quantum Field Theory - but no need to go into that) and via decoherence you get a mixed state which means its not a superposition - but an ordinary probability a particle will be detected or not. This is where the central mystery lies. Technically its how an improper mixed states becomes a proper one. Colloquially though its why we get any outcomes at all. Different interpretations explain it in different ways but that's the basic mystery - or non mystery depending on your view. After that everything is common-sense classical. Of course you are faced with the issue of how this common-sense classical world comes about - but that is another issue - and without going into details decoherence plays a big role as well.

BTW the information view of QM is indeed a popular modern interpretation from Fuchs and others. They have a particular view of the quantum state that it is just about information and the observation is the critical thing - the technical details are along the lines of post 137 in the following:

There is also a relative view of QM that takes a different tack - its along the lines of Quantum Darwinism advocated by Zurek:
http://arxiv.org/pdf/0903.5082v1.pdf

It has a different starting point to the information view where observations are the primitive and states come from that. It starts from states and derives observations. There is some controversy if he succeeds - I think he does - but others are not so sure.

My view is more along the information lines.

Thanks
Bill

Last edited: Apr 18, 2015
5. Apr 18, 2015

### atyy

Yes, that is possible.

Tsirelson, http://cds.cern.ch/record/260158/files/P00021853.pdf?version=1: "Our physical reality, being nothing but the totality of testable predictions is observer-dependent, that is a relative reality."

Leifer, http://mattleifer.info/wordpress/wp-content/uploads/2008/11/commandments.pdf: "Do not be envious of your neighbor's state . Do not be envious of your neighbor's dynamical CP-map $\mathcal{F}$, his POVM elements $\{N_{j}\}$, his update CP-maps $\mathcal{F}_{j}$ , his Kraus operators $\mathcal{F}_{jk}$, his donkey, or anything else that is your neighbor's, for they only describe his beliefs (except for the donkey), which naturally differ from yours."

It has even been argued that in Bohmian mechanics, the quantum state is at least partly subjective.

Harrigan and Spekkens, http://arxiv.org/abs/0706.2661: "On the other hand, it has been suggested by Wiseman that there exists an unconventional reading of the deBroglie-Bohm approach which is not ψ-ontic [78]. A distinction is made between the quantum state of the universe and the conditional quantum state of a subsystem, defined in Ref. [79]. The latter is argued to be epistemic while the former is deemed to be nomic, that is, law-like, following the lines of Ref. [80] (in which case it is presumably a category mistake to try to characterize the universal wave function as ontic or epistemic)."

Last edited: Apr 18, 2015
6. Apr 18, 2015

### Staff: Mentor

These interpretations of observations along the lines of Zureks Quantum Darwinism are possible. But I don't think they contain the following:

I don't think any observer in those interpretations would ever consider a macro object like a cat in a superposition.

Thanks
Bill

7. Apr 19, 2015

### Ilja

Sorry, but decoherence solves nothing here.

Decoherence shows only that there will be no nontrivial interference effects. Thus, the evolution equation of the superpositional state would be the same as of a state described by the classical Liouville equation of statistical physics.

Now, the interpretation of this would be not a problem - it could be interpreted - and has been interpreted in the Born probablity interpretation - a a probabilistic state. With probability 0.5 it is a dead cat, with probability 0.5 a living cat.

But this interpretation is also incompatible with many worlds - where this gives a probability density $\rho(p,q)$ as describing not a probability, but the complete reality.

8. Apr 19, 2015

### Ilja

That's what my paper http://arxiv.org/abs/1103.3506 is about.

9. Apr 19, 2015

### stevendaryl

Staff Emeritus
The original paper by Hugh Everett was "The Relative State Formulation of Quantum Mechanics". It's available here: http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html [Broken]

In it he derives a notion of the state of one subsystem relative to another subsystem. But his notion of state is not the wave function, but a quantum density matrix.

Last edited by a moderator: May 7, 2017
10. Apr 19, 2015

### stevendaryl

Staff Emeritus
Clarification: Everett assumes that the composite system is described by a wavefunction, but the relative state is not a wave function, but a density matrix.

11. Apr 19, 2015

### atyy

Actually I was just thinking of Copenhagen. I don't think anything rules out a cat in superposition. There already are macro objects in superposition http://www.nature.com/news/2010/100317/full/news.2010.130.html.

12. Apr 19, 2015

### craigi

Schrodinger presented his thought experiement as a reductio ad absurdum. However, we now know that macroscropic superposition is possible. We still have no reason to believe that with a sufficiently good box, that the cat shouldn't be in a superposition of states, relative to an external observer. What it means for a cat to be in a superposition of states is still not trivial. Just trying to understand how C60, with so many internal degress of freedom can form an interference pattern in a double slit experiment is complicated enough.

13. Apr 19, 2015

### atyy

Another example, but I'm not sure whether it really is an example, is the universe itself is (before you observe it) in a superposition of states. The theory behind this is Mukhanov and Chibisov's wonderful calculation about inflation and anisotropy. In a sense it doesn't count, since one always collapses the universe in a sensible basis. On the other hand, the calculation really does contain the universe in superpositions of macroscopically distinct states. http://gruber.yale.edu/cosmology/press/2013-gruber-cosmology-prize-press-release

14. Apr 19, 2015

### jerromyjon

Are there any interpretations where entanglement is the "normal"? I mean in the sense that "decoherence" is the special case where no entanglement exists? I don't want to go off the wall with "crazy theories" but I see every system as "group entanglement" does anyone know of anyone else?

I'm not sure how to elaborate but I'm curious about the density matrix... I have avenues to pursue. ;-)

Last edited: Apr 19, 2015
15. Apr 19, 2015

### stevendaryl

Staff Emeritus
I had to refresh my memory about how this relative state business works. Suppose that you have a composite system, with two subsystems, the first (representing the observer) described by a complete set of states $|\alpha\rangle$ and the second described by complete set of states $|j\rangle$. Let the composite system be described by the state:

$|\Psi\rangle = \sum_{\alpha j} C_{\alpha j} |\alpha\rangle |j\rangle$

Now, let $O$ be some operator corresponding to a measurement on just the second subsystem. For example, a measurement of the spin of an electron. Then, the effect of $O$ on a composite state $|\alpha\rangle |j\rangle$ is given by: $O |\alpha\rangle |j\rangle = O_{jj'} |\alpha\rangle |j'\rangle$ (implied sum over $j'$). $O$ has no effect on $|\alpha\rangle$

Then the expectation value of $O$ in state $|\Psi\rangle$ is

$\langle \Psi| O|\Psi \rangle = \sum_{\alpha j j'} C^*_{\alpha j'} C_{\alpha j} O_{jj'}$

At this point, we can introduce a "relative state" for the second subsystem:

Define $P_\alpha = \sum_j C^*_{\alpha j} C_{\alpha j}$
Define $|\psi_\alpha\rangle = \frac{1}{\sqrt{P_\alpha}} \sum_j C_{\alpha j} |j\rangle$

Then the above expectation value can be written as:

$\langle \Psi| O|\Psi \rangle = \sum_{\alpha} P_\alpha \langle \psi_\alpha | O |\psi_\alpha \rangle$

This expression is exactly the same as if the second system "collapsed" into one of the states $|\psi_\alpha\rangle$ with probability $P_\alpha$

So Everett's relative state formalism reproduces the same expectation values as the "collapse" interpretation, but without assuming collapse. It does, however, assume the Born rule, in the sense of assuming that the expectation value of an operator $O$ is given by $\langle \Psi|O|\Psi\rangle$

16. Apr 19, 2015

### underworld

I think the following is kind of what I was getting at in the original post:

Are there any interpretations where entanglement is the "normal"? I mean in the sense that "decoherence" is the special case where no entanglement exists? I don't want to go off the wall with "crazy theories" but I see every system as "group entanglement" does anyone know of anyone else? I'm not sure how to elaborate but I'm curious about the density matrix... I have avenues to pursue. ;-)

Perhaps there is no "normal", much like there is no "normal" frame of reference, vis-a-vis traditional relativity. But instead, is the concept of quantum states, or the concept of decoherence something relative to the frame of reference. In the case of relativity, it is often considered as the different observation and thus reality for different observers, based on their FOR. In the case of quantum states, decoherence, or any other observation of a system, why shouldn't the FOR be considered, and thus why shouldn't they be relative to the FOR of the observer?

17. Apr 19, 2015

### atyy

As I understand it, that is the standard interpretation. The quotes from Tsirelson and Leifer in post #5 are pretty much in this line of thought.

The wave function is not necessarily real, but measurement outcomes are. In relativistic quantum mechanics, a measurement outcome is a classical event, and absolute in the sense of classical special relativity. In contrast, the wave function is more like simultaneity, a useful tool for an observer. Thus the wave function collapses across a plane of simultaneity. The wave function is an observer-dependent tool to calculate the probabilities of measurement outcomes.

http://arxiv.org/abs/1007.3977 which shows how the wave function and collapse are not absolute, but used to calculate probabilities of things which are absolute.

18. Apr 19, 2015

### jerromyjon

And the density matrix?? Or is that completely irrelevant to the wave function?

19. Apr 19, 2015

### jerromyjon

Hmmm... I wonder, if those really cold vibrating and not vibrating paddles could be used as sensors to simultaneously detect and not detect electrons passing through slits?

20. Apr 19, 2015

### Staff: Mentor

I know Atty posted it but again here is what they had to do to get a macroscopic superposition:
http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

How do you think doing that to a cat will affect the Scrodinger's Cat experiment?

Thanks
Bill