You have noticed what few others seem to.  Conservation laws are not obeyed by the Born interpretation except over many events.  It is possible to fudge in some kind of back reaction but then the details of this are again obscure.  Assuming decoherence is right, which I doubt, the conserved quantities will be spread among the many branches.  I deviced a theory of "slicing" that is somewhat related to many-worlds that took this into account in my Ph.D. thesis and gives some corrections to Born for very small devices (micron sized grains collapsing wavefunctions).  Great question.  

Thanks. It seems to me that there is another problem related to conservation of energy that is not related to measurements on entangled particles. We talk on decoherence between two different pointer states of measuring device etc. But take the detection process where a charged particle is rapidly decelerated and emits photons. The total energy in the radiation emitted from the location of detection is related to the magnitude of the charge and to the initial energy of the charged particle. If in different "universes" the particle is observed at different positions, then the total energy in emitted radiation is infinite. 

I think you should weight the energy by the norm of each such universe that measurement branches into.  This would preserve the net energy among the universes.  

With all respect, what are you colleagues talking about? Decoherence only occurs in open systems, which are not bound to obey any conservation laws, not even on average.

Plimak,

The usual explanation for correlated outcomes in a spin measurement on entangled photon pair goes like this: Before and after the process of creation of the entangled pair of photons, the angular momentum of the atom is zero. If we measure spin +1 for one of the photons then we obtain -1 for the other photon because the total angular momentum within the system of photon pair is zero. This is because the angular momentum should be conserved. On the other hand we say that during each individual measurement there is a decoherence process where the interactions between measuring device and environmental fluctuations are an essential part of the process as you say. If conservation laws do not apply at all then what is the reason for  the correlated outcome?  

What we are talking about is actually not the decoherence process itself but whether decoherence is a proper solution to the measurement problem, or in other words whether the decoherence process is a proper foundation for many world interpretation.

Conservation laws, such as spin or energy, are connected to symmetries; (spin to the SU(2) symmetry, energy to time-translation invariance, etc.). If a quantum-mechanical system exhibiting such a symmetry is subjected to observation and the device used to observe it breaks its symmetry then the corresponding conservation law does NOT apply. If, however, the device used to observe the system has the same symmetry as the system observed then the TOTAL system, namely the composition of the observed system and the device used to observe it, satisfies the corresponding conservation law. This is a statement that does not depend on the particular "interpretation of quantum mechanics" applied in the discussion of a specific measurement.

I would like to express a strong warning against the idea that the "Many-Worlds Interpretation" of quantum mechanics is a reasonable interpretation of quantum mechanics! I am convinced it is NOT. I am tempted to add that I consider it to be an intellectual scandal that there still is a kind of "Babylonian confusion" among most physicists as to what exactly quantum mechanics describes and how it should be "interpreted". There is no good reason why that should be so - except some kind of intellectual laziness that makes people avoid addressing difficult conceptual problems, such as the "interpretation of quantum mechanics".

As I understand Attila's last clarification, he is concerned about conservation in the measurement process.  The question is best answered by focusing on a specific measuring apparatus--say, a Stern-Gerlach apparatus for a fermionic massive particle, or a birefringent crystal for a photon.  In either case, the angular momentum/polarization is described by a spatial separation of the two branches.  The branches, as L.I. Plimak points out, are not de-cohered at all prior to the interaction with the measuring apparatus.  When the spatial separation occurs, who cares how much decoherence has occurred in the separation process?  The spatial separation is macroscopic.

It is somewhat disheartening that, apparently, many physicists are not even capable  to correctly describe a Stern-Gerlach spin-component measurement. In such a measurement, a specific COMPONENT of the quantum-mechanical spin of, e.g., an atom is measured - let's say the z-component. in this experiment, the measuring device does NOT exhibit full rotational symmetry, but only symmetry under rotations around the z-axis; (the device typically will involve an external magnetic field parallel to the z-axis, which breaks full rotational invariance, but preserves the symmetry of rotations around the z-axis). Hence, in the course of a measurement, only the z-component of the total spin of the observed system is conserved! The total spin, as measured by \vec{S}\cdot\vec{S}, is NOT conserved in the measurement. (For two atoms, each with spin 1/2, prepared in a spin-singlet initial state (i.e., s=0), the state AFTER a measurement of the z-component of one of the two atoms is a superposition of states of spin s=0 and spin s=1; but the z-component of the total spin remains 0!)

Obviously, it is IMPOSSIBLE to measure ALL components of a quantum-mechanical spin in a single measurement, because the operators representing these components do not commute among each other.

When one observes photons, instead of atoms, one measures HELICITIES of photons (rather than "spin"). The direction of propagation of the photons (as determined, for example, by some optical fiber through which they propagate) then breaks rotational symmetry. It is therefore inaccurate to say that the observed correlations between the helicities of two photons is a consequence of the initial state of the two photons having "spin = 0"!

The SG example is a great one.  The 10 globally conserved quantities are conserved in the total universe so there is no need to worry about subsystems here.  This is true classically or for quantum UP TO the point of measurement.  At this point the net angular momentum and center of mass of the total system (md + wavefunction) is shifted by the measurement event.  This can only be removed by included some unspecified back reaction on the measurement device in a fashion not expressed by QM (and I seriously doubt decoherence unless someone does it by fiat).  Many worlds can solve this by weighting each branch appropriately and conserving among these multiple branches.  

Sorry to plug my own work here.  In my thesis and followup work I give a purely quantum description that gives many worlds like results for long times.  It was exactly this conservation law problem that led me to this.  

Well, I am afraid I disagree with Clifford Chafin! It is actually NOT possible to measure a component of the spin (or angular momentum) of a quantum system along a given direction directly without breaking full rotational symmetry! (Incidentally, a statement like "the 10 globally conserved quantities are conserved in the total universe so there is no need to worry about subsystems here" does clearly not make sense!) I would like to add that it is not helpful to speak of something like the "measurement event" without explaining what one means by this expression. There IS an interpretation of quantum mechanics that clarifies all these notions and, in particular, provides an understanding of the "measurement event"; but it appears that its is not known to many people, yet. Since I am an optimist, I imagine this will change with time.

J.M.Fröhlich,

I am not a defender of many World interpretation (MWI). I asked this and two other related questions to see whether the answers could dispell my doubts on MWI. Until now they couldn't. (I must write a detailed reply to Clifford Chafin's explanations why I think so)

Why don't you give a link to some document explaining the interpretation you mentioned? 

The many worlds interpretation is more a philosophical interpretation than an actual testable theory. There is never an experiment you could do to disprove it without disproving quantum mechanics itself, however on the other hand there is no experiment which could show that it is the 'correct' interpretation of QM.

The operator algebras which give the classical commutation relations imply restrictions which prevent mixing of angular momentum sectors ( as long as whatever external interaction which is causing decoherence actually conserves angular momentum). The simplest way to see this is to imagine that you start with a singlet (of 2 spin 1/2) and show that no matter what you do to the off diagonal density matrix elements, you will never have a finite amplitude to have both spins pointing up.  In the many worlds interpretation, these would correspond to a 'world'  which has a different angular momentum than you started with, and indeed there is no way to get there without interacting with something external which exchanges angular momentum with the system.

Sounds like you might find this paper by Tim Spiller, Bill Munro and myself of interest:

Quantum measurement with chaotic apparatus

We study a dissipative quantum mechanical model of the projective measurement of a qubit. We demonstrate how a correspondence limit, damped quantum oscillator can realise chaotic-like or periodic trajectories that emerge in sympathy with the projection of the qubit state, providing a model of the measurement process.

http://arxiv.org/abs/0905.1867

http://www.sciencedirect.com/science/article/pii/S0375960110005700

From this one could argue that 

• We have present a fully quantum mechanical model of a projective measurement process.
• In the measurement device dynamics of expectation values are chaotic-like or periodic depending on the measured qubit state.
• The final state is selected (collapse of the wavefunction) as a consequence of environmentally induced symmetry breaking together with decoherence (ignorance of the environment implies this is effectively - but not fundamentally - probabilistic in nature).
• In this model no preferred basis was assumed to exist a priori, rather it emerges coupling between the measurement device and the quantum object.
• In ensemble language our measurement device and qubit attained the expected final mixtures.

We further demonstrate that individual classical-like trajectories of an open quantum system can act as a record of the measurement of an individual qubit, in line with the Born rule (NB: the Born rule is NOT assumed) and Zeno effect.

However, a limit of this approach is that, while projective measurement modelled in this way may appear irreversible it is in fact reversible as the full quantum dynamic (if we could model the environment quantum mechanically too) is assumed to follow Schrödinger evolution. Indeed, while quite interesting, all the decoherence models of measurement that I know of (including ours above) require a little bit of non-unitary evolution in order to work (there are a range of candidates for this from Penrose' musings on gravity through to Milburn's intrinsic decoherence). Quite often this is hidden in the details of the model. As to weather this will limit the sucess of decohence based models of measument and the quantum  to classical transition - this is yet to be determined. I will say this though - such approaches have been remarkably successful.

Clifford Chafin,

These are some of the reasons why I don’t consider decoherence based many world interpretation as the correct solution to measurement problem:

1.Consider a coherent macroscopic state namely a Bose-Einstein condensate like for example an amount of superfluid helium and lets assume that we obtain ordinary(decoherent) helium by rising the temperature. If decoherence based MWI were correct then somehow the intensity of the observed decoherent macroscopic fluid should decrease when compared to the coherent BEC state since we would observe only a branch of its "reality" in our world. However this is not the case. To solve this problem we should assume that even in the totally coherent macroscopic state we have (infinite) number of copies in the multiverse and we  observe only one of the copies. However it seems to me that such an idea has no foundation. Although it is obvious that decoherence in measurement namely the vanishing of the of-diagonal elements in density matrix is correct, I cannot agree that this can be interpreted as “The consequence is that we can observe only one of the diagonal elements namely only one of the pointer states of the measuring device and all the other diagonal elements simply disappear out of our world”.

2.Any interpretation that is based on a realistic interpretation of the wave function has to provide a mechanism that can explain how the correlation between distant measurements can be understood. Since decoherence is a local process any explanation inevitably is in conflict with special relativity. Dechorence approach doesn't provide any explanation for these correlations in space-like separated measurement events. 

Mark Everitt,

How do you explain the correlation between distant measurements in this model if one considers that decoherence is a local process?

I think that we may not need an extra irreversible element because I think that the mechanism of radiation reaction may already provide such a non-unitary evolution mechanism which is present in any measurement.

https://www.researchgate.net/publication/2190816_Source_Field_Effects_and_Wave_Function_Collapse

Article Source Field Effects and Wave Function Collapse

Atilla,

I did my PhD work on such gases and my main battle was with those who thought thermo and hydro applied to them naively.  I think the notion of measurement of these is not much like that of wavefunction collapse.  We usually run the experiments up to time t then blast (destroy) it with light to get images then rerun the experiment up to time t+delta t.  These are measurements of highly correlated many body systems, specifically of the one-body density function of it.  A huge amount of information is hidden/destroyed.  The "collapsed" features are not observed and one gets the same results every time.

I have worked out a theory of measurement for correlated systems in my thesis work but haven't published it yet and am not yet sure of its originality.  MW is a naive limit for a better theory but it requires a proper inclusion of measurement devices as proper QM objects.  This gives MW for a while, sometimes a long while!  Many spatial coordinates suggests a many times approach and our experience is best understood through an "equal times" picture.  Causality works for such this picture and, you are right, it does not for decoherence (of which I am no fan).  

Atilla Gürel: An interesting question - the correlation is contained within the entanglement of the quantum objects that are the subject of the experiment. As with conventional Copenhagen interpretation of measurement - decoherence as a local process is not a problem here (unless I have misunderstood your point). 

One can model radiation as a non-unitary process - indeed, this was one historical reason for people being interested in non-Hermitian Hamiltonians. However, while interesting, such approaches seem to raise more problems than they solve. In my view Radiation is better thought of a unitary process of an atom in a much larger system (e.g. coupled to a set of cavities or the vacuum field).

Mark,

Decoherence itself is not a problem but correlations remain a problem from decoherence perspective of measurement.. Since decoherence is a description based on wave function dynamics where the measured particle the measurement device and local environment is involved, it should be also able to describe how the wave function dynamics at one measurement site can influence the dynamics in another spacelike separated measurement event. 

Mark Everitt,

Why radiation reaction may be a candidate for nonunitary portion of time evolution: 

Classical case:

The radiation of an hertz-dipole is an irreversible process. The entropy increases while the electromagnetic energy dissipates into the infinity. Notice that “radiation reaction” is only a name given to the fact that -because of conservation of energy- the energy that was within the dipole initially must decrease while energy dissipates into the infinity. Although the Maxwell equations are symmetric in time, the reverse process does never occur. By reverse process I don’t mean the absorption of radiation that was emitted by some other distant source. By the reverse process I mean playing back exactly the same process by replacing t by –t that corresponds to the creation of a simultaneous coherent fluctuation on a sphere at infinity that propagates to the center where the hertz-dipole is located.

Quantum description:

In quantum description of interaction of radiation field with matter the concept of radiation reaction was almost forgotten. The reason for this is twofold:

1. In QED it is impossible to write down the electrostatic energy within the source field of a single pointlike charge because of infinite energy associated with pointlike charge.

2.The vacuum fluctuations seemed to suffice to explain the spontaneous emission which is the quantum equivalent of discharging of an hertz dipole by radiation. So after renormalization the problem 1 did not seem to be a real problem.

In sixties the semiclassical explanation of spontaneous emission by radiation reaction by E.T. Jaynes and coworkers caused much controversy on the subject. Later papers discussing the role of radiation reaction in spontaneous emission from QED perspective were published. However because of problem 1, a fundamental treatment of radiation reaction from first principles in QED perspective was never accomplished.

I think that the irreversibility I described in classical case is a universal fact. It is only obscured in quantum description which leads to missing of the opportunity of consideration of (in my opinion) a serious candidate for the nonunitary part of the time evoulution to explain the collapse process. The advantage of this viewpoint over the consideration of other candidates you mentioned is that it does not have any effect on stationary states and it is only in effect during interaction of radiation with matter. This eliminates a serious problem of other approaches because these approaches inevitably require a fundamental modification to quantum mechanics which could change also the calculated energy levels of stationary states. Thus the consideration of radiation reaction as a candidate may have the potential to leave everything what is already calculated successfully intact while only solving the problem.

All these are discussed in the paper of which the link I gave in my previous post.