Decoherence - Theoretical, Exper. and Conceptual Probs

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In its most familiar guise, the many-worlds interpretation MWI suggests that we live in a near-infinity of universes, all superimposed in the same physical space but mutually isolated and evolving independently. In many of these universes there exist replicas of you and me, all but indistinguishable yet leading other lives. The MWI illustrates just how peculiarly quantum theory forces us to think. It is an intensely controversial view. But when the MWI is in the picture, those passions can become so extreme that we must suspect a great deal more invested in the matter than simply the resolution of a scientific puzzle.

For the interpretation speaks not just to quantum mechanics itself but to what we consider knowledge and understanding to mean in science.

It asks us what sort of theory, in the end, we will demand or accept as a claim to know the world. The wave function is a mathematical expression that defines all possible observable states of a quantum system, such as the various possible locations of a particle. Up until a measurement is made and the wave function collapses whatever that means , there is no reason to attribute any greater a degree of reality to any of the possible states than to any other. Where, then, do they all go, bar one, when the wave function collapses? At first glance, the many-worlds interpretation looks like a delightfully simple answer to that mysterious vanishing act.

It says that none of the states vanishes at all, except to our perception. When we make a measurement, we really do get just one result out of the many that quantum mechanics offers. Wave function collapse seemed to be demanded in order to connect quantum theory to reality. But in fact all of them occur. We only see one of those realities, but the others have a separate physical existence too.

In effect, this implies that the entire universe is described by a gigantic wave function that contains within it all possible realities. As it evolves, some of these superpositions break down, making certain realities distinct and isolated from one another.


Rather, we should speak of the unraveling of two realities that were previously just possible futures of a single reality. The many-worlds interpretation is distinct from the multiverse hypothesis , which envisions other universes, born in separate Big Bangs, that have always been physically disconnected from our own. When Everett presented his thesis, and at the same time published the idea in a respected physics journal, it was largely ignored. If all the possible outcomes of a quantum measurement have a real existence, where are they, and why do we see or think we see only one?

This is where the many worlds come in. DeWitt argued that the alternative outcomes of the measurement must exist in a parallel reality: another world. You measure the path of an electron, and in this world it seems to go this way, but in another world it went that way. That requires a parallel, identical apparatus for the electron to traverse. You avoid the complication of wave function collapse, but at the expense of making another universe. This picture gets really extravagant when you appreciate what a measurement is.

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In one view, any interaction between one quantum entity and another — a photon of light bouncing off an atom — can produce alternative outcomes, and so demands parallel universes. In particular, after a measurement takes place, there are two or more versions of the observer where before there was one. But after that, who can say? Their universes go their separate ways, launched on a trajectory of continual unraveling. You can probably see why the MWI is the interpretation of quantum mechanics that wins all the glamour and publicity. It tells us that we have multiple selves, living other lives in other universes, quite possibly doing all the things that we dream of but will never achieve or never dare to attempt.

There is no path not taken. Parallel quantum worlds have split once they have decohered, for by definition decohered wave functions can have no direct, causal influence on one another. In this view, splitting is not an abrupt event. It evolves through decoherence and is only complete when decoherence has removed all possibility of interference between universes. What we can say a little more precisely is what kind of phenomenon causes splitting.

In short, it must happen with dizzying profusion.

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Just within our own bodies, there must be at least as many splitting events affecting each of us every second as there are encounters between our molecules in the same space of time. Those numbers are astronomical. The main scientific attraction of the MWI is that it requires no changes or additions to the standard mathematical representation of quantum mechanics. There is no mysterious, ad hoc and abrupt collapse of the wave function. And virtually by definition it predicts experimental outcomes that are fully consistent with what we observe.

Far from it. The MWI is surely the most polarizing of interpretations. It is simply what quantum mechanics is. My own view is that the problems with the MWI are overwhelming — not because they show it must be wrong, but because they render it incoherent. It simply cannot be articulated meaningfully. Other copies of me? Other world histories?

Worlds where I never existed?

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Honestly, whatever next! Who are we to say how the world should behave? But one of the most serious difficulties with the MWI is what it does to the notion of self. What can it mean to say that splittings generate copies of me?

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They sound transgressively exciting while being easily recognizable as plotlines from novels and movies. The physicist Lev Vaidman has thought rather carefully about this matter of quantum youness. But in what can that perception reside, if not in a conscious entity? For how can it do that when nothing else does?

Despite its confounding reputation, quantum mechanics both guides and helps explain human intuition

You can make these measurements as often as you like just by pushing the button on the device. That is, A is now maximally entangled with E 1 , whereas A and B are completely uncorrelated. A larger value of Dec A E thus corresponds to a larger amount of decoherence. In the quantum case, Dec A E can be computed using any semi-definite programming solver 29 , We remark that Dec A E does itself not depend on the dimension of the system A. Furthermore, we note that Dec A E does not depend on the particular physical realization of the system A , but merely the amount of information that it can hold.

We point out that this entanglement-preservation picture is equivalent to the picture in which the quantum state of a single system decoheres 31 see Fig. After the decoherence process, Eve who controls the environment performs an operation in order to reach a state that is as entangled with system A as possible. The decoherence quantity is a measure for how close Eve can get to being maximally entangled with A , measured by the square of the fidelity, F 2. It is known 31 that decoherence on a single quantum system can be understood fully as the process' inability to preserve entanglement for further background information see Supplementary Note 1. It is for this reason that our test for decoherence is fully general. In particular, it could also be applied to collapse models or any other form of decoherence. We emphasize gravitational decoherence, because here there is a pressing motivation for considering theories that modify or extend quantum mechanics. We hence see that in quantum mechanics, the relevant measure of decoherence is simply Dec A E see Fig. How can we estimate it in an experiment?