Figure 1

When a ballerina does a pirouette she must escape the friction of the ground in order to get the freedom to move. (Figure 1: Photo by Michael Garner, courtesy of English National Ballet.) She does this by restricting her contact with the ground to a point. In a recent paper I and my collaborators Andrew Garner and FQXi's Vlatko Vedral show that quantum theory in a very similar way escapes a fundamental constraint on movement by accepting uncertainty.

Quantum systems are associated with states which encode the statistics of future possible measurements. The collection of such states may be represented as a geometric shape. In the smallest possible quantum systems, single qubits (quantum bits), this shape is a sphere, called the Bloch sphere.

For example, think about a property of a qubit, such as its position: the qubit could be associated with two possible positions, A and B, say, or it can be in a fuzzy superposition where it exists in both of these mutually incompatible states simultaneously, before being observed. If it's in a superposition then although experimenters cannot know with certainty what position they will find it in when they make a measurement, they will have some sense of the probability of getting a certain outcome. The Bloch sphere helps to visualise this odd feature and the probabilistic nature of quantum mechanics. In the example, a vector pointing to the north pole of the sphere could represent position A, while the south pole represents position B. (In a classical system, this would represent the only two options available for a binary digit, or bit, to access). However, a qubit can also be represented by a vector pointing elsewhere on the surface of the sphere, corresponding to the fuzzy in-between states.

Figure 2

The maximal state space conceivable would actually be the cube outside of the sphere, as shown in figure 2. The quantum state space is the sphere, but if there were no uncertainty principle all states in the outer cube could be allowed. In this case certain measurements could all have predictable outcomes at the same time, in violation of the quantum uncertainty principle.

One may ask why quantum theory is restricted to the sphere, and accordingly to having the uncertainty principle.

We came across an intriguing answer when thinking about how the cube state space would handle an interferometer. In an interferometer the particle or photon is firstly placed in a superposition of being in two places and then operations are done on each site. Now when you have two different sites fundamental locality restrictions come into play. In particular, we point out that if a system has 0 probability of being found on site B, then an operation on site B must leave the state of the system invariant. Otherwise we could do action at a distance. Contrary to some popular science depictions, quantum theory does not allow action at a distance. The universe would be almost inconceivably odd and complicated if action at a distance were possible. We would not be able to make a statement about an individual system without taking into account what happens everywhere else in the world.

On the Bloch diagram, state transformations move points around, e.g. by rotating the shape. So, if one accepts that this locality restriction holds, it turns out that operations on site B must leave all points (states) on the lower plane of the cube invariant. It is like the points are stuck by total friction between the shape and the lower plane. As a result the cube has a big disadvantage over the sphere because if the entire square face touching the ground is restricted, then the whole cube gets stuck and no states can change.

But now imagine metamorphosing the cube into a sphere, or indeed something else with only one point on the lower plane, like how the ballerina goes up on one toe. Then the shape, with all the quantum states in it, can move. The quantum sphere has the advantage over the cube that it can rotate even if there is full friction with the lower (and/or upper) plane, just as the ballerina accepts the uncertainty of only having a point in contact with the ground in return for the ability to pirouette.

One may say that uncertainty, rather than being just limiting, liberates quantum states to change.

--

Oscar Dahlsten is affiliated with Oxford University

The paper appears in Nature Communications.

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"Contrary to some popular science depictions, quantum theory does not allow action at a distance. The universe would be almost inconceivably odd and complicated if action at a distance were possible. We would not be able to make a statement about an individual system without taking into account what happens everywhere else in the world."

The above statements are grossly misleading, if not outright wrong.

To be sure, one cannot send a signal violating special relativity with the so-called quantum non-locality, but nonetheless quantum theory is not a locally causal theory.

But here is a good news: Quantum theory can be completed (in a manner espoused by Einstein) into a locally causal theory, as done, for example, in this paper and this simulation.

For a more compete discussion, see also this page of my blog, or this discussion of mine.

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The good thing about quantum action is that any number of complete or even mostly complete basis sets are solutions to the reality of the Schrödinger equation. The bad thing about quantum action is that any number of complete or even mostly complete basis sets are solutions to the reality of the Schrödinger equation.

Just as the Heisenberg approach is equivalent to Dirac's approach, science can and does argue endlessly about which basis set or approach or interpretation is better. These kinds of arguments are really not that all that useful since action is all about the Schrödinger equation, not really about which basis set you choose or which approach or which interpretation. But the arguments about basis sets go on and on and on...

After all, it is not even necessary to consider action in space as a priori since matter action as exchange is a complete basis for quantum action without space. Locality is simply a convenient and very intuitive representation of phase for the quantum action of matter waves and there are any number of equivalent ways to deal with the issue of locality in quantum action.

The really important goal in all of this is not to to find a better basis set for quantum action, the goal for science is to find a gravity exchange force that scales in a very nice way from that of the quantum action of charge force.

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"One may ask why quantum theory is restricted to ... having the uncertainty principle."

Quantum Theory has an uncertainty principle, because it employs Fourier Transforms to describe systems. Since the uncertainty principle is a property of a Fourier Transform, it is inevitable that any system, being described via Fourier Transforms, will also exhibit the uncertainty principle. Regardless of whether or not the uncertainty principle is a property of the system itself, it is a property of the chosen means for describing systems; hence it will inevitably exist, within the description of the system.

Rob McEachern

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North and South poles are relative positions. Somewhere, A and Nowhere, B are absolute positions. From cosmology, our universe seems to tell us that both states, A and B can be occupied, viz. 'Before' Big bang (Nowhere), the current epoch with 'Somewhere' increasing in size, and a Big crunch back to Nowhere (equal to non-existence).

I am not a professional Quantum Machinist, but if it can be contemplated on this blog and stated that, "For example, think about a property of a qubit, such as its position: the qubit could be in two different positions, A and B", why must the choice of positions only be relational and not absolute, when a geometric system as big as the Universe, and which itself is a collection of all that exists, including '…the smallest possible quantum systems, single qubits (quantum bits)', can occupy the two absolute positions, A and B, how much more a qubit? Does anything prevent a qubit from disappearing to Nothing (Nowhere) and appearing from Nothing (Somewhere)? Are virtual particles not said to behave similarly?

Akinbo

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As a sort of meta-observation, might it be worth considering the dichotomy of information and energy, in that because information is static, we assume it must have some Platonic permanence, yet when dynamic conditions are being described statically, the potential information goes to infinity. Now our neural functions are designed to extract and process information, so this creates an infinite feedback loop, but if we want to put it in context, then we need to acknowledge that dynamical basis.

Writing this on a phone, so pardon run on sentences.

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Hi Oscar,

"The crisis of representation and interpretation" (T.Romanovskaya) in quantum mechanics - the crisis of the philosophical foundations of the QM and all fundamental physics. It is true, the way to overcome the crisis - is a further deepening of the Geometry, but rather in the "origin of Geometry" (E.Husserl) and the dialectical- ontological unification of matter, search for the absolute foundations of physics and knowledge, the absolute generating structure. Necessary to consider limiting (absolute, unconditional) state of matter: absolute motion (rotation, "vortex", discretuum) + absolute rest (linear state, continuum)) + absolute becoming (absolute wave -"figaro" of states = discretuum + continuum).

Then geometrized basis of QM: "sphere" + "cube" + "cylinder". Each limit (absolute, unconditional) state of its way - the absolute vector, the vector of the absolute state. This "triangle" of absolute states of matter - the ontological representation of the triune foundation - "origin of geometry", the beginning of physics, the beginning, framework and carcas of knowledge. This is what David Gross calls - "general framework structure" (D.Gross, an interview "Iz chego sostoit prostranstvo-vremya/What is in the space-time) the same for the QM and for GM. Today QM and GM are parametrical theories without ontologic justification.

All best,

Vladimir

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Overcoming the "crisis of understanding" in fundamental physics is only possible through the introduction of standard ontological justifications addition to the empirical standard. Requires broadening and deepening of the limits of knowledge through a deeper ontological interpretation and representation of of the experimental data for the formation of the ontological framework, carcas and foundation of knowledge. "Quantum" is not ontologically grounded concept - this parametric concept. Accordingly, the "quantum theory" - a theory is not ontologically grounded, it is not fundamental in the full sense of the word.

The information revolution requires the introduction of the conceptual structure of the Universum the new ontological concepts that represent the deepest meanings of the "LifeWorld". Otherwise, the "uncertainty" "will hold by a throat" fundamental knowledge, first of all physics and cosmology.. This is indicated by the results of the fifth Contest FQXi. The winner of the fourth contest FQXi Robert Spekkens concluded: «Rest in peace kinematics and dynamics. Long live causal structure! . But where is it - «causal structure» with the ontological justification? I offered "The Absolute generating structure". But where open competition of alternative, ontologically and empirically based "general framework structure" of the Universum and knowledge that will enable to overcome the ontological uncertainty ?

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Dear Oscar,

Thanks. I really like the connection you make to the ballerina and quantum non-locality indeterminacy. You apparently seem to refer to a "Swan lake" type of dance and for instance not to "Le Sacre du Printemps". I might be mistaken there too. Modern dance isn't exactly similar to a Tsjaikovski ballet. But ok.

My question to you relates back to an arXiv paper of mine http://arxiv.org/abs/1409.0740 or\and (much more elaborated) to my loophole CHSH paper Results in Physics 4, (2014), 81-82. I appologize for this self-referring approach, however, I see no other way.

If we have Swan lake escapes from determinism then why can one arrive at the quantum correlation from Bell's correlation formula (maybe that formula is far too primitive to describe what is needed ?) or why is it then possible to see that CHSH holds a probability loophole. The arXiv paper shows a numerical argument for the derivation of a.b = cos(phi_a-phi_b) from Bell's formula.

I think it is time to realize that lhv and go-away-lhv are perhaps both wrong. The lhv camp served to show the way however.

It is concrete mathematical incompleteness that is bothering us here. Discussions in our quarters often degenerate to ordinary exchanges of nothing between, most of the time, adversaries with a hearing problem. Some of the adversaries also show a kind of "Gilles de la Tourette" type of response to criticism on a favourite theorem. I am- and probably Joy also is- sorry for all the inconvenience.

For your convenience to kill me off instantly, I attach the RinP paper (although it is very densly written one can verify the argument easily).

attachments: 1-s2.0-S2211379714000254-main.pdf

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