Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem

Palmer, Tim

doi:10.1098/rspa.2019.0350

Cited by 25 publications

(38 citation statements)

References 41 publications

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“…This will involve abandoning the distinction between initial conditions and laws, which is a central principle in scientific theories. Palmer seems to advocate such an approach [19,20]. However, his model still appears to assume an equilibrium distribution over certain parameters, a distribution which could in principle be different.…”

Section: Discussionmentioning

confidence: 99%

Superdeterministic hidden-variables models II: conspiracy

Sen

Valentini

2020

Proc. R. Soc. A.

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We prove that superdeterministic models of quantum mechanics are conspiratorial in a mathematically well-defined sense, by further development of the ideas presented in a previous article A . We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of N devices to determine the local measurement setting. We prove, without assuming any features of quantum statistics, that superdeterministic models of this scenario must have a finely tuned distribution of hidden variables. Specifically, fine-tuning is required so that the measurement statistics depend on the measurement settings but not on the details of how the settings are chosen. We quantify this as the overhead fine-tuning F of the model, and show that F > 0 (corresponding to ‘fine-tuned’) for any N > 1. The notion of fine-tuning assumes that arbitrary (‘non-equilibrium’) hidden-variables distributions are possible in principle. We also show how to quantify superdeterministic conspiracy without using non-equilibrium. This second approach is based on the fact that superdeterministic correlations can mimic actual signalling. We argue that an analogous situation occurs in equilibrium where, for every run, the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used. This results in extremely large superdeterministic correlations, which we quantify as a drop of an appropriately defined formal entropy. Non-local and retrocausal models turn out to be non-conspiratorial according to both approaches.

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Section: Discussionmentioning

confidence: 99%

Superdeterministic hidden-variables models II: conspiracy

Sen

Valentini

2020

Proc. R. Soc. A.

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“…Invariant Set Theory (IST) [34,35] arose from an earlier realization [36] that, suitably formulated, non-linear dynamics could provide the basis for a deterministic theory of quantum physics which was not counterfactually complete and therefore could violate Statistical Independence thus avoiding non-locality. More specifically, IST is a deterministic theory based on the assumption that the laws of physics at their most primitive derive from the geometry of a fractal set of trajectories, or histories, I U , in state space.…”

Section: Invariant Set Theorymentioning

confidence: 99%

Rethinking Superdeterminism

2020

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Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical description of the measurement process. This "measurement problem" indicates that quantum mechanics is at least an incomplete theory-good as far as it goes, but missing a piece-or, more radically, is in need of complete overhaul. Here we describe an approach which may provide this sought-for completion or replacement: Superdeterminism. A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent non-locality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way.

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“…However, the assumption of statistical independence does more than ensure that sub-ensembles are statistically independent; it implies a strong form of counterfactual definiteness [ 29 , 30 ]. Consider two measurements performed on two sub-ensembles of particles: counterfactual definiteness assumes that in principle, one could have performed the second measurement on the first sub-ensemble (even though in practice one did not).…”

Section: Why Is Quantum Physics So Unintuitive?mentioning

confidence: 99%

“…However, there is no reason for the Euclidean metric to be the correct metric of distance in state space rather than physical space. In particular, there is a deterministic theory of quantum physics based on fractal geometry, where the relevant metric on state space is p-adic rather than Euclidean [ 30 ]. Relative to this metric, putative states which lie in the gaps in the fractal geometry are necessarily distant from points on the fractal set, even when a fractal gap appears very slender and hence insignificant from a Euclidean perspective.…”

Section: Why Is Quantum Physics So Unintuitive?mentioning

confidence: 99%

“…To make better sense of contemporary physics, it is better to avoid using counterfactuals at all, e.g., by saying that I am free if there are no constraints preventing me from doing what I want to do [ 24 ]. Certainly, such real-world definitions are vital if we are to explain the violation of the Bell inequality in a causal theory where experimenters are free agents [ 29 , 30 ].…”

Section: Why Is Quantum Physics So Unintuitive?mentioning

confidence: 99%

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Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

Palmer

2020

Entropy

Self Cite

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It is proposed that both human creativity and human consciousness are (unintended) consequences of the human brain's extraordinary energy efficiency. The topics of creativity and consciousness are treated separately, though have a common sub-structure. It is argued that creativity arises from a synergy between two cognitive modes of the human brain (which broadly coincide with Kahneman's Systems 1 and 2). In the first, available energy is spread across a relatively large network of neurons. As such, the amount of energy per active neuron is so small that the operation of such neurons is susceptible to thermal (ultimately quantum decoherent) noise. In the second, available energy is focussed on a small enough subset of neurons to guarantee a deterministic operation. An illustration of how this synergy can lead to creativity with implications for computing in silicon are discussed. Starting with a discussion of the concept of free will, the notion of consciousness is defined in terms of an awareness of what are perceived to be nearby counterfactual worlds in state space. It is argued that such awareness arises from an interplay between our memories on the one hand, and quantum physical mechanisms (where, unlike in classical physics, nearby counterfactual worlds play an indispensable dynamical role) in the ion channels of neural networks. As with the brain's susceptibility to noise, it is argued that in situations where quantum physics plays a role in the brain, it does so for reasons of energy efficiency. As an illustration of this definition of consciousness, a novel proposal is outlined as to why quantum entanglement appears so counter-intuitive.

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Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem

Cited by 25 publications

References 41 publications

Superdeterministic hidden-variables models II: conspiracy

Superdeterministic hidden-variables models II: conspiracy

Rethinking Superdeterminism

Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

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