A Novel Interpretation of the Klein-Gordon Equation

Wharton, K. B.

doi:10.1007/s10701-009-9398-2

Cited by 31 publications

(32 citation statements)

References 30 publications

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“…'Retrocausation' refers to the possibility of causal influences that act in a direction contrary to the standard arrow of time. It has been proposed as a means of resolving the mystery of Bell-inequality violations [34][35][36][37][38] by purportedly saving the relativistic structure of the theory: rather than having causal influences propagating outside the light cone, they propagate within the light cone although possibly within the backward light cone.…”

Section: Retrocausationmentioning

confidence: 99%

The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning

2015

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An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles. 4 Other work in the field of machine learning has appealed to statistical features besides CI relations, but not the features of correlations that are relevant for Bellʼs theorem. Peters et al [8] demonstrate that if one is promised an additive noise model, then features of the joint distribution can often distinguish cause from effect in the case of a distribution on a pair of variables, where there are no CI relations to guide the analysis. Other approaches have appealed to the complexity of conditional distributions [3][4][5]. 5 A defining feature of a common cause is that if the statistical dependence between two variables is to be explained entirely by a common cause, then it must be the case that conditioning on the common cause makes the variables statistically independent. As we will see, this feature is built into the framework of causal models. Statements of Reichenbachʼs principle often assert it explicitly. New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens

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Section: Retrocausationmentioning

confidence: 99%

The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning

2015

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“…, given the Cartesian components ofq. The former equation (5), however, is not invertible; inserting the form of q from (4) into (5), one finds that the global phase α always disappears exactly.…”

Section: A Spinor-quaternion Mapmentioning

confidence: 99%

“…. Eqn (5) then indicates that the Bloch sphere vectorq can be found by rotating the vectorẑ by an angle −2β around the axisŵ.…”

Section: A Spinor-quaternion Mapmentioning

confidence: 99%

“…As before, we shall assume the map M i [|χ>] = q, and enforce the continued normalization of q by only multiplying exponential quaternions. Using the notation q = q L q, the simplest case is the left multiplication q L = exp(iγ/2), which simply changes the global phase of q. Eqn (5) indicates that this does not lead to any Bloch sphere rotation, becauseq =q.…”

Section: Left Multiplicationsmentioning

confidence: 99%

“…It is straightforward to generalize Section 2 to work for any map M v (|χ>) ≡ uM i (|χ>) between spinors and quaternions. Inserting q =ūq into (5), and dropping the primes, one finds simplyq =qvq,…”

Section: The Generalized Mapmentioning

confidence: 99%

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Unit quaternions and the Bloch sphere

Wharton¹,

Koch²

2015

J. Phys. A: Math. Theor.

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The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to "second order qubits" would imply either a larger gauge freedom or a natural space of hidden variables. ‡

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Fundamental is Non-random

Wharton

2019

The Frontiers Collection

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A Novel Interpretation of the Klein-Gordon Equation

Cited by 31 publications

References 30 publications

The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning

The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning

Unit quaternions and the Bloch sphere

Fundamental is Non-random

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