Indeterminism and Undecidability
- URL: http://arxiv.org/abs/2003.03554v3
- Date: Wed, 24 Mar 2021 11:07:20 GMT
- Title: Indeterminism and Undecidability
- Authors: Klaas Landsman
- Abstract summary: Chaitin's follow-up to Goedel's (first) incompleteness theorem can be proved.
The main point is that Bell and others did not exploit the full empirical content of quantum mechanics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The aim of this paper is to argue that the (alleged) indeterminism of quantum
mechanics, claimed by adherents of the Copenhagen interpretation since Born
(1926), can be proved from Chaitin's follow-up to Goedel's (first)
incompleteness theorem. In comparison, Bell's (1964) theorem as well as the
so-called free will theorem-originally due to Heywood and Redhead (1983)-left
two loopholes for deterministic hidden variable theories, namely giving up
either locality (more precisely: local contextuality, as in Bohmian mechanics)
or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's
cellular automaton interpretation of quantum mechanics). The main point is that
Bell and others did not exploit the full empirical content of quantum
mechanics, which consists of long series of outcomes of repeated measurements
(idealized as infinite binary sequences): their arguments only used the
long-run relative frequencies derived from such series, and hence merely asked
hidden variable theories to reproduce single-case Born probabilities defined by
certain entangled bipartite states. If we idealize binary outcome strings of a
fair quantum coin flip as infinite sequences, quantum mechanics predicts that
these typically (i.e.\ almost surely) have a property called 1-randomness in
logic, which is much stronger than uncomputability. This is the key to my
claim, which is admittedly based on a stronger (yet compelling) notion of
determinism than what is common in the literature on hidden variable theories.
Related papers
- Bell vs Bell: a ding-dong battle over quantum incompleteness [0.0]
This paper aims to bring clarity to the debate via simple examples and rigorous results.
It is first recalled, via quantum and classical counterexamples, that the weakest statistical form of locality consistent with Bell's 1964 paper is insufficient for the derivation of determinism.
Attention is then turned to critically assess Bell's appealing to the Einstein-Rosen-Podolsky incompleteness argument to support his claim.
arXiv Detail & Related papers (2024-06-27T11:11:28Z) - A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device.
Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
arXiv Detail & Related papers (2024-05-10T19:30:23Z) - Internal causality breaking and emergence of entanglement in the quantum realm [1.1970409518725493]
We investigate the quantum dynamics of two photonic modes coupled to each other through a beam splitting.
We find that when the initial wave function of one mode is different from a wave packet obeying the minimum Heisenberg uncertainty, the causality in the time-evolution of each mode is internally broken.
arXiv Detail & Related papers (2024-03-14T13:16:00Z) - Connecting classical finite exchangeability to quantum theory [69.62715388742298]
Exchangeability is a fundamental concept in probability theory and statistics.
We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
arXiv Detail & Related papers (2023-06-06T17:15:19Z) - Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
We show that there does not exist a finite set of resource monotones which completely determines all state transformations.
We show that totally ordered theories allow for free transformations between all pure states.
arXiv Detail & Related papers (2022-12-05T18:28:36Z) - Quantum Instability [30.674987397533997]
We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system.
An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
arXiv Detail & Related papers (2022-08-05T19:53:46Z) - On the Common Logical Structure of Classical and Quantum Mechanics [0.0]
We show that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account.
We show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions.
arXiv Detail & Related papers (2022-06-21T18:31:53Z) - Discretised Hilbert Space and Superdeterminism [0.0]
In computational physics it is standard to approximate continuum systems with discretised representations.
We consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics.
arXiv Detail & Related papers (2022-04-07T18:00:07Z) - Why we should interpret density matrices as moment matrices: the case of
(in)distinguishable particles and the emergence of classical reality [69.62715388742298]
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs)
We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way.
We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
arXiv Detail & Related papers (2022-03-08T14:47:39Z) - Branch-counting in the Everett Interpretation of quantum mechanics [0.0]
Well-known branch-counting rule, for realistic models of measurements, fails this test.
New rule hinges on the use of decoherence theory in defining branching structure.
arXiv Detail & Related papers (2022-01-16T16:50:07Z) - Depth-efficient proofs of quantumness [77.34726150561087]
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover.
In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
arXiv Detail & Related papers (2021-07-05T17:45:41Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.