Related papers: Solving the Hard Problem of Bertrand's Paradox
We construct games of chance from simpler games of chance. We show that it may happen that the simpler games of chance are fair or unfavourable to a player andyet the new combined game is favourable -- this is a counter-intuitive…
We propose a solution to the quantum measurement paradox by first identifying its classical counterpart.
The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…
We can overcome uncertainty with uncertainty. Using randomness in our choices and in what we control, and hence in the decision making process, could potentially offset the uncertainty inherent in the environment and yield better outcomes.…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
We present an improved version of Berry's ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture…
The "measurement problem" of quantum mechanics, and the "hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science…
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without…
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…