Modal Logic for the Everett Many-Worlds Interpretation

In this paper, we present a (propositional) modal-logic approximation to Quantum Mechanics from a reduced and characteristic number of crucial experi ments and so independently of the lattice of subspaces of Hilbert s'pace. Kripke's semantics, which determinates this system, allows to define, from a new point of view, the notions of process and virtual world and admits a natural interpretation which in turn can help us to understand the measurement problem. In this way, we can attempt a many-worlds interpretation of Quantum Mechanics, in the way of Everett.In this paper, we present a (propositional) modal-logic approximation to Quantum Mechanics from a reduced and characteristic number of crucial experi ments and so independently of the lattice of subspaces of Hilbert s'pace. Kripke's semantics, which determinates this system, allows to define, from a new point of view, the notions of process and virtual world and admits a natural interpretation which in turn can help us to understand the measurement problem. In this way, we can attempt a many-worlds interpretation of Quantum Mechanics, in the way of Everett.

Apr 1, 19850 citations

Many-worlds Interpretation from a Mathematical Viewpoint

Euich Miztani

Jul 5, 20260 citations

Measurement and Quantum States

Yorick Hardy, Willi-Hans Steeb

The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Basel eBooksJan 1, 20010 citations

Quantum Immortality and Non-Classical Logic

Phillip L. Wilson

The Everett Box is a device in which an observer and a lethal quantum apparatus are isolated from the rest of the universe. On a regular basis, successive trials occur, in each of which an automatic measurement of a quantum superposition inside the apparatus either causes instant death or does nothing to the observer. From the observer's perspective, the chances of surviving $m$ trials monotonically decreases with increasing $m$ . As a result, if the observer is still alive for sufficiently large $m$ she must reject any interpretation of quantum mechanics which is not the many-worlds interpretation (MWI), since surviving $m$ trials becomes vanishingly unlikely in a single world, whereas a version of the observer will necessarily survive in the branching MWI universe. Here we ask whether this conclusion still holds if rather than a classical understanding of limits built on classical logic we instead require our physics to satisfy a computability requirement by investigating the Everett Box in a model of a computational universe running on a variety of constructive logic, Recursive Constructive Mathematics. We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe. Thus we argue that Everett's argument is strengthened and any counter-argument must be strengthened, since it holds not only in classical logic (with embedded notions of continuity and infinity) but also in a computable logic.The Everett Box is a device in which an observer and a lethal quantum apparatus are isolated from the rest of the universe. On a regular basis, successive trials occur, in each of which an automatic measurement of a quantum superposition inside the apparatus either causes instant death or does nothing to the observer. From the observer's perspective, the chances of surviving $m$ trials monotonically decreases with increasing $m$. As a result, if the observer is still alive for sufficiently large $m$ she must reject any interpretation of quantum mechanics which is not the many-worlds interpretation (MWI), since surviving $m$ trials becomes vanishingly unlikely in a single world, whereas a version of the observer will necessarily survive in the branching MWI universe. Here we ask whether this conclusion still holds if rather than a classical understanding of limits built on classical logic we instead require our physics to satisfy a computability requirement by investigating the Everett Box in a model of a computational universe running on a variety of constructive logic, Recursive Constructive Mathematics. We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe. Thus we argue that Everett's argument is strengthened and any counter-argument must be strengthened, since it holds not only in classical logic (with embedded notions of continuity and infinity) but also in a computable logic.

arXiv:2007.09847Jul 20, 20201 citation

Modal quantum logic and its dialogic foundation

F. J. Burghardt

International Journal of Theoretical PhysicsNov 1, 19804 citations

m

trials monotonically decreases with increasing

m

. As a result, if the observer is still alive for sufficiently large

m

she must reject any interpretation of quantum mechanics which is not the many-worlds interpretation (MWI), since surviving

m

trials becomes vanishingly unlikely in a single world, whereas a version of the observer will necessarily survive in the branching MWI universe. Here we ask whether this conclusion still holds if rather than a classical understanding of limits built on classical logic we instead require our physics to satisfy a computability requirement by investigating the Everett Box in a model of a computational universe running on a variety of constructive logic, Recursive Constructive Mathematics. We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe. Thus we argue that Everett's argument is strengthened and any counter-argument must be strengthened, since it holds not only in classical logic (with embedded notions of continuity and infinity) but also in a computable logic.