Abstract I thought today that I would stress the positive side of quantum theory. We began our meeting with the principle of skepticism. In order to be skeptical of something, first you must notice it. It’s very hard to be skeptical of things you do not notice. The hardest part of each dramatic change that has occurred in physics since 1600 has been to become aware of the assumptions of the old theory that had to be given up. The most confusing state of affairs is during the early days of a new theory, when you still cling to some of the old assumptions, and yet some re- wards of the new theory are attracting you further. I used to think of 1924, the year in which Heisenberg discovered the quantum theory, as a kind of abyss, a Grand Canyon, separating the old physics from the new, or a desert separating two fertile regions. But this is too symmetric. The two sides of an abyss are on the same level. The two sides of a desert are symmetric in respect to each other.Abstract I thought today that I would stress the positive side of quantum theory. We began our meeting with the principle of skepticism. In order to be skeptical of something, first you must notice it. It’s very hard to be skeptical of things you do not notice. The hardest part of each dramatic change that has occurred in physics since 1600 has been to become aware of the assumptions of the old theory that had to be given up. The most confusing state of affairs is during the early days of a new theory, when you still cling to some of the old assumptions, and yet some re- wards of the new theory are attracting you further. I used to think of 1924, the year in which Heisenberg discovered the quantum theory, as a kind of abyss, a Grand Canyon, separating the old physics from the new, or a desert separating two fertile regions. But this is too symmetric. The two sides of an abyss are on the same level. The two sides of a desert are symmetric in respect to each other.

Mar 25, 20040 citations

Critique of Quantum Theory

C. G. F. Simkin

BRILL eBooksJan 1, 19930 citations

On quantum theory

Berthold‐Georg Englert

arXiv:1308.5290The European Physical Journal DNov 1, 201356 citations

A skepticism on the concept of quantum state related to quantum field theory on curved spacetime

Hideyasu Yamashita

Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a $C^{*}$ -algebra $\mathfrak{A}$ , but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of $\mathfrak{A}$ w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a $C^{*}$-algebra $\mathfrak{A}$, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of $\mathfrak{A}$ w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.

quant-pharXiv:2604.11830Apr 14, 20260 citations

Who Needs Category Theory?

Andreas R. Blass, Yuri G. Gurevich

In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical majority. In a muted form this split applies to the authors of this note. When we learned that the only mathematically sound foundation of topological quantum computing in the literature is based on category theory, the skeptical author suggested to "decategorize" the foundation. But we discovered, to our surprise, that category theory (or something like it) is necessary for the purpose, for computational reasons. The goal of this note is to give a high- level explanation of that necessity, which avoids details and which suggests that the case of topological quantum computing is far from unique.In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical majority. In a muted form this split applies to the authors of this note. When we learned that the only mathematically sound foundation of topological quantum computing in the literature is based on category theory, the skeptical author suggested to "decategorize" the foundation. But we discovered, to our surprise, that category theory (or something like it) is necessary for the purpose, for computational reasons. The goal of this note is to give a high- level explanation of that necessity, which avoids details and which suggests that the case of topological quantum computing is far from unique.

arXiv:1807.11399EPiC series in computingMar 7, 20201 citation

C^{*}

-algebra

\mathfrak{A}

, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of

\mathfrak{A}

w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.