452,841 research outputs found
Machines, Logic and Quantum Physics
Though the truths of logic and pure mathematics are objective and independent
of any contingent facts or laws of nature, our knowledge of these truths
depends entirely on our knowledge of the laws of physics. Recent progress in
the quantum theory of computation has provided practical instances of this, and
forces us to abandon the classical view that computation, and hence
mathematical proof, are purely logical notions independent of that of
computation as a physical process. Henceforward, a proof must be regarded not
as an abstract object or process but as a physical process, a species of
computation, whose scope and reliability depend on our knowledge of the physics
of the computer concerned.Comment: 19 pages, 8 figure
Physics and Proof Theory
Axiomatization of Physics (and Science in general) has many drawbacks that are correctly criticized by opposing philosophical views of Science. This paper shows that, by giving formal proofs a more promi- nent role in the formalization, many of the drawbacks can be solved and many of the opposing views are naturally conciliated. Moreover, this ap- proach allows, by means of Proof Theory, to open new conceptual bridges between the disciplines of Physics and Computer Science
Physics, Topology, Logic and Computation: A Rosetta Stone
In physics, Feynman diagrams are used to reason about quantum processes. In
the 1980s, it became clear that underlying these diagrams is a powerful analogy
between quantum physics and topology: namely, a linear operator behaves very
much like a "cobordism". Similar diagrams can be used to reason about logic,
where they represent proofs, and computation, where they represent programs.
With the rise of interest in quantum cryptography and quantum computation, it
became clear that there is extensive network of analogies between physics,
topology, logic and computation. In this expository paper, we make some of
these analogies precise using the concept of "closed symmetric monoidal
category". We assume no prior knowledge of category theory, proof theory or
computer science.Comment: 73 pages, 8 encapsulated postscript figure
The SCET_II and factorization
We reformulate the soft-collinear effective theory which includes the
collinear quark and soft gluons. The quark form factor is used to prove that
SCET reproduces the IR physics of the full theory. We give a
factorization proof in deep inelastic lepton-hadron scattering by use of the
position space formulation.Comment: 14 pages. The revised version which modifies largely will appear in
PL
Quantum Locality?
Robert Griffiths has recently addressed, within the framework of a
'consistent quantum theory' that he has developed, the issue of whether, as is
often claimed, quantum mechanics entails a need for faster-than-light transfers
of information over long distances. He argues that the putative proofs of this
property that involve hidden variables include in their premises some
essentially classical-physics-type assumptions that are fundamentally
incompatible with the precepts of quantum physics. One cannot logically prove
properties of a system by establishing, instead, properties of a system
modified by adding properties alien to the original system. Hence Griffiths'
rejection of hidden-variable-based proofs is logically warranted. Griffiths
mentions the existence of a certain alternative proof that does not involve
hidden variables, and that uses only macroscopically described observable
properties. He notes that he had examined in his book proofs of this general
kind, and concluded that they provide no evidence for nonlocal influences. But
he did not examine the particular proof that he cites. An examination of that
particular proof by the method specified by his 'consistent quantum theory'
shows that the cited proof is valid within that restrictive version of quantum
theory. An added section responds to Griffiths' reply, which cites general
possibilities of ambiguities that make what is to be proved ill-defined, and
hence render the pertinent 'consistent framework' ill defined. But the vagaries
that he cites do not upset the proof in question, which, both by its physical
formulation and by explicit identification, specify the framework to be used.
Griffiths confirms the validity of the proof insofar as that framework is used.
The section also shows, in response to Griffiths' challenge, why a putative
proof of locality that he has described is flawed.Comment: This version adds a response to Griffiths' reply to my original. It
notes that Griffiths confirms the validity of my argument if one uses the
framework that I use. Griffiths' objection that other frameworks exist is not
germaine, because I use the unique one that satisfies the explicitly stated
conditions that the choices be macroscopic choices of experiments and
outcomes in a specified orde
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