Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity

Németi, Péter; Székely, Gergely

doi:10.1007/978-3-642-30870-3_53

“…The Hungarian project is also fruitful in respect of the predictions of the science. For example, they prove that the existence of particles (bodies/ objects) travelling faster than the speed of light is consistent with the theories of relativity (Németi and Székely 2012;Székely 2012aSzékely , b, 2013.…”

Section: Introductionmentioning

confidence: 79%

On the epistemological significance of the hungarian project

Friend

¹

2014

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There are three elements in this paper. One is what we shall call 'the Hungarian project'. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini's philosophical work on the nature of mathematical explanations in science. The third is my pluralist approach to mathematics. The theses of this paper are that (1) the Hungarian project gives genuine mathematical explanations for physical phenomena. (2) A pluralist account of mathematical explanation can help us with appreciating the significance of the Hungarian project. (3) The significance consists in the fruitfulness and spread of the project. The spread is wide because the explanations are written in the very familiar language of first-order logic with identity. For this reason, the explanation is understandable to many mathematicians. (4) Because of the methodology adopted in the Hungarian project, the explanations are fruitful in another sense. In the Hungarian project certain questions are asked that would not be asked with a more usual methodology. The Hungarians are distinguished from other scientists in asking logical and mathematical questions, and these both deepen our understanding of the physical theories and induce further spread to mathematics and philosophy.I should like to thank Molinini and Nait-Abdallah for reading early draft versions of the paper, and giving several helpful corrections and suggestions. I should also like to acknowledge the helpful comments from members of the audience at the conference celebrating István Németi's 70th birthday, and for the enthusiasm and inspiration I received from Andréka, Németi, Székely and Madarász. They also paid careful attention to a better draft, and gave many helpful suggestions. Lastly, I should like to thank the anonymous reviewers for careful and invaluable comments. M. Friend (B)

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“…The distinction between inertial observers and more general body types emerges in these more advanced theories. For example, we demonstrate below that inertial observers can never travel faster than (what they consider to be) the speed of light, but this property need not be provable of more general bodies [18,19].…”

Section: Axioms (Axiomsthy Approx 260 Lines)mentioning

confidence: 88%

Using Isabelle/HOL to Verify First-Order Relativity Theory

Stannett

¹

,

Németi

²

2013

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Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem "no inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

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“…The distinction between inertial observers and more general body types emerges in these more advanced theories. For example, we demonstrate below that inertial observers can never travel faster than (what they consider to be) the speed of light, but this property need not be provable of more general bodies [NS12,Szé12].…”

Section: Axioms (Axiomsthy Approx 260 Lines)mentioning

confidence: 88%

Using Isabelle to verify special relativity, with application to hypercomputation theory

Stannett,

Németi

2012

Preprint

0

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Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally undecidable questions such as the Halting Problem and the consistency of set theory.The Hungarian theories are very extensive, and their associated proofs are intuitively very satisfying, but this brings its own risks since intuition can sometimes be misleading. As part of a joint project, researchers at Sheffield have recently started generating rigorous machineverified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate an Isabelle proof of the theorem "No inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs: (a) we can be certain our intuition hasn't led us astray (or if it has, we can identify where this has happened); (b) we can identify which axioms are specifically required in the proof of each theorem and to what extent those axioms can be weakened (the fewer assumptions we make up-front, the stronger the results); and (c) we can identify whether new formal proof techniques and tactics are needed when tackling physical as opposed to mathematical theories.

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Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity

Abstract: Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals.

Cited by 9 publications

References 24 publications

On the epistemological significance of the hungarian project

On the epistemological significance of the hungarian project

Using Isabelle/HOL to Verify First-Order Relativity Theory

Using Isabelle to verify special relativity, with application to hypercomputation theory

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