A logic road from special relativity to general relativity

Andréka, Hajnal; Madarász, Judit X.; Németi, István; Székely, Gergely

doi:10.1007/s11229-011-9914-8

Cited by 40 publications

(65 citation statements)

References 8 publications

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“…Let us note that usually a more general axiom system called SpecRel is used for axiomatizing special relativity, see, e.g., [3,5,36]. SpecRel does not contain SPR + but it captures the kinematics of special relativity, i.e., it implies that the worldview transformations are Poincaré ones.…”

Section: Axioms For Kinematicsmentioning

confidence: 99%

The existence of superluminal particles is consistent with relativistic dynamics

Madarász

Székely

2014

Journal of Applied Logic

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Within an axiomatic framework, we prove that the existence of faster than light (FTL) particles is consistent with (does not contradict) the dynamics of Einstein's special relativity. The proof goes by constructing a model of relativistic dynamics where FTL particles can move with arbitrary speeds. To have a complete picture, we not only construct an appropriate model but explicitly list all the basic assumptions (axioms) we use.

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Section: Axioms For Kinematicsmentioning

confidence: 99%

The existence of superluminal particles is consistent with relativistic dynamics

Madarász

Székely

2014

Journal of Applied Logic

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“…However, the extension to general relativity is elegant and easy. In Andréka et al (2011), the Hungarians weaken the theory special relativity (to make a, so called, 'local' theory of special relativity) and introduce two new axioms, one for accelerated observers, and one for Einstein's postulate, which together act as a bridge to take us from special relativity to general relativity. 2 The sources I use are part of a much larger project, involving other researchers, and many other papers.…”

Section: The Relativity Theory Projectmentioning

confidence: 99%

On the epistemological significance of the hungarian project

Friend

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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“…Here we are going to use a sightly modified framework of [5]. We will use the following two-sorted language of first-order logic parametrized by a natural number d ≥ 2 representing the dimension of spacetime:…”

Section: The Language Of Our Axiom Systemmentioning

confidence: 99%

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

Székely

2013

Reports on Mathematical Physics

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Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.A detailed history of the tachyon concept tracing back even to pre-relativistic times can be found in [15]. 2This observation is the basis of several causal paradoxes (i.e., seemingly contradictory statements) concerning FTL particles.

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A logic road from special relativity to general relativity

Cited by 40 publications

References 8 publications

The existence of superluminal particles is consistent with relativistic dynamics

The existence of superluminal particles is consistent with relativistic dynamics

On the epistemological significance of the hungarian project

The Existence of Superluminal Particles is Consistent with the Kinematics of Einstein's Special Theory of Relativity

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