Axiomatizing relativistic dynamics using formal thought experiments

Molnár, Attila Károly; Székely, Gergely

doi:10.1007/s11229-014-0545-8

Cited by 3 publications

(3 citation statements)

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“…8 These inertial observers are only potential and not actual observers, in the same way as the light signals required in every coordinate points by axioms AxPhc and AxEther below are only potential light signals. For a discussion on how actual and potential bodies can be distinguished using modal logic, see (Molnár and Székely 2015). 9 We do not need this axiom for the interpretation, but we do need it for the definitional equivalence.…”

Section: Axioms For Classical Kinematicsmentioning

confidence: 99%

Comparing Classical and Relativistic Kinematics in First-Order Logic

Lefever¹,

Székely²

2017

Preprint

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The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics.We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics.We will also show that if we distinguish a class of observers (representing observers stationary with respect to the "Ether") in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent (i.e., they become equivalent theories in the sense as the theory of lattices as algebraic structures is the same as the theory of lattices as partially ordered sets).Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with "Ether" is definitionally equivalent to classical kinematics.So within an axiomatic framework of mathematical logic, we explicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no "Ether", accompanied by a redefinition of the concepts of time and space.

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Section: Axioms For Classical Kinematicsmentioning

confidence: 99%

Comparing Classical and Relativistic Kinematics in First-Order Logic

Lefever¹,

Székely²

2017

Preprint

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“…cannot distinguish actual and potential particles only existing in some thought experiments. See (Molnár and Székely, 2013) for an axiomatic framework where this distinction can be made and the idea of thought experiments can be captured formally.…”

Section: Formulating the Thought Experimentsmentioning

confidence: 99%

On the Possibility and Consequences of Negative Mass

Madarász,

Székely,

Stannett

2014

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We investigate the possibility and consequences of the existence of particles having negative relativistic masses, and show that their existence implies the existence of fasterthan-light particles (tachyons). Our proof requires only two postulates concerning such particles: that it is possible for particles of any (positive, negative or zero) relativistic mass to collide inelastically with 'normal' (i.e. positive relativistic mass) particles, and that four-momentum is conserved in such collisions.

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“…In the informal explanations of the examples below we freely use such modal expressions as "can set down" and "can send out", in place of "coordinatise", to make the experimental idea behind scenarios intuitively clearer, and to illustrate how the dynamical aspects of making experiments are captured in our static framework. See also (Molnár & Székely, 2015) for a framework where the distinction between actual and potential bodies is elaborated within first-order modal logic.…”

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confidence: 99%