Search arXiv⌕ Search

arXiv · 0907.3531

On Kant's first insight into the problem of space dimensionality and its physical foundations

Abstract

In this article it is shown that a careful analysis of Kant's "Thoughts on the True Estimation of Living Forces" leads to a conclusion that does not match the usually accepted interpretation of Kant's reasoning in 1747, according to which the Young Kant supposedly establishes a relationship between the tridimensionality of space and Newton's law of universal gravitation. Indeed, it is argued that this text does not yield a satisfactory explanation of space dimensionality, actually restricting itself to justify the tridimensionality of extension.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Francisco Caruso, Roberto Moreira Xavier. 2015-04-25. On Kant's first insight into the problem of space dimensionality and its physical foundations. https://doi.org/10.1515/kant-2015-0051

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Relational Observables and Physical Perspectivalism in General Relativity: The View from Nowhere vs. The View from Everywhere

In General Relativity, relational constructions yield gauge-invariant Dirac observables by expressing physical fields relative to reference frames. This leaves open how the physical situations represented in different frames should be understood. I articulate two ontological interpretations within a common fibre-bundle framework, distinguishing \emph{frame-independence} from \emph{frame-freedom} to clarify appeals to perspective-neutrality. The \emph{View from Nowhere} treats the situations characterised by relational observables as partial aspects of a shared physical situation represented by a frame-free gauge-equivalence class. The \emph{View from Everywhere} takes each relational observable to characterise a comprehensive physical situation in its own right, without commitment to a shared frame-free reality. They articulate a qualified realisation of moderate and strong physical perspectivalism within GR, respectively. Using two GPS reference frames as a working example, I show that a physically constrained, frame-independent inter-frame map supplies a constructive counterexample to the claim that connecting perspectives requires frame-free structures in the ontology. The choice between the two interpretations remains open, with their ontological commitments made explicit. I conclude by outlining possible implications for quantum reference frames and relational quantum mechanics.

physics.hist-ph↗

What is Physics For? Why Classical Physics is not the Limit of Quantum Mechanics

Quantum mechanics is justifiably held to be the most successful physical theory ever created; yet no universally accepted interpretation of its mathematical formalism exists after a century of debate. We examine the specific claim that classical physics stands as the low-action limit of quantum mechanics, arguing that the deep interpretive difficulties exposed by the quantum formalism, the measurement problem, the subject-object divide, and the nature of scientific representation, were already latent in classical physics, constituting what we call a blind spot of objectivity. Taking quantum theory as an invitation to re-examine the implicit metaphysical commitments bundled with 'classical physics', we explore two key issues-the objective/subjective split and the nature of theoretical representation-and argue that quantum mechanics does not represent a break with classical physics per se but rather brings previously unacknowledged philosophical assumptions into the limelight. We discuss the London-Bauer interpretation and QBism as exemplars of interpretations that embrace this broader reconceptualisation.

physics.hist-ph↗

From Mass to Energy-Momentum: The Field-Theoretic Perspective on the Energy-Mass Relation

The paper examines the energy-mass relation of Special Relativity (SR), its status and interpretation, through the lens of classical/non-quantum relativistic field theory. The latter arguably constitutes the fullest embodiment of SR as what Einstein labelled a "principle theory". It forms, we propose, the most appropriate perspective also for understanding the energy-mass relation. In a field-theoretic setting, the key notion is a system's energy-momentum (in local/differential or global/integral form, defined via a suitable energy-stress complex). The energy-mass relation then expresses the role that a system's _rest_-energy (provided it exists) plays as the functional counterpart of mass: thanks to important theorems, rest-energy qualifies as its field-theoretic generalisation or successor term. That is, while mass is dispensed with as a fundamental notion, rest-energy retains some---but not all---of its salient functional roles; for special cases, it turns out to be directly correlated with mass. In field theory as a general framework for more specific relativistic theories, energy-momentum replaces mass as the essential notion---a profound, yet often overlooked revision in basic physical concepts. Conservation in particular is guaranteed only for energy-momentum, but no longer for mass. In several regards, energy-momentum fuses energy, momentum and mass, with novel connections amongst them and concomitant physical effects. Situating the energy-mass relation within field theory is a surprisingly neglected, but deeply insightful vista for clarifying and philosophically reflecting on SR's foundations. The field-theoretic interpretation achieves a compelling inner coherence and unifying power, and ties it to the rich heuristic resources of field theory, crucial for post-1905 developments in physics.

physics.hist-ph↗