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The classical space-time structure is derived from the structure of an abstract infinite dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H* of functions of abstr...
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. T...
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved...
The main thesis of this paper is that Platonism is inherent in classical infinitary reasoning and that strict formalism inevitably leads one to the author's non-Aristotelian finitary logic (NAFL) prop...
In this paper we address two problems in Boltzmann's approach to statistical mechanics. The first is the justification of the probabilistic predictions of the theory. And the second is the inadequacy ...
Why don't we see large macroscopic objects in entangled states? Even if the particles composing the object were all entangled and insulated from the environment, we shall still find it almost always i...
The implications for the substantivalist--relationist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the conte...
In this paper we argue that the emergence of the classical world from the underlying quantum reality involves two elements: self-induced decoherence and macroscopicity. Self-induced decoherence does n...
intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Se...
This paper, part I of a two-part project, aims at answering the simple question 'what is spontaneous symmetry breaking?' by analyzing from a philosophical perspective a simple classical model. Related...
David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that...
Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle sta...
Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it p...
This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the applicat...
We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the o...

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