The origin of space and time is the deepest question in fundamental physics. This paper addresses it from quantum-theoretic perspective, deriving both concepts from elementary principles. Time appears as a measure for the stream of decision acts, collapsing quantum potentialities of the future to actual reality. Guiding of this construction is identified as fundamental function of life, thus obtaining definition in cybernetic style. This entails specific geometric structure of subjective meaning identical to that of the simplest quantum state, the qubit. Alignment of individual meaning spaces then produces 3-dimensional Euclidean space as biologically fixed format of common sense. The problem of space-time is thereby triangulated with the nature of life, identifying these three concepts as integral sides of the same fundamental phenomenon. The theory opens new prospects for scientific and ethical progress.
Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics (QM) and `classical' (Newtonian) space and time (NST). We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily \ita{different}, which implies that they are \ita{discernible} (in classical logic, identity is defined by means of indiscernibility) --- we say that the space is
T2, or "Hausdorff". But when enters QM, sometimes the systems need to be taken as \ita{completely indistinguishable}, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an \ita{identity} to them by means of their individuation, which seems to be contra the physical situation, where individuation (isolation) does not entail identity (as we argue in this paper). Here we discuss this topic by considering a case study (that of two potentially infinite wells) and conclude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems to be relevant for a more detailed discussion on the interplay between physical theories (such as quantum theory) and their underlying mathematics (and logic), in a simple way apparently never realized before.
According to classical physics particles are basic building blocks of the world. Classical particles are distinguishable objects, individuated by physical characteristics. By contrast, in quantum mechanics the standard view is that particles of the same kind ("identical particles") are in all circumstances indistinguishable from each other. This indistinguishability doctrine is motivated by the (anti)symmetrization postulates together with the assumption (``factorism'') that each single particle is represented in exactly one factor space in the tensor product Hilbert space of a many-particles system. Although the factorist assumption is standard in the literature, it is conceptually problematic. Particle indistinguishability is incompatible with the everyday meaning of ``particle'', and also with how this term is used both in classical physics and in the experimental practice of physics. The standard view requires quantum particles of the same kind to remain indistinguishable even in the classical limit, so that a transition to the classical picture of the world seems impossible. Earlier we have proposed an alternative conception of quantum particles that does not rely on factorism and that avoids these and other problems. We further explain and develop this proposal here. In our view, particles in quantum theory are not fundamental but \emph{emergent}. However, in those situations where the particle concept is applicable, quantum particles---identical or not---are distinguishable in the same way as classical particles.