Axiomatic causal theory of space-time

arXiv (Cornell University), 2003

All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or heterogeneous in function of the distribution of the physical magnitudes. Applying the principle of causality to the homogeneous space we observe that its more important qualities are: their metric does not depend of the 4coordeninate where it is measured and the light speed constancy [1]. However, to apply the principle of causality in the heterogeneous space is very much fruitful. Thanks to the presence of physical magnitudes that vary in the 4space we can find the equations that this magnitudes should verify so that it takes place their space and time evolution. Working on the principle of causality like axiom for describe our physical systems, we will obtain the most basic expression of evolution of the magnitudes of the physical system. This expression coincides with the principle of action expressed for a tensorial action [2]. The scalar form of this principle coincides, in its turn, with the traditional relativistic and quantum expression, of the principle of action or principle of least action according to other authors.

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemmanian space-time.

arXiv: General Relativity and Quantum Cosmology, 2019

We propose a generalisation of the local causality principle of space-time, asserting that it holds for all regimes of motion, including superluminal motions. It assumes the existence of a countably infinite set of metrical null cone speeds, $c_k$, where the first one, $c_1=c$, corresponds to the speed of light in vacuum. Our associated space-time measures do not diverge at the maximum speed of each interval of speeds and implies a generalisation of Einstein's rule for velocities addition. We construct a causal structure for each regime of motion. After introducing a simple dynamical measure, we derive an expression for the energy of material particles, which approaches the relativistic one when $v<c$. An experiment to energise photons in an 1-1 process is proposed as a test of our interpretation of the non divergence at the speed of light of present space-time measures. We discuss also the possible transition of a material particle from the subluminal regime $v<c$ to the ...

2002

We start from the well-known form of the interval of the special relativity, stare it, and build up an attempt to implement the causality from it. Some features appear to be new, they involve the mass of the particle and the structure of space-time. erev Tishrei, 10th.

arXiv: History and Philosophy of Physics, 2020

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wuthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.

arXiv (Cornell University), 2012

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally-ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.

2010

We present a derivation of special relativity based on the quantification of causally-ordered events. We postulate that events are fundamental, and that some events have the potential to influence other events, but not vice versa. This leads to the concept of a partially-ordered set of events, which is called a causal set. Quantification proceeds by selecting two chains of coordinated events, each of which represents an observer, and assigning a valuation to each chain. An event can be projected onto each chain by identifying the earliest event on the chain that can be informed about the event. In this way, events can be quantified by a pair of numbers, referred to as a pair, that derives from the valuations on the chains. Pairs can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. From this pair, we derive a scalar measure and show that this is the Minkowski metric. The Lorentz transformations follow, as well as the fact that speed is a relevant quantity relating two inertial frames, and that there exists a maximal speed, which is invariant in all inertial frames. Furthermore, the form of the Lorentz transformation in this picture offers a glimpse into the origin of spin. All results follow directly from the event postulate and the adopted quantification scheme.

2016

Since the moment Boethius meditated on the nature of time in his fifth book on The Consolation of Philosophy, we have more tools to reflect on the subject. The onset of relativity and quantum physics provides us with the best insight, to date, that guides our reflections on the philosophical debates that attempt to theorize a definition of time. To clearly address the problems related to the theoretical models that account for the nature of time, adjustments to our interpretation of the contextual issues involved in special relativity are in order if we are going to preserve our notion of causal reality. As the construction of string theory emerges as the reigning theory for quantum gravity, a precise picture of causal reality can be accounted for through theories such as Dyson’s Chronological Protection Agency, Hořava’s theory of gravity, and new insight to how simultaneity is interpreted in relativity theory. With this model, the question about time in the philosophical debates ca...

I present a discussion of some open issues in the philosophy of space-time theories. Emphasis is put on the ontological nature of space and time, the relation between determinism and predictability, the origin of irreversible processes in an expanding Universe, and the compatibility of relativity and quantum mechanics. In particular, I argue for a Parmenidean view of time and change, I make clear the difference between ontological determinism and predictability, propose that the origin of the asymmetry observed in physical processes is related to the existence of cosmological horizons, and present a non-local concept of causality that can accommodate both special relativity and quantum entanglement.

2011

In this paper, we present a derivation of special relativity based in the quantification of events. We postulate that events are fundamental, and that some events have the potential to be influenced by other events. However, this potential is not reciprocal, nor are all pairs of events related in such a way. This leads to the concept of a partially-ordered set of events, which is often called a causal set. Quantification proceeds by distinguishing two chains of coordinated events, each of which represents an observer, and assigning a numerical valuation to each chain. By projecting events onto each chain, an event may be quantified by a pair of numbers, referred to as a pair. We show that each pair can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. We show that one can map a pair to a scalar and that this gives rise to the Minkowski metric. The result is an observer-based theory of special relativity that quantifies events with pairs of numbers. Events are fundamental and space-time is an artificial construct designed to make events look simple.