Four-Dimensional Newtonian Relativity

Reviews of Modern Physics, 1964

REVIEWS OP 1lttt. 013ERN PHYSICS~OCTOBER 1964 equations. In the quantized version of this formulation of the theory one would look for an operator representation for the I" s which would reproduce the classical commutator algebra between the various F's obtained from their Pb's. Since now one has many more observables than degrees of freedom the observables are not all independent of one another and so one has certain consistency conditions to satisfy that are not present when one eliminates degrees of freedom from the theory directly. It is not clear at present whether or not one can satisfy these consistency requirements.

ISRN Mathematical Physics, 2013

We present two models combining some aspects of the Galilei and the Special relativities that lead to a unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a se...

Relativity theory is often said to support something called 'the four-dimensional view of reality'. But there are at least three different views that sometimes go by this name. One is the B-theory of time, according to which the past, present, and future are all equally real and there is nothing metaphysically special about the present. A second is 'spacetime unitism' (as we call it), according to which there is a spacetime manifold, and if there are such things points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A third is perdurantism, according to which persisting material objects (rocks, trees, human beings) are made up of different temporal parts located at different times. We sketch routes from relativity to the B-theory and to unitism. We then discuss some routes to perdurantism, via the B-theory and via unitism.

2015

The four dimensional spacetime continuum, as originally conceived by Minkowski, has become the default framework within which to describe physical laws. Due to its fundamental nature, there have been various attempts to derive this structure from more fundamental physical principles. In this paper, we show how the Minkowski spacetime structure arises directly from the geometrical properties of three dimensional space when modeled by Clifford geometric algebra of three dimensions Cℓ(ℜ 3). We find that a time-like dimension, as well as three spatial dimensions, arise naturally, as well as four additional degrees of freedom that we identify with spin. Within this expanded eightdimensional arena of spacetime, we find a generalisation of the invariant interval and the Lorentz transformations, with standard results returned as special cases. The power of this geometric approach is shown by the derivation of the fixed speed of light, the laws of special relativity and the form of Maxwell's equations, without any recourse to physical arguments. We also produce a unified treatment of energy-momentum and spin, as well as predicting a new class of physical effects and interactions.

We put forward a new view of relativity theory that makes the existence of a flow of time compatible with the four-dimensional block universe. To this end, we apply the creation-discovery view elaborated for quantum mechanics to relativity theory and in such a way that time and space become creations instead of discoveries and an underlying non temporal and non spatial reality comes into existence. We study the nature of this underlying non temporal and non spatial reality and reinterpret many aspects of the theory within this new view. We show that data of relativistic measurements are sufficient to derive the three-dimensionality of physical space. The nature of light and massive entities is reconsidered, and an analogy with human cognition is worked out.

In Special Theory of Relativity time is considered to be the 4 th dimension of space -time as a consequence of Lorentz invariance and Minkowski metric, in turn based on the invariance of light speed c. In this paper we'll show that, starting only from universal postulates as homogeneity of space and time and Principle of Relativity, we can obtain space and time transformations (as the Lorentz and Tangherlini -Selleri ones) characterized by an invariant speed generally different than c. These results determine crucial difficulties in the assumption of Minkowski metric and consequently in the interpretation of physical time t as the 4 th component of space -time, also introducing a "relativity" feature in the velocity of light c in vacuum being no longer considerable as a necessarily universal invariant quantity and depending on the physical properties of space which originate from quantum vacuum. A novel interpretation of time, coherent with these results, defined as duration of material change in space, i.e. motion, is finally proposed.

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension ict, with the unit imaginary producing the correct spacetime distance x 2 {c 2 t 2 , and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary i~ffi ffiffiffiffiffiffi ffi {1 p , with the Clifford bivector i~e 1 e 2 for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis e 1 and e 2 . We find that with this model of planar spacetime, using a twodimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.

Journal of Modern Physics, 2018

The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of space and time, a model which, unlike the current one, is based solely on Euclidean geometry. In the new model, the pseudo-Euclidean spacetime is replaced with a specific subset of four-dimensional Euclidean space. The work shows that four-dimensional Euclidean space allows explanation of known relativistic effects that are now explained in pseudo-Euclidean spacetime by Einstein's Special Theory of Relativity (STR). It also shows simple geometric-kinematical nature of known relativistic phenomena and among others explains why we cannot travel backward in time. The new solution is named the Euclidean Model of Space and Time (EMST).

International Journal of Modern Physics A, 2013

We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute or property, to space-time location.

Foundations of physics, 2003

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications.