## The 3D World vs the 4D World

It is important to make a clear distinction between the dimension of space-time and the dimension of the physical world, that is, the set of all material things that can be perceived by our sense organs or by extensions of our sense organs. There is no doubt about the dimension of space-time - the discussion in the preceding section establishes that the space-time of relativistic physics is 4D, as demonstrated by the geometry of the space-time interval (and the unified measurement procedure...

## Physical Space Time

Within the framework of general relativity, the dynamics of the physical space-time is actually related with the history and evolution of the Universe. The mathematical description of space-time does allow for a wide range of scenarios however, recent developments in observational cosmology do indicate that our Universe is well described by a flat Robertson-Walker metric, meaning that the energy density of the Universe is fairly close to the critical one, pc 3H 8nG 10-29g cm3, where H0 73 km...

## Campbell and His Theorem

Whatever the form of a new theory which unifies gravity with the forces of particle physics, there is a consensus that it will involve extra dimensions. In section 2, we considered mainly the 5D approach, which by the modern names of induced-matter and membrane theory is essentially old Kaluza-Klein theory without the stifling condition of compactification. The latter, wherein the extra dimension is rolled up to a very small size, answers the question of why we do not see the fifth dimension....

## Dimensions and Fundamental Constants

Minkowski made a penetrating contribution to special relativity, and our view of mechanics, when by the simple identification of x4 ct he put time on the same footing as the coordinates x123 xyz of the ordinary space of our perceptions. Einstein took an even more important step when he made the Principle of Covari-ance one of the pillars of general relativity, showing that the 4 coordinates traditionally used in mechanics can be altered and even mixed, producing an account of physical phenomena...

## Eddington and His Legacy

In studying dimensions and fundamental constants over several decades, the writer has come to realize that much modern work on these topics has its roots in the views of Sir Arthur Stanley Eddington 1882-1944 for a recent interdisciplinary review of his contributions to physics and philosophy, see the conference notes edited by Price and French, 2004 . He was primarily an astronomer, but with a gift for the pithy quote. For example We are bits of stellar matter that got cold by accident, bits...

## Dynamical Emergence of Instantaneous 3Spaces in a Class

Of Models of General 13.2 Newton's AbsoluteDistant-Simultaneity 235 13.3 Special Relativity Conventional Distant Simultaneity 237 13.4 General Relativity Dynamically Determined Distant 14 Lorentzian Space-Times from Parabolic and Elliptic Systems of 14.2 Analogue Models of General 14.3 A Simple Parabolic 14.4 A Simple Elliptic Model 14.5 Characteristic

## Classical Mechanics

In Greek physics, a concept of time similar to the absolute time of Newtonian theory seems to have been assumed. Also, a preferred state of rest with respect to the earth was taken as natural. Thus, observers that is, coordinate systems were at rest on earth. Within this theory, this is interpreted to mean that there are observer-independent concepts of fixed points in space and simultaneity of events. In this sense, space and time were absolute. To enable a precise description of the universe...

## List of Contributors

Instituto de Fisica Te rica - UNESP, Sao Paulo, Brazil H. Arcos Instituto de Fisica Teorica - UNESP, Sao Paulo, Brazil Carlos Barcelo Instituto de Astrof sica de Andaluc a CSIC , Spain e-mail carlos iaa.es Departamento F sica, Instituto Superior Tecnico, Lisbon, Portugal e-mail orfeu cosmos.ist.utl.pt Institute for Gravitation and the Cosmos The Pennsylvania State University e-mail bojowald gravity.psu.edu Perimeter Institute and University of Oxford e-mail joy.christian wolfson.oxford.ac.uk...