A Cinematic Model of

Instantaneous Action-at-a-Distance

Index | Abstract | Introduction | Action-at-a-Distance (Sections 1-6) | Special Relativity: The Cinematic Deduction | Philosophical Background (Sections 1 to 4) | Implications for Cosmology | Relevant Publications | Curriculum Vitae

The standard consequences of Special Relativity can be deduced from the Cinematic
Model in the following very simple way. According to the model, at every stage
in the motions of objects, those objects are instantaneously interconnected by
the angular momentum balancing relations described in the ACTION-AT-A-DISTANCE
section of this homepage. The ultimately irreducible, finite bits of these angular
momenta, are what we have referred to as the quantum stills in which, by definition,
there is no motion, as such, but only extension. The motions of physical objects
are then due to the changes, in time, of their positions in successive stills,
in which those 'still' dimensions are, as it were, 'lateral' to the comparatively
'longitudinal' or reel-length time-dimension. Both the change in spatial position
and the time taken for that change are therefore, implicitly, time-measures.
This space-time relation (expressed by Herman Bondi's space-time conversion factor
*c*)* between those two dependent,
co-exclusive and therefore orthogonal components of motion is thus geometrical
(or, more precisely, geometro-temporal). The resultant, by Pythagoras, of those
two components answers precisely to the relativistically dilated time of Special
Relativity:

*t*R = [(*s/c*)2
+ *t*P2]½

where *t*R is the relativistically dilated
time, as measured by the observer of the motion, *t*P
is the time registered by the moving body (called proper time), and *s/c*
is the (also proper ** )
distance-time in seconds.

* Any attempt to measure the velocity of light,' says Bondi, ' is ... not an attempt at measuring the velcocity of light but an attempt at ascertaining the length of the standard metre in Paris in terms of time-units.' (H. Bondi, Assumption and Myth in Physical Theory, CUP, 1965, page 28.)

** By 'proper distance', here, is meant the distance as measured in Newtonian, or pre-relativistic, terms of the length parameters of balanced angular momentum systems, as described on the 'ACTION-AT-A-DISTANCE' page of this website. (For simplicity, that angular momentum is assumed sufficiently large for the velocities in these equations to be regarded as approximately rectilinear.)

From this simple Pythagorean formula the well-known Einsteinian formula follows
in just a few lines of schoolboy algebra. For instance, substituting for s the
definitional equivalent in terms of the relative velocity and time *vt*R
we have

*t*R = [(*vt*R)
2 + *t*P2]
½

which simplifies straightaway to

*t*R = *t*P[
1 - (*v*2/*c*2)]
-1/2

This is easily recognisable as the standard formula from which follow all the usual consequences of relativistic physics.

Mathematicians such as Herman Bondi and Clive Kilmister, to name but two, have unreservedly agreed with this deduction which, as another mathematician, Peter Analytis, put it, was 'the simplest deduction of Relativity I have ever seen.' He also warned, however, as many others have done, of the psycho-social problem (indeed, the virtual impossibility) of fitting-in this extremely radical but simple option with the established way of thinking, based as that is on jargonised historical presuppositions in favour of 'photons', 'electromagnetic fields', 'Lorentz transformations' and so on (see PHILOSOPHICAL BACKGROUND and the 'Reception to Date' section of CURRICULUM VITAE).