A number of experiments based on the general idea of Galilean relativity were performed to determine the speed of light. Michelson and Morley, in 1887 found that the velocity of a beam of light moving from east to west is the same as that of a beam of light moving from north to south. The east-west velocity might have been expected to be influenced by the velocity of the earth, but such was not the case. About 20 years later, H. A. Lorentz provided the solution by suggesting that material bodies contract when they are moving and that this foreshortening is only in the direction of the motion and also that if the length is

Although the contraction hypothesis successfully accounted for the negative result of the experiment, it was open to the objection that it was invented for the express purpose of explaining away the difficulty and was too artificial [5]. The contraction in length is concomitant with modification in time elapsed by the factor,

i.e., moving clocks run slower.

Based on the above hypothesis of linear contraction and time dilation in moving objects, Lorentz showed that Maxwell's equations retain their symmetry, i.e., remain unchanged when the following Lorentz transformations are applied.

*y'=y**z'=z*

(1)

Lorentz's transformations
introduced into the laws of mechanics, the speed of light, basically an
electromagnetic constant.

The corresponding Galilean transformations are

which relates the space and time coordinates
(* x, y, z* and

Einstein, following a suggestion originally made by Poincare, then proposed in his

where ** m_{0}** is the rest mass
and

The two basic postulates of Einstein's *special
theory of relativity* are as follows [3].

(1) The laws of electrodynamics and of mechanics
are the same in all inertial frames. This includes the requirement that
** c**,
the velocity of light in free space, is invariant.

(2) It is impossible to devise an experiment, which defines a state of absolute motion. There is no special "rest" frame of reference.

In his

There is only a minute difference between the predictions of general relativity and Newtonian gravity [6,7].

Nottale (1996) has discussed the implications of
the *fractal* spacetime characteristics on fundamental physical laws
[8].

Dynamical systems in nature exhibit selfsimilar
spacetime *fractal* fluctuations of all scales down to the microscopic
scales of the subatomic world, i.e., the vacuum zero point energy fluctuations.
Selfsimilarity implies long-range correlations, i.e., nonlocal connections
in space and time. The ubiquitous *fractal* spacetime structures found
in nature imply a self-organization or self-assembly process which is independent
of microscopic details such as physical, chemical, physiological, etc.,
of the dynamical system. Selvam and Fadnavis [9,10] have proposed a cell
dynamical system model for atmospheric flows which may be directly applicable
to all dynamical systems in general and in particular to the subatomic
dynamics of quantum systems. The model is based on the concept [11] that
spacetime integration of enclosed small scale (turbulent) fluctuations
results in the formation of large scale (eddy) circulations (Fig 1.).

Figure 1: Physical concept of eddy growth process by the self-sustaining process of ordered energy feedback between the larger and smaller scales, the smaller scales forming the internal circulations of larger scales. The figure shows a uniform distribution of dominant turbulant scale eddies of length scale 2r. Larger-eddy circulations such as ABCD form as coherent structures sustained by the enclosed turbulent eddies.

Large eddies are visualised as envelopes enclosing inherent small scale eddies, thereby generating a continuum of eddies, the spatial integration at each level generating the next level (large scale) and so on. The relationship between the root mean square (r. m. s. ) circulation speeds

The primary perturbation *w*_{*}
is constant and generates a continuum of eddies of progressively increasing
radii ** R**. The r. m. s. circulation speed

in the Lorentz transformation at Eq.(1) becomes equal
to 1, since the relative velocity ** u **=

Einstein's principles of

(1) Spacetime *fractal* structures are signatures
of string-like energy flow in a hierarchy of vortices tracing an overall
logarithmic spiral trajectory with the quasiperiodic *Penrose* tiling
pattern for the internal structure.

(2) The logarithmic spiral energy flow structure
can be resolved as a continuum of eddy circulations, which follow *Kepler*'s
laws of planetary motion, in particular the third law. The inertial masses
of eddies representing gravitational masses, therefore follow *Newton*'s
inverse square law of gravitation. *Fractal* spacetime fluctuations
are related to gravity and is consistent with El Naschie's [12] conjecture
that gravity is caused by '*fractal*' fluctuations of time.

(3) Instantaneous non-local connection, prohibited
in Einstein's special theory of relativity, is possible and consistent
in the context of eddy circulations which are considered as extended objects
as explained in the following. The bidirectional energy flow intrinsic
to eddy circulations is associated with bimodal, i.e., formation and dissipation
respectively of phenomenological form for manifestation of energy such
as the formation of clouds in updrafts associated with simultaneous dissipation
of clouds in adjacent downdrafts, thereby generating discrete cellular
geometry to cloud structure.

Gravitation is defined as a property
of spacetime geometry in Einstein's general theory of relativity. The concept
of pointlike particle of zero dimensions in classical physics introduces
infinities or singularities in the smooth spacetime fabric representing
gravitational field [13]. Further, pointlike particles are associated with
trajectories, where, the speed of the particle cannot exceed the speed
of light according to Einstein's *special theory of relativity*.

The cell dynamical system model
[9,10] discussed in this paper introduces the concept of extended objects
thereby avoiding singularities and also possessing instantaneous nonlocal
connection.

The eddy circulations follow

2. Weinberg, S., *Dreams of a Final Theory*.
Vintage, 1993.

3. Kip, A. F., *Fundamentals of Electricity and
Magnetism*. McGraw-Hill Book Company, New York, pp 630.,1969

4. Schroeder M., *Fractals, Chaos and Power Laws***,
**1990**,
**W.H.
Freeman and Co., N.Y.

5. Feynman, R. P., Leighton, R. B and Sands, M.,
*Lectures
on Physics*, 1963, Volume I, pp. 52-11.

6. Narlikar, J. N., *Violent Phenomena in the Universe*.
Oxford University Press, Oxford, 1982, pp. 213.

7. Narlikar, J. N., 1996: *The Lighter Side of
Gravity*. Cambridge Univeristy Press, Cambridge,1996, pp. 217.

8. Nottale, L., Scale relativity and fractal space-time:
application to quantum physics, cosmology and chaotic systems. *Chaos
Solitons and Fractals*,1996, **7(6)**, 877-938.

9 Selvam A. M., Fadnavis, Suvarna, Signatures of
a universal spectrum for atmospheric inter-annual variability in some disparate
climatic regimes, *Meteorology and Atmospheric Physics* ,1998, **66,**
87-112. http://xxx.lanl.gov/abs/chao-dyn/9805028

10. Selvam, A. M., and Fadnavis, Suvarna, Superstrings,
cantorian-fractal spacetime and quantum-like chaos in atmospheric flows,
*Chaos
Solitons and Fractals **Chaos,1999*,**10(8)**,
1321-1334.

11. Townsend, A. A., *The Structure of Turbulent
Shear Flow*. Cambridge University Press, London, U. K., 1956.

12. El Naschie, M. S., Dimensional symmetry breaking
and gravity in cantorian space. *Chaos Solitons and Fractals*,1997,
**8**,
753-759.

13. Argyris, J., Ciubotariu, C. and Andreadis, I.,
Complexity in spacetime and gravitation I: From chaos to superchaos . *Chaos,
Solitons and Fractals *(in press) 1998.

14. Mathews, R., Nothing like a vacuum. *New Scientist*
1995, **25 Feb.**, 30-33.