# Special and General Theory of Relativity

## Einstein's Misconceptions of Space and Time

### Special Relativity

The special theory of relativity, as developed by Einstein, is directly based on the Lorentz Transformation formula and attempts to transfer the 'equation of motion' for light signals to the space- time coordinates of moving material bodies. Not only is this generalization completely unjustified, but it has to be considered as invalid as the Lorentz- Transformation formula implicitly contains the assumption of the invariance of the velocity (of light) in moving coordinate systems, which obviously does not apply for material objects (for which the classical vectorial addition of velocities holds).
The inconsistencies go however further than this and are to some extent already contained in the Lorentz Transformation (as formulated by Einstein): it actually contradicts the invariance of c if one scales the space and time coordinates in order to re-establish a kind of vectorial (albeit normalized) velocity addition for light: the invariance of c strictly means that the time for a light signal to travel from the source to the observer does not depend on the velocity of either of them but only on their distance at the time of the emission (more). As the usual addition of velocities does not apply, the propagation of light has therefore to be considered strictly separately in each reference frame and it is incorrect to map its 'path' in one frame into the other by means of a Galilei- transformation and subsequently 're-normalizing' the velocity of light by scaling the space and time coordinates accordingly (Einstein's basic assumption of identical and synchronized clocks obviously has to imply t'=t). In other words: a contradiction to the invariance of c when using identical space and time coordinates in the two reference frames arises only if one initially chooses the wrong frame for calculating the arrival time of the light signal (two points may coincide mathematically in different frames at a certain time instant, but they are physically not identical as they belong to different objects moving relative to each other). However, important consequences arise from the possibility to pass from one reference frame to the other (by means of acceleration or deceleration), as then the arrival time of the light signal does not only depend on the space point considered but on the whole spatial history of the observer.
Einstein's re-scaling of space and time leads to similar nonsense (e.g. the existence of a maximum speed for material objects) as the one applied by the ancient philosopher Zeno of Elea (who 'proved' in his paradoxes that Achilles should be unable to overtake a tortoise, or that an arrow can never reach its target). Any alleged experimental 'evidence' for the existence of length contradiction and time dilation has therefore to be explained by other physical phenomena or instrumental effects (if the observed 'relativistic' behaviour of charged particles in high energy accelerators for instance is indeed real, this would have to be interpreted as a velocity dependence of the electric and magnetic fields involved, i.e. E=f(E0,v/c) and B=f(B0,v/c) where v is the velocity of the particle relative to the object creating the electric or magnetic field); even this does however not limit the speed which particles can reach through successive accelerations in fields related to objects moving with different velocities) (more).
The only direct consequences of the invariance of c must obviously be restricted to the propagation and properties of the light signal itself (e.g. the Doppler Effect and the 'spatial history' effect mentioned above).
(see also Speed of Light Postulate and Lorentz Transformation, Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation, Regarding the 'Light Sphere' Derivation of the Lorentz Transformation, Mathematical Flaws in Einstein's 'On the Electrodynamics of Moving Bodies', Time Dilation and Twin Paradox, Relativistic Interpretation of Magnetic Fields and Lorentz Force, Aberration of Starlight, Retarded Fields and Global Positioning System (GPS) and Relativity, Error in the Commonly Accepted Classical Theory for the Michelson-Morley Experiment).
Discussions

### General Relativity

In his Special Theory of Relativity, Einstein attempted to establish space and time as physical objects in their own right, making them scaleable quantities in order to conform with the observed invariance of c in reference frames moving uniformly relative to each other. In his General Relativity, he extended this concept to forces and the related accelerated coordinate systems (in particular with regard to gravitation) by means of his Equivalence Principle regarding gravity and acceleration. However, as shown on the linked page, such a principle is logically flawed as an acceleration can also be due to other (non-gravitational) forces which do not depend on the mass m (e.g. the electrostaic force). Furthermore, with his interpretation, the motion of a mass is determined by the curvature of space-time which in turn is caused by the presence of other masses. This view is inconsistent in several respects:
a) it claims that a physical action can result from a 'subject' (i.e. space-time) which has no physical reality but exists only as an idealized, mathematical concept;
b) although physical forces are frequently described by gradients of some potential function, this is in principle not acceptable as the fundamental form for the interaction, as it implies a non-local nature (if one assumes that the acceleration a(s) at location s depends on the gradient of some function f(s), then this would imply that a point mass at location s would also be affected by the location s+ds as the gradient is defined as (f(s+ds)-f(s))/ds (with ds being infinitesimally small but different from zero));
c) there is no reason why a motion due to gravitational forces should be described by a different concept than those for electrostatic interaction for instance; however for the latter the force does not depend on the mass (whereas the resultant acceleration does), therewith invalidating the concept of space-time curvature as an objective and unique quantity for describing the motion of objects in force fields;
d) Einstein claims that the alleged space-time curvature around massive objects will affect the path of light rays as well. Even ignoring the points above, this is an unallowed generalization as the concept was derived to describe the gravitational interaction, but electromagnetic waves are immaterial and massless physical objects. Effects that apparently confirm this prediction of General Relativity could well be explained by other mechanisms (see for instance the page Plasma Theory of Gravitational Lensing of Light on my site plasmaphysics.org.uk).
(see also Curved Space, Equivalence Principle and the page Global Positioning System (GPS) and Relativity).
Discussions

Thomas Smid (M.Sc. Physics, Ph.D. Astronomy)
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