Einstein's Elusive Gravitational Waves
- LIGO, LISA Destined to Detect Nothing
by Stephen J. Crothers
August 7, 2009
It is claimed that the LIGO and LISA projects will detect
Einstein's gravitational waves. The existence of these waves is entirely
theoretical. Over the past forty years or so no Einstein gravitational
waves have been detected. How long must the search go on, at great expense to
the public purse, before the astrophysical scientists admit that their
search is fruitless and a waste of vast sums of public money? The fact
is, from day one, the search for these elusive waves has been destined
to detect nothing. Here are some reasons why.
Einstein's gravitational waves do not have a unique speed of propagation. The speed of the
alleged waves is coordinate dependent. A different set of coordinates yields a different speed
of propagation. Einstein and his followers deliberately choose a set of coordinates that gives
the speed of propagation as that of light in vacuum. There is no a priori reason why
this particular set of coordinates is better than any other. The sole reason for their choice is to
obtain the desired result. Such a method has no validity in science. Here is what the late
British scientist Arthur S. Eddington pointed out in his book, The mathematical theory of
relativity, Cambridge University Press, Cambridge, 2nd edition, 1960:
The statement that in the relativity theory gravitational waves are propagated with the speed
of light has, I believe, been based entirely upon the foregoing investigation; but it will be seen
that it is only true in a very conventional sense. If coordinates are chosen so as to satisfy a
certain condition which has no very clear geometrical importance, the speed is that of light;
if the coordinates are slightly different the speed is altogether different from that of light.
The result stands or falls by the choice of coordinates and, so far as can be judged, the
coordinates here used were purposely introduced in order to obtain the simplification which
results from representing the propagation as occurring with the speed of light. The argument
thus follows a vicious circle.
In their calculations for Einstein's gravitational waves, the relativists utilise a mathematical
entity called Einstein's pseudo-tensor. In the words of the late British physicist Paul A. M.
Dirac (General Theory of Relativity, Princeton Landmarks in Physics Series, Princeton
University Press, Princeton, New Jersey, 1996),
It is not possible to obtain an expression for the energy of the gravitational field satisfying
both the conditions: (i) when added to other forms of energy the total energy is conserved,
and (ii) the energy within a definite (three dimensional) region at a certain time is
independent of the coordinate system. Thus, in general, gravitational energy cannot be
localized. The best we can do is to use the pseudotensor, which satisfies condition (i) but not
condition (ii). It gives us approximate information about gravitational energy, which in
some special cases can be accurate.
Now Einstein realised that his field equations do not satisfy the usual conservation of energy
and momentum and so, in order to save his theory from this catastrophe, he simply invented
something, ad hoc, to make his theory satisfy the usual conservation laws; namely, his
pseudo-tensor. Not only is this unscientific, it is also unconscionable, and completely
fallacious for the following reason. Assumption of the validity of Einstein's pseudo-tensor
implies the existence of a mathematical entity called a linear invariant, which is dependent
solely upon the components of the metric tensor and their first derivatives. One does not even
have to know the details of this; all one needs to know is that the pure mathematicians,
Georgio Ricci-Curbastro and Tullio Levi-Civita, inventors of the tensor calculus, proved, in
the year 1900, that such invariants do not exist! Thus, by reductio ad absurdum,
Einstein's pseudo-tensor is a meaningless concoction of mathematical symbols, and consequently
everything relying upon it, such as Einstein gravitational waves, is meaningless. Here is T.
Levi-Civita's demonstration of the invalidity of Einstein's pseudo-tensor:
Let us consider the energy of these waves. Owing to the pseudo-tensor not being a real
tensor, we do not get, in general, a clear result independent of the coordinate system. But
there is one special case in which we do get a clear result; namely, when the waves are all
moving in the same direction.
According to Einstein and his followers, his Principle of Equivalence and his laws of Special
Relativity must manifest in sufficiently small regions of his gravitational field, and such
regions can be located anywhere therein. Now the Principle of Equivalence and the laws of
Special Relativity are defined in terms of the a priori presence of multiple arbitrarily
large finite masses, and so neither the Principle of Equivalence nor the laws of Special Relativity
can manifest in a spacetime that by construction contains no matter. Here is what Einstein
enunciated in his book, The Meaning of Relativity, Science Paperbacks and Methuen &
Co. Ltd., 1967, pp. 56-57:
Let now K be an inertial system. Masses which are sufficiently far from each other and from
other bodies are then, with respect to K, free from acceleration. We shall also refer these
masses to a system of co-ordinates K', uniformly accelerated with respect to K. Relatively to
K' all the masses have equal and parallel accelerations; with respect to K' they behave just
as if a gravitational field were present and K' were unaccelerated. Overlooking for the
present the question as to the 'cause' of such a gravitational field, which will occupy us later,
there is nothing to prevent our conceiving this gravitational field as real, that is, the
conception that K' is 'at rest' and a gravitational field is present we may consider as
equivalent to the conception that only K is an 'allowable' system of co-ordinates and no
gravitational field is present. The assumption of the complete physical equivalence of the
systems of coordinates, K and K', we call the 'principle of equivalence'; this principle is
evidently intimately connected with the law of the equality between the inert and the
gravitational mass, and signifies an extension of the principle of relativity to co-ordinate
systems which are in non-uniform motion relatively to each other. In fact, through this
conception we arrive at the unity of the nature of inertia and gravitation. For, according to
our way of looking at it, the same masses may appear to be either under the action of inertia
alone (with respect to K) or under the combined action of inertia and gravitation (with
respect to K').
Now the alleged field equations Ric ≡ Rμν = 0 describe
a spacetime that by construction
contains no matter. It is from these equations that the black hole was conjured.
Stated more exactly, there are finite regions, where, with respect to a suitably chosen space
of reference, material particles move freely without acceleration, and in which the laws of
special relativity, which have been developed above, hold with remarkable accuracy.
Black holes were first discovered as purely mathematical solutions of Einstein's field
equations. This solution, the Schwarzschild black hole, is a nonlinear solution of the Einstein
equations of General Relativity. It contains no matter, and exists forever in an asymptotically
And so Ric = 0 violates the requirement that the Principle of Equivalence and the
laws of Special Relativity must manifest in the gravitational field. So Ric = 0
is inadmissible. It immediately follows as a consequence of this that the total energy of
Einstein's gravitational field is always zero, and so it is impossible for his gravitational
energy to be localised, i.e. Einstein gravitational waves do not exist. Moreover, it follows
that Einstein's field equations violate the usual conservation of energy and momentum, putting
them into direct conflict with the experimental evidence on an even deeper level.
Einstein's ad hoc pseudo-tensor can't be used to save it from this result, since
the pseudo-tensor is meaningless.
DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY, Edited by Richard A. Matzner, CRC
Press LLC, Boca Raton, USA, 2001.
Thus, the LIGO and LISA projects and their international counterparts are destined to detect
nothing. Undaunted, the astrophysical scientists however, never let the truth get in the way of
a good story.
[Editor's note: This is a shortened version of a paper recently written by Stephen J. Crothers.
The full paper is available on his website at
More of Crothers' work can be accessed via
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