Albert Einstein said, “We can’t rule out anything strictly a priori.”  Naturalistic humanism rests on the polarization of the growing disparity between the natural and the supernatural.  In 1962, the physicists O.M. Bilaniuk and E.C.G. Sudarshan began to speculate on the consequences of superluminal velocities (faster than light).  Consider the effect of a particle with a velocity of 2c in the Lorentz equation:  the proper mass, M, is therefore equal to M1 x 1.74 x -1.  High school algebra tells us that there exists no real -1 but that a logically consistent geometry exists with an axis based on these imaginary numbers.  So we can now also construct a logically consistent universe by assigning imaginary proper masses to particles with superluminal velocities.  Ordinary particles in our universe always have masses that are positive (or in special cases, zero; neutrinos, antineutrinos, photons).  An imaginary mass can have no imaginable significance in our universe.  Does this negate their existence?  Not necessarily.  Dr. Isaac Asimov states that, “allowing the existence of imaginary proper masses, we can make such faster-than-light particles fit all the equations of Einstein’s Special Theory of Relativity.”  (Isaac Asimov, Asimov’s Guide to Science (NY: Basic Books, 1972), p. 857-876).  (See Hawking and Jaki on “Time.”)


Such faster-than-light particles have been given the name “tachyons” by the American physicist Gerald Feinberg.  (Note:  It has been argued that anything that is not forbidden is compulsory, i.e., any phenomena that do not actually violate an observed law must at some time or another occur; ergo, since tachyons do not violate special relativity, they must exist.  This reasoning would be valid if the assumptions of this line of thought were true.  This line of reasoning pre-supposes an infinite universe and eternal time; neither of these being true (actually a Riemannian hyper sphere and a beginning and an end of time). 


Dr. Asimov summarizes by saying that—


We may then imagine the existence of two kinds of universes.  One, our own, is the taredyon-universe (slow) in which all particles go at subluminary velocities and may accelerate to nearly the speed of light as their energy increases.  The other is the tachyon-universe, in which all particles go at superluminal velocities and may decelerate to nearly the speed of light as their energy increases.  Between is the infinitely narrow “luxon wall” (Latin for light) in which there are particles that go at exactly luminal velocities.  The luxon wall can be considered as being held by both universes in common . . . .  A literal interpretation of God as light could be sued as an evidence of God’s ability to create even an infinite universe.  Beginning with the Lorentz transformation of mass:  M1 = M we have an existence at the speed of light implying an infinite mass.  Plugging infinite mass into the classical formula for Kinetic energy produces infinite energy.  Finally, using Einstein’s relation of mass and energy we have God physically possible of creating an infinite universe.  (Asimov, p. 876)


Tachyons would exhibit a seemingly paradoxical property:  velocity would be inversely proportional to energy (you add energy; it slows down, with a lower limit of c).  Theoretically, if a tachyon had a high energy level and was therefore moving slowly enough it might have sufficient energy and stay in one location long enough to give off a detectable burst of photons.  (“Tachyons would leave a wake of photons even in a vacuum as a kind of Cerenkov radiation.”  (Asimov, p. 876)  Scientists are watching for those bursts, but the chance of having detecting instruments in the right location and time of such a burst of only a trillionth of a second or less, is very slim.  Evidence of this non-forbidden beyond nature would support the Christian claim that there is an existence that transcends time and space, but so far it has not been detected, just postulated.


Evidence of a Riemannian Universe: How could it be determined that space was curved?  If we could make a ray of light travel over a long enough distance, we could perhaps see whether it curved or not.  In actuality, the universe deviates from the Euclidian so slightly, due to the great radius, hence the curve is very small, that a ray of light long enough for the purpose would be difficult to handle, not to mention the tact that our criterion for straightness is light itself.


The decision among the possible universes must therefore be more indirectly made.  Einstein knew that his physics implied a Riemannian universe and by 1917 had worked out its consequences, trying to find some that would deviate measurably from a Euclidian universe as a proof for his theories.  He devised three experiments that would point to a Riemannian universe.  They involved:  (1) the bending of light around the sun; (2) a loss in energy by light traveling against a gravitational field, now referred to as the Einstein shift and (3) a rotation of the ellipse that the planets make around the sun, especially Mercury.  All three experiments followed Einstein’s predictions, as will be discussed.


Einstein’s “General Theory of Relativity” was primarily an attempt to unify the effects of acceleration and gravitation under the laws governing the special theory.  For his first proof of his new geometry and physics, Einstein calculated that a ray of starlight which grazes the edge of the sun bends (curves with the curvature of the universe which is due to gravitation of the bodies in the universe) due to the sun’s gravitational field, through a very small angle of 1.7 second of an arc.  (Each degree of an angle is divided into minutes and seconds like an hour.  There are 90 degrees in a right angle.  This tiny angle is approximately five-millionths of a right angle.)  due to this bending the star’s apparent position in the sky differs slightly from its true position.  Einstein suggested that his calculation could be checked by comparing, during an eclipse, the apparent position of a star that is almost in line with the sun with the position of the same star at night.  Calculations from photographs taken during the eclipse of May 29, 1919, apparently confirmed Einstein’s figure for this bending and made Einstein world famous.  Two sets of observations were taken during that eclipse, one at Sobral, Brazil, and the other on the island of Principe off the coast of West Africa.  The angles of bending obtained were 9.98 seconds of arc at Sobral and 1.6 seconds at Principe, the average (1.79) being extremely close to Einstein’s figure (1.7), in view of the extreme smallness of the angle.


Stronger evidence in confirmation of Einstein’s theory has come recently in the phenomena known as the Einstein shift.  (Frequency is reduced and since velocity is constant the wavelength must correspondingly be increased, and hence there must be displacement of the spectrum.)  He showed that in a Riemannian universe, light would lose energy in traveling against a gravitational field.  But ordinary gravitational fields would produce a shift too small to measure and at the time he advanced his theory, he did not realize that any sufficiently strong field might exist.  A breakthrough came with the discovery that the white-dwarf Sirus B was made u almost exclusively of degenerate matter, and that this super-density would generate a surface gravity 2500 times that of the sun.  Under such conditions the Einstein shift would be measurable.  In 1925, W.S. Adams checked the spectrum of Sirus B and carefully measured the position of various spectral lines after allowing for the star’s radial motion and the Einstein shift was verified.


Einstein’s third proof is one of the strongest experimental supports for his general theory; here he calculated in strict detail.  His theory explains and accurately accounts for a divergence between the observed motion of the planet Mercury and its calculated motion on the basis of Newton’s law of gravity.  According to Newton’s law, a single planet would orbit the sun in an elliptical path, always remaining in the same plane.  Now the gravitational influence of the other planets, all much less massive than the sun, will slightly deflect Mercury’s path out of its original plane.  Newton based calculations show that due to the other planets the plane of Mercury’s orbit should rotate very slowly through an angle of 531 seconds per century.  (Accurate astronomical observations go back for so many years that it is permissible to consider rotation during a century.)  But in fact, the observed rotation is 574 seconds per century, an excess of 43 seconds over the Newton based figure.


Now Einstein’s formula for the motion around the sun of a single planet show that (disregarding the effects of the other planets) its orbit will not remain precisely in one plane, but will rotate slightly; in the case of Mercury, Einstein calculated this angle of rotation to be 43.03 seconds per century—precisely the excess rotation that had been observed, but not explained.  Mercury, being the nearest planet to the sun, travels through a stronger gravitational field than the others.  Venus also confirms Einstein’s theory, although since it moves in a weaker gravitational field the rotation of its orbit is smaller, hence observation and calculation are less accurate than for Mercury.  Einstein’s theory predicts a rotation of 8.63 seconds per century and the observed rotation has been calculated to be 8.4 seconds of arc per century, once again supporting Einsteinium physics and a Riemannian universe.


In summary, Peter Hamilton states, “Taken together, the various items of experimental evidence offer strong and impressive confirmation of Einstein’s general theory of relativity which is now fairly generally accepted.”  (Hamilton, p. 48)


Dr. Isaac Asimov states that—


In  all tests made of Einstein’s general theory of relativity, the theory has been borne out.  Not one observation going clearly against it has been made and it is generally accepted among astronomers that the universe as a whole follows a Riemannian geometry although one that deviates so slightly from the Euclidian that under ordinary circumstance Euclidian geometry is perfectly satisfactory.  (I. Asimov, The Universe: From Flat Earth to Quasar (NY: Discuss Books, 1966), p. 201)


The Riemannian Universe and the Christian Claims:  In conceptualizing the universe as a hyper sphere, science gives evidence to the possibility of a transcendent existence.  The Riemannian cosmos liquidates the naturalist claim that all that exists exists in this time and space.  (See Stephen Hawking, A Brief History of Time and Stanley Jaki’s critique, The Only Chance)


The concept of an evolutionary cosmos is refuted by Einstein’s theory and hence the Biblical doctrine of an overall uniform existence is supported.  Asimov further states—


Einstein further pictured a Riemannian universe that was static, one that did not undergo an overall change.  The individual components within it might move around, but the overall density of matter, if all were smoothed out evenly, would remain the same.  Since, in Einstein’s view, the curvature of the universe (the extent to which it is Riemannian) depended on the density, a ray of light would travel in a perfect circle if not interfered with.  (I. Asimov, Understanding Physics, Vol. II.  Light, Magnetism and Electricity (NY: Walker and Co., 1966), p. 876)


A third and the final consideration for the Christian claims and the Riemannian universe involves the ontology of possibility.  “There are those physicists who maintain that anything not forbidden is compulsory.  In other words, any phenomenon that does not actually break a conservation law, must at some time or another take place.”  (Asimov, The Universe, pp. 201-202)  This line of reasoning is similar to the statement that it is possible for a monkey typing away at random to type out the Bible.  Here I would say two things:  this is a true claim if (1) the monkey has an infinite amount of time, or (2) there are an infinite number of monkeys typing at typewriters.  In fact, mathematics probability laws tell us that given either infinite time or infinite typing monkeys, one of them will type out (or in the case of the single monkey), someday the entire King James version of the Bible.  Now if the universe is infinite in size we are faced with the same range of possibility, i.e., anything which is technically possible will happen somewhere.  This smacks of freedom talk and runs counter to the Christian claim.  But the Riemannian view of the universe, i.e., its finiteness, re-establishes the Christian claim.  As a learned friend of mine once said, “The Riemannian universe fits like an Italian glove on the Christian world view.” And later, “Many things are thought possible that are in fact not possible.  Many things could occur that do not.” 


The history of Western civilization suggests that it is always dangerous to try to correlate science and the Bible.  No doubt soon advancement will be made in the notion of a Riemannian universe and a new outlook will be proposed for the cosmos, one that fits even better with the Christian Weltansicht.  The nature of scientific breakthrough is not to negate previous truth, but rather to expand the previous statement.  Newton’s Theory of Absolute Space claimed the observer’s position did not affect the results.  Now Einstein’s Theory of Relative Space does not negate this tenant but rather spherically expands its partial statement concerning reality.  Einstein’s theory states that the relative position of the observer does not affect the results.


Reid summarizes the nature of the problem by saying—


In this case, one of the problems is the lack of proven knowledge from science.  Science still has not supplied solid facts that are common knowledge.  One can only say that both science and the Bible seem to indicate the next step, which underlines that man has to go even further in knowledge in order to be able to find all the facts in the Bible.  And, what is even more important, Christians do not have to fear the abstract analyses of mathematics and advanced science. (Reid, p. 82; see my work, “Mathematics and the Progress of Science” and “Transcendence, Philosophy of Mathematics and Goedel’s Theorem” at http://www.worldvieweyes.org/strauss-docs.html).


James D. Strauss