The Law of Repetition may be used to predict behavior in different branches of science. If one branch of science is developed fully, while a second branch is not yet fully developed, and if the two branches agree in their basic laws up to a certain point, then we may be able to extend the second branch based upon our knowledge of the first branch. This concept will be applied to include repetitive phenomena in aerodynamics and relativity. Aerodynamics is fully developed below and above the speed of sound, while the relativity is developed only below speed of light. The aerodynamic model may be applied on the relativity model, leading to a very interesting conclusion. The analogy of aerodynamics and relativity can be shown as follows:
1. In aerodynamics, Mach number (M) is defined as the speed of an object divided by the speed of sound. And in relativity, the speed parameter (R) is defined as the speed of an object divided by the speed of light.
2. In aerodynamics, Prandtl-Glauert factor is defined as 1/√ 1-M2. And in relativity, Lorentz factor is defined as 1√ 1-R2.
3. Both factors are used to predict quantities at different speeds, and both factors reach infinity if M=1, R=1.
The theory of relativity advocates that the maximum speed of any object is the speed of light. This is based upon the fact that Lorentz factor reaches infinity at the speed of light and there should not be an infinite value in the physical laws. But, as it was mentioned before that at the Big Bang the speed of the universe rushed out at a speed that is faster than the speed of light. It was suggested that speed of light is a limitation on objects in space, but not on space itself. This statement negates the notion that the ultimate speed is that of the speed of light in all conditions.
In aerodynamics, before approaching the speed of sound, it was thought that aircrafts would never reach the speed of sound. The air resistance of aircrafts increases dramatically as the speed of sound is approached. Theoretically, this air resistance should become infinite at the speed of sound, hence the term "sonic barrier." However, wind tunnel testing of aircraft models showed that the air resistance increases when approaching the speed of sound, but it does not reach infinite value at the speed of sound. The coefficient of air resistance reaches a finite high value at the speed of sound, then starts decreasing at speeds higher than the speed of sound. Actually, Prandtl-Glauert factor is changed from (1/√ 1-M2) at subsonic speeds to (1/√ M2 -1) at supersonic speeds.
In 1964 Bertozzi conducted an experiment of accelerating electrons to various measured speeds and – by an independent method – also measured their kinetic energies. He found that as the force that acts on a very fast electron is increased, the electron’s measured kinetic energy increases to very large values but its speed does not increase appreciably. He concluded that no matter how much energy an electron is subjected to, its speed should not exceed the "light barrier."
From the above, the similarity of the aerodynamic and relativity models is quite obvious below the speeds of sound and light.
So the following questions arise:
Is it possible that two models are similar at speeds higher than the speeds sound and light?
Is it possible that Lorentz factor behaves like that of Prandtl-Glauert factor at speeds higher than the speeds sound and light?
Is it possible that Lorentz factor becomes (1√ R2 -1) at speed larger than the speed of light?
If the answers of the above questions are affirmative, then the Law of Repetition is much more powerful than we ever imagined!
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