The effect of Einstein's Special theory of relativity on the Universal Constants.

I) Introduction: Einstein's Special theory of relativity (STR) has shown us that many entities we had thought to be absolute are actually not and are relative. Entities such as time, length, mass and with this showed us the relativistic nature of our Universe. Here, we like to find out, what effect, if any, does the STR has on the Universal Constants. For this we will consider a few of the well-known and common Universal Constants. This can only be for illustrative purposes as there are just too many Universal Constants for us to consider in a single paper.

II) Here we will consider three well-known Universal Constants, (1) The speed of light in vacuum, C, (2) The Universal Gravitational Constant, G, and (3) The Planck's constant, h.

Before we delve into the details, let us first set up the stage. Following in the tradition laid by Einstein himself, let us take two inertial reference frames S and S'. Let us have S' move along the +x-axis of S at a uniform speed v, relative to S, with the +x'-axis of S' being parallel to the +x-axis of S. Let us put two physicists P and P' at the origins 0 and 0' of S and S', respectively. These physicists will be the observers relative to whom we will be discussing the effects of STR on our Universal Constants.

(a) The speed of light in vacuum. C: It is a postulate of the Special theory of relativity that the speed of light in vacuum is the same relative to any inertial reference frame. This means the speed of light in vacuum, C', as measured by P' will be the same as the speed of light, C, as measured by P. In other words, we have C'=C. Since the aim of this paper is to find any effect of STR on the Universal Constants, we can say that the STR does not have any effect on the Universal Constant that is the speed of light in vacuum.

(b) The Universal Gravitational Constant. G: To find the effect of STR on G, let us put a spherical object of mass M' at 0' that is at rest, relative to S'. This also means, M' = M0, relative to S'. Now, this object has a spherical gravitational field, GF', relative to S', around it that, theoretically, extends to infinity. Since the GF' of M' extends to infinity, relative to P', it also must be spherical and extend to infinity relative to P. The gravitational field of M', relative to P, we will designate as GF. Let us put an object, μ', of unit mass, i.e. μ' = 1, relative to S', at rest, relative to S', at a distance x' from O'. Now, P' will measure the Newtonian gravitational force, F' (M', μ', x'), on μ' by M' as, F' (M', μ', x') = -G' M' μ'/x'2, G' is the Universal gravitational constant relative to S'. Given the principle of relativity, our physicist P in S will write his Newtonian gravitational force equation as F(M, μ, x) = -G Mμ/x2, where G is the Universal gravitational constant relative to S and the other quantities are the equivalent, relative to S, of the corresponding quantities in F' (M', μ', x'). According to STR, we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], P will notice length contraction, as per STR, and he will measure the distance between M and ì, i.e. x, as given by the STR, namely, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Substituting the expressions for M, μ and x into the equation for F(M, μ, x), we get, after simple manipulation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (equation #1). The equation #1 is the transformation of the equation for the Newtonian gravitational force from S to S'. Again, as per the principle of relativity of STR, the form of the equations representing physical laws must be similar in all inertial reference frames. This means, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. From this we can conclude that, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This is not what we had expected for a supposedly Universal Constant. One can easily see the tremendous and profound consequences of the above relationship between G and G'. However, for now we will defer further discussion for later and look at our last Universal Constant, the Planck's constant.

(c) The Planck's constant, h: Let us have an object of mass m', relative to S', traveling at a uniform speed u', relative to S', along the +x'-axis. Our physicist P' will write the De Broglie equation for this object as λ' = h'/m'u', where ë' is the wavelength of the object and h' is the Planck's constant relative to S'. For this same object, our physicist P will write his De Broglie equation as λ = h/mu. From STR we know the relation between λ and λ'. It is nothing else than the length contraction equation, because A and A are lengths or distances between two consecutive peaks or troughs of the De Broglie wave of the object we are considering. Using the same argument we used in the previous section on the gravitational constant to obtain the relation between x and x', we get, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Substituting the expressions for λ and λ', respectively, we get, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (equation #2). Since equation #2 has to be valid for all m, u, m', u' and again as per the principle of relativity, which is the basis of the STR, the form of the equations representing physical laws must be similar in all inertial reference frames, we must conclude that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Here again, we see that a supposed Universal constant is not constant universally! In the discussion section, we will look at the consequences of this result also.

III) Discussion: In the above section we have looked at the effect of Einstein's Special theory of relativity on some common Universal Constants. We have found that if we accept the relativistic nature of the Universe, as per the Special theory of relativity (STR), then we must also accept the conclusion that some of our well-known Universal Constants cannot be constant universally. Let us now discuss the consequences of what we have found.

(a) The speed of light in vacuum, C: For this Universal Constant we found C'=C and that the STR has no effect on C. Therefore, there is no need for any further discussion regarding C.

(b) The Universal...