CHAPTER 1
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 gravitational constant, G: Regarding this Universal Constant we found that, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Thus, the STR has a profound effect on G and that G cannot be constant universally. We can easily see the following consequences: (1) For v « c, G'=G as we would expect. (2) A moving object has a stronger gravitational field simply due to its motion compared to its gravitational field at rest. (3) The gravitational effect of the Sun on the planet Mercury is higher than its effect on Earth not just because Mercury is closer to the Sun, but also because the relative motion of the Sun is greater relative to Mercury than its motion relative to Earth. (3) For a photon we have v=c, which makes G' = ∞. This leads to the conclusion that a photon cannot have a gravitational field or, in other words, pure energy cannot have a gravitational field. This is not surprising since a photon does not have an inertial mass to produce a gravitational field. (4) In the gravitational field equation of Einstein's General theory of relativity, we need to replace the G by G' for non-terrestrial objects, such as our Sun. (5) We can speculate that perhaps it is the non-constancy of G that is responsible for the phenomenon we have so far attributed to the mysterious Dark Matter and Dark Energy. (6) One can easily see that there has to be innumerable sub-atomic black holes all around us simply due to the speed with which they are traveling, just as Stephen Hawking had predicted before. (7) There are many other consequences that one can derive which I am going to have to leave for the reader.
(c) The Planck's constant, h: Here also we have found the profound effect of STR on this supposed Universal Constant. We saw that according to STR, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The following consequences can be derived from the above expression: (l)For v « c, we get h'=h, which is as expected. (2) We see that h' -> ∞ as v -> c. This means if one is traveling in a spaceship at a speed that is very close to C, then, according to Heisenberg's uncertainty principle for position and momentum, the uncertainty of the position and momentum of a particle should increase compared to what we determine for the same particle on Earth. (3) In the Schrodinger's wave equation and other equations describing quantum mechanical processes, we will need to replace the h by h' when using those equations for non-terrestrial objects, such as the Sun or near the Event Horizon of a black hole.
IV) Testing the theory and final thoughts: As we have been able to test some of the results of Einstein's Special theory of relativity, it would be very helpful if we can test these results of the theory also. One way to test the non-constancy of G is using our particle accelerators. One can take a collection of identical particles, say protons, and have them in a spherical formation. We then gradually accelerate our spherically distributed protons to near the speed of light in vacuum, i.e. C, and see if the protons come closer to each other throughout and not just in the direction of motion, which is due to the length contraction effect of the STR. We then slow them down and see if the particles move away from each other to the original spherical distribution. In this way, we can get an indirect evidence for the non-constancy of G. We can also use the General theory of relativity and substitute G' for G in the gravitational field equation and observe for cosmic phenomenon that support the non-constancy of G.
To test the non-constancy of h, we can do experiments on the International Space Station or observe cosmic phenomenon that can best be explained using a value of h the is different that what we know it to be here on Earth. One can also do experiments involving our Sun and see if using a value of h that is greater by a factor of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where v is the apparent speed of the Sun relative to Earth, compared to the value of h on Earth, best explains our experimental results. Finally, the most important point of this paper is to show that if we accept that our Universe is relativistic as described by Einstein's Special theory of relativity, then we should also be ready to accept that not all Universal Constants can be constant universally.
CHAPTER 2
On some of the defects in Einstein's Special Theory of Relativity.
For the sake of keeping this a short paper, I will forgo the usual introduction and go directly to some of the gross defects present in Einstein's Special Theory of Relativity (STR). I will assume that the reader is familiar with the English translation of Einstein's original paper that was published in Annalen der Physik in 1905.
I) A problem in the derivation of the equation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
We will start with the following equation from Einstein's original paper on the STR: (a) 1/2 [τ(0,0,0, t) + τ (0,0,0, t + x'/c-v + x'/c+v)] = τ (x',0,0,t + x'/c-v). The problem that is present in this equation is the following:
Einstein says that a beam of light, starting at O' in S', reaches x'/[c-v], in time relative to an observer in S. Similarly, he also says that the time for the same beam of light to reflect at x' and reach O', again relative to the same observer in S, is given by x'/[c+v]. This cannot be valid. By doing this Einstein is in effect applying the Galilean addition of velocities to the speed of light in vacuum. This clearly contradicts his postulate of the constancy of the speed of light in vacuum relative to any inertial frame of reference that may or may not be in relative motion with respect to a beam of light traveling in vacuum.
This problem in Einstein's derivation of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is enough to make the entire derivation of the equation invalid.
II) Problems with the equation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
The following problems can be seen with the above equation relating t' and t:
(1) Unlike for S, where we have a single time 't', that applies to the entire S, we have an infinite number of times t' for S' due to the infinite number of values for the x in the equation for t'.
(2) To derive his famous time dilation equation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), Einstein placed a clock at O', thereby making x=vt, in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and obtained [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This means, the time dilation equation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], is valid only for x=vt and not generally, i.e. for x ≠ vt.
(3) Since, both x and t are independent variables, we can see that for any given time, t, in S, there will always exist an x, in S, equal to c2/v t, making t'=0 at that x. This means, for the observer in S, the time t' at x = c2/v t will be at a standstill. Not only this, we can also see that for x > c2/v t, we get t'<0, i.e. the observer in S will notice the time t' moving backwards!
From the consideration of the above problems with the equation for t', we can conclude that using the Special Theory of Relativity one can actually determine an Absolute Inertial Frame of Reference, S, by measuring (t')'s, of any given non-absolute inertial frame of reference S', at various points x of S. This contradicts the basic assumption of the STR that there is no Absolute Inertial Frame of Reference. In other words, the STR has a built-in self-contradiction.
III) Conclusion:
The above sections detail just two of the gross defects that are present in Einstein's Special Theory of Relativity. I will not go into the many other defects that are present in the STR, for the sake of keeping this a brief paper. This year, the physics community and the world is celebrating the 110th birthday of the STR and yet all the brilliant minds throughout the world are keeping quiet concerning the most basic and blatant defects that are present within this theory. Even Einstein's General Theory of Relativity (GTR) has to be a flawed theory for the simple reason that one of it's basic assumptions is that the STR should be locally valid.
In the end, I like to say that if the human society is interested in genuine further scientific progress, then it must discard both of Einstein's relativistic theories, whose time came and went, and replace them with theories that are mathematically, logically and physically correct and self-consistent.
CHAPTER 3
A relativistic theory based on the invariance of Newton's second law for motion and the constancy of the speed oflight in vacuum.
I) Introduction:
Let me begin by saying that it was never my intention to develop a new relativistic theory in order to somehow supersede Einstein's Special Theory of Relativity. My only intention was to find out, if possible, a relationship between the Newtonian Time and Einstein Time. After obtaining the said relationship, I noted that I could develop a set of relativistic transformation equations between two non-Newtonian inertial reference frames, S and S' with S' moving at a constant speed, Γ, along the + x-axis of S. These equations turned out to be quite different from the Lorentz-Einstein equations in Special Theory of Relativity and had consequences that in some cases were qualitatively similar to those of Special Theory of Relativity and others that were very different both qualitatively and quantitatively.
