|Thursday, 20 November 2003|
The physical basis of Relativity
by Viraj Fernando
From the end of the 17th century to the beginning of the 20th century, most physical problems found answers in terms of Newtonian mechanics, and it was considered a fully comprehensive theory requiring no further development. However, at the beginning of the 20th century, scientists realised that there are certain phenomena known as 'relativistic phenomena' which cannot be explained in terms of Newtonian mechanics.
Einstein, found a mathematical methodology (the Theory of Relativity), to obtain answers to these phenomena. However, Einstein's theory is kinematic, that is to say it does not explain the physical factors behind these phenomena.
In contradistinction to it, the theory I have discerned obtains the exact same results mathematically, as in Einstein's theory, and in addition it also explains, from a consistent point of view, how these phenomena occur physically and what physical factors are involved.
I have discerned that a 'Relativistic' phenomenon is what occurs when one and the same mass of matter is acted upon by two discrete quantities of energy at primary and secondary levels in a local system.
A 'relativistic' phenomenon occurs due to a fraction of energy at the secondary level getting dysfunctional in a certain proportion of the energy acting at the primary level.
To explain the above statements let us take the case of the planet Mercury. Mercury moves round the Sun in an elliptic orbit. The energy of this motion acts at the primary level. As Mercury orbits, the other planets pull it backwards. The energy of this latter motion acts at a secondary level.
The effect of this backward motion manifests as if the major axis of the orbital ellipse of Mercury turns backwards as it orbits. This backward motion is known as the 'precession of perihelion of Mercury'. The French scientist Leverrier was the first to explain how the perihelion motion occurs due to the gravitational pull of the other planets.
However, he found that his predicted rate of the perihelion motion falls short by 43" (about 0.012 of a degree) per century. We contend that this shortfall occurs due to the dysfunction of a fraction of energy acting at the secondary level.
When a fraction of energy becomes dysfunctional, there is less energy available for action. Therefore, the displacement is less than that if the total energy were fully available. This is the reason for the shortfall in the backward motion of Mercury.
In order to explain the physical basis of relativity from first principles, we must first discuss how kinetic energy undergoes transmission following the same patterns as other forms of energy. In particular we make an analogy between transmission of heat and kinetic energy.
Pattern No. 1: Transmission from higher to lower level - In the transmission of electricity, energy flows from a higher potential to a lower potential, in heat transfer it flows from a higher temperature to a lower temperature, in gravitational falling of a body it moves from a higher level to a lower level.
We contend that kinetic energy too is no exception to the above pattern of transmission of energy from a higher level to a lower level.
Modern physics has however considered kinetic energy to be an exception to the above pattern. This is because empirically kinetic energy does not manifest such a flow. The secret is that kinetic energy has virtual states along with its empirical state of 1/2 mv2 (when moving a mass m at velocity v).
To explain the matter of kinetic energy having both empirical and virtual states, let us take the following example. Suppose you have a bundle of money in Sri Lankan Rupees.
This is the empirical or bodily form in which your money exists. You can at the same time have a computer program, which gives the value equivalent of your rupees in Euros, Iraqi Dinars, U.S. Dollars, Cuban Pesos, Yen, Indian rupees etc.
From these you get different numbers giving the value equivalent of the actual number of Sri Lankan rupees you have.
Similarly, the virtual states of kinetic energy are imaginary value equivalents of 1/2 mv2, where the same quantity of energy is expressed in a different form, hypothetically considering it to move different masses at different velocities.
Let the quantity of kinetic energy be Ei. Then Ei = 1/2mv2. From this m = 2Ei/v2. So when a quantity of kinetic energy is applied to a given mass and when it is moved at a certain velocity, the value of that mass can be expressed as Mass = 2 x energy/ (velocity)2 So in a virtual states where Ei is hypothetically considered to move a certain mass at velocity c, the value of the equivalent mass is given by 2Ei/c2. Or for one that corresponds to a velocity u the equivalent mass is 2Ei/u2.
Pattern No 2. Intensive and extensive components of energy - Heat energy consists of the two internal components, temperature and entropy. Temperature is the intensive component and entropy is the extensive component. Intensive component is independent of the quantity of substance. And extensive component is dependent on the quantity of substance. Just like other forms of energy, we contend that kinetic energy Ei too must consist of intensive and extensive components.
The intensive component of kinetic energy is 1/2 v2 which is 'kinetic energy per unit mass' and the extensive component is 'inertia of energy' given by 2Ei/v2 = m.
In the virtual state where Ei is considered to move a mass at velocity c, the intensive component is 1/2c2 and the extensive component (inertia of energy) is 2Ei/c2. Similarly where it is considered to move a mass at velocity u, the intensive component is 1/2 u2 and the extensive component (inertia of energy) is 2Ei/u2.
Pattern No.3: Transmission between upper and lower limit of intensive component of energy - In the transmission of heat energy transmission occurs between two limits of the intensive component (temperature). It occurs between the temperature of the source T1 (upper limit) and temperature of the sink T2 (lower limit).
We contend that kinetic energy too must transmit between upper and lower limits of intensive components. For kinetic energy, the upper limit is 1/2c2 and the lower limit is 1/2 u2. The significance of 1/2 c2 and 1/2 u2 is explained below.
Pattern No. 4: Conjugate relationship between magnitudes of intensive and extensive components of energy - In the transmission of heat energy of quantity Q, from the upper limit of intensive component T1 to the lower limit T2, the magnitude of the extensive component changes from the lower limit S1 to the upper limit S2 conjugately, that the product of the two components remains constant such that the total quantity of heat Q = T1S 1 = T2S2
We contend that kinetic energy in the form of Ei = 1/2 mv2 also has an intensive component ( 1/2 v2) and an extensive component (m = 2Ei/v2).. Just like with a quantity of heat energy, where the intensive component (temperature) and the extensive component (entropy) vary in a conjugate manner, in kinetic energy too intensive and extensive components vary conjugately so that the product of intensive and extensive components is always constant.
Ei = (2Ei/v2). 1/2v2 = (2Ei/c2). 1/2c2 = (2Ei/u2). 1/2 u2
Pattern No. 5: The unattainable datum in the measure of intensive component of energy - In heat energy, there is the lower datum for the measure of the intensive component (temperature) in the from of 0K. And this temperature is unattainable empirically by material particles. Similar to heat energy, we contend that kinetic energy has an upper datum in the measure of the intensive component equal in value to 1/2 c2 and this is unattainable by material particles (therefore velocity c is unattainable by material particles).
0K is the limiting intensive component in the transmission of heat energy. Likewise, 1/2c2 is a limiting intensive component in the transmission of kinetic energy.
Pattern No. 6: The adaptation of limits of transmission of energy - In the transmission of heat, the intensive component (temperature T2) of background energy is adapted as the lower limit of transmission of the source energy.
We contend that in the transmission of kinetic energy too it adapts the intensive component of the background energy as the lower limit of transmission.
To illustrate how this adaptation occurs, suppose an ant is crawling at velocity v on a window of a train moving at velocity u. The moving train is the local reference frame of the motion of the ant. The energy of motion of the train is the background energy in relation to which the ant moves. The intensive component of kinetic energy of motion of the train is 1/2 u2. Kinetic energy of motion of the ant attains a virtual state where its intensive component is 1/2 u2.
This acts as the lower limit of the intensive component in the transmission of ant's kinetic energy.
Also we postulate that irrespective of what the empirical velocity v at which kinetic energy is moving a mass of matter, it adapts 1/2 c2 as the upper limit of the intensive component.
This is true for any quantity of kinetic energy irrespective of whether the quantity is big or small.
That is, no matter whether it is a speck of dust moving at a very low velocity, or a rocket of a great mass moving at a great velocity, in each case its kinetic energy has a virtual state whose intensive component is 1/2 c2. For each and every quantity of kinetic energy, there is a virtual state whose intensive component is 1/2 c2 and this acts as the upper limit of the intensive component universally in the process of transmission.
This is why c2and hence c also is a universal constant.
Pattern No. 7: The dysfunction of a fraction of energy - In heat transmissions, it is well known that inevitably a fraction of the quantity of energy Q becomes dysfunctional given by Q times the ratio of lower and upper limits of the intensive component = Q. T2 /T1. It will be noticed that if the internal energy were absent, then the material particles of the thermal system would be acted upon by the background energy and these particles would have remained at the level of temperature T2. It is because these material particles, which are already acted upon by the background energy are acted upon over and above that by a second level of energy, that they form into a system having a higher temperature T1.
So, we find that when the same material particles are acted upon by two levels of energy, a fraction of the internal energy (determined by the intensive component of background energy) becomes dysfunctional. (We have demonstrated mathematically how this dysfunction occurs, elsewhere).
In our analogy, background energy too can be in any form empirically.
And its intensive component remains true to its empirical form, (as we saw in the example of the photon, where the intensive component of field energy was considered as GM/R) when it enters as a determining factor of the dysfunctional fraction of internal energy in the form of the lower limit of the intensive component internal energy.
As in the case of Einstein's relativity, we do not need two theories to cover different phenomena.
One simple theory covers them all. The lag in the Perihelion Motion of Mercury.
There are two energy levels acting on Mercury:
a) Energy acting on Mercury at the primary level Energy of orbit due to the action of the Sun Es
b) Energy acting on Mercury at secondary level Energy of perihelion rotation by the action planets - Ep
We contend that the energy of perihelion rotation operates between upper and lower limits of its intensive component. The upper limit = 1/2 c2. For the lower limit it adapts the intensive component of the background energy. Background energy in this case is the energy of Mercury's orbit. The intensive component of the energy of orbit is 1.5GM2/R (where G = gravitational constant, Ms = Mass of the Sun and R the mean distance of Mercury from the Sun).
The fraction of energy of perihelion rotation that gets dysfunctional = Total energy Ep times the ratio of lower and upper limits of the energy in action (1.5GMs/R) / 1/2 c2 = Ep. 3GMs /Rc2. Let be the angular distance that perihelion rotation lags by, due to the dysfunction of the fraction of energy.
In general, area moved is proportional to the energy available (or area unmoved is proportional to the fraction of energy that has become dysfunctional).
The area proportional to the dysfunctional fraction of energy:
Ei. 3GMs / Rc2 1/2 R2 ----------(1)
The total area that would be moved proportional to total energy Ei if it were to be fully available:
E p R2 --------------------(2)
From equations (1) and (2) we get:
= 6 GMs/Rc2 ----------------(3)
This equation conforms to the observed results and is effectively the same as the equation derived by Einstein through rigorous method for a fictitious rotation of Mercury's orbit by the masses of the Universe. This shows how the relativistic phenomenon of the lag in the Perihelion Motion of Mercury occurs due to the action of two quantities of energy on one and the same material body simultaneously.
We have obtained mathematical results identical to Einstein's theory for the gravitational redshift and the time dilation of a fast moving muon which are well known relativistic phenomena. The lack of space restricts us from showing these here.
Our theory is an extension of principle of thermodynamics into rest of physics. Einstein wrote in his Autobiographical Notes (p. 33).
"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and more extended is its areas of applicability.
Therefore, the deep impression, which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of applicability of its concepts, it will never be overthrown".
Our theory is modelled in analogy with thermodynamics.
Its premises are simple and the areas of its applicability are more extended, covering phenomena explained in terms special and general theory of relativity under one single principle.
So our theory conforms to Einstein's own criteria, of being an indisputable theory.
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