Updates to "The Einstein Hoax" [January 2006]
2.12- (Updated January 2006) In 1915, Dr. Einstein published his General Theory of Relativity. In deriving this theory he combined a new and apparently original concept, the Principle of Equivalence, with the Principle of Relativity upon which Special Relativity was based. Simply stated, the Principle of Equivalence asserts that gravitational acceleration can be considered to be equivalent to inertial acceleration. Unfortunately, Dr. Einstein failed to recognize that Tensor Calculus cannot be used to derive a relativistic theory unless no mathematical error (update) is made (as discussed later) and incorrectly employed that mathematical technique in the theory's derivation. Its use for such a purpose introduced a mathematical error of a type which, if persistently made by a student of Elementary Calculus, would result in a failing grade for the course. As a result of this error, the derivation of General Relativity was impossible in terms of our observable three dimensional Euclidian Space.
5.3- In the article it was stated that attempts to use the apparatus to communicate at velocities greater than the velocity of light resulted in the transmission of noise instead of information. Their failure to achieve communication resulted from the fact that, while they were obviously good quantum physicists, they were not good communication engineers. In analogous electronic terms, they were attempting to communicate by phase modulating a randomly phased carrier. In such an arrangement, the randomly phased carrier injects white noise that prevents the information, which is actually present in the received signal, from being decoded. The experiment did demonstrate that, if the carrier had been coherent, the desired propagation of information at translight velocity would have been achieved. (Correction as of January 2004. The success of the basic experiment established that information was actually being transmitted faster than the velocity of light. The failure to successfully receive that information can only be attributed to an improper processing of the information or a poor signal to noise ratio.)
5.10A- Update to Text as of 02/19/04 A recent E-mail asserted that the assumption that the addition of the 45 degree polarizers would not affect the polarization coupling of the paired photons was incorrect. The E-mail asserted that such coupling is destroyed when the photons pass through polarizers. If this is the case, the experiment of Figure 5.3 would obviously not work. A closer examination however, reveals that all is not lost. Not only are the 45 degree polarizers unnecessary, removing them improves the signal to noise ratio by 40%. (This illustrates a tongue in cheek truth the writer learned as a teenager. A mechanism being repaired quite often works better with some parts left out.)
6.8a- A clarification as of February 2004 - It is repeatedly asserted that photons are massless particles because they have zero rest mass. This assertion is partially true, they do have no rest mass, but they also do not exist at any velocity different from C so the assertion is true but meaningless. The inertial mass of the photon, as determined by the force exerted when it is reflected or absorbed, may be determined by dividing the accepted equation defining the momentum of the photons in terms of its energy by the velocity of light, C. If one divides both sides of that equation by the velocity of light one obtains M=E/C^2, a rearrangement of the well known equation, E=M*C^2. If one applies the Lorentz Transformations for Mass to determine the mass of a photon at zero velocity to determine its rest mass, one finds that he has divided the mass of the photon at the velocity C by infinity! Since dividing any actual number by infinity produces a value of zero, the fact that the photon has no rest mass should surprise no one. Special Relativity requires that conclusion but does not prevent the photon, as it exists from having mass!
6.14- The time required for sound to travel though water between two points is determined by three parameters, one of which is dependent on the velocity of the points of transmission and reception through the water. First consider the case of the round trip signal between the following boat to the leading boat. While the signal is traveling through the water, it propagates at the velocity of sound in the water, C. When the signal is sent from the following boat to the leading boat which is a distance L ahead, the receiving point is running away from the signal at the speed of the boat, V, and the time required for the outward trip is given by To=L/(C-V). When the signal is returned, the following boat approaches the signal at the speed of V, and the time required for the return trip is given by Tr=L/(C+V). The time for the round trip, T, is the sum of these times, T=2*L*C/(C2-V2), or T=2*L/(C*Bv2) [Corrected January 2006 was T=2*L/Bv2 ] where BV = (1-V2/C2)0.5.
7.2- In order to insure that the basic system of units represent directly observable entities, it is necessary to convert the familiar Mass-Length-Time system of units to a Force-Length-Time system. (For a definition of the basic units of this system see Table 7.2.1.) Unlike force, which is directly observable and is a fundamental entity in its own right, mass has no independent existence and cannot be directly observed. The mass of an object (or particle) can be observed in one or more of three ways. It can be observed in terms of its inertia as the incremental impulse (force-time product) required to produce an incremental change in velocity (length/time ratio). It can be observed in terms of the gravitational force between the energy (force-length product) [Corrected January 2006 - was incorrectly given as force-time product] equivalents of two masses divided by the square of their separation (length-length product). Or it may be determined by the energy (force-length product) released when the object is converted to radiation. Accepted texts on Special Relativity correctly provide the Lorentz Transformations for Time, Parallel Length, Transverse Length, and Parallel Force. Unfortunately, an unrecognized error was been made in the derivation of the Lorentz Transformation for Transverse Force. The transformation provided in texts is 1/Bv whereas the correct transformation is Bv. The existence of this error is revealed by the Right Angle Lever Paradox discussed below. (A rigorous derivation of the Lorentz Transformations for Parallel and Transverse Force is provided in "Corrections to Errors in Special Relativity" as provided at this Website.)
7.6a- An objection was raised by an individual who used Maxwell's Equations to derive the Lorentz Transformation for Transverse Force. He asserted that he had rederived the Minkowski's version iof the Lorentz Transformation of Transverse Force using Maxwells' Equations and found the expression ot be correct. What this individual failed to recognize is that his derivation depended upon the ABSOLUTE velocity of light to be unchangeable. This assertion is not correct and any derivation between refernce frames which relies on Maxwell's Equations will be defective. (Discussed later in this chapter.)
8.20- The correct effect of changes in elevation on the velocity of light is provided by the Gravity Transformation for Velocity in Table 8.13.1 as a function of the ratio between the distance, R, to the center of a gravitationally attracting object and its Horizon Radius, Rh, both as measured with the units of measurement existing at an infinite radius. The departure of the velocity of light from its nominal value of C when R approaches Rh is provided in Figure 8.4. It will be noted that, because of the minus sign in the transformation, as the radius approaches the Horizon Radius, the velocity of light abruptly approaches zero. The effect of this drop in the velocity of light causes the path of a ray of light to be refracted by the gravitational field for the same reason that the lenses in your eye refract the light to bring the image of this text to a focus on the retina of your eye. The velocity of light is slowed down by the nature of the space through which the light is passing. This change in the velocity of light is concealed from a local observer who, of necessity, measures the velocity of light with units of measurement which have been altered by the gravitational field. (Added January 2006) - If one refers to Table 8.13.1, one finds that the effect of the proximity of energy which produces gravitation acts entirely on the permeability of space. The dielectric constant of space is unaffected.
9.2- In deriving the General Theory of Relativity, Dr. Einstein employed a mathematical tool called Tensor Calculus. Properly applied, this tool is extremely useful and normally insures that the effects of all possible variables are considered. It does have a limitation however, it cannot be blindly (word added January 2006) used for deriving a relativistic theory. Tensor Calculus, in its simplest form, is a process in which partial derivatives of the variables of interest are arranged in a set of simultaneous equations similar to those encountered in conventional algebra. A typical group of Tensor Calculus equations is illustrated below:
A11*(dX)+A12*(dY)+A13*(dZ)=W1
A21*(dX)+A22*(dY)+A23*(dZ)=W2
A31*(dX)+A32*(dY)+A33*(dZ)=W3
9.3- In this group of equations, the symbols A11 through A33 are constants determined by the problem, the symbols X, Y, and Z are the variables whose value is to be determined, W1, W2, and W3 are the sums of each of the equations, and the symbol d within parenthesis indicates that the term is a partial derivative. Solution of equations of this type requires a mathematical procedure known as integration. Therein lies the rub. To perform that integration, it is necessary to know that the coefficients (e.g.:- A11 through A33) of the partial derivatives are independent of the variables. To understand why, consider the use of the rules of Elementary Calculus to integrate the expression K*(dX). If K is independent of the value of X, the result of the integration is K*X+C", where C" is the constant of integration. However, if K is equal to X, the result is X2/2+C", an entirely different result. A basic rule of all types of Calculus, including Tensor Calculus, is that the variable to be integrated must be completely defined in the expression itself and not be hidden within other terms, in this case, K.
9.4- It is because the solution of a problem in Tensor Calculus requires the performance of mathematical integration that Tensor Calculus is unsuitable, without additional information (added January 2006) for the derivation of a relativistic theory. The partial derivatives in the Tensor Calculus matrix used to derive the General Theory of Relativity involve length. It has been demonstrated that the units of measurement of length change between reference frames which differ in velocity. Since the derivation of General Relativity is based upon the Principle of Equivalence, it follows that the effect of a change in elevation on the units of measurement for length must be taken into account (corrected January 2006, was "known") in order for a meaningful, mathematically valid, integration to be performed. (The size of the units of measurement are analogous to the "size" of K in the previous paragraph.) Unfortunately, the effect of a change in elevation on the units of measurement for length cannot be known until the integration has been performed correctly and a valid integration cannot be performed until the effects of a change in elevation on the units of measurement for length are known. Consequently a valid derivation of gravitational theory is not possible by this method. When the attempt is made, it arbitrarily forces the Gravity Transformation for Length to equal unity regardless of its correct value. Until the Tensor Calculus equations have been solved, the required information needed to solve them is not available. It is difficult to understand, however, why Dr. Einstein did not recognize that, in employing Tensor Calculus to derive General Relativity, he was incorporating an erroneous loop of circular reasoning. Dr. Einstein's approach in solving this basic error is described in the next paragraph. (January 2006) If an undergraduate student of elementary calculus persistently made an equivalent error he would receive a failing grade for the course.
10.16- As the internally observed expansion phase proceeds and the temperature drops below its limit of 4.25 trillion Kelvins, matter can no longer reduce the absolute energy represented by individual particles of matter, as required by the Principle of Relativity, by creating additional matter. After this point has been reached, matter has no choice but to release energy in the form of radiation. For the small portion of its energy which is electromagnetic in nature (electrons/positrons, charge of protons/antiprotons, and the electromagnetic energy associated with the orbiting of electrons/positrons) there is no problem. The resulting radiation consists of photons and adds to the observed background electromagnetic radiation of space or, if the matter is contained within an object such as a planet or star, serves to warm that object. (Planets, for example, are observed to radiate more energy than they receive from the Sun.) The 99.95% of the energy content of matter that is contained within atomic nuclei is a different matter. Based upon the arguments provided in Chapter 13, it would seem that the required shedding of energy must be accomplished by broad spectrum radiation of neutrinos similar to the black body radiation of electromagnetic energy. Such a broad spectrum radiation of neutrinos, however, is not directly observable within the current state of the art and, indeed, may never be observable. Neutrinos are currently detectable only by their absorption by atomic nuclei. Since that interaction occurs at sharply defined frequencies, analogous to the electromagnetic spectral absorption lines of atoms, only a small percentage of the emitted neutrino radiation traversing space can be detected. (Gravitationally induced time dilation between the center of the Sun and the Earth can easily provide enough frequency shift to account for the failure of experiments designed to detect the expected emission level of neutrinos produced in Sun.) Unlike photons, neutrinos are not trapped by matter and they escape directly to space without heating the object through which they are passing. It seems reasonable to expect that the distribution of energy between photons and neutrinos in the background radiation of space would closely match the ratio of electron mass to nucleon mass of atoms. If this is the case, 99.95% of the background radiation level of space would consist of undetectable neutrinos. While this conclusion may seem extreme, in terms of background radiation temperature it is not hard to accept. Since the energy of radiation varies as the 4th power of absolute temperature, the required energy ratio is achieved if a very reasonable background neutrino radiation temperature of 22.3K coexisted with our Universe's background electromagnetic background temperature of 3.5K. [Further work, Fall 2005, suggests that the energy represented by matter, notably by quarks, is entirely represented by loops of electromagnetic radiation. If this is the case, then the expected numbert of neutrinos in the Universe would be small. This is discussed further in Chapter 13.]
11.3- Since astrophysicists teach that only objects having an
externally observed size larger than 4.5 Solar Masses will undergo gravitational
collapse, it is reasonable to use the Gravitational Transformations to examine
the interior of such objects after they have undergone that collapse but have
not radiated energy to external space. Late in its locally observed expansion
stage we would find that:
- The object consists of mostly empty space filled with radiation.
- Nucleons within the object are organized in strings of varying lengths up
to a significant portion of the size of the object. If the object is
sufficiently large, these strings eventually contain stars and galaxies.
- Workers in the field of plasma physics have shown that electric and
magnetic fields in space are capable of organizing matter in this manner.
("The Big Bang Never Happened" by Eric Lerner, Times Books.)
- The object will be observed to be expanding towards an infinite radius
with the fraction of its total energy which is in the form of radiation, #,
approaching unity.
- Extrapolation of observations of the expansion process backwards in time
will lead to the conclusion that the object began with an eruption of matter
into existence. Simplistically, it would be concluded that the matter was
created from nothingness at a single point in space.
- The radius of the object will appear to be increasing at the velocity of
light.
- The object will be composed entirely of normal matter or of anti-matter
but it will not contain both types.
- Mutual annihilation will cause matter and anti-matter in the original
cloud to annihilate each other until only the predominant type of matter
remains.
- Workers in the field of plasma physics have shown that electric and
magnetic fields in space are capable of organizing matter in this manner.
("The Big Bang Never Happened" by Eric Lerner, Times Books.)
- Mutual annihilation will cause matter and anti-matter in the original
cloud to annihilate each other until only the predominant type of matter
remains.
This description might well apply to our own Universe if it were not for one difficulty. Our Universe contains 1080 nucleons. As shown in Figure 11.2A, the nucleon content of a collapsed object is determined by its actually observed size and, for the collapsed object to contain 1080 nucleons, the actually observed size of the collapsing object would have to be on the order of 2*1012 kilograms (approximately that of a rock having a diameter of a kilometer), as shown in Figure 11.2B. Since gravitational collapse does not occur in objects smaller than 4.5 actual solar masses, our Universe could not be formed in this manner unless an additional factor was present.
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