The Discovery of First-Degree Relativity First written June 2001 as a compression of my longer original paper of November 2000. One or the other was submitted in 2001-2002 to PRL, ADP, CERN, Nature, and JPL, where it was either refused or ignored. For example, it was submitted November 2001 to
Special Relativity is widely considered one of the most famous physical theories in history, as well as one of the most perfect. Quantum mechanics, or QED, the only other theory that is as famous, has been corrected a countless number of times in the 20th century. In that time, Special Relativity has not been corrected once. Einstein's derivations of 1905 stand to this day. Part One
Relativity is caused by motion. An object in motion relative to a second object no longer shares the co-ordinate system of that object. We must therefore create two systems to explain them. Specifically, the length and time variables will differ, and at least one transformation equation will be required to go from one to the other. The transformation equation(s) must include the speed of light, since the finite speed of light is what makes them necessary in the first place. If c were infinite, then all space would be one co-ordinate system, as with Galileo. This is Einstein's set-up, which I fully accept. It implies that clocks and measuring rods will not match up across systems. The result is length contraction and time dilation, which I also do not question. Part Two
But let us start at the beginning. Let us start with an illustration. Part Three
This leads us to the third major problem. Everyone knows that Einstein used the Lorentz equations to find that time appeared to slow down and x appeared to get shorter. Length contraction and time dilation. But let's look for a moment at the two light equations above. The light equations Lorentz and Einstein both used: Part Four
We are finally ready to derive new transformation equations. Going in, we know two things. 1) The current equations are mathematically flawed. 2) They are not far off, since they have been verified by many experiments. Part Five
First I will show why Einstein's proof does not work. In his 1905 paper he did not differentiate his ξ equation in order to find his relative velocity equation, like they do now in textbooks. He simply combined his equations algebraicly, like this: 1 - w/c - v/c + wv/c ^{2}= 1 - wv/c^{2}1 - w/c - v/c + wv/c ^{2}t/τ' = c
=
^{2} - wv 1 - wv/c^{2}(c - w)(c - v) (1 - w/c)(1 - v/c) Similar, but not gamma. Not surprising, since gamma only has one velocity variable. But in Einstein's derivation of gamma, regarding x and t, he already had two velocities. His set-up for the addition of velocity section is exactly the same as his set-up for x and t, in the first section. The only difference is he had a light ray moving—as his second velocity—in the first part, and a point in the second part. But in both sections he is seeking equations for two degrees of relativity. So what if we substitute the speed of light for w in the last equation above? Does it then resolve to gamma? t/τ' = (c ^{2} - cv)/ c^{2} - c^{2} - cv + cvNo, it resolves to infinity, just like Einstein's t-transformation. What does Einstein's addition of velocity equation resolve to if w is replaced by c? V = w + v
=
c + v
=
c(c + v)
=
c1 + wv/c ^{2}
1 + v/c
c + vV resolves to c, in that case. The velocity of light is c whether it is measured from k or K. That is Principle 2 again. But then that means that Einstein's adding and subtracting of v from it in the tau expansion was pointless. My final equation for V also resolves to c if w is c, but I did not get there like he did. Now, you may say, why not use "equation 5" above? It looks very much like Einstein's equation, except that we are adding the velocities in the denominator rather than multiplying them. At most speeds this would only be a small correction to Einstein and would seem to imply that his math was not that far off. We can't use that equation for one very important reason. The velocity variables don't match Einstein's. Mine are prime, his were not. Mine are the local velocities of k and the point. The other reason not to use equation 5 is that in most real situations we will not be given the local velocities. In using the relativity equations on quanta, for instance, the givens are not local velocities. We have no local knowledge of quanta. We would be given relative, or measured-from-a-distance, numbers to begin with, and would need an equation to determine the addition of these numbers. The famous experiment of Fizeau (explained by Einstein) is another example. We are given the speed of the liquid. But this is our determination of the speed of the liquid, not the liquid's. The given is not a local measurement of the system. Please notice that my new equation for the addition of velocities gives us numbers that are very close to Einstein's in most situations. It differs from his in having another easily comprehensible term in the numerator and a minus sign instead of a plus sign in the denominator. But it may be used with confidence, since it has been derived from a thoroughly analyzed situation, as above, from five different co-ordinate systems. My first-degree equation for velocity also gives us a fraction more slowing at the speed of a space satellite, which answers the Jet Propulsion Lab's decades-old problem. ^{1}"On the Electrodynamics of Moving Bodies", Annalen der Physik, 17, 1905.^{2}"On the Electrodynamics of Moving Bodies", Annalen der Physik, 17, 1905, p. 8.^{3}Relativity, Ch.XII, last page. ^{4} Historical Note: Max Born used gamma without the square root, perhaps for this reason. But this does not address the other substitution errors I have shown.
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