Mr. Babin,
I have read your papers on Special Relativity and find them very informative. I especially like your point on averaging, which is a critique of Michelson I had not heard before. It is utterly crushing to him and Einstein.

I have also read most of the papers on the site. Some of them are also informative and correct. However, I have an addition to the conversation, a paper that makes some points not found in any of the papers on your site, or, as far as I know, in history. In some ways it mirrors your paper, but in a language that is geared slightly more to the uninitiate. In other ways, it diverges. I accept time dilation and length contraction as a fact, but explain them as a by-products of the distant measurement of clocks. In this way, relativity can be seen as an extension of the Doppler effect. It is the Doppler effect applied to clocks. It is therefore an effect of measurement, not of "reality." What may interest you more than this, however, is my specific albegraic critique of Einstein's and Lorentz' derivation of gamma. I follow the derivation (one still published in textbooks) line by line, and show the mathematical errors. I also explode the various diagrams used to explain SR and the interferometer, showing in detail, and clear language, the mistakes made. I especially recommend you to the part where I show that x'=ct' is not a viable equation, in relation to the other mathematical givens and conclusions of SR. I am also quite proud of the philosophical link I have made clear between the Heisenberg Uncertainty Principle and the measurement of the velocity of light by Michelson.

Dec. 3, 2002: Walter
Here is a recent posting on the site forum in case you missed it.

Dec. 3, 2002: Miles
Yes, I know that Mr. Urovski is very excited about Relativity. He has emailed me many times. I am glad for the support. I am curious to know what you think of the paper. Especially the part exploding the equation x' = ct'. I think that may be the crux of the argument, and I feel it may be the most explosive and incontrovertible fact. Einstein's whole derivation falls with it. One can argue with theory. One cannot argue with mathematics.

Dec. 3, 2002: Walter
I agree entirely with you that the x' in galilean and relativistic formulas are not the same. The transformation can be on the basis of time (lack of synchronism which is usually used), of space (which is as you point out) or compound speeds. They all produce the same result, that of expanding or dilating first order quantities (c-v and c+v for compound velocities) so that the speed of light is constant in some substratum common to both frames. That is, the expansion and contraction due to motion is first order, and gamma only applies in second order configurations such as the MM experiment. Applied to linear motion, it is useless.

If the transformations are used for wavelengths and frequencies, it is exactly right. Even gamma applies in cases where there are interactions and the waves are modified by induction fields which is almost always. I cover basically the same thing in my kinematics paper under "Dimensional Considerations". In the 2nd paper, I show that the first order changes are wavelength and frequency under Lorentz transformations, and the last paper identify induced fields as gamma, even in the spectrometric experiments in 1901.

Dec 3, 2002: Miles
I don't believe that gamma applies, ever. It is an outcome of improper math. Have you read yet the section where I critique the illustration of the spaceship and the light projector? Or the appendix where I critique the Michelson Morley illustration. Gamma comes from the pythagorean theorem. But the "legs" of the triangle are not conceptually equivalent. The whole experiment was a hash. And Lorentz's math is completely faulty. No fringe effect should have been expected. Gamma is a mathematical mirage.

Dec 3, 2002: Walter
I agree the derivation is wrong, but you get the same quantity by solving the squared momentum-energy equation which devolves to v₁² = v₂²-v₂⁴/4c²where v₁ is the momentum velocity and v₂ = the "kinetic energy" speed. This relates to a primary field less an induced field ending in the experimentally determined momentum velocity.

Dec. 4, 2002: Miles
Of course you get the same quantity. In your paper you start by assuming that e = mc² But that equation is derived from the equations of special relativity, which Einstein presented first. That is to say that gamma was derived, then used in the equations which ultimately led to e = mc². e = mc² contains a presumption of gamma, so of course if you use it in the right way, you can re-derive gamma.

Dec. 4, 2002: Walter
No, it relies on experimental result. I first show that an electron in a magnetic field has a velocity component to the 4th power which denotes an induced field, take the energy-momentum equation and remove the mass and show that there is a 4th power component in it, specifically the velocities required for a squared induction field (v₂⁴/4c²) which results in the experimental momentum velocity. Then infer from this a spin, reverse spin energy from which is inferred an energy of transfer between potential and kinetic. The thesis is that relativistic effects are field effects only, which in the Compton treatment infers that it applies to time and space as well. The inferences are the result of not being able to complete the paper in time. I posit, like you, that relativistic effects are real, but due to other causes, effects and interpretations of the math.

I do not derive gamma. I remove it, then get the same quantitative result.

Dec. 5, 2002: Miles
What I meant was that in your first paper, equation 6 reads like this

(m - mo)c = ½mv_k²

I deny that that equation is valid, since if Einstein's and Lorentz's derivations of gamma are invalid, so is Einstein's derivation of e = mc².

Dec. 5, 2002: Walter
It is definitely invalid since it is tautological. b = (1-v₂²/2c²) = gamma
(mc²/b)- mc² = mv₂²/2b
= c²/b - v₂²/2b = c²
= c² - v₂²/2 = c² - v₂²/2

Dec. 5, 2002: Miles
Your equation 7 is this, m/m_o = 1 – (v_k²/2c²) = b₁, but this does not follow from equation 6. By my math either,

m/m_o = 1 + (v_k²/2c²) or m_o/m = 1 – (v_k²/2c²),

depending on whether you make the mass in the right side of equation 6, m or m_o. But it doesn't matter, since you say you want to drop the mass increase from the momentum equations. The mass increase is m - m_o, not m/m_o.

Then, equation 9 is this,

b = (1-v_m²/c²)^1/2 = b₁ = (1-v_k²/2c²)

I don't understand this. b is similar to b₁ but they are not equivalent. There is an extra 2 in there, not to mention the square root. But again, I don't see that it matters, since b₁ was derived from a non-working equation. It is therefore also a non-working equation. Dropping it out of the momentum equations cannot tell us anything. Likewise, equation 8

(Pc)²+(m_oc²)² = (K+m_oc²)²

is also non-working, for the same reason that equation 6 is non-working. If gamma is compromised, then e = mc² is compromised, in which case equation 8 is also compromised. Equation 8 is just as faulty as equation 6.

Dec. 5, 2002: Walter
Thank you, I had the masses transposed and have updated my papers. But I am sure you understood the tautology.

The form of b₁ and gamma is not the same (3-dashes) but quantitatively, are precisely equal (2-dashes). In fact, the only important aspect of the math in that series of equations is the relationship of v_k to v_m (and later, v_n) which emerges once we remove the masses from equation 8. The paragraph containing "increase in mass" does not logically relate to (7) but to the balance of the sentence, the "incremental field".

Also, E as a total energy does not enter into it at all. The relationship is between v_k (assumed scalar) and v_m which may be derived solely from the squares of gamma and b₁. v_k is an internal speed which is presumably spin. Later, we see in the Compton section that [c] disappears on impact (as it should) and becomes v_n.