this may be old but did anyone win?
Sounds like a loaded question. Who's the judge?
Without having reviewed his entire argument, I'd bet this comes down to "acceptable" assumptions. I am very interested in hearing what our heavyweights have to say here.
Unsurprisingly, the "refutation" is pure junk.
Section 1 on special relativity:
This entire section is based on equation set A. The first two are the familiar Lorentz transforms and the latter two are the equations of the light-cones originating from the origin in each reference frame. (Of course, a 2-d cone is simply a pair of intersecting lines)
The defining property of the Lorentz transformation is that it maps lightcones onto lightcones, so, for example, the solution set of x^2=(ct)^2 gets mapped onto the solution set of x'^2=(ct')^2 when you change coordinates.
In other words:
x^2=(ct)^2 if and only if x'^2=(ct')^2
The author, however, totally misunderstands what is going on, and takes the above two equations as being equations that must always be true. Unsurprisingly, the author derives contradictions from this flawed hypothesis.
Section 2 uses the same flawed hypothesis.
It's clear yet again that the author doesn't understand what's going on, through his terminology. Cutting things from axes? Attaching them? Worth of a segment?
He seems to be trying to avoid having to properly handle reference frames by inventing things like cutting a segment from a moving axis and making it stationary.
His flaw in this section is that he is speaking gibberish, but taking my best guess at what he is trying to say, he has obscured the fact that we're working in two different reference frames, and doesn't realize he's trying to set equal the velocity measured by different observers.
His first listed option is just the fallacy of simultaneity; he cannot tolerate that simultaneous events in one frame (t'2-t'1=0) are not simultaneous events in another frame (t2-t1[ne]0). However, he mistakenly stated that it is mathematics that cannot tolerate it.
In option two, he asserts that
x2-x1 = v(t2-t1)
is always true... but, of course, this is not always true. In particular, it is true when the two events are on the trajectory of a particle, but the two considered events are not on the trajectory of a particle.
I imagine the rest would be even more nonsensical.
Reference to A. Einstein's "On the Influence of Gravitation on the Propagation of Light" is an anachronism, being published before Einstein's learning about Riemannian geometry. In this paper, time is warped by different gravitational potential values at different places, while space remains serenely Euclidean. So Einstein had to assume a variable lightspeed c and attempted to develop a new gravitation law from that. That was all given up by the time Einstein got into second and third gear with General Relativity (late 1912 and on). The editors of the Principle of Relativity anthology probably included this paper in their collection in order to document Einstein's early conception of light-bending near the Sun.
See Pais,Subtle Is The Lord,Oxford(1982);p. 199,eq. 11.6 and pp. 202-203,eqs. 11.9-11.10
I especially love the part where they screw up the equivallence principle. They say something along the lines that one cannot distinguish between a mass generated gravitational field and the mechanical acceleration of a steady body. In other words, acceleration is similar to gravity. I guess they forgot that this only applies for uniform fields. A mass gravity field is curved. Objects dropped will get closer together. Oops!
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