Difference between revisions of "Special relativity considered as a reconciliation"
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Latest revision as of 21:53, 4 July 2016
Having considered the math in special relativity considered as an average, we can point out another way of thinking about special relativity – as a reconciliation between Newtonian effects and flat spacetime.
Conflict
If we start with the Newtonian relationships for the energy and momentum of a moving body, and extrapolate from them to get the energy and momentum of light, we get the same Doppler relationships that appear in C19th ballistic emission theory, but without committing to a particular propagation model for light. These energetics are usually indistinguishable or nearindistinguishable from those of special relativity, and include much of the same "good" phenomenology as SR (including things like E=mc^2).
 [math]\frac{frequency'}{frequency} = \frac{(cv)}{c}[/math] (longitudinal), [math]= 1\frac{v^2}{c^2}[/math] (transverse)
Although these Newtonian relationships obey the principle of relativity, they are incompatible with flat spacetime and with a globally fixed lightspeed.
On the other hand, if we assume that the speed of light is always globally fixed w.r.t the observer's state of motion , we get
 [math]\frac{frequency'}{frequency} = \frac{c}{c+v}[/math] (longitudinal), [math]= 1[/math] (no transverse effect)
Reconciliation
If we want to reconcile the conflicting predictions of both flat absolute spacetime and Newtonian mechanics, we can again synthesise an intermediate prediction that is the geoemtric mean of the two earlier conflicting predictions, and declare both to be equally correct … and equally off the mark, by the same Lorentz ratio.
By adopting this synthesised intermediate set of relationships we can say that a lightspeed fixrf uin the observer's frame is correct (as long as the opticial predictions are reddened and shortened by the Lorentz factor),and the the Newtonian predictions are a correct startingpoint, which then have to be modified with a Lorentz factor for the energy and momentum of a movign body, in order to correspond to the same intermediate result.