http://www.relativitybook.com/w/index.php?title=Special_relativity_considered_as_a_reconciliation&feed=atom&action=historySpecial relativity considered as a reconciliation - Revision history2022-08-14T15:14:24ZRevision history for this page on the wikiMediaWiki 1.26.3http://www.relativitybook.com/w/index.php?title=Special_relativity_considered_as_a_reconciliation&diff=387&oldid=prevEric Baird: 1 revision imported2016-07-04T21:53:01Z<p>1 revision imported</p>
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</td></tr></table>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Special_relativity_considered_as_a_reconciliation&diff=386&oldid=prevErkDemon at 17:13, 6 June 20162016-06-06T17:13:08Z<p></p>
<p><b>New page</b></p><div>{{SR}}<br />
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'''.<br />
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==Conflict==<br />
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 near-indistinguishable from those of special relativity, and include much of the same "good" phenomenology as SR (including things like [[E=mc^2]]). <br />
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::: <math>\frac{frequency'}{frequency} = \frac{(c-v)}{c}</math> (longitudinal), <math>= 1-\frac{v^2}{c^2}</math> (transverse)<br />
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Although these Newtonian relationships obey the principle of relativity, they are [[incompatible with flat spacetime]] and with a globally fixed lightspeed. <br />
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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<br />
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::: <math>\frac{frequency'}{frequency} = \frac{c}{c+v}</math> (longitudinal), <math>= 1</math> (no transverse effect)<br />
==Reconciliation==<br />
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.<br />
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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 starting-point, 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.<br />
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==Modified relationships==<br />
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==References==<br />
* <br />
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==See also:==<br />
* [[Geometric mean]]<br />
* [[Special relativity considered as an average]]</div>ErkDemon