confused2 > Oct 12, 2018 11:22 PM
Syne > Oct 13, 2018 12:04 AM
confused2 > Oct 13, 2018 12:47 AM
Syne Wrote:Your analogy to converting between different units of measurement does the opposite; it holds the measuring units invariant while changing the factor needed to make each specific conversion.If we choose to measure distance in light years and time in years then the conversion factor © becomes 1. Where s is the invariant spacetime interval, we'd have
Syne Wrote:..as one contracts and the other dilates in SR)This is implicit in s²=x²-t², s² is invariant (betwen frames) so if x² increases then t² must decrease - this is where your contraction and dilation actually come from.
Syne > Oct 13, 2018 04:20 AM
(Oct 13, 2018 12:47 AM)confused2 Wrote:That's a choice of convenient units; it still leaves c invariant.Syne Wrote:Your analogy to converting between different units of measurement does the opposite; it holds the measuring units invariant while changing the factor needed to make each specific conversion.If we choose to measure distance in light years and time in years then the conversion factor © becomes 1. Where s is the invariant spacetime interval, we'd have
s²=x²-t²
which is often done, depending on the forums and individuals you encounter.
Quote:Syne Wrote:..as one contracts and the other dilates in SR)This is implicit in s²=x²-t², s² is invariant (betwen frames) so if x² increases then t² must decrease - this is where your contraction and dilation actually come from.
The OP derived the the standard (accepted) equation for time dilation of one frame seen from another using s²=x²-c²t² as a starting point.
The muon experiment involves just two events located in spacetime (first and second counters), the geometry is entirely linear between those events so I don't think there is any need for the complexity of the full Lorenz Transform - it will (inevitably) give the same result (try it!).
Secular Sanity > Oct 13, 2018 03:12 PM
(Oct 13, 2018 04:20 AM)Syne Wrote: Contraction and dilation mean space and time are dependent upon relative velocity, and the spacetime interval is wholly mediated by c. So again, you've given no reason to assume spacetime more fundamental than causality.
Syne > Oct 13, 2018 08:47 PM
(Oct 13, 2018 03:12 PM)Secular Sanity Wrote:(Oct 13, 2018 04:20 AM)Syne Wrote: Contraction and dilation mean space and time are dependent upon relative velocity, and the spacetime interval is wholly mediated by c. So again, you've given no reason to assume spacetime more fundamental than causality.
He’s right, you know. Read the speed of light and causality and then the speed of light as a limit.
"These considerations show that the speed of light as a limit is a consequence of the properties of spacetime, and not of the properties of objects such as technologically imperfect space ships. The prohibition of faster-than-light motion, therefore, has nothing in particular to do with electromagnetic waves or light, but comes as a consequence of the structure of spacetime."
https://en.wikipedia.org/wiki/Minkowski_..._causality
Secular Sanity > Oct 13, 2018 09:46 PM
(Oct 13, 2018 08:47 PM)Syne Wrote: No one claimed that electromagnetic waves of light are fundamental, deary. That's why we've been talking about whether spacetime or causality is more fundamental, where causality relates all frames via spacetime intervals and is what limits the speed of light...not equivalent to light. Try to keep up.
Syne > Oct 13, 2018 11:29 PM
It is popularly imagined that Special Relativity forbids travel faster than the speed of light or the propagation of signals faster than the speed of light. However, the actual theory does not contain this assumption. The original theory, framed by Einstein in 1905, states that the speed of light in free space is constant in all inertial frames of reference so how did people in general come to believe that this implies a speed limit? The idea of a speed limit comes from two predictions of the theory, that inertia increases towards infinite as velocity approaches light speed and that causality, the succession of cause and effect, is violated if we could signal at speeds above the speed of light.
The inertial constraint does not apply to particles without a rest mass, such as the photon, or to particles that might oscillate between massless and massive forms. The possibility that causality would be violated if signals could travel faster than the speed of light is a more interesting problem however. The relationship between Faster than Light signal speeds and causality will be considered and it will be shown that if a Faster than Light signal were ever discovered then either Special Relativity or Causality will be false.
- https://en.wikibooks.org/wiki/Special_Re...Relativity
The Lorentz transformations have a mathematical property called linearity, since x' and t' are obtained as linear combinations of x and t, with no higher powers involved. The linearity of the transformation reflects a fundamental property of spacetime that we tacitly assumed while performing the derivation, namely, that the properties of inertial frames of reference are independent of location and time. In the absence of gravity, spacetime looks the same everywhere. All inertial observers will agree on what constitutes accelerating and non-accelerating motion. Any one observer can use her own measurements of space and time, but there is nothing absolute about them. Another observer's conventions will do just as well.
- https://en.wikipedia.org/wiki/Spacetime#...formations
Secular Sanity > Oct 13, 2018 11:33 PM