[...]
On 2/13/24 5:37 AM, JanPB wrote:
[...]
Note also that for deriving the equations of SR, Einstein's second
postulate can be replaced with any appropriate experimental observation,
JanPB wrote:
We perform the experiments described below far away from any external forces >> (including gravity) so objects when left alone travel uniformly in straight >> lines.
Thanks. I had never thought of SR being based purely on
the results of experimental measurement.
In a previous thread ("Einstein's Relativity contains a HUGE Loophole. Its Implications Can't Be Ignored") a common assumption is made that clock synchronisation is essential to setting up and defining special relativity.
Then an argument is presented critiquing the relevant clock synchronisation (typically, Einstein's) as in some ways deficient or arbitrary or impossible to
verify experimentally. This then "leads" to the conclusion that special relativity is circular at best and self-contradictory at worst.
But this is an incorrect
is a theory which is based on a geometry (whether this is a sensible thing to do is another topic) and therefore it does not need coordinate axes, or clock sync, for its definition. It's the same with Euclidean geometry: it existed just fine before Rene Descartes.
So I'll describe below the relevant experimental setup that necessarily implies
special relativity holds (to the experiment's error bars) WITHOUT EVER referring to, or relying on, synchronising clocks. It only assumes a bunch of rulers (identical in construction) and a bunch of clocks (identical in construction).
Note also that for deriving the equations of SR, Einstein's second
postulate can be replaced with any appropriate experimental observation,
such as:
a) pion beams exist that are longer than ~20 meters (both
CERN and Fermilab have had pion beams more than a kilometer
long).
b) No matter how much energy is pumped into a charged particle in
an accelerator, its speed relative to the lab never exceeds c
while its kinetic energy increases correspondingly.
c) The observed trajectories of high-energy charged particles in
magnetic and electric fields, as a function of their kinetic
energy.
Or his second postulate can be replaced with a more abstract,
theoretical statement: there is a finite upper bound on the speed of information transfer.
(In discussing this last, one should note that it is
inspired by (b).
It should also be pointed out that
arbitrarily-large speeds can destroy energy/momentum
conservation, and common notions of causality, because
objects could "zoom in from infinity".)
Tom Roberts
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