[I respond to several of your posts in this thread.]
On 6/27/17 6/27/17 10:41 AM, Nicolaas Vroom wrote:
> I agree Nature has nothing to do with coordinates, however still there is
> an issue if you want to describe certain physical phenomena.
>
> [Two supernovas, each orbiting a different galaxy, and discussion
> of their "light spheres"]
> My question is will neutron star A be positioned (and stay) at the
> center of its sphere. The same for neutron star B > IMO both will not stay at the center of their respectivily spheres.
> They are only at the center a short time after the SN.
This is really too complicated to discuss, as it inherently requires GR, and
ambiguities arise due to the presence of gravitation. For example, nether source
actually has a light SPHERE, because the light paths are distorted by the
gravitation.
Let me simplify the scenario so it can be analyzed in SR.
Consider two pulsed omnidirectional light sources, A and B, each mounted on the
rim of a circular table. The two tables are identical, and they rotate in the
X-Y plane of an inertial frame S, with centers at rest in S. They are separated
by more than their diameter, and are counter-rotating at identical speeds
relative to S; they are synchronized such that A and B cross the line between
their centers simultaneously in S, and that is when they both emit a light pulse
(once per rotation). At the instant of each emission, A and B are both at rest
in inertial frame S' -- let us only discuss one such emission and use it to
define Minkowski coordinates in S and S', with the x and x' axes along their
velocity relative to S, and with the emission happening at (x,t)=(0,0) and
(x',t')=(0,0). Everything is in vacuum; spacetime is flat throughout the region
of interest. Ignore shadows from the apparatus.
This is a more precise description than yours, but I think
it captures the situation you had in mind.
Relative to S, A and B each have a light sphere that expands at c, but
observations of them at points with x>>0 will see the light blueshifted, and
observations at points with x<<0 will see the light redshifted.
Relative to S', A and B each have a light sphere that expands at c, and all
observations of either see no redshift or blueshift.
Note that after the light pulses are emitted, neither A nor B remains at the
center of its light sphere, relative to either S or S'. As expected -- once
emitted, light has no connection to its source.
> This raises an issue related to SR (if I understand correctly)
> SR claims that the speed of light is the same in both directions.
> That may be true for a certain reference frame, but IMO
> that same reference frame cannot be used to describe both SN.
But either S or S' can be used to describe light sources A and B. The speed of
light is isotropically c in S, and isotropically c in S'. You could choose any
other inertial frame as well, and the light from each source would expand in a
sphere relative to it.
The same would apply to your supernovas, ignoring the
effects of gravity.
> If this is correct then it is very important to select a one and only
> reference frame to describe this whole "experiment".
To perform an analysis, one must indeed select coordinates. But for the
situation I described one can select ANY inertial frame. It's just that S and S'
will make the analysis simpler than any of the others, because these are
directly related to the physical situation.
> The point is that measurements (observations) are highly subjective
> to human activities.
Some are, some aren't. But to test a physical theory one must ensure that
external actions/activities, human or otherwise, do not affect the result.
> The laws of nature are highly mathematical.
What God whispered in your ear and told you this?
Our MODELS of nature are indeed highly mathematical. But it seems HIGHLY
doubtful that nature actually uses mathematics, she just does her thing
(whatever that is).
See: Wigner, "The Unreasonable Effectiveness of Mathematics in the
Natural Sciences", Communications in Pure and Applied Mathematics,
vol. 13, No. I (February 1960)
> [excessively simplistic attempt to discuss "measurement and control"]
Tom Roberts