Re: Circular motion in SR

On Mar 20, 9:53 pm, rbwinn <rbwi...@xxxxxxxx> wrote:
On Mar 20, 3:24 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:

On Mar 20, 4:53 pm, rbwinn <rbwi...@xxxxxxxx> wrote:

On Mar 20, 1:13�pm, PD <TheDraperFam...@xxxxxxxxx> wrote:

Special relativity does not and can not describe a satellite's orbit,
regardless of your uneducated suggestion. You want to use GR, which
you also do not understand.

Sorry, Eric, go try to snow someone else. �All you are doing is trying
to tell me that because you went to school and took some classes, you
are better than me. �This is a legal argument used by Europeans. �Here
in the United States people have equal rights. �As far as mathematics
is concerned, there is no obligation for anyone to follow your
dictates. �If special relativity can be applied to motion in a
straight line, it can also be applied to motion in a curved line.
That is one of the applications of calculus. �I can remember that
much.

And there is the boundary between math and physics. For while a
straight line and a curved line can have some of the same applications
mathematically, physically they are quite distinct. An object in
straight line motion can be accelerationless and inertial. An object
in a curved line cannot possibly be inertial. Newton understood this
point enough to distinguish the first and second laws of motion.

Well, all right, but there is still experiment. �Scientists claim they
orbited a clock in a satellite and when they recovered it, it had run
slower than an identical clock on earth. �So there is some correlation
between Special Relativity and a curved orbit.

Some, but it's not as tight as you think. Oh, and there is that
General Relativity business, too.

�According to
scientists, a moving clock is slower than a stationary clock whether
it is orbiting or moving in a straight line.

Well, no, that's not quite what it says, though I'm sure it's put that
way in comic-book versions of SR.
What it does say is that a non-straight path through spacetime has the
shorter proper time than a straight path through spacetime. This is
precisely also why the traveling twin comes back younger. It doesn't
have anything to do with whether one is moving and the other is not.
That is precisely the misconception that the twin puzzle is aimed to
correct. The neophyte looks at the traveling twin and says, "But
motion is relative, and I can take the traveling twin to be still and
the earth twin to be moving, and then the rule that the moving twin's
clock runs slower doesn't work." And the moral of that little story
is: that's right, and that's because which one shows lower elapsed
time has NOTHING TO DO with which one is moving, so erase that from
your wee little mind.

Well, that is interesting, but I never did think much about the
twins.  My equations indicate that according to the rotation of the
sun, they would both be the same age.

But the rotation of the sun is not the standard. The standard is
defined in terms of reproducible physical processes that can be
replicated locally.

Well, The Galilean transformation equations can be referenced to the
rotation of the sun, but not to reproducible physical processes
replicated locally.

By choosing some distant reference, one can *always* impose an
absolute time, sacrificing all locally consistent behavior. That,
however, is not an obviously superior position. It leaves you with the
situation that, in terms of rotations of the sun, an observer at rest
can measure radioactive half-lives, the growth of trees, the
population of bacteria, an AC-circuit resonance period; but as soon as
you go to a frame in which the sun is moving, then you need to *first*
redefine seconds to be in terms of that distant sun's rotation, and
then after doing so you note that all your local radioactive half-
lives, the growth of the trees, the population of bacteria, and the AC-
circuit resonance period have all changed in terms of the new second.
Seems rather stupid, just to preserve the rotation rate of the distant
sun and to preserve a Galilean transformation.

If you make this change just to preserve the Galilean transformation,
and as a result you find that all local physical phenomena now have
different rates, then this *normally* would be an indication that the
Galilean transformation is not a good one to insist on. And in fact,
the Galilean transformation was thought to have value when it was
believed that you would not *have to* do the goofy redefinition of the
second you propose. When it was found out that you'd have to, most
reasonable people began to look for a better transformation than the
Galilean one. You on the other hand, want to preserve the Galilean
transformation, even though it would mean that all local physical
processes would now have different rates. Why you think that's better
is beyond me.

 That is why the scientific definition of time as
transitions of a cesuim isotope molecule cannot be defined by the
Galilean transformation equations except by the way I do it.

If the traveling twin comes back, his heart having beaten only half as
many times as his Earth twin's, his hair still brown where the Earth
twin's has turned gray, and with the traveling twin's box containing a
radioactive isotope with an activity rate twice that of the Earth
twin's equivalent box, and the traveling twin's crystal-growing tank
exhibiting half the crystal growth of the Earth twin's equivalent
tank, it makes no sense to say that the traveling twin and all those
processes are nevertheless 40 years older even though by any standard
measure they match what would be expected of those process after 20
years.

Well, think of it this way, suppose both twins observe a planet
revolving around another star during the trip the one twin makes.  The
planet revolves around the star the same number of times during the
trip as seen from the frame of reference of either twin.  So consider
it from the perspective of a scientist on the planet being obeserved.
What is more important to him in terms of measurement of time, the
number of times the traveling twin's heart beats, The color of his
hair, the box containing a radioisotope, the time on the traveling
twin's clock, or the number of times his own planet orbited its star.
The Galilean transformation equations agree with the scientist on the
planet orbiting the star.  Local differences may be interesting, but
they do not control the universe the way scientists on this earth
maintain they do.

That's why we HAVE standards for time that are based on locally
reproducible physical processes, so we don't HAVE to use some
ridiculous and arbitrary standard like the number of rotations of one
star in one galaxy chosen for no particular reason.

That is fine, but if you are going to use the Galilean transformation
equations, there will be a preferred frame of reference.

Agreed. It's just not obvious that the Galilean transformation needs
to be upheld, or that it even really does apply.

 Generally
speaking that seems to be controlled by the gravitation of the
system.  So if ground control tells an astronaut, Your velocity is 30
miles per second, and the astronaut comes back saying, No, my clock
shows I am going faster than that, then we know which clock to
believe.  

It is not a matter of needing to believe one or the other. It is a
frame-dependent quantity and is known to be frame-dependent, and so
there is no need to assign one or the other as being the one to
believe.

Or else the altitude of the satellite is different in the
frame of reference of the astronaut, or the value of pi changes.  You
scientists never did say which you prefer.

 The traveling twin would just
have a clock that registered less time than the clock of the one on
earth.

[rest ignored because of expiring attention]

Well, I know how boring reality must seem to scientists.  It probably
has a purpose, nonetheless.
Robert B. Winn

.

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