Re: the heart of a paradox

From: Ken and Vicki (kavs_delethis__at_sysmatrix.net)
Date: 07/30/04 

Date: Fri, 30 Jul 2004 09:09:48 -0400

"Jim Black" <ghytrfvbnmju7654@mail.com> wrote in message
news:cb623e6.0407291930.22fd1dc2@posting.google.com...
> "Ken and Vicki" <kavs_delethis_@sysmatrix.net> wrote in message
news:<_7GdncnJ3qvs6pTcRVn-pg@sysmatrix.net>...
> > We are so very sorry if our original inquiry was misinterpreted!
> >
> > So you have this exactly symmetrical, albeit unlikely, binary star
system
> > out in no-man's land. Or they could be two heavy spacecrafts likewise
> > circling about one another, out where other gravitation is negligible.
What
> > evidence leads the pilot inside one of those crafts from presuming his
is a
> > non-inertial FoR? so that he can therefore *justify* the
denial/dismissal of
> > SR mutual Lorentz transform as the end-all-be-all ciphering of the
situation
> > (which would lead to a contradiction). In a loosely analogous
scenario --
> > that of Terrence and Stella in this group's FAQ GR Explanation of Twin
> > Paradox -- each of the twins can *justify* figuring in a massive GR
> > correction at Stella's turnaround because you could literally have a
machine
> > onboard Stella's craft that measures the g-force felt (or degree of
local
> > bending of light) and thence ciphers the resulting clock tick rate
> > disparity. An actual quantitative analysis can be done by machine alone,
and
> > the two twins apprised that by fully applying GR AS WELL AS SR (don't
deny
> > it), the paradox is perfectly resolved.
>
> Even on Usenet, writing it in all capital letters doesn't make it
> true. Special relativity contains no internal contradictions, and you
> do not need general relativity to resolve paradoxes, or even to
> understand them. Quite the contrary. You need to understand special
> relativity to see why accelerated observers see gravitational time
> dilation.
>
> > Conversely, no hypothetical machine aboard the inner cabin of either of
> > these
> > aforementioned mutually encircling stars or heavy crafts could sense any
> > pseudo force or witness any local bending of light -- so where, oh
where,
> > does the necessary inference of any GR effect derive... in their view?
How
> > would
> > those pilots know to differentiate their's from an inertial frame?
Without
> > application of GR, an SR paradox results.
> >
> > -kjs
>
> The whole world isn't inside the cabins of the two spaceships.
> There's a whole lot of curved space-time in between them.
>
> In the special relativistic scenario, the acceleration of the
> spaceship is causing the spaceship's idea of simultaneity to change.
> The spaceship's idea of what time on the other spaceship's worldline
> is "now" is becoming further into the other spaceship's future. This
> effect cancels out the effect of time dilation.
>
> In curved space, simultaneity is even harder to define. One thing you
> could do is draw a bunch of geodesics perpendicular to the worldline
> of the spaceship. Near the spaceship, the surfaces formed by the
> geodesics would be parallel, just like in a normal inertial reference
> frame. But as you move away from the spaceship, through curved
> space-time, the surfaces get bent away from each other. So the
> spaceship's idea of what time on the other spaceship's worldline is
> "now" is moving forward faster than it would otherwise. This cancels
> out the effect of special relativistic time dilation.

Thank you kindly for your thoughtful response -- it is mighty helpful.

I've reread the Usenet FAQ at
http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html and at
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html , which
address how SR handles acceleration... I hadn't read those pages in some
years and they are noteworthy. I find their concepts somewhat hard to grasp.
I know SR solely as what the Lorentz Transform describes, and I thought
acceleration was handled by integrating that, but apparently I was wrong. If
the transform were merely integrated, then some constant time dilation would
be attributed to any clock that is in relative motion, regardless if that
motion is toward, away or transverse; and regardless if that motion is
steady or accelerating. Yes, I am also aware of some time dissynchronicity
(what relativists term "the relativity of simultaneity") entering into that
figuring. In fact, I can resolve the Twin Paradox with SR alone, but I
prefer the GR explanation with its attendent uniform gravitational
pseudo-force that "suddenly permeates the universe" as the thrusters are
fired.

Yes, "the whole world isn't inside the cabins of the two spaceships", but I
was wishfully thinking that Relativity allows for a purely local reckoning
from one's arbitrary choice of a reference frame. You are saying that with
SR alone, each pilot can do that?? You are saying that each pilot, feeling
no G-force, can presume his to be an *inertial* frame, and resolve any
apparent paradox based on the accelerating relative motions that he
*observes* of the other craft -- and thence attributing a quantitative SR
analysis of the lines of simultaneity betweem him and that *other*
obviously-accelerating craft whilst presuming himself inertial??

Oh well; perhaps well-enough is best left alone. Tom Roberts was 100% right
when he accused me of wanting a "sound bite approach". I found the sound
bite approach so easy to grasp as it was described in the Usenet FAQ GR
Explanation of the Twin Paradox, and I so hoped that an equally simple
explanation could be had re the binary star paradox -- which I NEVER
believed to constitute an actual contradiction, because I accept Relativity
wholeheartedly.

I'm sure you can at least appreciate my being somewhat confused by the total
lack of physical evidence that each pilot has at his disposal that would
unequivocally differentiate his from an inertial frame, eg. the lack of
G-force felt. If each pilot then presumes himself inertial, then the lack of
any longterm clock discrepancy between his and the other encircling craft's
clock is satisfactorily resolved based on (1) his observation of the motions
of the other craft, without assessing their causations, and (2) SR ciphering
alone. Is that your assertion, sir??

Again, thank you.

Relevant Pages

  • Re: quibbles with special relativity
    ... >> The paradox I'm thinking of is that the Earth twin and travelling twin ... the acceleration can't be neglected. ... >> problem with relativity, only with our undertanding of how to apply it. ... there are several ways to pose the twin paradox problem ...
    (sci.physics)
  • Re: Letter to Dirk Van de moortel
    ... > SR is a subset of GR, just as Newtonian mechanics is a subset of SR. ... paradox, not about GR itself. ... >> basic relativity issue. ... >> Acceleration is handled fine because you invoke the clock principle. ...
    (sci.physics.relativity)
  • Re: quibbles with special relativity
    ... Admit the contradiction and then the theory is at the best ... Reject the contradiction but drop the name Relativity. ... > The paradox I'm thinking of is that the Earth twin and travelling twin ... the acceleration can't be neglected. ...
    (sci.physics)
  • Re: twin patadox question
    ... > The usual explanation as to why the twin paradox ... > spaceship 2 accelerated to .99c before we began this experiment. ... > acceleration, '1' and '2' would appear to be in symmetric situations, ...
    (sci.physics.relativity)
  • Re: Van Flandern & Rethinking Relativity?
    ... What relative aging do you get from the Earth frame and the ... >The calculation from the accelerated spaceship frame gives the ... Well, now you're mentioning acceleration. ... >> Of course it can be treated with special relativity only. ...
    (sci.physics)