🚀 go-pugleaf

"Wolfgang G. Gasser" <z@z.lol.li> wrote in message 
news:enjf3m$q39$1@atlas.ip-plus.net...
>> Wolfgang G. Gasser wrote:
>
>>> Two distant observers with each a (transversal) LIGHT CLOCK orbit
>>> at a constant distance around their common center (assumed at rest).
>>> Special relativity postulates that the light beams in both light
>>> clocks propagate at c relative to both (almost inertially moving)
>>> observers. This requires that for each observer the clock rate of
>>> the opposite clock CAN be lower than the clock rate of his own clock.
>>> Because of symmetry and unchanging distance, clock rate CANNOT differ.
>
> Tom Roberts in news:dSymh.10793$yC5.9487@newssvr27.news.prodigy.net :
>
>> For approximately inertial motion, the basic equations of SR are only
>> APPROXIMATELY valid. You ignored the approximation you, yourself, made.
>
> Let us assume a relative speed of v = 0.99995 c (with gamma = 100)
> of each observer with respect to the other. Deviation from inertial
> motion can be made as small as we like by choosing a large enough
> radius of the orbit in relation to the height of the light clock.
> Applying the simple and transparent LIGHT CLOCK reasoning, we get:
>
> With respect to each observer the light beam in the opposite clock
> can only propagate at c, if the rate of this clock is gamma = 100
> times lower than the observer clock rate*. On the other hand, if
> the clock rates of both light clocks are equal, then with respect
> to each observer the velocity of the beam in the opposite clock is
> composed of the two orthogonal components c and v, resulting in a
> speed of light of c_v = sqrt(v^2 + c^2) = 1.41c.
>
> So we have a real contradiction and not something caused by an
> approximate calculation.
>
>> At a deeper level, however, such orbiting observers cannot be treated
>> as inertial observers, because a circle is different topologically from
>> a line.
>
> Also this attempt to remove the contradiction leads to an untenable
> consequence: Let us assume that at a given moment the observers start
> moving inertially instead of further orbiting. When still orbiting,
> the time of each observer runs identically with respect to the other.
> Just after the start of inertial movement however, the time of each
> observer runs one hundred times slower with respect to the other!
>
> Cheers, Wolfgang
>
>
> * This gamma time dilation leads to a gamma reduction in the speed
>  of the opposite clock beam from c to c/gamma. This opposite clock
>  is moving at v with respect to the observer, and this movement
>  is orthogonal to the light beam direction. Therefore the velocity
>  of the beam with respect to the opposite observer results in
>  the hypotenuse of the right-angled triangle with the legs v and
>  c/gamma_v, and we get: c_v = sqrt(v^2 + (c/gamma_v)^2) = c
>
>

  Only two blackholes could possibly orbit each other, and hold orbit, at 
anything like the orbital speed you speak of. So you are defeated before you 
begin. Anything else would have begun spiraling outward from a circle long, 
long, before reaching a relative velocity, each relative to the other, of 
0.99995c. Then you have to deal in the increasing distance factor on top of 
and inlaid into the increasing velocity factor taking you up into dimensions 
of hyperspace-time. Therein you are getting into a far wider scope of 
interpretation of the principle of uncertainty regarding both the postions 
and the velocities of both observers (relative to each other).

  For one observer to just happen to detect the other and measure a velocity 
for the other of 0.99995c relative to himself, that relative velocity of v = 
0.99995c for observer(2) would still be relative to no other very local 
velocity than v = 0 for the observing observer(1)! If both had reached the 
same relative velocity in the same time, the spiraling away from each other, 
as they gain distance from each other, still matters and so neither would 
come up with anything like v = 0 for the other though they were both doing a 
relative velocity of v = 0.99995c (relative to some third observer's v = 0). 
(Did I get enough relatives in there?)

  I don't know what the observed relative velocity for the distance gain in 
lengthening straight line between the two observers (in spiraling out from 
each other), would probably be, but it would probably be no less than a 
third of, and probably be no greater than half of, 0.99995c (velocity v = 
0.99995c relative to observer(3)'s own very local v = 0).

  The concrete cosmological constant of c, which will be measured as such 
within each observer's local frame, can and will shatter position and 
velocity of travelers into any number of differing [relatives] for any 
number of differing observers (in scenarios such as this one). None of the 
observers will be isolated from their observable universes. And the map is 
never the territory.

GLB