Everyone knows the original Twins Paradox experiment where one identical twin, Fred, leaves Earth on a rocket ship and eventually returns after many years to his stay at home twin, Jim, on Earth. Due to time dilation, predicted by the Special Theory of Relativity (STR) as a function of velocity, Fred is expected to return younger than his twin.
This original form of the Twins Paradox has unnecessary disadvantages, in particular the three acceleration periods of the rocket. A simplification which still retains the essence of the paradox employs three identical clocks, A,B and C, is described in Fig 1.
The relative velocity between A and B is +V and between A and C it is -V. A and B are initially zeroed across near zero distance. C is later synchronised to the reading of B across near zero distance such that these two clocks combined effectively equate to one single clock B,C. Finally A and C pass each other at near zero distance.
During the journey either clock, A and B, C, may and indeed should make observations of the other clock, using the Radar method, over the separation distance. Because the relative velocity V is reciprocal, these observations (ignoring for the moment the velocity reversal ) should be identical for either clock, based on the predictions of either the STR or its competitor theory, the Aether Theory of Velocity Effects ( ATVE) . Each clock will read the other to be slow by an amount -TV2/2c2 , where T is the elapsed time up to that observation.
But two clocks cannot both be slow with respect to each other (hence the paradox). The reality is that clock B,C finally reads A to be fast by the same amount that it is predicted to be slow. Thus there is a difference between prediction and observation of +TV2/c2 . So where does this effect occur. It can only occur at the velocity reversal as this operation has not yet been covered by either theory. The effect cannot happen to clock A as the reversal affects only clocks B and C. Also B and C cannot be affected internally as they would need to run backwards, which no theory predicts. Hence the effect can only be an observation effect on reading clock A due to the change in the observer's velocity.
The key to the Twins Paradox lies within the velocity reversal as an observation effect.
The STR cannot predict a pure observation effect
The ATVE predicts exactly this effect via the eqn;
Tobsdif = vd/c2
where velocity ‘v' is the change in the observer's velocity in the direction of and between the observations. In the case of the Twins Paradox this is 2V. It is not material that the two observations are made by two different clocks so long as they are synchronised. Hence:-
This is exactly the amount required to give the correct final observation (or indeed all observations after the reversal)
The derivation of Tobsdif is found in the Aether Theory of Velocity Effects on the website WWW.AETHERTHEORY.CO.UK .
The reading of a distant clock is affected by the communication delay between the observer and that clock over the unknown separation distance. This problem is overcome by employing the ‘radar' method of interrogation. A light pulse is emitted by the observer which strikes the face of the distant clock and reflects back with the reading. The reading is delayed by the time for the light pulse to reach the distant clock from the observer. But this communication delay can be considered to be one half the round trip time of the radar pulse. Hence the delay error can be accounted for. This is irrespective of the separation distance and whether it changes with time, as the delay is recalculated every reading.
However, the assumption made above, that the ‘out' delay equals the ‘return' delay, is only true if the speed of light is isotropic. But if the observer has a non-zero Aether velocity this is no longer true and the ‘out' delay does not equal one half the ‘out and return' delay. This difference is the ‘observation effect '. It is an unknowable effect as Aether velocity is unknowable. This effect can be simply calculated to be:-
Tobs = dpVe/c2
where dp is that component of the separation distance which is in line with Ve, the observer's Aether velocity.
The change in Tobs where the Aether velocity of the observer changes between the two observations (this results in a change of velocity through the IRF of the observed clock which is taken to possess constant velocity) calculates to be:-
Tobsdif = dv/c2
where ‘d' is the separation distance (a constant, as the two observations are made at the same point, either side of the velocity reversal) and ‘v'is the change in velocity of the observer in the direction of the observation. These two factors are measured in the IRF of the observed object.
It can be seen that the equation for Tobsdif does not involve unknown factors where-as that for Tobs does.
The ATVE predictions agree with observations throughout the Twins Paradox experiment.
Explanations which deal only with the final readings aren't worth looking at.
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