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The front and rear of an accelerating spaceship would be at two different (but not independent) velocities with respect to an inertial frame. This is a consequence of SR, not an assumption

Subtle distinction there between different and independant

originally austin0

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In light of your interpretation I have a question.

What is the difference btween proper acceleration in the system and coordinate acceleration as viewed from another frame??

.They are equal if the other frame is the instantaneously co-moving inertial frame. But since that frame is different from moment to moment, they are rarely used as reference frames in a scenario, except sometimes one of them. Proper acceleration depends on force applied (thrust) and the mass accelerated, and is the same value in any frame. Coordinate acceleration, like coordinate velocity, depends on reference frame

I understand the definitions of proper and coordinate acceleration. That was not my question. If acceleration of a frame results in dilation what difference does the semantical distinctions make with regard to its observation from another inertial frame.

Ie: Whether you call it proper acceleration or coordinate acceleration or consider it a velocity differential due to acceleration,,, why is it not detectable in the acceleration testing performed so far???

original quote austin0

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I dont think this analogy really applies. It is not a question of 1 in =2.54 cm but 4.67cm in S being equivalent to 7.9cm in S'

I think we completely disagree on this one. The Lorentz math is no more a convention than the inverse square proprtionality in gravity and electrostatics. There is no other possible expression. This is a description of fundamental aspects of reality and physicists of Andromeda would inevitably discover the same expressions although undoubtably with different conventional units.But the reason for that is convention as well. It's based on the SR simultaneity convention. If the proper length of my spaceship is 20 ft long, and an observer in relative motion at 0.6c measures the spaceship length by using light signals, he would use the SR simultaneity convention to determine the location of each end, and determine the ends to be 16 ft apart at a specified moment. Assuming a constant invariant light speed, the length of the ship in the other frame is 16 ft by convention. Length contraction is a result of convention, and invariant light speed.Only in the same way as the standard method for converting inches to cm. The SR simultaneity convention, like other conventions, isn't a law of physics.

ThanksThese conventions are used in a physical theory not as claims, but as useful tools. Alternative conventions could be used, and the final results would be the same, if the theory using the other conventions was otherwise equivalent to SR/GR.