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The question of the reality of motion and the Lorentz effects came up again in a recent thread where it was correctly pointed out that these subjects often devolve to arguments of semantics and subjective interpretations.

It was also suggested that frame independence was a criteria with a more valid objective meaning which certainly makes sense to me.

In that light I am going to attempt a basis for discussion of the reality of inertial motion.

Given:

A) AN arbitrary inertial observation frame Lab.

B) An inertial system F'(ast) moving 0.7c --->+x wrt Lab

C) Inertial system S''(low) moving 0.3c -->+x wrt Lab

D) At Lab (0,0)..... F' is passing S'' and at this point of coincidence both systems initiate equal proper acceleration as determined by onboard accelerometers.

E) From this point Lab simply tracks and lpots the course of acceleration of both systems F' and S''

Premises:

1) As measured in L the initial coordinate acceleration of both systems would diminsh by a factor of [tex]\gamma[/tex]^{ 3}

Coordinate acceleration eventually falling off to the practical limit of 0 . Further measurement of changes in instantaneous velociities requiring such huge intervals, both spatially and temporally, as to be uneasonable.

If we call this point T (erminal) then the interval from initial acceleration to T for F is then T'

and the comparable interval for S'' is T''

2) That measured in Lab the (dt,dx) of (S) T'' will be longer than the same for (F) T'

This would seem to be reasonable if we assume the two systems equivalent to two systems starting out at rest in Lab with the same constant proper acceleration and identical overall (dtt, dx) in which case F would be a system having already traveled a greater percentage of this total course with a comparably smaller percentage left to reach T' than system S''

3) That all possible observing inertial frames would agree that S'' took a longer time and over a longer distance to reach T'' than F' took to reach T'

There are clearly any number of systems that would measure S''(low) as having a greater relative velocity than F'(ast) but as far as I can see they would all still agree that the overall course of acceleration was longer for S''

If I have not made some huge error in thought in the above it would seem to indicate a basis for the statement F' was initially traveling inertially at a different velocity than S'' at Lab (0,0).

Not based oin any quantitative relative measurements of velocity but on the physics of the subsequent acceleration. In would appear that all frames would agree that S'' required more energy to acheive T''

and required more time and distance to reach that point.

This would seem to be a strong argument that there was some unquantifieable but still real difference in their initial states of inertial motion . perhaps??

There is the question of T and this point contains a degree of indefiniteness when applied to frames that were already approaching c -->+x and their measurement of acceleration falloff as well as the question of unlimited proper acceleration.

a)This would also apply as far as measuring any acceleration from those frames in the case of the frame independance of acceleration and the assumption of its reality wouldn't they??

So any comments or areas where I have gone astray???

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# REAL inertial motion?

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