Real Inertial Motion: A Discussion of Frame Independence

[Austin0]

REAL inertial motion?

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 \gamma 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 achieve 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?

 

[Passionflower]

Apart from the fact that you really should quantify T, I get the impression based on several of your postings, that you really have not fully come to terms with the fact that inertial motion is completely relative.

In other words if A accelerates away from B it does not make one shred of a difference how fast B moves with respect to C, D or whatever other frame you fancy. Second, while proper acceleration is absolute, inertial acceleration is not, different frames can 'see' different inertial accelerations in relation to the same object. But they would always agree on the rate of proper acceleration for that object.

 

[Austin0]

Apart from the fact that you really should quantify T, I get the impression that you really have not fully come to terms that inertial motion is completely relative.

In view of what you have written below , why would it be relevant to quantify T??
The point is not what any particular frame would calculate the short interval acceleration to be.
It is based on the assumption that all frames would agree when the systems went from inertial states to accelerated states and would agree when they reached a point of extrme reduced acceleration.
Then a comparison of the spacetime interval between those points . Not agreement on the quantitave interval but only on the comparative interval. The interval observed for S'' being longer than the interval for F'
If you will notice I made NO statements whatever regarding the quntitative relative measurements of relative velocities and suggested absolutely no conclusions inconsistent with the relativity of velocity measurement.

In other words if A accelerates away from B it does not make one shred of a difference how fast B moves with respect to C, D or whatever other frame you fancy.

What possibly gives you the idea that I am basing anything at all on the type of relative measurements youare referring to here?

Second, while proper acceleration is absolute inertial acceleration is not, different frames can 'see' different inertial accelerations for the same object. But they would always agree on the rate of proper acceleration for that object.

by inertial accelerations I assume you mean coordinate accelerations?
In any case once again the quantitative evaluation of rates is irrelevant.
The only important factor is the purely comparative evaluation of the total space and time interval for the complete acceleration course for the two systems.

 

[Passionflower]

by inertial accelerations I assume you mean coordinate accelerations?

An observed acceleration between an inertial test observer A and an unknown test object B. In flat spacetime this implies B undergoes a proper acceleration, in curved spacetime B could have undergone proper acceleration or it is caused by spacetime curvature (or both).

For now I will get out of the way and give others a chance to comment on what you have written.