- #1

Grimble

- 485

- 11

*local*time scale, that measured by a stationary, local obsever, situated at the origin of that frame's coordinates compares with the local time scale of another IFoR

The coordinates of any Inertial Reference Frame, employing stationary clocks, will be measured in proper units and have the same magnitude in any such frame.

A stationary clock situated at the origin of the frame's coordinates will, by definition, measure proper time.

The distance from that clock to any other stationary clock showing the same time, in that same frame of reference, will, by definition, measure proper distance.

It has to be the same in any IFoR for the following reasons:

i.If two IFoRs are at rest with one another they are both effectively in the same IFoR and share the same proper time.

ii.If they are moving relative to one another, i.e. have a relative velocity, each can still be considered to be at rest and must, therefore, still measure the same proper time.

iii.Every IFoR obeys the same simple physical laws, therefore identical, synchronised, clocks situated in such frames must keep identical time.

iv.If the proper time in IFoRs COULD be anything other that identical, then the differences could negate the need for Special Relativity! As any conflicts between Einstein's first and second postulates could, possibly, be explained by the differences in the measurements of time.

v.The proper times of two IFoRs can be calculated from a third IFoR by means of the Lorentz Transformation equations; and, if that third IFoR was permanently positioned at the midpoint between the two IFoRs in question, those calculated proper times would have to be identical. Otherwise we would be contravening the Special Principal of Relativity, Einstein's 1st Postulate, - The laws of physics are the same in all inertial frames of reference, in other words, there are no privileged inertial frames of reference.

vi.If two IFoRs are moving with a constant relative velocity with respect to one another, then the movement of one, being a combination of time and distance relative to the second, must be the reciprocal of the movement of that second one with respect to the first. Therefore they must be using the same proper units.

I don't know whether this will be considered to be ATM or not, but no doubt some will claim so, but to me it is what Einstein described.

Grimble