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During discussions in other threads I have been coming to the conclusion that the idea proposed here may be true.

Consider a plane with constant z coordinates. All measurements of length are made relative to the x and y coordinates that lie on the plane. It seems that all measurements of length, time, velocity and acceleration (linear or angular) that are made entirely within the plane, by observers that remain on the plane, are independent of any linear velocity

Extensions:

a) This remains true even if the plane is rotating with constant proper angular velocity.

b) This remains true if the observers on the plane are moving relative to the plane (as long as they remain on the plane).

c) This remains true even if observers are accelerating relative to the plane (as long as they remain on the plane).

d) This remains true even if the observers are undergoing circular motion relative to the plane around an axis orthogonal to the plane.

e) It may be possible to extend the idea to higher derivatives of motion.

Of course angular motion that has tangential velocity parallel to the plane has an angular velocity vector orthogonal to the plane, but for the purposes of this idea, angular motion with tangential velocity that remains in the plane counts as a measurement on the plane.

This hypothesis has far reaching claims and would greatly simplify many relativistic calculations and proofs if true. Can anyone think of any counter examples besides the implication that it is denied by the Hergotz-Noether theorem which is under discussion in other threads currently?

I think it will be an interesting discussion to discuss where some of the extensions fall down, which extensions may be valid and where there are issues, how they can be 'made to work'. I think any conclusions that remain valid (even with additional qualifications) will be make it a useful hypothesis.

This hypothesis can be thought of as extending the accepted clock postulate http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html in ways that have probably been done instinctively in the past as part of other work, but never as a subject in its own right.

Consider a plane with constant z coordinates. All measurements of length are made relative to the x and y coordinates that lie on the plane. It seems that all measurements of length, time, velocity and acceleration (linear or angular) that are made entirely within the plane, by observers that remain on the plane, are independent of any linear velocity

**or acceleration**in the z direction.Extensions:

a) This remains true even if the plane is rotating with constant proper angular velocity.

b) This remains true if the observers on the plane are moving relative to the plane (as long as they remain on the plane).

c) This remains true even if observers are accelerating relative to the plane (as long as they remain on the plane).

d) This remains true even if the observers are undergoing circular motion relative to the plane around an axis orthogonal to the plane.

e) It may be possible to extend the idea to higher derivatives of motion.

Of course angular motion that has tangential velocity parallel to the plane has an angular velocity vector orthogonal to the plane, but for the purposes of this idea, angular motion with tangential velocity that remains in the plane counts as a measurement on the plane.

This hypothesis has far reaching claims and would greatly simplify many relativistic calculations and proofs if true. Can anyone think of any counter examples besides the implication that it is denied by the Hergotz-Noether theorem which is under discussion in other threads currently?

I think it will be an interesting discussion to discuss where some of the extensions fall down, which extensions may be valid and where there are issues, how they can be 'made to work'. I think any conclusions that remain valid (even with additional qualifications) will be make it a useful hypothesis.

This hypothesis can be thought of as extending the accepted clock postulate http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html in ways that have probably been done instinctively in the past as part of other work, but never as a subject in its own right.

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