Dear Peter,
I hope you are well. Before I address the problem with inertial frames, let me state: Frames of reference in which Newton's first law (law of inertia) holds are inertial frames. You may mean something else by inertial frames, which would explain my 'confusion'!
The purpose of my 'thought experiments' was to bring a certain problem within GR to your attention, as your theory deals with inertial frames. The problem is this:
Freely falling frames anywhere in our real, gravity-endowed Universe, are equivalent to inertial frames in an idealised, gravity-free universe. The problem is that Einstein ignored tidal gravity, and 'justified' this by insisting that the reference frame be very small. However, Hans Ohanian (H.C. Ohanian, "What Is the Principle of Equivalence?" American Journal of Physics 45 (1977):903-909) has shown that tidal effects persist even when the object in question is arbitrarily small. An observer in a freely falling elevator could in principle deduce that he is in a gravitational field by detecting tidal bulges in a liquid drop. In other words inertial (gravity-free) frames do not in principle exist.
I don't know if detecting tidal bulges in a liquid drop is consistent with your use of inertial frames. Perhaps it is but I am just to blind to see it.
In any case here is how my theory addresses this problem.
Newton's three laws:
1) First law (law of inertia): Every body continues in its state either of rest or of moving uniformly unless acted upon by a net force (F=0). (What about the force of gravity?)
2) Second law: The rate of change of the momentum of a body is proportional to the force acting and takes place in the direction of that force (F=dp/dt=ma).
3) Third law: Forces are caused by the interaction of pairs of bodies. The force exerted by A upon B and the force exerted by B upon A are equal in magnitude and opposite in direction (F=-F).
Laws 2 contains all of Newton's laws of motion as shown, and the laws of motion were necessary for Newton's 'discovery' of the 'force of gravity' to correctly account for Kepler's 3 laws.
Now, Law 2 is what we get when we 'mathematically differentiate' Newton's definition of momentum p=mv. Thus Newton's laws of motion, and hence law of Gravity, ultimately depend upon the 'existence' of p=mv! In my paper I have shown that p=mv disappears of its own accord, given the de Broglie equation, and consistently that F=ma disappears to leave us with a = g, given 'the Light'. Thus the absence of Newtonian mechanics means inertial frames ARE fictitious. What then of SR? In the subatomic realm, where gravity (space-time 'curvature') is negligible, 'the Light' supersedes SR. Both 'the Light' and a = g (the foundations of Relativity) NECESSITATE the observer detect tidal bulges in a liquid drop!
I hope this brief explanation gives you a better understanding of my paper. If your theory also necessitates the 'tidal bulge in a liquid drop', then our theories share common ground. The problem (as I see it) is that in order for your inertial frames to exist, tidal gravity must be nonlocal, contrary to the above. Am I wrong?
All the best old friend,
Robert
All the best
