a reference to relativity
The twisted string theory doesn't seem to be related to the general or special theory of relativity. The world of twisted strings is completely undisturbed, straight and without forces or fields.
On the contrary, the development of the twisted theory started with the strange behaviour of the curvature of spacetime. I struggled with the idea, if the Planck constant could also be disturbed. What would be the consequences and how could this be verified? There is a clearly evidence, that the physical principles across the universe must be the same. The Planck constant should also be the same at every point. But if the constant is related to distortion, then the physical principles are still the same, but the Planck constant would be a function of the distortion of the surrounding spacetime. If the spacetime is disturbed the Planck constant is higher, if there is fewer distortion its decreasing.
A hint is the formula of the Planck-Einstein relation
\[ E = h f \]
and the distortion of the frequency by the relativistic Doppler effect. The special relativity claims the curvature of space time for the frequency shifting. But if there is just a distortion of objects itself and the space is always completely undisturbed, the only possibility to disturb the frequency of a photon by a given energy is to change the Planck constant.
If there is a minimum of an undisturbed Planck constant, this would be the base of an inertial frame of reference that should be intermediate between all other inertial frames of references, even if there are accelerated.
Now we have some nice questions and an initial point to start.
The basic assumption of the special relativity is, that a relativistic moving object will be disturbed by the Lorentz transformation, while the lengths of its inertial frame of reference shrinks. The distortion exists only in the inertial frame of reference of the observer, the inertial frame of reference of the relativistic moving object stays undisturbed.
Because of this strange behavior the passage of time between a relativistic moving object and our slow motion world has to be different. That is not common sense, but nobody expects a regular behaviour of a relativistic moving object.
It looks like the distortion of space time is outside the object and the space time is treating the object. But if the structure of the object itself is disturbed, there is no need for an outside impact of space time any more. It's obvious that increasing kinetic energy could disturb the structure of an object. If there is an interaction between stored kinetic energy, distortion and gravitation, then a moving object is not treated by space time, its manipulating its environment. For calculating the effects of gravitation and time dilatation, this question doesn't matter. But if you are looking for the mechanics, that causes this effects, it's crucial.
In this case a variability of the Planck constant would yield to a minimum for the stationary object and a maximum for the relativistic moving object.
If we assume, that the space is always undisturbed and only objects itself can be disturbed, then the relativistic object has to be at most disturbed. But the inertial frames of references doesn't fit and there is a need for a disturbed space time.
The trapped momentum theory assumes, that only the free moving of a particle reveals the undisturbed momentum. That means, a standstill is a disturbed state, because there is a force that cushions the momentum. That sounds reasonable, because a straight movement of a short distance should be the exact opposite of a distortion.
Let's flip the whole thing.
relativistic motion as the only undisturbed motion
A standstill is the maximum of a distortion and acceleration decreases the distortion. Just particles moving by speed of light are not disturbed.
But the theory of trapped momentum has a more complex explanation. A standstill has a distortion and it could be described by a perfect sphere. Motion disturbs this shape and the distortion increases. The higher the speed, the more particles will escape from the accelerated cluster. The cluster will radiate, disintegrate and its distortion shrinks. This effect is called Lorentz contraction and the length of the inertial frame of reference are shrinking because of the omission of the uncertainty.
The measuring of the photon is disturbed by the uncertainty of the observer.
Disturbed object are oscillating. If a disturbed observer is measuring a traveled distance the value should increase. But the distance for an undisturbed photon stays short. An object isn't disturbed by space time, it is the uncertainty of the observer, which is influencing the measurement and produces the image of a disturbed object.
The train example: We are not watching at the train, we are sitting in the train of uncertainty and are watching through the window at the undisturbed photon.
the Planck constant is not a constant is disturbed by our space time. The Doppler effect of light describes the distortion of our space time of the Planck constant.
trapped momentum and uncertainty
The basic idea is to find a relation between shape, distortion and constant motion without the construct of a disturbed space time. The reason is simple. If there is a relation between shape and motion, a distortion of shape will cause motion. The difference between the special relativity and the trapped momentum is the source of the momentum. Is it the surrounding space time, that alters the momentum, or is it a distortion of an object itself? The trapped momentum theory tries to explain the relativistic effects with a different mechanism. Not the surrounding space time is curved, but each trap of momentum.
The trapped momentum theory describes the relation between shape and motion as proportional. This effect is derived from the constant momentum.
A standstill object is a cluster of trapped momenta, but the vector sum is zero. Such an object could just freeze. This would happen if all trapped momenta are oscillating by chance. But clusters are the result of a disturbed chaining process and these distortions resulting in at least one unbalanced part. Every cluster of trapped momenta has sources of unbalanced oscillations. That causes a shaking of the whole cluster [A].
If a cluster is accelerated, the shape of the traps in the moving direction shrinks. The cluster itself shrinks and this causes the switch of the inertial system, because the measured length are now disturbed and have to be rectified by changing the inertial system. Because of if this adjustment, the distances of the front and the rear shrinks and objects get disturbed [B]. The more a cluster is accelerated, the more the shape is forming a vector. The motion get less and less undisturbed [C]. But only the motion of a free moving particle is completely undisturbed [D].
the frame of reference
The underlying theory is a world of quantum matter. This has to be the frame of reference and it has to be the place, where a photon is moving at the speed of light.
This approach contradicts the general and the special relativity. But the frame of reference is the special case for undisturbed moving objects like a photon. All other standstill shaking or moving objects are exposed the effects of relativity.
what about the constancy of the speed of light?
The constancy of the speed of light is crucial. It is the fundamental verified fact on which the special theory of relativity is successfully founded. But this approach should predict a velocity of the light in relation to the observer. Sounds like the death knell for the twisted string theory.
The solution is, that the acceleration is disturbing the measurement of velocity. The trapped momentum theory says, that motion shrinks the distortion shape. This is the crucial factor of an inertial frame of reference. All objects belonging to this inertial frame, like an observer, measuring devices or a "racing track" for measuring velocity, are shrinking. The distance between the start and finish line decreases. Hence the velocity of any object should increase. But simultaneously the observer, the measuring devices and the "track" are moving during the measurement. The distance of moving is exact the length of the decreasing measuring line. This proportional relationship is the core of the trapped momentum theory and is derived from the constant momentum. The measurement of a photon stays constant. That's comprehensible, because the motion of a photon is undisturbed and straight, it is just a vector.
The effect of the measurement of disturbed objects is complicated, because the "race track" of the velocity measurement and the real motion observed from an hypothetical undisturbed photon and its frame of reference is not a line or a track, but a very complex oscillating scene. The measurement of an disturbed observer of an oscillating moving object depends on the involved distortions.
inertial frame of reference
Observers measure everything in their inertial frame of reference, but this is nothing else than a shared distortion. When a distance shrinks, not the space is contracting, only the measuring is less disturbed. And there is a real distance, which only a photon would see correctly. There is an absolute reference for all inertial frames.
Each inertial frame of reference can have different sources of distortions. One or more distortions by gravity, the moving of gravity. Electromagnetic fields, Kinetic. There are unlimited sources and their temporary modification and interaction with other sources .
The absolute frame of reference of a photon [A] , a standstill cluster [B] and a cluster moving in a gravitational field [C]. It is just a two dimensional perspective.
[A ↔ B] The photon and the standstill cluster are seeing each other as a shaking point. While photon is undisturbed, the cluster is permanently moving.
[A ↔ C] The photon and the gravitational disturbed cluster are seeing each other a oscillating wave. But the wave length depends on the gravitational distortion. If the gravitational field is moving, the wave length changes.
[B ↔ C] The standstill and the disturbed cluster are seeing each other as two superimposed waves. If the gravitational field is moving, one of the wave length changes.
In a three dimensional world the observed oscillations are transformed to helixes.
Minkowsky space and uncertainty
The forth dimension of the Minkowsky space isn't time, but it is distortion and it is a shape.
The distortion of the referential inertial frame of an undisturbed moving object is zero. The distortion of a nearly standstill moving object is the Planck constant and it is nearly a sphere.
All object of an inertial frame of reference are disturbed, thus a time measuring device also will be disturbed. If two observers are moving in different inertial frames, their clocks will measure their disturbed time. If one of them visits the inertial system of the other and they compare their watches they will see different times. The effect of time dilatation still exists.
But there is a frame of reference and there could be assigned a reference time for each disturbed measured time. The problem of simultaneity is solved.