Quantum is not only "uncertainties". Quantum also means quantum correlations, which are able to violate Bell inequality, So any local classical theory could not reproduce quantum correlations. Relativity theory is local classical theory.

quantum mechanics was initially formulated without any use of Special nor General Relavity.  Dirac once suggested that the electron spin which appears in his Dirac equation was a consequence of special relativity but this was shown to be false by Feynman and reiterated by J.J. Sakurai.  General Relavity and quantum mechanics are actually axiomatically incompatible: that is why for almost a century we have created superstring theory and loop quantum gravity in attempts to reconcile them.  The closest I have every seen in a derivation of quantum mechanics was in finding out that a gravitational dilaton was governed by a Schroedinger equation but none of this stuff explains the uncertainties resulting.  These results come from Poisson bracket relations where quantization, a conerstone of quantum theory, applies.  

Although some aspects of quantum uncertainties in principle can be modeled by some ingenious classical systems (hidden variable models), this is not always possible if one restricts to local interactions only (as required by causality in relativity theory). Any classical hidden variable model with local interactions would obey the Bell inequalities, which are experimentally observed to be violated. 

No-Planck's constant, that controls quantum effects, is independent of the speed of light, that controls relativistic effects. 

Quantum Field Theories attempt to make the connection you asked about, but have not succeeded so far because of disagreements between General Relativity and Quantum Mechanics about how much energy is contained in space compared to the observed cosmological constant. I have proposed a remedy in Vacuum Partition Theory such that stress energy is partitioned into nearly equal amounts of gravity like curvature and reversed curvature, giving a small net cosmological constant. It is not widely accepted or discussed. http://vixra.org/abs/1512.0277

Remi, you shouldn't seriously bother about historical statements from anyone who claims that for almost a century we have created superstring theory and loop quantum gravity.

To Remi Cornwall: I am stuck in Taiyuan China and cannot readily access the reference but you will find it in J.J. Sakurai's book "Advanced Quantum Mechanics"  (not to be confused with Sakurai's other books).  Therein Sakurai presents an alternative derivation of the Dirac equation.  

To continue with Remi: I have lecture notes taken from Sakurai which explains the gist.  I will be happy to email them to you if you give me an email address.

Tony, this is not Sakurai's 'Modern QM' Revised?  Just want to make sure your's is the correct title and that I do not have in my library. Thanks 

Answer to Mark S. Rogers.  No it isn't.  Sakurai wrote more than one book.  Sakurai's "Advanced Quantum Mechanics" covers the Dirac equation.  His modern QM book is mostly on basic non-relativistic quantum mechanics.  You can find Sakurai's "Advanced Quantum Mechanics" mentioned on-line.  I think Amazon.com has it.

Quantum is not only "uncertainties". Quantum also means quantum correlations, which are able to violate Bell inequality, So any local classical theory could not reproduce quantum correlations. Relativity theory is local classical theory.

Spin *is* a classical property of matter, just like mass, since it's one of the two invariants of the Poincaré group, that labels particles, independently of Planck's constant, the other being mass. What's a consequence of special relativity and quantum mechanics, is the spin-statistics relation, in four spacetime dimensions. Once more, historical evolution and technical content are two different things.

Dear Mark S. Rogers,

Yes you are right; quantum mechanics be shown to be an effect of a relativistic system. Read my paper http://vixra.org/abs/1509.0059

All of the comments which says no here, they are built on the Lorentz transformation. Lorentz transformation is not describing the motion well neither in gravity nor in quantum. The real transformation which describing the reality is 

x=R^2(x'-vt'), t=R^2(t'-vx'/c^2), y=Ry'  and z=Rz'

R is the Lorentz factor, and in this case speed of light is locally constant. In this case if you consider space is invariant as in my transformation, it is resulted this transformation is vacuum energy dependent, and it expressing exactly about the uncertainty principle, and globally the speed of light is vacuum energy dependent. 

According to that light have no aberration and only fields have one, and the constancy of light be suitable with Galilean transformations. 

So all the problems in physics now solved from Higgs to Galaxies. Also that illustrates to you why Aether field rejected by Michelson Morley experiment in 20th century, but now in 21st century Higgs field is accepted. 

In my interpretation to the Lorentz transformation I refuse the reciprocity principle which was adopted by Einstein in the SRT. Refusing the reciprocity principle in my theory leads to disappearing all the paradoxes in the SRT; the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship

paradox. Furthermore, according to my interpretation I could interpret the experimental results of quantum tunneling and entanglement (spooky action), Casimir effect and Hartman effect. My new interpretation to the Lorentz transformation equations leads also to the wave-particle duality as in quantum theory, and thus agrees with Heisenberg uncertainty principle.

So you are completely right in your comment, and for more information review my equivalence principle in my paper which expressing about the escape velocity of the free falling object under the gravitational field must be described as relativistic not classical as in Einstein's GR. In fact GR is not completely relativistic!!!!

http://vixra.org/abs/1509.0059

Azzam, thank you for your insight and kind words. I will give your paper my full attention. I also look forward to additional reviewer comments. 

Welcome Mark S. Rogers!!

I recommend also to read these 3 papers which are related to my transformation.

1- The Hafele-Keating experiment, velocity and length interval transformations and resolution of the Ehrenfest paradox, J.H. Field http://arxiv.org/abs/1405.5174

2- On the Origin of the Lorentz Transformation, Wolfgang Engelhardt

http://arxiv.org/abs/1303.5309

3- Classical and Relativistic Derivation of the Sagnac Effect, Wolfgang Engelhardt

http://arxiv.org/abs/1404.4075

These 3 papers are related to each other. All together illustrate to you how  light have no aberration and only fields have one, and the constancy of light be suitable with Galilean transformations as in my transformation.

Physics is very simple now, and quantum and relativity are one theory, each one will lead to the other.

Thank you again Azzam. By the way, do you have a comment on my above thought experiment. If this thought experiment is plausible, it should be possible to compute an gravitational analog length (or mass) to the Planck length when considering a large mass diameter of a gravitational 'system' such as Earth to a small mass object from my thought experiment. Yes/no?

Yes Mark S. Rogers!!!

And the uncertainty principle plays the rule in macro same as in micro. Actually what causing the light bending by gravity, precession, Shiparo delay and the Pioneer anomaly is the uncertainty principle, when we considering space is invariant and that computed exactly according to my theory. And thus the zero point energy explains the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius. As you see my transformation is vacuum energy dependent which lead to the wave-particle duality and Heisenberg uncertainty principle, and then photon mediates gravitation according to this transformation and my new equivalence principle in which acceleration equivalent to vacuum fluctuations. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well. Thus the zero point energy explains the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius. Also the dark matter explained.

If there is precession, then gravity must be viewed as a 'static' field absent of 'Waves' thoughts?

If quantum theory could b shown to be a consequence of relativity, then Einstein would not have wasted so many years in the search for a unified theory, and a satisfactory Quantum Gravity would have been developed a long time ago. I'm afraid that, for the moment , Relativity and Quantum Theory remain unassimilated opponents, in theory and in practice.

It's easy to misinterpret what I just said.  For 'static field' clearly I mean a collapsed 4-space geometry.  By static, I mean there's no radiating, oscillating, or rippling within any single gradient line.

Precession observed globally!

Here there must be a connection point between the location of the free falling bodies at a certain point in space in the gravitational field which is depending on the gravitational potential at this point in space, and when the particle observed globally changes his position from this point in space in the gravitational  field because of  the effect of free falling. This connection point must be related to the uncertainty principle, because here we are dealing with energy (gravitational potential) at a certain point in space at the gravitational field and the changing of the location of the object from the certain point in space in the gravitational field. Here if we want to consider time dilation where t' not equal to t as in Lorentz transformation. In this case space must be invariance but that is in contradiction with SCHW. 

But the fact that the SCHW solution cannot be applied for free falling bodies because the geodesic motion of massive bodies in a gravitational field simply violates the energy conservation law, the geodesic motion can work only with massless entities.

The violation of energy conservation law is resulted  from the violation of the reciprocity principle in Lorentz transformation, when computing the proper time when we considering time dilation. in this case we consider the Lorentz length contraction in one side ( for one observer) and then we  ignoring the Lorentz length contraction in the other side (for the other observer), and after that we proposing the objectivity and continuity in the macro world implicitly, and that violates the reality in the reciprocity principle in the Lorentz transformation. The  objectivity and then the continuity and the reciprocity principle in Lorentz transformation are one thing. There is no objectivity and then no continuity without the reciprocity principle in Lorentz transformation.

To solve this problem. we must consider space is invariant, and we must look for a transformation considering space is invariant.

Because of that Lorentz transformation does not describe the physical reality well neither in gravity nor in quantum physics. 

In fact motion in macro and micro world must be defined always according to 4-D and because of that the motion always  as observed globally  must be governed by the wave-particle duality and the uncertainty principle in micro  and macro. The problem here when you make a measurement at a certain point in space for the moving object, in this case the wave-function which describes the motion is collapse, and in this case it is translating from 4-D to 2-D, and in this case the uncertainty principle plays the rule.

That interprets the double slit experiment. As in my paper, Figs 1 & 2, every motion in constant speed v for micro and macro, are governed by two pictures are separated in space and time because of the effect of time dilation, but these two pictures are entangled with each others by the energy moment four vectors. According to these two pictures the motion are governed by the wave-particle duality. For me on the ground, I see one picture now according to my time on the ground, for example when the plane arrives Paris now for me. But there is another picture is hidden relative to me, which is related to where is the plane now for the observer on the moving plane according to his time. Here t' not equal to t (my time), and thus also x' must not equal to x. This interprets for you hidden variable theory.