Dear Remi Cornwall,

I think you understand my question in a wrong way. For example suppose a train at rest, when the velocity of the train changed from zero to v, then according to the concept of quantum physics and the quantization of energy, the train absorbed an energy of frequency f1, and then it will move with kinetic energy equivalent to hf1, and then if the train absorbed another energy of frequency f2, then it will move with velocity equivalent to kinetic energy h(f1+f2). Now where is the concept of classical acceleration according to the point of view of quantum physics and the concept of quantization of energy. The Goal of my question is to understand the equivalence principle of Einstein in GR according to the point of view of quantization of energy. Is energy continuous in the case of classical motion, and thus in case of uniform acceleration as in classical physics, the particle will move in a continuous path 1/2at^2, and then what is the formula of the relativistic quantized Newton's second law? In stead of inform me about the de Broglie relations, it is more interested inform me about the Schrodenger equation, and how it is related to the equivalence principle in GR according to my question.

Interesting and important discussion. 

If the mean value of the momentum of the particle is time dependent then the time derivative of this mean value gives you acceleration or decceleration. Otherwise, you can not speak about it.

Dear Remi Cornwall,

The problem is in the interpretation of Einstein to the Lorentz transformation according to objectivity.

Objectivity means "event occurs, then it occurs for all observers" Event is independent of the observers. For example suppose a plane flies from London to Paris in a constant speed v. Now ignore the concept of classical acceleration or deceleration, because it is related to some thing in quantum. Now according to objectivity, when the plane flies from London, then the plane flies from London for the observer on the ground, and for the Pilot of the plane. And when the Plane arrives Paris, then the Plane arrives Paris for the observer on the ground and for the Pilot of the plane. Both the observer on the ground and the pilot on the plane will agree at the location of the plane at any point in space between London an Paris, and from that it is resulted the continuity as observed according to objectivity for both the observers on on the ground and on the plane basis on symmetry. Symmetry is only to keep on objectivity.

Basis on objectivity Einstein defined the Lorentz transformation depending on the concept of the relative simultaneity and the constancy of the speed of light depending on the difference between two events in space and time, which resulted the concept of space-time continuum. The Minkowski diagram provides an illustration of the properties of space and time in the special theory of relativity basis on objectivity which leads to continuity. So in GR by the equivalence principle we confined with objectivity and the Lorentz symmetry which leading to continuity, and from here it is resulted the confusion of seeing photon of spin 1 mediates gravitation, and there is no graviton of spin 2.

Dear Nuri Ünal ,

yes I mean value of the momentum of the particle is time dependent then the time derivative of this mean value gives you the force, not acceleration. This force must be defined as quantized and relativistic. Quantized means defining the force in terms of frequency. The approximate form of the relativistic quantized force in case low change in the velocity (classical) -where the change in the relativistic mass is negligible- will give you 1/2 the Newton's force. Because of that in order to define the classical acceleration from the quantized relativistic force, you must multiply the  acceleration derived from the quantized relativistic force by the factor of two. Since Einstein depended  in his equivalence principle in GR on the concept of classical acceleration, because of that you find the factor of 2 in the Schwarzschild solution in the Lorentz factor. And since GR is not relativistic, you think the Schwarzschild radius is 2GM/c^2 not GM/c^2. And why according to GR graviton must mediates gravitational not photon, while photon mediates gravitation, and there is no graviton.

Remi, 

I think you need to grasp. Do you mean I need to grasp why Einstein must be right? There is no path in QM, there are conjugate pairs subject to the uncertainty principle. How that related and violates the Einstein interpretation to the Lorentz transformation equations in SRT, and then how the concept of acceleration is related to that according to the equivalence principle of Einstein in GR. This what I try to let you understand.

Read my paper and then we can discuss. "The Quantization of General Relativity: Photon Mediates Gravitation" http://dx.doi.org/10.14299/ijser.2014.10.002

Let's study this thought experiment of Einstein!

Suppose a plane flies from London to Paris in constant speed v . Now According to SRT, the observer on the ground and the observer on the plane are agreed that plane flies from London, and when the plane arrives Paris, they will be agreed that the plane arrives Paris. They agree that the plane arrives at any point in space within the distance between London and Paris. Because of that and under the postulate of the constancy, of the speed of light and the Lorentz transformation equations, the length of the plane must be contracted in the direction of the velocity of the plane, and according to the reciprocity principle, the distance between London and Paris must be contracted.

Now if we consider the Lorentz contraction is not exist in the length of the moving plane, but it exists in the passed distance of the moving plane for the observer on the plane comparing to the measured passed distance of the plane for the observer on the ground because of the effect of the time dilation. Suppose the velocity of the plane is 0.87c. Thus if the observer on the ground sees the plane arrives Paris, then according to our postulate, the observer on the plane does not see the Plane arrives Paris yet, it is still in the middle distance between London and Paris. And in order to keep on the constancy of the speed of light Locally for all observers, we must multiply the y and z coordinates by the Lorentz factor, and by removing the reciprocity principle, we get disappearing all the paradoxes in SRT. In this case space is invariant, and thus both the observers on the ground and the observer on moving plane will agree at the measured distance between London and Paris, and they will agree also at the length of the moving plane in x,y and z same if the plane is stationary. During the motion of the plane in constant speed v, it is impossible that both observer on the ground and the observer on the moving plane agree that plane arrives at the same point in space between London and Paris at the same time, and this is the core of the Heisenberg uncertainty principle when we deal with the four vector according to our new transformation. According to our new transformation the Lorentz transformation becomes vacuum energy dependent. When the observer on the ground sees the Plane arrives Paris, and then he could stop the plane, where the plane's speed becomes zero, in this case the observer on the plane finds his plane arrives Paris, where his Plane transformed from quantum state of motion when it was in the middle distance between London and Paris to the stationary state in Paris in a zero time separation. And because of the effect of time dilation and according to the clock of the plane, the measured speed the plane passed the distance between London and Paris if the velocity of plane was 0.87c is 1.74c which is faster than light which is not true but depending on the effect of time dilation. According to our new transformation the concept of acceleration or deceleration becomes vacuum fluctuations, which is related to gaining energy or loosing energy of frequency f, and that is clear when dealing with the four vector according to our new transformation. Where according to our new transformation when the plane stopped, then it lost all of its kinetic energy which is equivalent to hf. it is same from transforming from quantum state to other quantum state, and that leading to vacuum fluctuation. According our new transformation, we removed the Lorentz symmetry, but we keep on the Lorentz invariance.

Now it is easy according to our new transformation the quantization of gravity and understand how photon mediates gravitation by our new transdormation

Dear Dr. Azzam,

Your question is profound, as usual.  It would make an exciting kick-off for a thorough discussion of the issues involved in a classroom of advanced students.  In response to it, I would like to mention very briefly the following points.

First, the concept of acceleration is very well-defined in SR; otherwise, the theory would not have survived, in A. P.  French's words, "a bump on the road"!

Second, it is equally well-defined in QM; otherwise, what would all these particle-accelerators in CERN and elsewhere be doing? For, the analysis of the collisions involved, which is undertaken routinely on a daily basis, stands on both QM and SR.

Third, the concept of path or trajectory is again well--defined in QM; otherwise the path-integral formulation of the theory would not make sense.  True, the concept is 'fictitious'; but so is that of momentum space and phase space for that matter.  The point is that, instead of using equations of motion and kinetics in the Newtonian sense, you use here energetics in the Lagrangian and Hamiltonian sense.  The full story behind all this is well-known, of course.

So, there it is!

Kindest regards.

Dear Dr. Humam B. Ghassib,

SRT is for an inertial frames of reference and it is not related to accelerated frames. relative to the definition of the acceleration in quantum physics and then in Cern is related to absorption or loosing energy only. Where if a particle absorbed an energy of frequency f1, then it will move with kinetic energy hf1, and if it absorbed another energy of frequency f2, then it will move with kinetic energy h(f1+f2). Now according to SRT and because of SRT is for none accelerated frames, it is only concerned for the kinetic energy which is related to hf. Here where is the concept of acceleration which is adopted by Einstein in his equivalence principle in GR. The collision is related to gaining energy or loosing energy hf which is quantized, and then it related to changing velocity according to changing energy.

Here is the idea; Since repulsion and attraction in electromagnetic mediate photons of spin 1, in this case the new equivalence principle must be related to changing velocity according to changing energy by absorption or loosing energy of frequency f. In this case Newton's second law must be defined in terms of frequency, that means it must be quantized and relativistic, and thus the inertial force must be defined as relativistic and quantized. In this case you get by the equivalence principle the escape velocity must be relativistic also and it depends on the amount value of the rest mass of the free fall particle under gravitational field that changed to photons, these photons let the free fall object to move in a relativistic speed equals to the relativistic escape velocity. In weak gravitational field this velocity can be approximated to the classical form of escape velocity, But in strong gravitational this speed is relativistic. GR is not completely relativistic. Review the Pond-Rebka experiment, and why the gravitational time dilation is equivalent to free fall object in gravitational field as moving with the escape velocity.

Believe me and trust in me; The problem is related to the interpretation of Einstein to the Lorentz transformation basis on objectivity and continuity. And then when he generalized his interpretation according to his equivalence principle which violated by many experiments, it is resulted the problem in quantization of gravity. Because of that according to GR it must be graviton of spin 2, not photon of spin 1.