V.6 No 1 73 The problem of physical time in today physics
 6.4.2.3. The features of revelation of inertial forces in a freely falling reference frame in a homogeneous gravity field As we showed in the previous subsections, the phenomenology of physical processes in non-inertial frames generally does not corroborate the hypotheses which Einstein has put forward to substantiate the general theory of relativity. And if Einstein based on some premises, we can surely say, he built his premises namely on the regularities that reveal themselves in the homogeneous field of acceleration, and regularities described not from the view of relativistic conception but just on the basis of classical formalism. To show it, consider from two points of view – relativistic and classical – a trivial problem of some amount of masses in an external homogeneous field of gravity, how the conservation laws work in passing from the inertial frame to that non-inertial that falls in this field together with masses. Begin with the classical representation. Let in some region of space that is under affection of a homogeneous gravity field, there is located some compact amount n of masses mi , i = 1. 2, 3, ... , n each of which at the initial moment of time t0  has the velocity  'i  relative to the freely falling reference frame S' . The frame S'  and the considered masses move relative to the inertial frame S with some acceleration caused by the mass forces – for example, with the axis x, and this additional velocity rel = gtx  is same at each moment of time both for the frame and studied bodies. So from the view of classical physics, if in the frame S'   the impulse of each body was
 (6.34)
 then in S
 (6.35)
 Noting that from the view of classical physics
 (6.36)
 we yield from (6.35)
 (6.37)
 Thus, if in one frame the law of impulse conservation
 (6.38)
 is true, where 1 and 2 denote the sum of impulses before and after some process occurring in this frame, then in the another frame, according to (6.36), the equality
 (6.39)
 will be true, too. Since on one hand
 and on the other
 joining the yielded expressions gives (6.39). Similarly, from the point of classical physics, we, basing on the energy conservation law, may not select a non-inertial frame being in the homogeneous field of mass forces. To show it, consider the same amount of n masses. Let the total kinetic energy of the amount of bodies, before some interaction in the resting frame S be equal
 (6.40)
 In passing from one frame to another, in classical physics we vectorially subtract the velocity of frame having the same value rel  from the velocities of all bodies, so for the total energy in the freely falling frame S'   we will yield
 (6.41)
 From (6.40) and (6.41) it automatically follows that if in one frame the energy conservation law was true, then, noting that all bodies of the studied amount have an additional velocity together with frame S'  , in the moving frame the energy conservation law will remain. Actually, let in the resting frame the energy conservation law is true; then we may write
 (6.42)
 where, as before, 1 and 2 mean the total energy of the system before and after some process. In (6.42) we can transform the left part as follows:
 (6.43)
 and the right part, relatively:
 (6.44)
 Now, to yield from (6.43) and (6.44) the energy equation for the moving frame, we only have to account that the second summands in the right parts of these expressions are equal and the third summands are equal, which follows from the conservation of the impulse of system. So we yield
 (6.45)
 We also see from (6.43) and (6.44) that if in passing from one frame to another the law of impulse conservation is not true, the law of energy conservation will be untrue, too, as the situation is impossible when in some formalism one conservation law is true and another is not. Both laws must be true or not. It also follows from our consideration that in the inhomogeneous gravity field, in passing between the inertial and non-inertial frames, the conservation laws will not be in such agreement with each other, as each of considered bodies will have its own acceleration of free fall proportional to the strength of gravity field at the place of location of this body. As the value of this acceleration for separate bodies will not be same as the acceleration of the frame’s origin, in (6.39) and (6.45) the non-compensated summands will appear, and they will make the frames non-equivalent. And in the relativistic formalism this correspondence, even approximate and even in the homogeneous gravity field, is not true. We can easily make sure of it if we consider the same conservation laws for impulse and energy in limits of this conception. Let us begin with the conservation law of impulse of the system of bodies. The law of impulse conservation to remain true in passing from one frame to another, two conditions have to be satisfied: – the conservation law has to be true in the initial frame; – the transforms have to remain the parallelogram law. The Lorentz transforms and Einsteinian kinematics satisfy neither. Actually, let at some, even inertial, frame some amount of bodies moves arbitrarily and their trajectories cross each other in extrapolation, which implies interaction between these bodies. And let the total impulse before the interaction be
 (6.46)
 “Relativistic mechanics proceeds from the premise that in the coordinate system K' , in which the material point is resting at the considered moment, the following equations of motion of old mechanics are true:
 (6.47)
 [23, p. 170]. It immediately follows from this that if at the next moment of time the material body has gained the speed (which is predestined by the equations of motion (6.47)), then (6.47) is already untrue. Nothing to say of considered problem where we consider some amount of material bodies moving with different speeds which we cannot think resting in this frame even at the initial moment. Really, “… introducing the hypothesis that the mass mv   depends on the energy, which means – also on time, we encounter the difficulty that for this case the equations of mechanics are already unknown; the first equality in the relationship
 (6.48)
 is already untrue. None the less, we have to assume that the difference
 (6.49)
 is in proportion to the second order of speed. So, if all speeds are so little that we can neglect the second-order terms, in the change of mass mv  the equation
 (6.50)