Are Dark Matter and Dark Energy the result of uncalculated addition derivatives? The need to introduce dark matter dark and energy becomes unnecessary if we consider that, the phenomenon of dark matter and dark energy is a result of not computing the
additional derivatives of the equation of motion. For this purpose, we use higher derivatives in the form of non-local variables, known as the Ostrogradsky formalism. As a mathematician, Ostrogradsky considered the dependence of the Lagrange function on acceleration and its higher derivatives with respect to time. This is the case that fully correspond with the real frame of reference, and that can be both inertial and non-inertial frames. The problem of dark matter and dark energy presented starting from basic observations to explain the different results in theory and experiment. The study of galactic motion, especially the rotation curves, showed that a large amount of dark matter can be found mainly in galactic halos. The search for dark matter and dark energy has not confirmed with the experimental discovery of it, so we use Ostrogradsky formalities to explain the effects described above, so that the need to introduce dark matter and dark energy disappears.
Physics of non-inertial reference frames is a generalizing of Newtons laws to any reference frames. The first, Law of Kinematic in non-inertial reference frames reads: the kinematic state of a body free of forces conserves and determinates a constant
n-th order derivative with respect to time being equal in absolute value to an invariant of the observers reference frame. The second, Law of Dynamic extended Newtons second law to non-inertial reference frames and also contains additional variables there are higher derivatives of coordinates. Dynamics Law in non-inertial reference frames reads: a force induces a change in the kinematic state of the body and is proportional to the rate of its change. It is mean that if the kinematic invariant of the reference frame is n-th derivative with respect the time, then the dynamics of a body being affected by the force F is described by the (n+1)-th differential equation. The third, Law of Static in non-inertial reference frames reads: the sum of all forces acting a body at rest is equal to zero.
Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary reference fra
mes postulating the description of body dynamics by differential equations with higher derivatives of coordinates with respect to time but not only of second order ones and follows from Mach principle. In that case the Lagrangian $L(t,q,dot{q},ddot{q},...,dot {q}^{(n)},...)$ depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if n-th derivative of the body coordinate with respect to time is a constant (i.e. finite). First, kinematic state of a free body is postulated to invariable in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the n-th order derivative of coordinate with respect to time, then the body dynamics is describes by a 2n-th order differential equation. For example, in a uniformly accelerated reference frame all free particles have the same acceleration equal to the reference frame invariant, i.e. reference frame acceleration. These bodies are described by third-order differential equation in a uniformly accelerated reference frame.
Which non-local hidden variables could complement the description of physical reality? The present model of extended Newtonian dynamics (MEND) is generalize but not alternative to Newtonian Dynamics because its extended Newtonian Dynamics to arbitrar
y reference frames. It Is Physics of Arbitrary Reference Frames. Generalize and alternative is not the same. MEND describes the dynamics of mechanical systems for arbitrary reference frames and not only for inertial reference frames as Newtonian Dynamics. Newtonian Dynamics can describe non-inertial reference frames as well introducing fiction forces. In MEND we have fiction forces naturally and automatically from new axiomatic and we neednt have inertial reference frame. MEND is differs from Newtonian Dynamics in the case of micro-objects description.
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields background. We are f
inding to the imagined Feynman Path a classical model of test particles as geodesic trajectory in the curved space of Projected Hilbert space on Blochs sphere.
Refined are the known descriptions of particle behavior with the help of Hamilton function in the phase space of coordinates and their multiple derivatives. This entails existing of circumstances when at closer distances gravitational effects can pro
ve considerably more strong than in case of this situation being calculated with the help of Hamilton function in the phase space of coordinates and their first derivatives. For example, this may be the case if the gravitational potential is described as a power series in 1/r. At short distances the space metrics fluctuations may also be described by a divergent power series; henceforth, these fluctuations at smaller distances also constitute a power series, i.e. they are functions of 1/r. For such functions, the average of the coordinate equals zero if the frame of reference coincides with the point of origin.
