lobal Journal of Science Frontier Research, A: Physics and Space Science, Volume 24 Issue 4

entropy σ s , but in principle for all forms of partial energy U i , including chemical elements and countless of their compounds that arise or disappear during chemical reactions. They also exist for polarization charges arising under the influence of an external field, as well as for electrons and positrons, as evidenced by the predominance of the latter in fluxes of cosmic particles [20]. Sources also appear in various phases of matter, including baryonic matter as a product of “condensation” of non-baryonic (hidden) matter. Thus, from the law of conservation of energy it follows that it is possible to interconvert not only any forms of partial energy, but also their energy carriers. In this case, a natural question arises about the origin of statements of an opposite nature, moreover, claiming to be laws of nature. III. I nconsistency of the L aws of C onservation of M omentum and M omentum It is known that Newtonian mechanics did not consider internal processes occurring in accelerating bodies (material points), believing that they remained in a state of internal equilibrium. In this case, ji = 0 for any energy carrier, and the only reason for the change in momentum P = M υ was the external force F [4]: F = d Р /dt. (8) However, by (1), this expression refers to the source of momentum ∫ р . dV= d с р ./dt. Indeed, in the general case of open systems (exchanging matter with the environment), a change for internal motion in the system M υ is also possible through the diffusion of matter at a rate different from v. Thus, in reality, I. Newton from the very beginning limited himself to the case when the change in the momentum of bodies M υ is caused exclusively by long-range forces F, i.e., in a way different from the “convective” exchange of it with the environment. Hence Newton’s definition of force (8), relating it to the source of momentum σ i , and not to its convective term ∇⋅ j i . Such sources σ i should be called “external” σ ie in contrast to “internal” sources σ ii, caused by the action of thermodynamic (internal) forces X i . In this case, the correspondence of the momentum M υ to the balance equation (1) with sources, i.e., its belonging to non-conserved quantities, would not raise any doubts. Let us now show that the law of conservation of momentum Р = M υ at F =d Р /dt does not exist in nature. Formally, this becomes clear already when applying the balance equation (1) to the components Р =M υ of the impulse M υ ( = 1,2,3), in which in this case the terms σ е of the external source of impulse appear. The same is true for the components of angular momentum L=I ω ω , expressed as the product of the moment of inertia I ω and the angular velocity ω . However, it may seem that to preserve energy carriers Θ i , the homogeneity of the system (x i = 0) is sufficient. In this case, equation (4) takes the form: d ρ е /dt=- Σ i ψ i ∇⋅ j i (9) Since in homogeneous systems the potentials ψ i are identical at any point in the volume of the system V and can be taken out of the integral sign (2), and ∫ ∇⋅ j i dV = ∫j i ⋅ df = d Θ i /dtin accordance with equation (6), then in integral form this expression is a combined equation of the 1st and 2nd principles of classical thermodynamics in the form of the generalized Gibbs relation: dU = Σ i ψ i d Θ i ,. (10) In such systems, energy carriers Θ i can change due to their transfer across the system boundaries (∫ ∇⋅ j i dV≠0), which does not contradict the balance equations (1). However, this does not exclude the presence of external forces F i and their internal sources σ ii, i.e., violation of conservation laws. To verify this, let us write relation (6) in integral form, having previously taken out a certain average value Х i = - ψ i ∇ force x i from the integral sign (6): dU/dt= Σ i ∫ ψ i σ i dV = Σ i Х i J i , (11) where J i = ∫j i dV is the impulse of the system as a whole. It follows that the movement of the system as a whole (J i ≠ 0) can only occur if the main vector Х i of internal forces xi is not equal to zero, i.e., there are external forces causing this movement. This position is fully consistent with Newtonian mechanics, but again emphasizes the presence of internal sources of σ ii, i.e., a violation of conservation laws. This conclusion seems to contradict the well- known theorem of E. Noether [15], according to which the laws of conservation of momentum and its momentum are a consequence of the homogeneity and isotropy of space. However, we should not forget that these properties of space do not at all mean that the distribution of mass filling this space is uniform. It is known that the density of matter in the space of the universe ranges from 10 -31 g cm -3 in space free from celestial bodies to 10 18 g cm -3 in celestial bodies such as “white dwarfs”. Therefore, by general relativity, the properties of space (its curvature and the associated energy-momentum tensor) depend on the distribution of matter in it. Consequently, in real outer space, where the density of matter differs by tens of orders of magnitude, there can be no talk of homogeneity of space. Global Journal of Science Frontier Research ( A ) XXIV Issue IV Version I Year 2024 87 © 2024 Global Journals On the Incompatibility of the Laws of Energy and Pulse Conservation