<\/p>\n\n\n\n
Special relativity does not deal with acceleration, general\nrelativity does not deal with non gravitational acceleration, which leave the\ntheory of relativity imperfect. We will demonstrate some relativistic dynamical\nlaws that specify relativistic acceleration, force and kinetic energy. Also,\nbased on equivalence principle does gravitational mass vary with inertial mass?<\/p>\n\n\n\n
Newtonian kinematics defines motions of objects\nwith velocity and acceleration, Newtonian dynamics defines force with acceleration and mass, which makes Newtonian mechanics the most complete theory\nin physics. Special and general relativity\nare extremely successful, but they lack the capability of dealing with acceleration and force. For relativity mass increases to infinity\nwhen u=c<\/em>, which makes energy and momentum\nto become incorrectly infinity. Also, general relativity is based on equivalence\nprinciple according to which inertial mass is equivalent to gravitational\nmass. Then does gravitational mass increases when inertial mass increases? So, relativity\nneeds new laws to deal with acceleration and\nforce.<\/p>\n\n\n\n In previous studies of relativity [1][2][3][4][5],\nwe have already correctly treated acceleration,\ninertial mass, kinetic energy. Below we will demonstrate the laws that describe them. For setting the\ndemonstrations on a strong base, we begin with rigorously proving the equality of\ndifferential momentum in 2 relatively moving frames of reference.<\/p>\n\n\n\n In relativity, a change\nof velocity has different value in\nrelatively moving frames. However, differential momentum\nhas the same value in such frames,\nwhich we call equality of differential momentum and\nhave explained in \u00ab Velocity, mass, momentum and energy<\/a> of an accelerated object<\/a> in relativity \u00bb [2]. <\/p>\n\n\n\n For rigorously proving this equality, let us take 2\nidentical objects labeled a<\/em> and b<\/em>. The object b<\/em> moves at the velocity u<\/em><\/strong>\nwith respect to a<\/em>, the frame of reference of the object b<\/em> is labeled frm. b<\/em>, see Figure 1. If the object b<\/em> gets an infinitesimal impulse,it gets a differential\nmomentum and a differential change of velocity labeled du<\/strong>b<\/sub><\/em>.<\/p>\n\n\n\n Notice that in\nthe frame frm. b<\/em> the velocity\nof b<\/em>\nis constantly zero. Then, how can its\nchange of velocity du<\/strong>b<\/sub><\/em> be nonzero? In fact, du<\/strong>b<\/sub><\/em>\nis with respect to an inertial frame, not\nto frm.\nb<\/em>. For defining du<\/strong>b<\/sub><\/em> we have to create\na new type of inertial frame that\ncoincides with b<\/em>. We name this type\nof frame \u201cProper inertial frame\u201d.\n<\/p>\n\n\n\n For example, the\nobject b<\/em> moves at the instant velocity u<\/em><\/strong>t<\/sub><\/em>\nat a given time t<\/em>. At this time we create the proper inertial\nframe of b<\/em> labeled Ref. b<\/em> which moves at constant velocity\nthat equals u<\/em><\/strong>t<\/sub><\/em>. The trajectory of Ref. b<\/em> is a straight line while that\nof\nb<\/em> is a curve, see Figure 2.\nAfter the infinitesimal impulse b<\/em> moves at the instant velocity u\u2019<\/em><\/strong>t<\/sub><\/em> and the\nchange of velocity equals du<\/strong>b <\/sub><\/em>= u\u2019<\/em><\/strong>t<\/sub><\/em>– u<\/em><\/strong>t<\/sub><\/em> with u<\/em><\/strong>t<\/sub><\/em>\nbeing the velocity of the inertial frame Ref. b<\/em>. In the same way the proper\ninertial frame of the object a<\/em> is labeled Ref. a<\/em>.<\/p>\n\n\n\n \u2026<\/p>\n\n\n\n Figures and equations are in the article below:<\/p>\n\n\n\n \u00abRelativistic\ndynamics<\/a>: force, mass,\nkinetic energy, gravitation and dark matter<\/a>\u00bb<\/p>\n\n\n\n https:\/\/www.academia.edu\/49921891\/Relativistic_dynamics_force_mass_kinetic_energy_gravitation_and_dark_matter<\/a><\/p>\n\n\n\n https:\/\/pengkuanonphysics.blogspot.com\/2021\/07\/relativistic-dynamics-force-mass.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Special relativity does not deal with acceleration, general relativity does not deal with non gravitational acceleration, which leave the theory of relativity imperfect. We will demonstrate some relativistic dynamical laws that specify relativistic acceleration, force and kinetic energy. Also, based … Continue reading