| Physik Prof. Dr. Geilhaupt -------------------------------------------------------------------------------- (1984) UNIFIED FORCE EQUATION f=(m`r`+mr``)u +(m`r+2mr`)u`+mru`` m = m(t), r = r(t), u = u(t) (breathing-oscillation-rotation /t: time (mathematically) u is the unit vector of a special frame of reference in the center of the physical quantity ` means derivation in time Einstein's definition of force f=dP/dt with P=mv with v=d(ru)/dt 5 internal forces Respects Coulomb, Newton / Einstein, Maxwell / Lorentz, Coriolis, Orton 1. m`r`u : charge (Coulomb potential) (+-)eE Coulomb (fe) 2. mr``u : mass (gravitational potential) -mg Newton (fm) 3. m`ru` : current (charge spin) (+-)e[vxB] Lorentz (fi) 4. 2mr`u` : stream (mass spin) (+-)2m[vxw] Coriolis (fcor) 5. mru`` : compression m[-wx (rxw)] Orton (fradial) internal dynamics of a single (non point like) particle with ists (virtual) centre of mass relatively at rest u is in the centre of any particle or U = -u outside anywhere the external velocity (vext) relative to SR-frame of references is (assumed to be) about zero. EINSTEIN / POISSON Fo*Dg44=8p*r*c2 (Fo=(c4/gamma)) SR Force Equation F?/strong> = (d/dt)[m(t,v)(dX?/strong>/dt)] Notice: Einstein explicitly excluded the time dependence of the mass m(t,v)! GR Force Equation F?/strong> = (d/dt)[m(r,t,E,Q)(dX?/strong>/dt)]+ Glm?/sup> (dmXl/dt) (dmXm/dt) Notice: The Relativistic Quantum Thermodynamik of a single particle need to be discussed! (02.04.2000) Concept of Force "In many cases we observe the motion of one particle. In this situation it is rather difficult to use the principle of conservation of momentum. However, there is a practical way of circumventing this difficulty, by introducing the concept of force. We shall designate the time rate of change of momentum of a particle by the name force. That is the force acting on a particle, well known as the second law of Newton F=dp/dt. The word acting is somewhat misleading because it suggests the idea of something applied to the particle. The force here is a mathematical concept which, by definition, is equal to the rate of change of momentum of a given particle. Which in turn is due to the interaction of the particle with other particles. Therefore, physically, we may consider force as an expression of an interaction. If the particle is free, p=const and F=0. Hence we can say that no force acts on a free particle. Newton`s second law of motion is more a definition than a law, and is a direct consequence of the principle of conservation of momentum that yields actio=reactio" Extension of the concept of force Assuming that the conservation of momentum is a fundamental law in physics - no doubt and physically well accepted - then this law is determining nature or objective existence at all and without exception. Therefore a free particle appearing as a real entity must show an internal interaction of (minimum) two parts! Otherwise the conservation of momentum has no meaning! And now? We need to distinguish between single non zero internal forces as well as external forces. The net force to be zero is allowed. At least: The UFE above might have been written down on many sheet of papers by many people during the last 400 years but I am not sure whether anybody until today has been discussing it physically while applying my principle. yes? The "law of inertia," Newton's First Law states that body at rest remains at rest and a body in motion continues to move at a constant velocity unless acted upon by an external force. If we ask where remains the angular momentum the answer leads us to Einstein's GR. So our extension is the cause of the internal forces. (Geilhaupt/Orton) To understand the difference, you should combine Hamilton's funktion H(q,q',t)=q'*p-L(q,q',t) due to mass density with the Maxwell Equations due to charge density. Here external interactions are the starting point but internal action of one single free particle at rest forces a new discussion. The UFE is very useful here to solve how to calculate mass and charge of the electron. Hamilton H = Ekin(t) + Epot(t) =const Poynting Vektor S = 1/my*(E(t) x B(t)) Hamilton Action+Internal Action [t1,t2]intgral(H*dt)=H*(t11-t12) + H*(t12-t13) + ... = H*(t2-t1) M.G.2001 Visits to this Page: Main Menue -------------------------------------------------------------------------------- oder schreiben Sie mir! M. Geilhaupt -------------------------------------------------------------------------------- last review / Letzte 膎derung: 16.09.1998 |