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Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The reconciliation of gravity to the current particle physics theory is not solved; many theories have addressed this problem, such as loop quantum gravity, string theory and supersymmetry theory. Experimental particle physics is the study of these particles in radioactive processes and in particle accelerators such as the Large Hadron Collider.
String Theory. A possible candidate for the theory of everything, this theory combines the theory of general relativity and quantum mechanics to make a single theory. This theory can predict about properties of both small and big objects. This theory is currently under the developmental stage.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The configuration space and the phase space of the dynamical system both are Euclidean spaces, i. e. they are equipped with a Euclidean structure.The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass = is equal to the sum of kinetic energies of the three-dimensional particles with the masses , …,:
There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities. [12]
However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, bound states , and solitons . The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.
In Cartesian coordinates the Lagrangian of a non-relativistic classical particle in an electromagnetic field is (in SI Units): = ˙ + ˙, where q is the electric charge of the particle, φ is the electric scalar potential, and the A i are the components of the magnetic vector potential that may all explicitly depend on and .