is lorentz force conservative?

is lorentz force conservative?


The Lorentz force does not depend only on the position of the particle. However also on its velocity (speed and direction). Thus the force is not conservative.

The Lorentz factor, a term used in special relativity. One that describes how time, length, and mass change for an object that is moving at a significant fraction of the speed of light relative to an observer.

Hendrik Lorentz (right) with Albert Einstein (1921) Did Feynman ever meet Einstein?

The Lorentz factor denoted by the symbol γ and defined as:

γ = 1 / sqrt(1 – v^2/c^2)

where v is the velocity of the object, c is the speed of light, and sqrt refers to the square root function.

As an object’s speed approaches the speed of light. Moreover, its Lorentz factor approaches infinity. Thus, meaning that its time, length, and mass are all significantly affected by its high velocity. For example, time dilation occurs at high speeds, meaning that time appears to pass more slowly for an object that is moving at a high velocity relative to an observer who is at rest.

γ starts at 1 when v equals zero and stays nearly constant for small v's, then it sharply curves upwards and has a vertical asymptote, diverging to positive infinity as v approaches c.
The Lorentz factor γ as a function of velocity. It starts at 1 and approaches infinity as v approaches c.

The Lorentz factor also has important implications for the behavior of particles at high energies. In particle accelerators, for example, particles can be accelerated to very high speeds and energies, approaching the speed of light. At these energies, the Lorentz factor becomes very large, and the particles can exhibit behavior that is not observed at lower energies.

Overall, the Lorentz factor is a fundamental concept in special relativity that plays a crucial role in understanding the behavior of objects and particles at high speeds and energies. It is intimately related to the speed of light, which is a fundamental constant of the universe.

One of the last and most accurate time of flight measurements, Michelson, Pease and Pearson’s 1930–35 experiment used a rotating mirror and a one-mile (1.6 km) long vacuum chamber which the light beam traversed 10 times. It achieved accuracy of ±11 km/s.

is lorentz force conservative?