[ home ] | Einstein's Equivalence Principle | General Relativity. Note: « 1 » |
Inertial (fictitious) forces are the forces which are thought to affect the bodies when looking at their motion from an non-inertial frame. Centrifugal, Coriolis and elevator forces are the examples.
Consider the motion of a free test body in an inertial frame K: its equation of motion is x''=0 which is an equation for a straight line. Frames, where free bodies move along a straight lines are called flat.
Consider the same body from a frame K° that accelerates with respect to K with acceleration a. In this frame the equation is x''=-a which is an equation for a parabola. Frames, where free bodies do not move along a straight lines are called curved. This equation can be written with the help of a fictitious inertial force FI=-ma as the Newton's law: mx''=FI. Inertial forces are useful if one for some reason must work in a non-inertial frame.
Inertial forces have the following properties:
Galileo's "Pisa experiment" showed that all bodies move in a gravitational field with the same acceleration (which is the first property of inertial forces). Einstein has postulated that all three properties of inertial forces are fulfilled also for gravitational forces. In other words, gravitational forces are physically equivalent to inertial forces. This is called the Einstein's equivalence principle. It can also be formulated as:
Consider the motion of a particle with charge e and mass m in a constant uniform electric field E which is, say, in X direction.
dp/dt = e(E + 1/cv×H), |
p = mv (1/√[1-v2/c2]) |