Elementary Particles in the theory of relativity Section 15

The field was first conceived by Faraday to explain action at a distance In classical physics, the field is a convenience for describing interactions between particles In relativity, due to the finite velocity of propagation of interactions, the field has physical reality. – A particle first acts on the field – Then the field acts on other particles at later times.

Rigid bodies don’t exist In classical physics, rigid non-deformable bodies exist In relativity, the existence of rigid bodies is impossible.

Assumption of rigidity leads to absurdity Consider a rotating disk, and suppose it to be rigid. Imagine a reference frame fixed to an infinitesimal element of the disk. This frame can be considered inertial during a moment. Different elements have different inertial frames in the given moment.

Consider line elements along a radius of the rotating disk – The elements are perpendicular to their velocity – No Lorentz contraction The total radius of the disk is the same as when it was at rest. v

Now consider line elements a long the circumference of the disk The assumption of rigidity means that the proper length of each element is the same as would be observed by a viewer at rest. However, an observer at rest sees that the length of each element is contracted. v

The circumference of the rotating disk is smaller than that of the disk at rest. Thus, due to rotation circumference/radius does not equal 2  This cannot be, unless the moving disk is no longer a disk, i.e. it must have deformed.

Apply an external force to one spot on an extended body. Speed of propagation of interactions is finite. F ext is not applied to all points simultaneously. Body must deform as it accelerates. F ext

Elementary particles are described completely by position r and velocity v. No independent motion of parts. Elementary particles cannot have finite dimensions. They are mathematical points.

In its own reference frame, an object is a flat disk. An observer at rest observes it spin around its symmetry axis. What possible shape might the observer see it deformed into? A bowl. A flat oval. A ruffled circle.

In its own reference frame, an object is a flat disk. An observer at rest observes it spin around its symmetry axis. What possible shape might the observer see it deformed into? A bowl. A flat oval. A ruffled circle.