Elementary Particles in the theory of relativity

1. Elementary Particles in the theory of relativity Section 15

2. 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.

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

4. 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.

5. 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

6. 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

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

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

9. 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.

10. 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.

11. 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.