9. [C] Circularly Polarized Gravitational Waves If a linearly polarized electrom

Question

9. [C] Circularly Polarized Gravitational Waves If a linearly polarized electromag- netic wave with a given frequency is added to a wave of the same amplitude and frequency propagating in the same direction but polarized in a perpendicular direc- tion and 90° out of phase, the result is a circularly polarized wave in which the tip of the electric field vector moves in a circle at any one position in space. By analogy, the superposition of a + polarized gravitational plane wave with another of the same amplitude, frequency, and propagation direction but with x polarization and 90° out of phase is called a circularly polarized gravitational wave. Show that a circularly polarized plane gravitational wave with frequency o that is normally incident on an ellipse of test the elliptical pattern rotates with a constant angular frequency. What is that angular frequency? particles causes each test particle to rotate in a small cirele such that

Explanation / Answer

1. circularly polarized waves carry angular momentum the amount of which is (2/?) times the energy carried by the wave.

2. If we consider the gravitational field, then, according to quantum field theory, the waves are associated with fundamental particles responsible for the gravitational interaction, and a quantum of the field will have energy h? and consequently spin 2. This means that the quanta of the gravitational field, the gravitons, are spin 2.

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