Chapter 12: Problem 12

What common feature of the electromagnetic and gravitational interactions requires that their carrier (or exchange) particles bo massless?

Short Answer

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Answer: The common feature is that both electromagnetic and gravitational interactions are long-range forces, which follow an inverse-square law. Their massless carrier particles allow them to propagate effectively over large distances.

Step by step solution

Understanding the electromagnetic and gravitational interactions

Electromagnetic interactions are mediated by the exchange of photons, which are massless, while gravitational interactions are mediated by the exchange of gravitons, which are also believed to be massless. We need to identify the common feature between these interactions that necessitates their carrier particles to be massless.

Long-range forces

The electromagnetic and gravitational forces are both long-range forces, meaning that their strength does not vanish at large distances. Instead, their force laws follow an inverse-square law, which means that the force between two particles decreases as the square of the distance between them. For the electromagentic force, the law is given by Coulomb's law, F = k * q1 * q2 / r^2, and for the gravitational force, it is given by Newton's law of gravitation, F = G * m1 * m2 / r^2, where F is the force, q1 and q2 are electric charges, m1 and m2 are masses of two objects, r is the distance between them, k is Coulomb's constant and G is the gravitational constant.

Massless carrier particles for long-range forces

In order for a force to be long-range, its carrier particle must be massless. A massless particle, such as the photon or the graviton, can travel at the speed of light, which allows it to effectively propagate the force over long distances. If the carrier particles were to have mass, the range of the force would become finite, and the force would diminish much more rapidly with increasing distance. In fact, the force would acquire an exponentially decaying term, proportional to e^{-m * r} where m is the mass of the carrier particle.

Conclusion

The common feature of the electromagnetic and gravitational interactions that requires their carrier (exchange) particles to be massless is that they are both long-range forces. Their force laws follow an inverse-square law, which results from having massless carrier particles that can effectively propagate the force over large distances.

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What common feature of the electromagnetic and gravitational interactions requires that their carrier (or exchange) particles bo massless?

Short Answer

Step by step solution

Understanding the electromagnetic and gravitational interactions

Long-range forces

Massless carrier particles for long-range forces

Conclusion

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