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Chapter 1: Problem 44

Time is homogeneous so .............. law of conservation is the result of this (a) angular momentum (b) linear momentum (c) energy (d) charge

Short Answer

Expert verified
The conservation law resulting from time homogeneity is the conservation of \(energy\), as energy is the only quantity with a clear connection to time. Thus, the correct answer is (c) Energy.

Step by step solution

01

Understand the Concept of Time Homogeneity

Time homogeneity means that the laws of physics remain invariant under time translation. In other words, time homogeneity asserts that the behavior of a physical system will not change with time as long as the properties of the objects within the system and the interactions between them do not change. According to Noether's theorem, continuous symmetries lead to the conservation laws. In the case of time homogeneity, the continuous symmetry is the invariance of the system under time translation.
02

Identify the Conservation Laws Associated with Each Option

a) Angular momentum: The conservation of angular momentum states that the total angular momentum of a closed system remains constant if there is no net external torque acting on the system. b) Linear momentum: The conservation of linear momentum states that the total linear momentum of a closed system remains constant if there is no net external force acting on the system. c) Energy: The conservation of energy states that the total energy of a closed system remains constant if there is no exchange of energy with the surroundings (no net external work is done on the system). d) Charge: The conservation of charge states that the net electric charge of an isolated system remains conserved over time.
03

Determine Which Conservation Law is the Result of Time Homogeneity

According to Noether's theorem, time homogeneity leads to a conservation law associated with the uniformity of time. Since energy is the only quantity in the list that has a clear connection with time (via the work-energy theorem and the fact that the energy of a physical system is a function of time), the conservation law resulting from time homogeneity must be the conservation of energy.
04

Choose the Correct Answer

The correct option for the conservation law resulting from time homogeneity is: (c) Energy

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Most popular questions from this chapter

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