Question

Which of the following statement(s) is/are true?

• A. Newton’s laws of motion and Maxwell’s equations are both invariant under Lorentz transformations.
• B. Newton’s laws of motion and Maxwell’s equations are both invariant under Galilean transformations.
• C. Newton’s laws of motion are invariant under Galilean transformations and Maxwell’s equations are invariant under Lorentz transformations.
• D. Newton’s laws of motion are invariant under Lorentz transformations and Maxwell’s equations are invariant under Galilean transformations.

Hint:

Newton’s laws of motion are Galilean invariant, while Maxwell’s equations are Lorentz invariant.

Answer 1

The Correct Option is C

Step 1: Understanding the invariance of physical laws.
Newton’s laws of motion are formulated within classical mechanics and are invariant under Galilean transformations, which relate the coordinates of two inertial frames moving at constant velocity relative to each other. Maxwell’s equations, which describe electromagnetism, are invariant under Lorentz transformations, which are the appropriate transformations in special relativity.

Step 2: Analyzing the options.
(A) Newton’s laws of motion and Maxwell’s equations are both invariant under Lorentz transformations: Incorrect. Newton’s laws of motion are not Lorentz invariant, they are Galilean invariant.
(B) Newton’s laws of motion and Maxwell’s equations are both invariant under Galilean transformations: Incorrect. Maxwell’s equations are not invariant under Galilean transformations, they are Lorentz invariant.
(C) Newton’s laws of motion are invariant under Galilean transformations and Maxwell’s equations are invariant under Lorentz transformations: Correct. This is the correct statement, as it correctly describes the invariance properties of both Newton's laws and Maxwell’s equations.
(D) Newton’s laws of motion are invariant under Lorentz transformations and Maxwell’s equations are invariant under Galilean transformations: Incorrect. Newton’s laws are not Lorentz invariant.

Step 3: Conclusion.
The correct answer is (C) because it correctly describes the invariance of Newton's laws and Maxwell's equations.