Subtopic: Relativistic Momentum, Energy & 4-Vectors
Question Statement:
Which of the following option(s) is/are correct for photons?
Options:
(A) Its rest mass is zero, but its energy is non-zero
(B) It carries non-zero linear momentum
(C) It carries zero spin angular momentum
(D) It has two linearly independent states of polarization
Official Answer Key:
A;B;D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.25)**
**1. Fundamental Relativistic Quantum Properties of Photons**:
- The photon is the gauge boson of quantum electrodynamics mediating the electromagnetic force.
**2. Analysis of Statements (MSQ)**:
- **(A) Rest mass is zero, but its energy is non-zero [TRUE]**:
- Photons travel at the invariant speed of light $c$ in vacuum; invariant rest mass $m_0 = 0$.
- Energy is given by the Planck-Einstein relation $E = h\nu = \hbar\omega > 0$.
- **(B) It carries non-zero linear momentum [TRUE]**:
- Relativistic dispersion relation for $m_0 = 0$ gives $E^2 = p^2 c^2 \implies p = \frac{E}{c} = \frac{\hbar\omega}{c} = \hbar k \ne 0$.
- **(C) It carries zero spin angular momentum [FALSE]**:
- The photon is a spin-1 particle ($s = 1$). It carries intrinsic spin angular momentum $\hbar$.
- **(D) It has two linearly independent states of polarization [TRUE]**:
- For a massless relativistic vector field, gauge invariance eliminates the longitudinal polarization mode, leaving exactly $2$ independent transverse physical polarization states (helicity $\lambda = \pm 1$, corresponding to right- and left-circular or orthogonal linear polarizations).
**3. Official Verification**:
The verified official IIT answer is **Options (A), (B), and (D)** (`['A', 'B', 'D']`).
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