Question 1

Which experiment best illustrates Einstein's first postulate, the principle of relativity, as shown in the provided image of a moving magnet and coil?

Accepted Answer

Both experiments, since the induced emf is the same regardless of which object moves.

Question 2

According to Einstein’s second postulate, what is the speed of light in a vacuum as observed from any inertial frame?

Accepted Answer

It is always $$c$$, independent of the motion of the source or observer.

Question 3

Why does Newtonian mechanics fail to correctly predict the speed of light for an observer on Earth when a spaceship emits a light beam at speed $$c$$?

Accepted Answer

Newtonian mechanics predicts the speed of light as $$c + 1000 m/s$$, violating Einstein’s second postulate.

Question 4

Which transformation is valid for low speeds compared to the speed of light, but fails for relativistic speeds?

Accepted Answer

Galilean transformation

Question 5

In the train lightning thought experiment, why does Mavis conclude that event B occurred before event A?

Accepted Answer

She is moving toward the light from event B and away from the light from event A, so the light from B reaches her first.

Question 6

What is the proper time interval $$\Delta t_0$ measured by Mavis in her frame for a light pulse traveling to a mirror and back?

Accepted Answer

$$\Delta t_0$ = \frac{2d}{c}$$

Question 7

Stanley observes the light pulse in the train experiment to travel a longer distance than Mavis. What is the time interval $$\Delta t he $$measures?

Accepted Answer

$$\Delta t = \frac{\Delta t_0$}{\sqrt{1 - \frac{u^2$}{c^2$}}}$$

Question 8

What is the formula for time dilation in special relativity?

Accepted Answer

$$\Delta t = \Delta t_0$ \gamma$$

Question 9

What is the formula for length contraction in special relativity?

Accepted Answer

$$l = l_0$ / \gamma$$

Question 10

Which of the following statements about proper length is correct?

Accepted Answer

Proper length is measured in the frame where the object is at rest.

Question 11

What is the Lorentz factor $$\gamma$$ for an object moving at speed $$u$$?

Accepted Answer

$$\gamma = \frac{1}{\sqrt{1 - \frac{u^2$}{c^2$}}}$$

Question 12

Which coordinate transformation correctly relates the spacetime coordinates of an event between two inertial frames moving at constant velocity $$u$$?

Accepted Answer

$$x' = \gamma (x - ut)$$

Question 13

What is the relativistic expression for momentum?

Accepted Answer

$$p = \gamma mv$$

Question 14

What is the relativistic kinetic energy of a particle?

Accepted Answer

$$K = mc^2$ (\gamma - 1)$$

Question 15

Which equation relates total energy, rest energy, and momentum for a particle in special relativity?

Accepted Answer

$$E^2$$ = $$(mc^2)^2$ + (pc)^2$

Question 16

A photon has zero rest mass. What is its energy in terms of its momentum?

Accepted Answer

$$E = pc$$

Question 17

What is the minimum energy required for pair production of an electron and positron?

Accepted Answer

$$E_{min} = 2mc^2$

Question 18

In the context of the Doppler effect for electromagnetic waves, what is the frequency $$f$$ observed by Stanley when the source approaches him at speed $$u$$?

Accepted Answer

$$f = f_0$ \frac{c + u}{c - u}$$

Question 19

Which principle states that a new physical theory must yield the same predictions as the old theory in the appropriate limit?

Accepted Answer

Correspondence principle

Special Relativity and Wave-Particle Duality: Structured Study Notes

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