Question bank — Postulates of SR

False — by Postulate 2, light's speed is $c$ for every inertial observer regardless of source motion; only its frequency (colour) shifts via Doppler. See Relativistic Velocity Addition, where $u^{\prime }=(u+v)/(1+uv/c^2)$ collapses to $c$ whenever $u=c$.

False — it is geometric, derived from the constancy of $c$ alone (the diagonal-vs-vertical triangle above); even a flawless ideal clock (or a beating heart, or a decaying particle) dilates. It is time itself, not the device.

False — Postulate 1 covers only inertial (non-accelerating) frames; an accelerating frame feels pseudo-forces, so its rules differ. Special relativity can still describe such motion (e.g. via accelerated "Rindler" coordinates) — you do not need General Relativity — but Postulate 1's exact equivalence of frames no longer applies.

True — the situation is perfectly symmetric because neither is "really" moving (Postulate 1); each is a valid inertial frame, so each sees the other's clock dilated by $\gamma$.

False — since $v<c$ gives $v^2/c^2<1$, the square root $\sqrt{1-v^2/c^2}$ is between 0 and 1, so its reciprocal $\gamma$ is always $\ge 1$. See Time Dilation.

False — they are logically contradictory; keeping $c$ invariant forces you to abandon Galilean addition and the universality of time. See Galilean Relativity.

False — it proved the opposite; it detected no ether wind and no $c+v$ effect, which is exactly what pushed physics toward Postulate 2. See Michelson-Morley Experiment.

False in practice — $\gamma \approx 1+\frac{1}{2}(10^{-14})$, a correction far too tiny to detect; relativity is always on but invisible at everyday speeds.

False — simultaneity is relative; an observer moving relative to me can measure the same two events as happening at different times. This is what Einstein sacrificed to save $c$.

Error — no inertial frame moves at $c$, so a photon has no rest frame; as $v$ approaches $c$, $\gamma$ grows without bound, so the transformation breaks down. Light is $c$ in every frame, never at rest in any.

Error — it says the laws of physics are identical in all inertial frames, not that measured values (times $\Delta t$, lengths) agree. Observers famously disagree on durations and lengths while agreeing on the laws and on $c$.

Error — you multiply: $\Delta t_0$ is the proper time (shortest, measured in the clock's own frame), and any other frame measures the larger value $\gamma \Delta t_0$. Dividing would wrongly make the other frame's time shorter.

Error — unlike sound, light needs no medium; Maxwell's equations give $c$ with no reference to any ether, and Michelson-Morley Experiment confirmed none exists.

Error — the logic runs the other way: $c$ constant is the postulate, and time dilation is a derived consequence (via the light-clock triangle). You never assume the conclusion.

Error — the moving observer feels nothing unusual; their own clock ticks normally to them ($\Delta t_0$ in their own frame). Dilation is only ever measured by a different inertial frame, never by the clock about itself.

Step 1: Maxwell's Equations contain the constants ${\epsilon }_0$ and ${\mu }_0$ and predict a wave speed $c=1/\sqrt{{\epsilon }_0{\mu }_0}$ — a single fixed number, with no reference to any observer's motion. Step 2: Postulate 1 says those very equations (and hence that number) must be identical in every inertial frame. Step 3: therefore every inertial frame, applying the same Maxwell's equations, computes the same numerical $c$ — that is exactly Postulate 2.

Giving up the laws would collapse all of physics; time and absolute simultaneity are the "cheaper," less foundational assumptions to surrender while keeping the laws and $c$ intact.

While the light rises a height $L$, the mirror slides sideways by $v\Delta t/2$, so by Pythagoras the one-way path is $\sqrt{L^2+(v\Delta t/2{)}^2}$ — the hypotenuse of a right triangle whose vertical leg is $L$. Solving $c\Delta t=2\sqrt{L^2+(v\Delta t/2{)}^2}$ yields $\Delta t=(2L/c)/\sqrt{1-v^2/c^2}=\gamma \Delta t_0$, so the diagonal exceeds the vertical by precisely the factor $\gamma$. See Time Dilation.

Plugging $u=c$ into $u^{\prime }=(u+v)/(1+uv/c^2)$ gives $(c+v)/(1+v/c)=c$; the denominator scales exactly to cancel the excess, which is the algebra enforcing Postulate 2.

At everyday speeds $v\ll c$, $\gamma \to 1$ and the Lorentz Transformations reduce to Galilean ones; relativity contains Newton as its low-speed limit. See Galilean Relativity.

Because $\gamma$ grows without bound as $v\to c$, any massive object would need infinite energy to reach $c$; $c$ is the universal speed limit built into spacetime's geometry, and light merely rides it. See Mass-Energy Equivalence.

$v^2/c^2\to 1$, so $\sqrt{1-v^2/c^2}\to 0$ and $\gamma \to \infty$ — time dilation becomes unbounded, which is why massive objects can never actually reach $c$.

$\gamma =1/\sqrt{1-0}=1$, so $\Delta t=\Delta t_0$ — no dilation, and every relativistic formula collapses back to the classical one, as it must.

Yes — a fast muon's internal decay "clock" runs slow in the lab frame, so it lives long enough to reach the ground; this is real experimental confirmation, not a device artifact.

Neither — the question is meaningless because both are equally valid inertial frames (Postulate 1); each correctly measures the other's clock as slow. Only if one accelerates to reunite (breaking symmetry) does an absolute comparison exist.

No — vacuum light speed is exactly $c$ in every inertial frame; chasing the beam or fleeing it changes the frequency but never the measured speed.

They are in an accelerating (non-inertial) frame, so Postulate 1's exact frame-equivalence does not apply; the felt pseudo-force is precisely the signal that the frame is non-inertial (still describable within SR, not requiring GR).