Progressive Special relativity practice questions
Use Clevolab for progressive practice in special relativity. This page shows what the topic covers, what skills the current set targets, and a few real examples from the reviewed question bank.
About this topic
Clevolab treats special relativity as repeated practice with explanation, not just answer checking. This page is designed to make the topic legible before you open the app.
The current Progressive set covers time dilation, length contraction, and relativistic ideas. 158 reviewed questions currently published for this page.
What you can practise
- Relativity postulates
- Time dilation
- Length contraction
- Frames of reference
Real sample questions from the current set
These examples come from the reviewed questions currently stored for this topic. They are here so the page shows the actual flavour of Clevolab, not just a summary.
Sample question
For causally connected (timelike) events, what about time order?
- AOrder can reverse in fast frames.Answer option
- BOnly observers at rest agree on order.Answer option
- COrder is undefined.Answer option
- DAll inertial observers agree on which came first.Correct answer
Why this answer is right
Timelike separations keep causal order invariant under Lorentz transformations, so all observers agree on before and after.
For timelike intervals, $$s^2 = c^2\Delta t^2 - \Delta x^2 > 0.$$ Lorentz transformations cannot flip the sign of $\Delta t$ for timelike separations. Thus if one event can cause another, all inertial observers agree on which occurred first.
Sample question
What is the rest energy of a $1.00\,\mathrm{kg}$ mass?
- A$3.0\times10^8\,\mathrm{J}$Answer option
- B$9.8\times10^{16}\,\mathrm{J}$Answer option
- C$3.0\times10^{16}\,\mathrm{J}$Answer option
- D$9.0\times10^{16}\,\mathrm{J}$Correct answer
Why this answer is right
Rest energy is $E_0=mc^2$. With $m=1.00\,\mathrm{kg}$ and $c=3.0\times10^8\,\mathrm{m\,s^{-1}}$, $E_0=9.0\times10^{16}\,\mathrm{J}$.
Compute $$E_0=mc^2=(1.00\,\mathrm{kg})(3.0\times10^8\,\mathrm{m\,s^{-1}})^2=9.0\times10^{16}\,\mathrm{J}.$$ This is the energy equivalent of the mass at rest, independent of frame.
Sample question
Which of the following about the Lorentz group is correct?
- AIt is non-abelian; boosts in different directions do not commuteCorrect answer
- BIt is abelian; all boosts commuteAnswer option
- CIt contains spatial translationsAnswer option
- DIt preserves Euclidean distanceAnswer option
Why this answer is right
The Lorentz group is non-abelian. The commutator of boost generators yields a rotation, reflecting Thomas–Wigner rotation. It preserves the Minkowski interval, not Euclidean distance.
Generators satisfy $$[J_i,J_j]=\epsilon_{ijk}J_k,\quad [J_i,K_j]=\epsilon_{ijk}K_k,\quad [K_i,K_j]=-\epsilon_{ijk}J_k.$$ Nonzero $[K_i,K_j]$ shows noncommutativity of noncolinear boosts. Lorentz transformations preserve $\eta_{\mu\nu}x^\mu x^\nu$, not Euclidean norms, and do not include translations.
How this page fits into Clevolab
Clevolab is broader than any one exam mode. GCSE and A-level pages are useful entry points, while the wider project is about sharpening understanding through repeated topic practice.