Relativity, laboratory methods and specialised topics
| English | 中文 | Pinyin |
|---|---|---|
| covariance/ˈkɒveərɪəns/ | 协方差 | xié fāng chà |
| precision/prɪˈsɪʒn/ | 精密度 | jīng mì dù |
A decision before an answer
- A precise instrument can give consistently wrong results when its calibration is shifted.
- Your goal: Apply special-relativistic energy and spacetime relations.
Read the relationship
- Special relativity uses γ=1/sqrt(1−v²/c²). Rest energy is mc² and total energy is γmc².
- Propagate measurement uncertainty and analyse experimental data.
At v=0, the Lorentz factor is:
γ=1/sqrt(1)=1.
Use the defining rule
- For independent small uncertainties, combine contributions in quadrature; correlated uncertainties require covariance terms.
- Recognise nuclear, particle, condensed-matter and astrophysical concepts.
A fixed zero-offset error chiefly affects:
Calibration bias shifts readings from the true value.
Check the conditions
- Random scatter affects precision; calibration bias affects accuracy. A log plot can reveal a power law.
- Recognise nuclear, particle, condensed-matter and astrophysical concepts.
For v=0.6c, γ=1/sqrt(0.64)=1.25. Total energy is 1.25mc²; kinetic energy is (γ−1)mc²=0.25mc². For y=ab with independent small relative uncertainties 3% and 4%, relative uncertainty is sqrt(3²+4²)%=5%.
Independent relative uncertainties 6% and 8% combine to ____%.
sqrt(6²+8²)=10.
Apply the task format
- Nuclear, particle, condensed-matter and astrophysics questions require undergraduate vocabulary and models. School physics alone is not a complete preparation course.
- Recognise nuclear, particle, condensed-matter and astrophysical concepts.
Adding percentage uncertainties linearly gives a worst-case bound, not the independent statistical standard uncertainty.
Which answer fits this case?
Apply special-relativistic energy and spacetime relations
Greater precision always guarantees greater accuracy.
A biased instrument can give tightly clustered wrong readings.
Keep the distinctions
- precision 精密度 — Closeness of repeated measurements to each other.
- covariance 协方差 — A measure of joint variation used for correlated uncertainties.
- Apply special-relativistic energy and spacetime relations.
- Propagate measurement uncertainty and analyse experimental data.
- Recognise nuclear, particle, condensed-matter and astrophysical concepts.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.