Relativity, laboratory methods and specialised topics · 相对论、实验方法及专题内容
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| 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.
答案前的判断
- 当校准发生偏移时，精密仪器也可能给出始终错误的结果。
- 你的目标：应用狭义相对论的能量与时空关系。
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.
阅读关系
- 狭义相对论中 γ=1/sqrt(1−v²/c²)。静止能量为 mc²，总能量为 γmc²。
- 传播测量不确定度并分析实验数据。
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.
运用定义规则
- 对于独立的微小不确定度，按平方和开方（quadrature）合并各分量；相关不确定度则需要协方差项。
- 识别核物理、粒子物理、凝聚态物理及天体物理概念。
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%.
检查条件
- 随机离散影响精密度；校准偏差影响准确度。对数图可揭示幂律关系。
- 识别核物理、粒子物理、凝聚态物理及天体物理概念。
当 v=0.6c 时，γ=1/sqrt(0.64)=1.25。总能量为 1.25mc²；动能为 (γ−1)mc²=0.25mc²。若 y=ab 且存在相互独立的微小相对不确定度 3% 和 4%，则相对不确定度为 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.
应用题目格式
- 核物理、粒子物理、凝聚态物理及天体物理问题需要本科水平的词汇与模型。仅凭高中物理不足以作为完整的备考课程。
- 识别核物理、粒子物理、凝聚态物理及天体物理概念。
线性相加百分比不确定度得到的是最坏情况界限，而非独立统计标准不确定度。
Which answer fits this case? · 哪个答案符合此案例？
Apply special-relativistic energy and spacetime relations · 应用狭义相对论能量与时空关系
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.
保持区别
- precision 精密度 — 多次测量值彼此接近的程度。
- covariance 协方差 — 用于处理相关不确定度的联合变异度量。
- 应用狭义相对论的能量与时空关系。
- 传播测量不确定度并分析实验数据。
- 识别核物理、粒子物理、凝聚态物理及天体物理概念。
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.