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RA · Relativity, laboratory methods and specialised topics

GRE · GRE Subject Test · GRE 物理 · 知识点 6

训练
6.1

相对论、实验方法及专题内容

A precise instrument can give consistently wrong results when its calibration is shifted.

Prerequisites: 21, 22, 42, 43, 44.

  • Apply special-relativistic energy and spacetime relations
  • Propagate measurement uncertainty and analyse experimental data
  • Recognise nuclear, particle, condensed-matter and astrophysical concepts
6.2

Choose the system and model

Special relativity uses γ=1/sqrt(1−v²/c²). Rest energy is mc² and total energy is γmc².

6.3

Use the governing relation

For independent small uncertainties, combine contributions in quadrature; correlated uncertainties require covariance 协方差 terms.

词汇 训练
English 中文 拼音
covariance/ˈkɒveərɪəns/ 协方差 xié fāng chà
6.4

Apply the conditions

Random scatter affects precision 精密度; calibration bias affects accuracy. A log plot can reveal a power law.

词汇 训练
English 中文 拼音
precision/prɪˈsɪʒn/ 精密度 jīng mì dù
6.5

Check the conclusion

Nuclear, particle, condensed-matter and astrophysics questions require undergraduate vocabulary and models. School physics alone is not a complete preparation course.

6.6

Worked method

Proper time 固有时 is measured between events at one position in a frame. For a particle speed 0.60c,

$$\gamma=(1-v^2/c^2)^{-1/2}=(1-0.60^2)^{-1/2}=1.25.$$
If its mean proper lifetime is 4.0 microseconds,
$$\tau=\gamma\tau_0=1.25(4.0\,\mu\mathrm s)=5.0\,\mu\mathrm s.$$
$$\bar d=v\tau=(0.60)(3.00\times10^8\,\mathrm{m/s})(5.0\times10^{-6}\,\mathrm s)=900\,\mathrm m.$$
A lifetime is a mean of a distribution; it does not predict an individual decay time.

Relativity, laboratory methods and specialised topics: GRE original diagram
Relativity, laboratory methods and specialised topics: original GRE teaching diagram.
词汇 训练
English 中文 拼音
Proper time/ˈprɒpə taɪm/ 固有时 gù yǒu shí
6.7

Check conditions and vocabulary

Adding percentage uncertainties linearly gives a worst-case bound, not the independent statistical standard uncertainty.

precision: Closeness of repeated measurements to each other.

covariance: A measure of joint variation used for correlated uncertainties.

该知识点的互动课程

逐步完成，配合即时检查练习。

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