Относительность, лабораторные методы и специальные темы
GRE Subject Test · GRE Physics Тема 6 3:24 Английское озвучивание · Английский + китайские субтитры (встроенные)
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A precise instrument can give consistently wrong results when its calibration is shifted.
精密仪器如果校准发生偏移，就会持续给出错误的结果。
This topic applies special-relativistic energy and spacetime relations, propagates measurement uncertainty through experimental data, and introduces nuclear, particle, condensed-matter and astrophysical ideas.
本主题应用狭义相对论的能量与时空关系，在实验数据中传递测量不确定度，并介绍核物理、粒子物理、凝聚态物理和天体物理的概念。
Special relativity uses gamma equals 1 over the square root of 1 minus v squared over c squared.
狭义相对论使用γ等于1除以根号下1减v平方比c平方。
Rest energy is m c squared and total energy is gamma m c squared.
静止能量是mc²，总能量是γmc²。
For independent small uncertainties, combine contributions in quadrature; correlated uncertainties require covariance terms.
对于相互独立的微小不确定度，以平方和开方的方式合并各项贡献。 存在相关性的不确定度则需要加入协方差项。
Random scatter affects precision; calibration bias affects accuracy.
随机散点影响精密度。 校准偏差影响准确度。
A log plot can reveal a power law.
对数图可以揭示幂律关系。
Nuclear, particle, condensed-matter and astrophysics questions require undergraduate vocabulary and models.
核物理、粒子物理、凝聚态物理和天体物理问题需要本科水平的词汇和模型。
School physics alone is not a complete preparation course.
仅凭中学物理并不足以构成完整的预备课程。
Proper time is measured between two events at one place in a frame.
固有时间是在某一参考系中同一地点发生的两个事件之间测得的时间。
For a particle moving at 0.60 c, gamma is one over the square root of one minus 0.60 squared, which is 1.25.
对于速度为 0.60c 的粒子，γ 等于 1 除以根号下 1 减 0.60 的平方，等于 1.25。
If its mean proper lifetime is 4.0 microseconds, the lifetime in the lab is gamma times that: 1.25 times 4.0, which is 5.0 microseconds.
如果它的平均固有寿命为 4.0 微秒，实验室中测得的寿命就是 γ 乘以它：1.25 乘 4.0，等于 5.0 微秒。
In that time the particle travels v times tau: 0.60 times three times ten to the eight metres per second, times five microseconds, which is 900 metres.
在这段时间内，粒子走过的距离等于 v 乘 τ：0.60 乘每秒 3×10⁸ 米，再乘 5 微秒，等于 900 米。
A lifetime is a mean of a distribution; it does not predict an individual decay time.
寿命是分布的均值，它不能预测单个粒子的衰变时间。
A detector measures four hundred independent radioactive counts in a fixed interval.
一个探测器在固定时间间隔内测量到四百次独立的放射性计数。
State the Poisson standard uncertainty.
请写出泊松标准不确定度。
How many times longer must it count to halve relative counting uncertainty at the same stable rate?
若保持相同的稳定计数率，需要延长多少倍的时间才能使相对计数不确定度减半？
Explain whether this change removes a constant calibration bias.
请说明这种改变是否能消除恒定的校准偏差。
Sigma sub N equals the square root of N, which is 20 counts.
σ_N 等于 N 的平方根，即 20 个计数。
The relative uncertainty is 1 over the square root of N, which equals 0.05.
相对不确定度为 1 除以 N 的平方根，等于 0.05。
Half that relative uncertainty needs four times N, hence four times the interval.
要使相对不确定度减半，需要四倍的 N，因此测量时间也需增加四倍。
Repetition reduces random counting uncertainty, not constant calibration bias.
重复测量只能降低随机计数不确定度，无法消除恒定的校准偏差。
Award absolute uncertainty, relative uncertainty, time factor and bias distinction.
评分要点包括：绝对不确定度、相对不确定度、时间因素以及偏差的区别。
Adding percentage uncertainties linearly gives a worst-case bound, not the independent statistical standard uncertainty.
将百分比不确定度线性相加，得到的是最坏情况下的界限，而非独立的统计标准不确定度。
precision: Closeness of repeated measurements to each other.
精密度：重复测量值彼此之间的接近程度。
covariance: A measure of joint variation used for correlated uncertainties.
协方差：用于关联不确定度的联合变异度量。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆含义，然后改变原始传递中的一个参数并检验极限情况。