📚 IB Physics: Methods for Evaluating Uncertainties and Errors | IB 物理：不确定度与误差的评估方法
In IB Physics, evaluating uncertainties and errors is not an optional extra; it is part of the language used to communicate experimental results honestly.
测量是物理学的核心，但没有任何测量是完美的。像 5.02 g 这样的数值，如果不说明其可信程度，就是不完整的：应写成 5.02 ± 0.01 g。在 IB 物理中，评估不确定度和误差并非可有可无的步骤，而是诚实表达实验结果所必需的语言。
1. Why Uncertainties Matter | 为什么不确定度很重要
A result without an uncertainty cannot be compared with another result or with a theoretical prediction. If one experiment gives 9.81 m s⁻² and another gives 9.79 m s⁻², we cannot decide whether they agree unless each is accompanied by an uncertainty.
没有不确定度的结果无法与另一个结果或理论预测进行比较。如果一个实验得到 9.81 m s⁻²，另一个实验得到 9.79 m s⁻²，在没有各自不确定度的情况下，我们无法判断它们是否一致。
Uncertainty also tells us how much confidence we should place in a conclusion. It helps scientists decide whether a result is consistent with a law, or whether an unexpected outcome needs further investigation.
不确定度还告诉我们应对方结论抱有多大的信心。它帮助科学家判断结果是否符合某个定律，或者一个意外结果是否需要进一步调查。
2. Error versus Uncertainty | 误差与不确定度的区别
Error is the difference between a measured value and the true value. The true value may never be known exactly, so the actual error is often unknown.
误差 是测量值与真实值之间的差异。真实值可能永远无法精确得知，因此实际误差通常是未知的。
Uncertainty length of 12.0 ± 0.2 cm suggests the true length is probably between 11.8 cm and 12.2 cm.
不确定度 是真实值可能落在的一个数值范围。它不是错误，而是对怀疑程度的量化估计。例如，长度 12.0 ± 0.2 cm 意味着真实长度可能在 11.8 cm 和 12.2 cm 之间。
3. Random and Systematic Errors | 随机误差与系统误差
- Random errors cause readings to scatter above and below the true value. They may be caused by human reaction time, slight changes in conditions, or electrical noise. Random errors reduce precision and can be reduced by repeating measurements and averaging.
- 随机误差使读数在真实值上下分散。它们可能由人的反应时间、条件轻微变化或电噪声引起。随机误差降低精密度，可以通过重复测量并取平均来减小。
- Systematic errors push all readings in the same direction. They are caused by zero errors, poorly calibrated instruments, or incorrect technique. Averaging cannot remove systematic errors, and they reduce accuracy.
- 系统误差使所有读数朝同一方向偏移。它们由零误差、校准不良的仪器或不正确的操作方法引起。取平均不能消除系统误差，这类误差降低准确度。
4. Absolute, Relative and Percentage Uncertainty | 绝对、相对与百分比不确定度
unit. If a resistance is measured as 24.6 ± 0.4 Ω, then 0.4 Ω is the absolute uncertainty.
绝对不确定度与测量值一同记录，并带有相同单位。如果测得电阻为 24.6 ± 0.4 Ω，那么 0.4 Ω 就是绝对不确定度。
The relative uncertainty compares the uncertainty with the measured value. The percentage uncertainty is the relative uncertainty multiplied by 100 %:
相对不确定度将不确定度与测量值进行比较。百分比不确定度是相对不确定度乘以 100 %：
relative uncertainty = Δx / x
percentage uncertainty = (Δx / x) × 100 %
m, the relative uncertainty is 0.2 / 4.8 = 0.042, and the percentage uncertainty is about
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