111 votes
Accepted

How do you make more precise instruments while only using less precise instruments?

I work with an old toolmaker who also worked as a metrologist who goes on about this all day. It seems to boil down to exploiting symmetries since the only way you can really check something is ...
user avatar
  • 7,720
102 votes
Accepted

What reference clock is an atomic clock measured against?

This is a good and somewhat tricky question for a number of reasons. I will try to simplify things down. SI Second First, let's look at the modern definition of the SI second. The second, symbol s, ...
user avatar
  • 9,438
78 votes
Accepted

Why is a leading digit not counted as a significant figure if it is a 1?

Significant figures are a shorthand to express how precisely you know a number. For example, if a number has two significant figures, then you know its value to roughly $1\%$. I say roughly, because ...
user avatar
  • 95.5k
76 votes

Why should a clock be "accurate"?

why it is necessary for a reference clock to worry about this, if the definition of the second itself is a function of the number of ticks the clock makes. The concern is that somebody else (say a ...
user avatar
  • 23.2k
75 votes
Accepted

In nuclear physics, what length year in seconds is used?

A "year" without qualification may refer to a Julian year (of exactly $31\,557\,600~\rm s$), a mean Gregorian year (of exactly $31\,556\,952~\rm s$), an "ordinary" year (of exactly $31\,536\,000~\rm s$...
user avatar
  • 16.8k
65 votes
Accepted

Are random errors necessarily Gaussian?

Are random errors necessarily gaussian? Errors are very often Gaussian, but not always. Here are some physical systems where random fluctuations (or "errors" if you're in a context with the thing ...
user avatar
65 votes

How exactly do you avoid fooling yourself?

There are lots of different strategies that are employed by the scientific community to counteract the kind of behavior Feynman talks about, including: Blind analyses: In many experiments, it is ...
user avatar
59 votes

How do you make more precise instruments while only using less precise instruments?

The more you measure things and add or multiply those measurements, the greater your errors will become. Not necessarily. If the errors in a series of measurements are independent and there is no ...
user avatar
  • 35.5k
44 votes

What does the notation $8.9875517923(14)$ mean?

It's the uncertainty in the last two digits: $$8.9875517923(14) = \color{blue}{8.987\,551\,79}\color{red}{23} \pm \color{blue}{0.000\,000\,00}\color{red}{14}. $$
user avatar
  • 23k
42 votes

How exactly do you avoid fooling yourself?

My favorite story (which I learned about recently) is about Frank Dunnington and his measurements of electron properties in about 1930. He was measuring the ratio $e/m_e$. Experiments took quite a ...
user avatar
  • 4,019
42 votes

Why should a clock be "accurate"?

For most of human history, we had a single mechanical clock: the spinning Earth. Well, actually two mechanical clocks. The Earth’s spin rate is a good constant, but it’s tricky to measure directly. ...
user avatar
  • 74.3k
36 votes

What reference clock is an atomic clock measured against?

BIPM and TAI The International Bureau of Weights and Measures (BIPM) in France computes a weighted average of the master clocks from 50 countries. That weighted average then gives International Atomic ...
user avatar
36 votes

How long is a second?

A second is a second long by definition, but if you measure any time in seconds, the number of seconds you infer will be subject to an error of at least $\mathcal O(10^{-15})$ because of the ...
user avatar
  • 4,472
35 votes

Why aren't the 0's significant figures in 0.002?

Because significant figures measures uncertainty relative to the size of the number Suppose you take a measurement of something and it comes out to be 0.002 meters. You then measure something else ...
user avatar
  • 509
34 votes
Accepted

Uncertainty in parenthesis

The digits in parentheses are the uncertainty, to the precision of the same number of least significant digits. (The meaning of the uncertainty is context-dependent but generally represents a standard ...
user avatar
  • 456
29 votes

How do you make more precise instruments while only using less precise instruments?

One thing I haven't seen mentioned is amplification. Amplification: Imagine you have a lever that is 10 cm on one side of the pivot and 1 m on the other. Then any change in position on the short side ...
user avatar
27 votes

Why is the standard uncertainty defined with a level of confidence of only 68%?

We talk in terms of standard deviation because this is traditionally the quantity you use to specify the variance of a Gaußian distribution specifically and any random distribution more generally. You ...
user avatar
  • 108k
26 votes

How do you make more precise instruments while only using less precise instruments?

That's a really nice one! I'm not an expert on experiments and measurements but this is how I see it: The ultimate calibration tool is always nature. We pick special phenomena which rely on certain ...
user avatar
  • 1,441
25 votes
Accepted

How to deal with zero uncertainties?

Use the second derivative (or third, or whatever). The reason we use that formula is that $$ df \approx \frac{df}{dx} dx $$ is the first order Taylor approximation to df. If the first order term ...
user avatar
  • 7,611
25 votes

What is the accuracy of our knowledge about the planets orbits?

This one is tricky unless you know the magic term: ephemeris. An ephemeris gives the position of celestial bodies over time. Once you know that one, finding out information about their uncertainties ...
user avatar
  • 43.1k
25 votes
Accepted

The Electron at the End of the Universe

The calculations are done in Schwartz (2019), Lecture 3: Equilibrium (https://scholar.harvard.edu/files/schwartz/files/3-equilibrium.pdf) Here's a summary of the key equations, using the notation ...
user avatar
24 votes
Accepted

Why don't we use absolute error while calculating the product of two uncertain quantities?

It basically comes from calculus (or more generally just the mathematics of change). If you have a quantity that is a product $z=x\cdot y$, then the change in this value based on the change of $x$ and ...
user avatar
  • 53.8k
23 votes
Accepted

What does it mean to "bin" in a spectroscopy context

Suppose you are analysing the weights of people in the UK to see what the distribution of weights looks like. Suppose also you can measure the weight to arbitrary precision, so that no two people's ...
user avatar
23 votes

If a measurement has 5% error, can we say it has 95% accuracy?

Prefer “uncertainty” over “error.” When you say “error” you imply that Someone Out There has determined the Right Answer. This isn’t how it works outside of an introductory lab class. When you say “...
user avatar
  • 74.3k
23 votes

Why should a clock be "accurate"?

if the definition of the second itself is a function of the number of ticks the clock makes. Why don't we just use a single simple mechanical clock somewhere with a wound up spring that makes it tick,...
user avatar
  • 7,720
20 votes

Why aren't the 0's significant figures in 0.002?

The notion of "significant figures" is meant to communicate how much you know about a number. A number with one sig fig means you know it to roughly one part in $10$, two sig figs mean you know it to ...
user avatar
  • 95.5k
20 votes

How do you make more precise instruments while only using less precise instruments?

Measurement errors can accumulate, yes. But we are not talking about measurements here, we are talking about processes and tooling. That's another deal. If you fling off a piece of flint from a ...
user avatar
  • 47.2k

Only top scored, non community-wiki answers of a minimum length are eligible