# Tag Info

### Uncertainty Calculation: Applying Product Rule instead of Power Rule

The product rule assumes that the things being multiplied vary independently of one another, which is clearly not the case when multiplying something by itself. As such, the power rule is the correct ...
• 5,317

### How to understand measurement uncertainty (error) from scientific papers in this form 6.67430(15)?

If I read a scientific article and they publish some value like this here 6.67430(15)×10−11. How can I understand what is the real value with 95% confidence interval without knowing how many ...
• 81.8k

### Time and measurement relation to displacement

One way is: "...The unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s$^{−1}$" which ...
• 28.2k
Accepted

### Does the Sun or Moon affect weight measurements on Earth?

As I understand, your question is: at noon, the solar gravity attracts an object on a scale what would turn it lighter. At midnight its gravitational force adds to the Earth's one, and the object ...
• 13.7k
1 vote
Accepted

### Quantum measurement in a strong magnetic field

Measurement requires an interaction between the measured system and some apparatus/external system. In this case you're discovering that measurement would cost some energy to perform, with the cost ...
• 1,579
1 vote

### Time and measurement relation to displacement

Any physical phenomenon that changes in a predictable way over time will do. They don't have to be periodic. Some examples: a particle moving without any forces applying to it travels in a straight ...
1 vote

### Does the Sun or Moon affect weight measurements on Earth?

The Earth itself is in free-fall around the Sun. But people (and everything else) on the surface of the Earth are not quite in free-fall around the Sun because (a) the Earth is rotating and (b) things ...
• 40.9k
1 vote
Accepted

### Operation on one of the EPR particles

You might have gotten it wrong. Sabine says you can modify the state on one particle without modifying the state of the second particle. ChatGPT says the opposite, affecting a single particle in the ...
• 3,978
1 vote
Accepted

### Ideal quantum measurement

Yes orthogonality is required here, but it's basically a given because with the number of degrees of freedom in a macroscopic state, the probability of two macroscopic states having significant ...
• 6,448
1 vote

### Uncertainty measurements done with multiple devices

A better approach will be to do a weighted average. The weights should be the inverse of the variance. This will give greater importance to the more precise measurements. Once you have determined the ...
• 81.8k
1 vote
Accepted

### Uncertainty Calculation: Applying Product Rule instead of Power Rule

As was pointed out by Sandejo's answer, uncertainties only add in quadrature if the two quantities being measured are uncorrelated. The formulas for propagation of uncertainty have additional terms ...
• 43.8k
1 vote

### How to understand measurement uncertainty (error) from scientific papers in this form 6.67430(15)?

You would understand this to indicate that $1.5\times 10^{-11}$ is an estimate of the standard deviation of the mean (often called the standard error). The standard error would contain 68% of the ...
• 120k
1 vote

### What is the 'correct' way of determining uncertainty of an average value from multiple measurements?

None of the above if $n$ is small. John Darby's answer is correct if $n$ is sufficiently large that the departure from a normal distribution caused by the fact that you are trying to estimate the mean ...
• 120k

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