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Questions tagged [error-analysis]

Techniques and methods for computing, estimating, or placing bounds on the errors of expressions (formulas) based on knowledge of error distributions, error intervals or bounds of variables and parameters entering those expressions, and of methods used in the computations.

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Human error in wave experiment

I am trying to see what the fundamental frequency of a string is by slowly increasing the frequency on a function generator. This experiment relies on the experimenter to record the frequency as soon ...
risa's user avatar
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1 vote
1 answer
73 views

Combination of errors when $1/z = 1/a + 1/b$ [closed]

It is mentioned directly in every text I could find that, if $$\frac{1}{z} = \frac{1}{a} + \frac{1}{b}$$ then $$\frac{\Delta z}{z^2} = \frac{\Delta a}{a^2} + \frac{\Delta b}{b^2}.$$ How we came to ...
Omkar Deshmukh's user avatar
0 votes
3 answers
55 views

Significant figures when product is more by a factor of 10

A rectangular plate has a length of 21.3 cm and a width of 9.8 cm. Calculate the area of the plate. A straightforward question, which you multiply and arrive at 208.74 cm2. Taking significant figures ...
InquisitiveLad's user avatar
-1 votes
1 answer
72 views

Why do we use perturbation theory instead of statistical error?

In perturbation theory, the solution to a given quantum physical problem cannot be solved to an exact precission. But the approximate function which yields similar solutions can be improved by adding ...
groaking's user avatar
3 votes
0 answers
45 views

Is there a sigma for unexplained hypothetical discoveries?

I recently read that the Koide formula relating electronic leptons rest masses is often considered to be numerologic, since unexplained, even though recent years experiment data tend to narrow the ...
olivierlambert's user avatar
2 votes
2 answers
52 views

How can I determine an error on total noise?

I am analyzing the data for an experiment, where we measured the total noise in a system. The total noise is defined as the variance of the signal (and is equal tot the integral over the noise ...
LemanRussNL's user avatar
2 votes
0 answers
63 views

Vernier Caliper Measurement [duplicate]

My doubt is regarding the formula for measurement using a vernier caliper. In my class we were taught the following formula: $Reading = MSR + n(LC)$ (p) (here MSR stands for main scale reading and LC ...
entropy's user avatar
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14 votes
4 answers
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If gravitation is negligible for small masses, how was Cavendish's experiment successful with balls much smaller than celestial objects?

If gravitation is negligible for small masses, then how was Cavendish's experiment a success since the balls used were very small compared to the sizes of celestial objects?
JAYANT SINGH GBPP's user avatar
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1 answer
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What type of variable would you classify $a, b, c$ etc shown in the picture? Would I just call them random, insignificant real values? [closed]

The variables don't really represent anything
Yifan YIN's user avatar
1 vote
1 answer
73 views

Resolution and delta function

Any attempt to measure the value of a physical quantity is limited, by the finite resolution of the measuring apparatus used. on the one hand the physical quantity we wish to measure will be in ...
Hello's user avatar
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1 vote
2 answers
59 views

Numerical solution of differential equations, e.g. the three-body problem

What forms of differential equations have numerical solutions with errors that go to zero with sufficient computational power? For example, suppose I want to solve a differential equation $E$ for a ...
Alex's user avatar
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2 votes
1 answer
265 views

Are zeros to the right really significant? [duplicate]

In one of YouTube lectures about significant digits I saw this: I was completely shocked. Both scientific notation numbers when converted to integer would represent same quantity of $1200 \text{kg}$ ...
Agnius Vasiliauskas's user avatar
2 votes
0 answers
38 views

How are uncertainties of the quantum state/wavefunctions themselves modeled?

This question might be confusing so let me try to clarify this carefully. The wavefunction is a tool that allows us to calculate probability distributions that model uncertainties. Thus makes sense. ...
Maximal Ideal's user avatar
0 votes
1 answer
36 views

Does changing units affect Significant Figures

Does changing the unit of a physical quantity has no influence whatsoever on the number of significant figures? Suppose the mass of a particle is given as 0.060kg 0.060 has 2 significant figures as ...
Vignesh's user avatar
5 votes
2 answers
190 views

Why using sigmas instead of p-values in particle physics?

Motivated by this question in Statistics community: Why do physicists use sigma while biologists use p values/posterior probabilities?. After discussion it essentially reduces to: why assuming normal ...
Roger V.'s user avatar
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1 vote
2 answers
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Confidence level on excluded lifetime of decay

Could someone help me understand the ideas behind setting confidence levels on decay lifetimes. Like what Super K has been doing on the proton. Given the count rate of the decays is a poisson ...
Jasper amirante's user avatar
1 vote
1 answer
61 views

Why is the uncertainty of the Gravitational Constant $G$ many orders of magnitude larger than that of other important fundamental constants?

Why is the numerical range of uncertainty of the Gravitational Constant $G$ many orders of magnitude larger than that of other important fundamental constants? What are the challenges in precise ...
Alex's user avatar
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0 votes
1 answer
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How to add and subtract significant figures?

There are actually two ways given to add or subtract significant figures in different books .In books like concepts of Physics by HC Verma it is written that round of the numbers given first and then ...
ARNAV CHADHA's user avatar
0 votes
1 answer
34 views

Limiting factors in traditional microscopy

I have been researching Entanglement-Enhanced Microscopy, and the overall breakthrough seems to be obtaining a resolution of $1/N$ as opposed to $1/\sqrt N$. This led me to ask what the limiting ...
murtadee hughes's user avatar
1 vote
1 answer
25 views

Difference between these two equations to calculate uncertainty when multiplying

I have seen these 2 equations for how to calculate the uncertainty when 2 numbers (that have uncertainty) are multiplied. $$(A\pm a)\times(B\pm b)=(A\times B)\pm \left[\left(\frac{a}{A}\cdot100\right)+...
John Hon's user avatar
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3 votes
1 answer
82 views

Why is the term 'Accuracy of 1 part in $x$' used?

My question stems from how we measure the accuracy of Caesium clocks. Most Caesium clocks are said to have an accuracy of '$1$ part in $10^{14}$.' I understand that the terminology means to convey ...
Smarika Singh's user avatar
1 vote
0 answers
25 views

Does the mean of multiple measurements of one sensor reduce the sensor error, in the case of a data-logged K-type thermocouple?

I'm doing an experiment to measure steady-state heat transfer conditions. I have a hot plate connected to a power supply which supplies a constant current (~1.880A in this run). It is very precise, ...
Cloudyman's user avatar
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1 vote
2 answers
121 views

Question regarding error analysis of focal length of a lens [duplicate]

The question in whose context i am asking this question is as follows In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10 \pm ...
koiboi's user avatar
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1 vote
1 answer
45 views

Uncertainty due to assuming a variable is constant - Adiabatic Invariance

I am studying classical mechanics from Goldstein and I ran into a confusing equation in the textbook. In the third edition of the book, equation (12.92) calcucates the average change of the action ...
patrick7's user avatar
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2 votes
3 answers
53 views

How do I find the individual relative uncertainties of cubed terms in an equation and use this to find the absolute uncertainty of a value?

I'm currently conducting a physics project for school and I am really stuck on uncertainties. I am trying to calculate the overall uncertainty in Young's Modulus, with the Bending Beam experiment ...
Rose's user avatar
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2 votes
0 answers
63 views

What does the Jacobi identity *mean* statistically?

Given that the commutator of a pair of operators shows up explicitly in the lower bound of the Robertson-Schrodinger inequality, I am wondering what, if any, statistical meaning/significance one can ...
hyportnex's user avatar
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0 votes
1 answer
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Measuring distances between the stars

If we know how far away are the two known stars from Earth, then is it a safe bet that we can know how far apart those two stars are from each other using sine rules? Does that mean we must first ...
user6760's user avatar
  • 13k
0 votes
1 answer
65 views

Significant Figures when dealing with bearings

Significant figures are used to ensure that the value is precise, and fall in within error in the positive and negative direction. 327 degrees true can also be written as N33degreesW. As such, would ...
Jay Chen's user avatar
-1 votes
2 answers
111 views

Is there a physical cause of uncertainty? [closed]

The uncertainty principle is confusing me. Considering this image from the article: Is the particle believed to be physically moving with similar capriciousness in real space; and if so, what ...
jazamm's user avatar
  • 91
0 votes
1 answer
45 views

Determine the more accurate way of measuring the angle

I need to measure an acute angle in a right triangle. There are $2$ methods. Use a protractor with precision to $1^\circ$ to measure the angle. The result is $5^\circ$. Use a ruler with precision ...
youthdoo's user avatar
  • 147
0 votes
1 answer
63 views

How precisely can change in temperatute be modeled without a thermometer?

This is mainly a gastronomical question, however, it is not exactly trivial. I'll present the setting in the form of a problem: In order to make a dessert, the recipe states that we have to "...
Simón Flavio Ibañez's user avatar
0 votes
0 answers
58 views

Why is the inherent error in measurement of position of particle of the order of $\frac{\lambda}{2}$?

The setup is : To measure the position of a moving particle, we send a light beam and we calculate the time required ($t_0$) for the light to travel to the particle, reflect and come back. we can use ...
Thejas S's user avatar
0 votes
1 answer
92 views

Error on the calculation of area of a circle

I am currently writing an investigation for my high school diploma, and I am a little rusty on uncertainties and error propagation. So I was wondering whether I could get some help on a doubt I had. ...
Miles Jarra Gloekler's user avatar
0 votes
0 answers
26 views

How do you do error propagation for Logarithmic equations? [duplicate]

my equation is a=10log_10(x/10^-12). I have the error value for a, but I'm struggling to propagate the error for x
user391458's user avatar
2 votes
0 answers
84 views

Interpreting non-normalized covariance matrix eigenvalues as physical Actions

Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). Can we interpret this to obtain ...
user3716267's user avatar
0 votes
3 answers
203 views

Which of the classifications and different ways of expressing is correct?

I know that uncertainty in measurement is different from measurement error (1). But when it comes to classification (of uncertainty and error) and different ways of expressing uncertainty and error in ...
Altair25's user avatar
  • 103
7 votes
4 answers
2k views

What is the difference between "Error" and "Uncertainty"?

Error of measurement is defined as the result of a measurement minus a true value of the measurand (Source: Page no. 36) Uncertainty (of measurement) is a parameter, associated with the result of a ...
Altair25's user avatar
  • 103
3 votes
0 answers
39 views

Minimizing difference between two quantities with uncertainties

I'm a bit confused on how to approach a minimization/uncertainty problem. Say we have some function: $ a(b) = \int_{0}^{b} \frac{dx}{1 + C \cdot g(x)} $ And we have experimentally determined $ a_{\...
jimbertothy's user avatar
6 votes
3 answers
2k views

What is meant by precision of a measuring instrument?

I came across many definitions of the precision of a measuring instrument such as, "a precise measuring tool is one that can measure values in very small increments" and "The precision ...
Altair25's user avatar
  • 103
0 votes
0 answers
15 views

What is a simple way to estimate $σ_{RV}$ assuming photon noise in radial velocity measurements?

Hello there i have been trying to figure out what is wanted in the question "Simple way to estimate σ_RV assuming photon noise" for a presentation. But i can not seems to find much, but i ...
GodOfDemoting's user avatar
2 votes
2 answers
327 views

Errors when the quantity is an exponent

Errors add up in addition or subtraction. Relative errors add up in multiplication or division. When a quantity is raised to a power, the error is increased by times of the exponent. Now what if the ...
user avatar
1 vote
1 answer
79 views

How to use error propagation formula in equation with inseparable variables?

$$ R_i(t) = \frac{\mu_{s,E_i}+\mu_{s,E_0}}{\mu_{s,E_i}-\mu_{s,E_0}} \cdot \frac{e^{-\rho\sqrt2\mu_{s,E_0}}-e^{-\rho\sqrt2\mu_{s,E_i}}}{1-e^{-\rho\sqrt2(\mu_{s,E_0}+\mu_{s,E_i})}}. $$ How do I can find ...
Anchal Kumar Sharma's user avatar
7 votes
1 answer
1k views

Observation of the effect of gravity on the motion of antimatter

In a recent paper (https://www.nature.com/articles/s41586-023-06527-1), the authors state that we find that the local gravitational acceleration of antihydrogen is directed towards the Earth and has ...
Jim421616's user avatar
  • 316
0 votes
1 answer
88 views

Mass, time and length are measured with 5% accuracy each, what will be the total accuracy in torque? [closed]

I don't understand the solution of the above question, the solution i know is :- Accuracy in torque = [M%] + [2 × L%] + [2 × T%] Which will be equal to 25% I dont understand why 2 was multiplied to L% ...
nevedhya's user avatar
0 votes
0 answers
30 views

Estimation of errors in actual experiments

I encountered a statement in a research paper I read which confused me- “In order to estimate the random error in our data, we calculated the average distance between a line of best fit and the ...
Akarsh Sahay's user avatar
2 votes
1 answer
106 views

What is the error in a naive computation of a path integral? [closed]

If I were to try to brute force compute the following integral: $$F(t_{i-1}, x_{i-1})= e^{-r(t_{i}-t_{i-1})}\int_{-\infty}^{\infty} dx_{i} \cdot G(x_{i}, t_{i}|x_{i-1}, t_{i-1})F(t_i, x_{i}),$$ where $...
NX37B's user avatar
  • 239
26 votes
4 answers
6k views

What is the minimum temperature difference which can be measured?

All real things have temperature. Temperature can be measured in various ways. We have reached to a great precision in measuring change in time and space , however I am not sure to what extent change ...
SacrificialEquation's user avatar
0 votes
1 answer
108 views

Curve fitting and error propagation for non-independent quantities

I have measurement values $y_\mu$ at times $t_\mu$; the should follow a function $y(t) = f_t \, \cos (\Omega_t\cdot t - \delta)$ where $f_t, \Omega_t$ are slowly varying functions (currently I am ...
TomS's user avatar
  • 917
1 vote
2 answers
50 views

Optimizing accuracy of different basketball shots [closed]

I have a high school math project and chose to work on basketball trajectory because I thought I would enjoy it the most. But honestly, I have a hard time calculating a 3D trajectory. So I thought ...
Nicolas's user avatar
  • 11
0 votes
1 answer
54 views

What can one say about the precision of the experiment if horizontal error-bars are wide and vertical error-bars are very small?

After conducting a physics experiment I plotted the data with their respective uncertainties. My horizontal error-bars for the independent variable are wide but vertical error-bars for the dependent ...
Alex's user avatar
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