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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
-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
1 vote
0 answers
17 views

How do I calculate the significance level (in Gaussian Sigma) of a particle classification's classier results/

I'm doing a high school project for which I'm training a Neural Network to classify signal and background events with this dataset: https://www.kaggle.com/datasets/janus137/supersymmetry-dataset/data ...
SidKT's user avatar
  • 21
2 votes
0 answers
40 views

What is the interpretation of the covariance of two quantum observables?

I have been studying the covariance matrix in continuous variable quantum systems and I am struggling to understand the interpretation of this object. In statistics the covariance measures the joint ...
Hermitian_hermit's user avatar
1 vote
2 answers
63 views

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
2 votes
0 answers
43 views

Why does the entropy not decrease when inserting a partition into a macroscopic amount of different particles? [duplicate]

Here is a thought experiment. Imagine a box with 10^20 different particles, all different types of molecules, such that they are not indistinguishable according to QM. I insert a parition in the ...
Amit Levy's user avatar
  • 170
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
  • 2,356
1 vote
2 answers
120 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
  • 173
0 votes
0 answers
52 views

Standard deviation for a free path distribution

I would like to be able to describe a particles path before collisions with greater precision. We can calculate the "mean" free path of a particle before colliding moving particles, but I ...
Roman Grachev's user avatar
4 votes
0 answers
112 views

Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments

The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
Omid's user avatar
  • 342
0 votes
0 answers
66 views

Use of Binder Cumulant for Determining Critical Temperature

I am completing a computational project where I am simulating the Ising model using Monte Carlo methods, namely the Metropolis-Hastings algorithm, and the Wolff algorithm. For the Metropolis-Hastings ...
Thomas's user avatar
  • 155
1 vote
1 answer
110 views

Interpretation of a probability that does not normalize to one in stat mech?

I am trying to understand the meaning of the "n-particle distribution function" as defined by the three references below([1][2][3]), primarily those by Claudio Zannoni. Setup: For a system ...
McKinley's user avatar
0 votes
1 answer
58 views

Quantum Chemistry Help FWHM [closed]

I am struggling with this question and cannot find any resources to help me. Even the tutors at my school don't know how to help me and my professor just tells me to reference the slides, but I have ...
Lorena Alvarado's user avatar
0 votes
0 answers
7 views

Calculation of angular frequency and wave vector from time series data using minimum variance method

Suppose, I have 20 data for the velocity components Vx, Vy and Vz with 5 minutes interval of time, how to find the angular frequency and wave vector using minimum variance method for those data? What ...
Tasnim's user avatar
  • 31
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0 answers
32 views

Determine the entropy of an ideal bosonic gas

I am struggling with this problem. So we're told that any macroscopic state of a gas can be characterized by microscopic stated of a single particle. We divide the microscopic states into groups. So $...
PhysicsStudentInPain's user avatar
0 votes
0 answers
14 views

Statistics on Cauchy Distributed Data

So the Cauchy/Lorentz distribution is often used to describe distributions in physics (e.g. resonance). But theoretically, the Cauchy/Lorentz Distribution does not have a defined mean and variance, ...
Mars's user avatar
  • 1
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
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
1 vote
1 answer
28 views

How is the normalized probability function used in the variance? [closed]

For context this is the very beginning of stat mech. I understand how the definition of the mean was used but I don't know how we went from part 2 to 3 (going left to right in the series of equations)....
dingobruh's user avatar
0 votes
1 answer
57 views

Can someone please elaborate an answer about torque? [duplicate]

Please explain Michael Seifert's answer here I think $x,y$ are distances but what is $d$? How did he get this formula? x cos ⁡ θ + d sin ⁡ θ Does this ...
ChemistryLearner'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
1 vote
1 answer
104 views

Ising model and the axiomatics of Statistical Mechanics

I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
MsTais's user avatar
  • 1,184
1 vote
1 answer
46 views

What is the optimal measuring time split for limited measuring time between signal+background and background in a Poisson counting experiment?

I’m trying to figure out the best split of time between measuring either background or signal+background in a counting experiment in the case where we have no prior knowledge about the mean signal ...
Physicist_285'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
0 votes
1 answer
62 views

Distribution sampling from a trajectory

Consider a sequence of random variables $\{X_1, X_2,.., X_n\}$ corresponding to regular measurements of a single observable over time obtained from a laboratory or computer experiment. Assume that the ...
gatsu's user avatar
  • 7,262
4 votes
1 answer
531 views

How large a closed system does the 2nd law of thermodynamics require?

Does the second law of thermodynamics apply to a single electron in deep space? Or two electrons? Or 100? (assume the electrons are restricted in a finite area) From which point we can start to talk ...
Merci chao's user avatar
1 vote
2 answers
155 views

Mean squared displacement of a particle on a biased random walk [closed]

Given a particle on a 1-D random walk with some drift velocity $\nu_d = \frac{\Delta x_d}{\Delta t}$, the position in at some time step j is given by $$x_j=x_{j-1}+k_j L + \Delta x_d$$ where $L$ is ...
mertvy's user avatar
  • 13
0 votes
0 answers
40 views

Which statistical methods are better than basic random scans for studying and exploring the parameter space of extensions of the standard model?

Given a lagrangian of a new model beyond the standard model, and given a set of constraints, say the oblique parameters for instance and the decay of the higgs boson and some signal strengths and ...
Collector101's user avatar
0 votes
1 answer
490 views

Measurement Error Analysis in Gaussian distribution

I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet ...
Govind Prajapat's user avatar
0 votes
1 answer
62 views

From where does the uncertainty formula come from? [duplicate]

The uncertainty formula is the one used in the laboratories to find the uncertainty of a variable. Say $X$ is a function of $Y$ and $Z$ such that $X=X(Y,Z)$ then it's uncertainty can be found with: $$\...
Ulshy's user avatar
  • 69
2 votes
0 answers
39 views

Integral over rapidly randomly fluctuating function [closed]

As a part of my bachelor thesis on cosmic structure formation I have been dealing with a sum of many randomly distributed phase factors, so in principle with a pearson random walk. If there are $N$ ...
Ricardo Ochel's user avatar
2 votes
1 answer
130 views

Why don't I get a whole number when determining the vibrational energy level of F2?

So I was playing around with some data and formulas and wanted to calculate the index for the wave number of the vibration of F2 that I got from here, i.e. which allowed energy level n this ...
iwab's user avatar
  • 211
2 votes
2 answers
232 views

Median Uncertainty propagation

I have a data set of values each with a different associated error. If I take the mean, I can use standard error propagation to calculate a much smaller error. This will therefore incorporate the ...
Isaac Holst's user avatar
0 votes
1 answer
112 views

Error analysis for counting experiments

i am trying to refresh my knowledge in error analysis and stumbled over an interesting question. Suppose i have a radioactive compound and i want to measure the standard deviation of the decay count. ...
vreithinger's user avatar
4 votes
2 answers
853 views

Error analysis via two different methods

We have a quantity $a$ expressed in terms of two quantities $b $ and $c$ as $a = b/c$. It seems to me that there are two ways of estimating the error on $a$, the "physics" ...
Govind Prajapat's user avatar
0 votes
1 answer
56 views

Correct Way to Calculate Uncertainty [closed]

Given a function $f(x_1,x_2,...,x_n)$ of $n$ uncorrelated variables $x_1,x_2,...,x_n$, each of which has some small absolute uncertainty $\Delta x_1,\Delta x_2,...,\Delta x_n$, I know that the ...
SurfaceIntegral's user avatar
21 votes
7 answers
2k views

Line of Best Fit with or Without Constant Term

Some other physics teachers and I were discussing an AP problem about a potential experiment for measuring $g$ and disagreed on the best way to use a line of best fit to analyze the data. The ...
Luke Pritchett's user avatar
1 vote
2 answers
115 views

Units in a Poisson probability mass function

I'm trying to calculate a likelihood ratio test, but some of the units in the calculation don't make sense to me. I have a toy 1-dimensional X-meters-long photon detector, and I'm trying to calculate ...
radioactive.fade's user avatar
0 votes
2 answers
259 views

Can the standard errors in the slope and the intercept of a linear regression be used to get the uncertainty in the dependent variable?

I have bought a resistor that works as a heater when a voltage is applied to it, and the seller provided me these $ \left(V (\mathrm{V}), T (\mathrm{°C})\right)$ points: $(6.20$, $200)$, $(7.75$, $250)...
user21390097's user avatar
0 votes
0 answers
66 views

Why on the ATLAS Higgs discovery paper there are uncertanties on the expected cross section upper limits but not on the observed upper limits?

I was reading the ATLAS paper on the Higgs discovery and a question came to my mind. In the plot I attached, there are uncertainty bands on the background only hypothesis upper limits, and not on the ...
Matthew D.'s user avatar
1 vote
1 answer
219 views

Level spacing statistics of the quantum Ising model

Consider the quantum Ising model defined by the Hamiltonian \begin{equation} \hat H=-\sum_j\hat\sigma_j^z \hat\sigma_{j+1}^z-h\sum_j \hat\sigma_j^x-g\sum_j\hat\sigma_j^z. \end{equation} For $g=0$, ...
Noobgrammer's user avatar
2 votes
1 answer
625 views

Significant figures and angles

We measure an angle to be -55 degrees (2 sigfigs). Let us take the sine of this angle. We get sin(-55) (2 sigfigs). Now, since sin(-55)=sin(305), then we can also take the sin(305) (3sigfigs). Now, ...
wos's user avatar
  • 123
1 vote
0 answers
122 views

Wilson Coefficients in the Standard Model

I'm not particularly knowledgeable in this area of physics. From my understanding as an undergraduate, Wilson coefficients are sets of parameters that arise from an effective field theory which ...
probablysid's user avatar
4 votes
2 answers
526 views

How can I resolve this apparent paradox about the average age and the average lifetime?

I've got very much confused about distributions and am looking for quick help. Distributions are common in physics, so I humbly hope to receive an answer that will resolve my confusion. Let's suppose ...
Mitsuko's user avatar
  • 1,599
1 vote
1 answer
86 views

Uncertainty measurements done with multiple devices

so I need to calculate the volume of a cylinder. I have measured both the radius and the height with three different devices (ruler, calipers, micrometer), each of them 10 times (total 90 measurements)...
Charlie's user avatar
  • 11
2 votes
1 answer
142 views

Problem with the Fisher information matrix in case of $N$ measurements of two observables

Let consider two observables, $x$ and $y$. Suppose that $y$ depends on the independent variable $x$ through the model $m(x; \boldsymbol{\theta})$, where $\boldsymbol{\theta}$ is a vector of model ...
Wil's user avatar
  • 43
2 votes
2 answers
245 views

Uncertainty Calculation: Applying Product Rule instead of Power Rule

I use $\delta$ to represent absolute uncertainty. The power rule for the calculation of relative uncertainty in $t^2$ is $$\frac{\delta (t^2)}{(t^2)}=2\left(\frac{\delta t}{t}\right).$$ But if I treat ...
BoundaryCondition's user avatar
-1 votes
1 answer
91 views

Is there sufficient "content" in the field of econophysics to write a substantial undergraduate thesis/project on? [closed]

Okay, maybe the title is somewhat misleading. My university calls this a BSc Project, but it is limited to between 4000 and 6000 words, so it isn't particularly long. Anyhow, one of the projects ...
probablysid's user avatar

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