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1
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1answer
144 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
0
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1answer
52 views

Can the uncertainty principle be redefined for different standard deviations?

$$\sigma_x \cdot \sigma_p \ge {{\hbar} \over {2}}$$ Where the $\sigma$ is the standard deviation. What happens to the inequality if you use a different definition of $\sigma$. For instance what ...
0
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1answer
170 views

Is there a fundamental difference between the statistical methods of science, comparing medicine to physics?

Is there a fundamental difference between the statistical methods of science, comparing medicine/biology with small sample sizes(n < 10^2 or 10^3) to the statistics applied in Quantum Mechanics (h: ...
11
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1answer
278 views

Statistical analysis of data in Physics

Analysis of data is integral in bridging the gap between theory and experiment. How much do the results of the analysis depend upon the choice between Bayesian and frequentist methods? For instance, ...
0
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0answers
12 views

Averaging Multiple Load Graph Values

I'm aware this is a problem of statistical analysis, but given my background in physics and the physical nature of the problem I felt it was best to ask this question in this SE rather than ...
0
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0answers
19 views

How to describe frequency spectrum with samples?

I posted this same question in math, but nobody is answering, so I thought I'd give a try here too... To me the question is pretty straightforward, but nevertheless I have to explain its background ...
0
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0answers
19 views

Can I use the Chi squared test to see if my data fit to the Wigner-Dyson distribution indicating chaotic behaviour? [migrated]

I recently read the paper about Quantum Chaos in Feshbach resonance spectra of ultracold Erbium [1]. The authors analyze their data statistically using the random matrix theory framework for ...
1
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0answers
43 views

Statistical physics Susskind lecture question? Proof of Boltzmann distribution

In lecture 3 of the following series by Susskind on statistical physics, at 36 minutes in he takes the following step and spends the next 5 minutes discussing it, \begin{equation} f(P_i)=-N\sum ...
4
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5answers
6k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
3
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1answer
140 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
3
votes
1answer
37 views

Median filtering - cheating?

The concept is simple, and is used to remove non-typical data. A sample set is put in numerical order and the extremes discarded. For example, in an experiment I am doing I take batches of 10 ...
0
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0answers
41 views

how to handle errors in this high-school experiment?

I'd like to conduct some measurements with my pupils in the high-school I'm teaching in, but I ran into some conceptual problems. I'd like to measure the (approximately constant) speed $v$ of an ...
13
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2answers
4k views

How do we know that some radioactive materials have a half life of millions or even billions of years?

If a radioactive material takes a very long time to decay, how is its half life measured or calculated? Do we have to actually observe the radioactive material for a very long time to extrapolate its ...
7
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2answers
853 views

Is half-life a statistical average of variable decay times?

Is the half life of a material only accurate as long as you are still in a macroscopic regime? If I had 8 particles in a box would I observe a fluctuation in half lives, and what would occur within ...
0
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0answers
40 views

Wigner-Dyson vs Poisson level statistics in MBL effective Hamiltonian

Many-body localization (MBL) has been a hot topic recently. It was proposed that the MBL system can be describe by the following fixed-point Hamiltonian ...
0
votes
1answer
50 views

Can binary sequences generated from ergodic maps be chaotic?

Chaotic Sequences of IID Binary Random variables with their applications to Communications and related papers by the same author, Tohru Kohda, talk about the statistical properties of binary symbolic ...
4
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2answers
359 views

Physical experiments - False positives

How is it made sure that something has been discovered, and not just noise? Is one discovery of something that is predicted considered to be enough (Higgs-particle)? What are the probabilities of a ...
0
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0answers
26 views

What is normal fluctuation?

I was reading Statistical Mechanics (second edition) by Kerson Huang. On page 146, after equation 7.14, there is a reference to normal fluctuation. What is it? Here is the relevant part from the ...
2
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0answers
23 views

statistical property of light reflected from a coarse mirror

This is a problem comes up in my study in correlation reflectometry. I'm wondering if there is a straight-forward way to interpret the phase and amplitude of the reflected light from a perturbed ...
4
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1answer
185 views

Model Selection in Physics [closed]

My high-level understanding of the scientific method is that it can be summarized in the following steps, in no particular order: Make conjectures & hypotheses (theory) Make predictions ...
2
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1answer
84 views

Statistical Mechanics vs Statistics

Just how much of a representation of statistics do we get in a statistical mechanics curriculum. What are some of the useful facets of stat not in stat mech/quantum mech that physicists should really ...
4
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3answers
975 views

Why does positronium decay into 2 photons more often than into 3 photons?

I cannot find the answer to the above question. I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability ...
0
votes
1answer
37 views

Counting the number of microstates that there are for a given configuration. How to prove this result?

I'm doing some statistical physics and I came across a result which I'm not sure how to derive. Any help? The answer turns out to be: Can anyone help with this derivation? Thank you :D
0
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1answer
49 views

Propagation of uncertainty - which formula? [duplicate]

Can someone explain to me when do I use this formula ...and when do I use this one?
5
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2answers
134 views

Why is propagation of uncertainties quadratic rather than linear? [duplicate]

1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation: if $C = A+B$ or $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = ...
4
votes
1answer
71 views

What is the interpretatation of individual contributions to the Shannon entropy?

If $X=\{ x_1,x_2,\dots,x_n\}$ are assigned probabilities $p(x_i)$, then the entropy is defined as $\sum_{i=1}^n\ p(x_i)\,\cdot\left(-\log p(x_i)\right).$ One may call $I(x_i)=-\log p(x_i)$ the ...
0
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0answers
20 views

Are the random variables in a delay embedded phase space uncorrelated and independent?

Consider a smooth manifold $M=R^d$ embedded in a higher dimensional space $R^D$ using Takens Attractor reconstruction where $D > 2d+1$. Let, the Random Variable $X \in R^d$ have a Gaussian pdf and ...
1
vote
1answer
50 views

Uniform $p$-values in $\chi^2$ fit?

I seem to have gotten myself confused about uniform $p$-values assuming the null hypothesis. This is related to how we interpret the results. Say I have a $\chi^2$-distribution which I got from ...
2
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4answers
260 views

Are “uncertainties” in Heisenberg Uncertainity just standard deviations? [closed]

Can someone confirm that the uncertainties in Heisenberg's uncertainty relation are really just standard deviations based on the expectation values? For example, the $\Delta x$ can be computed by ...
0
votes
0answers
25 views

What does bispectrum mean?

I am working on a project that uses EEG signals of the brain to identify emotional states. While surveying the literature, I came across several references where "derived features of bispectrum" are ...
2
votes
1answer
44 views

Activity of a radioactive source - distribution of number of impulses per unit time

I have the following problem: The activity of a radioactive isotope was measured with the result $N=625$ impulses/second. If this measurement were to be repeated, state the interval where we can say ...
1
vote
2answers
44 views

Particle motion characteristic

I'm making a particle motion raffling normal numbers. The normal random numbers raffled are the angles of the directions that the particle is going. The particle speed is constant. Look how this is ...
0
votes
0answers
26 views

Regarding Chebychev and Gravity

I recently learned Chebyshev's Inequality (in statistics). He uses the inverse square to specify an upper bound to the proportion of entities of a set as it recedes on either side of the mean. I am ...
3
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1answer
28 views

Scale Factor on Error

I was gathering some data from the particle data group website and for many results it gives a value, an uncertainty and then a scale factor for the uncertainty. For instance, at here, where it gives ...
10
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2answers
275 views

Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
0
votes
1answer
63 views

A parameter to quantify instability in flight

Suppose I have plotted the body angles of a flying aeroplane.I have two such plots. One of a normal plane, and the other plot in which a primary sensor of the aeroplane is removed. So with the absence ...
1
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0answers
49 views

How to calculate the correlation function for a discrete series of data [closed]

Using a simulation, I have generated a random field, which is basically a list of complex numbers. How do I calculate the correlation function of the field? To be more specific: which are the ...
1
vote
1answer
45 views

Derivation of Fermi level for T>0

I am working through the derivation of the Fermi level $ \mu_0$ for T>0. However, at one point in the notes I have, it states without any explanation that: $$ \int_0^\infty F'(\epsilon) ...
0
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3answers
106 views

We don't know when a nucleus will decay. Then how can find its half life? [duplicate]

I mean how can we say that in 5730 years, 1/2 the no. of C14 nucleus will decay because in reality we don't know when a particular nucleus will decay
7
votes
2answers
265 views

Arrhenius Fit: Linear or exponential form?

I have a seemingly easy question about performing an Arrhenius fit to the equation $$y = A \times \exp \left( -\frac{E_A}{RT} \right)$$ I can either fit this in the exponential form using a ...
1
vote
1answer
41 views

Uncertainty of approximately sinusoidal voltage measurement

Say one is interested in measuring the mean value an approximately sinusoidal voltage with an instrument that has an accuracy of 0.01 V, according to its spec sheet. 10 periods of the oscillation have ...
3
votes
3answers
735 views

Should a Gaussian Curve Always Be Drawn Symmetrically?

This question is more about the appearance of a curve that comes up while I am analysing my data rather than an actual physics question, but I think it's relevant. I have analysed some data from an ...
1
vote
1answer
105 views

Probability distribution of phase-space reconstructions

I am unable to find resources regarding the probability density and distribution of non-linear chaotic systems in phase space. For example, if a discrete one-dimensional system, say the logistic ...
2
votes
2answers
97 views

How to properly read a measurement result if it is a number?

If the result of a measurement is i.e. $3.2 \pm 0.7$, what is 0.7? At which confidence level we know that the real result is inside of this interval?
0
votes
1answer
63 views

Resolution of experiment is lower than the detector, so how to weigh the data?

I am attempting to create an atomic model based on data from a transmission electron microscope (TEM). Basically you shoot electrons at bunch of identical molecules stuck to a grid, and look at the ...
8
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2answers
14k views

How do you find the uncertainty of a weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
0
votes
1answer
33 views

Help Understanding Gaussian Particle Distribution

I have a simple enough problem. I want to mathematically describe a Gaussian particle distribution of $N$ total particles with a spot size of 0.1 (sigma). I need a function that will tell me the ...
0
votes
1answer
33 views

To find the probability? [closed]

The mass of the earth is 5.975 X 10^27 g of average atomic weight 30.00 g. The fraction (by weight) of the earth that is gold has been estimated to be 3 X 10^-9. The atomic weight of gold is about ...
1
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0answers
203 views

how to draw mechanical engineering problems [closed]

Hello I'm not entirely sure if this is on topic, but does anyone know software (or methods) to draw mechanical engineering schematics? (For statics/dynamics, so things like beams joints, rollers, ...
1
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0answers
34 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...