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16
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2answers
6k 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 ...
12
votes
2answers
1k views

Use of Monte-Carlo simulation in High-energy Physics

I've been doing some research into the analysis used in particle physics when determining the significance of a finding (e.g. the recent Higgs candidate was announced as a boson in the 125-126 GeV/$c^{...
12
votes
1answer
324 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, ...
11
votes
2answers
19k 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 ...
11
votes
2answers
321 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 ...
10
votes
10answers
439 views

Could one measure a stick to an arbitrary precision by having its length estimated by enough people?

I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of ...
10
votes
3answers
9k views

How to combine measurement error with statistic error

We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction time....
9
votes
1answer
455 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
9
votes
1answer
3k views

Standard Deviation in Particle Physics

I'm familiar with sigma, and how its usually calculated and used, but would like to know how it's applied to particle physics. I recall reading that the discovery of the Higgs would only be credible ...
8
votes
2answers
1k 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 ...
8
votes
2answers
465 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 non-...
8
votes
3answers
458 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...
8
votes
2answers
259 views

How to predict how much data to collect

The same question on CrossValidated Apologies if I'm being a bit vague in what follows, I've been asked to keep certain aspects of the experiment confidential for the time being. An analogous ...
7
votes
3answers
252 views

Meaning of $5.1\sigma$ significance with regards to GW150914

I couldn't find any publication by LIGO that explains how we should interpret this value. The closest I have found is the following quote: This means that a noise event mimicking GW150914 would be ...
7
votes
5answers
11k 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 ...
6
votes
2answers
253 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 = \frac{A}{...
6
votes
1answer
4k views

Is there a stable numerical algorithm for FWHM that isn't 2.35*sigma?

This is a question that should have a simple answer, but which I can find no proper discussion of in the literature or on the internet. I start from the assumption that I have a noisy numerical ...
6
votes
1answer
448 views

Finding coefficient of proportionality

Recently in my AP Physics class I did a lab in which I measured k for a spring by setting up an oscillating system with it, and timing the period, repeating for different masses. Since $T=2\pi\sqrt{\...
6
votes
1answer
232 views

What is known about Higgs LHC machine learning algorithm for identifying Higgs events?

Recently many LHC-affiliated organizations and otherwise announced the Higgs ML learning challenge (in May) running over the summer. There are many competing teams and significant results posted ...
6
votes
2answers
724 views

statistics for photon counts in photomultiplier

It seems that a common statistical model for the count numbers of a photomultiplier is a Poisson distribution whose parameter $\lambda$ equals to the square-root of the number of counts.(e.g. http://...
6
votes
0answers
204 views

What statistical test should I use?

I have two differential cross sections $d\sigma_{1,2}/dM$ ($M$ is some invariant mass) corresponding to different hypothesis. What I want is to calculate how well the appropriate experiment would do ...
5
votes
6answers
1k views

Why don't experimental physics groups have statisticians in it?

Perhaps someone can clear up a bit a cognitive dissonance I am experiencing. Pollsters are under constant scrutiny of statisticians for even the most mundane of survey topics. With so much riding on ...
5
votes
3answers
2k 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 ...
5
votes
4answers
865 views

How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?

$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$ What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
5
votes
2answers
3k views

Averaging decibels

Wikipedia: The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. If I ...
5
votes
1answer
318 views

Advanced data analysis in Physics experiments

I know that regression, chi-distribution, covariance, error propagation, etc. are frequent tools for experimental physicists. So, I'd like to know if advanced statistics topics are used in data ...
5
votes
2answers
546 views

Photon statistics of an incandescent light source

We usually calibrate the cameras on our microscopes by capturing 20 images of a blurry (not sharp) fluorescent particle. For each pixel in this stack of 20 images we calculate the intensity variance. ...
5
votes
0answers
91 views

How does the “Look Else Where Effect” affect the chances of detecting a false diphoton excess at the LHC?

Back in December 2015, there was found a 750 GeV diphoton excess in both CMS and ATLAS at the same location with a significance well above $3\sigma$; a 0.13% chance of being false. However, there ...
5
votes
1answer
229 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 ...
5
votes
1answer
172 views

Is frequency or Bayesian interpretation used in quantum mechanics?

In quantum mechanics, we deal with probability. There are two kinds of interpretations: frequency and Bayesian. Which one is actually used in quantum mechanics? My impression is, it doesn't matter. ...
4
votes
3answers
301 views

why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero?

Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the ...
4
votes
2answers
389 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 ...
4
votes
2answers
110 views

What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?

What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle v_{i}\right\...
4
votes
2answers
10k views

How to combine the error of two independent measurements of the same quantity?

I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. $k$ is just the mean of $k_1$ and $k_2$. I thought ...
4
votes
1answer
487 views

How do I calculate the experimental uncertainty in a function of two measured quantities

I am performing an experiment where I'm measuring two variables, say $x$ and $y$, but I'm actually interested in a third variable which I calculate from those two, $$z=f(x,y).$$ In my experiment, of ...
4
votes
1answer
215 views

Products of Gaussian stochastic process variables

In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
4
votes
1answer
537 views

How is the theory of partial coherent light related to quantum-mechanics?

Background Let me start this question by a long introduction, because I assume that only few readers will be familiar with the theory of partial coherent light and concepts like a mutual coherence ...
4
votes
2answers
1k views

What do “local” and “global” mean when talking about standard deviations in experimental particle physics?

I found the following sentence: The excess is most compatible with a SM Higgs hypothesis in the vicinity of 124 GeV and below, but the statistical significance (2.6σ local and 1.9σ global after ...
4
votes
1answer
108 views

Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?

I've only recently started studying statistical mechanics and I'm quite confused with the MaxEnt and anti-MaxEnt ideas. I'm looking for a concise answer, if it is possible, not really a description ...
4
votes
1answer
92 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 ...
4
votes
2answers
61 views

Combining two data points with different uncertainties

I have two separate algorithms (call them "A1" and "A2") which reconstruct the $(x, y)$-position of an event in a particle detector. I can test both of these algorithms on simulated events from a very ...
4
votes
1answer
267 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
4
votes
0answers
58 views

Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical ...
4
votes
0answers
61 views

Appropriate fit function for $\phi$ meson mass from $K^{+}K^{-}$ pair

I am attempting to measure the mass of the $\phi$ meson using the decay mode $\phi \to K^{+}K^{-}$. I have isolated the $\phi$ meson candidates using this decay mode, and have constructed the graph ...
3
votes
3answers
882 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 ...
3
votes
3answers
585 views

Calculating uncertainties for a final result

Say you are dividing 2 times with uncertainties: $$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$ After doing the calculations you get: $$\frac{t_1}{t_2} ~=~ 0.774 \pm \ldots?...
3
votes
1answer
329 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 ...
3
votes
1answer
917 views

Is $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement?

I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$. But in ...
3
votes
2answers
577 views

Question about uncertainty

Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate ...
3
votes
1answer
5k views

Kolmogorov-Smirnov test vs Chi-squared test

What is the difference between the Kolmogorov-Smirnov test and the Chi-squared test? When should we use one instead of the other? I was reading this article, and I got confused a lot. It is hard to ...