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9
votes
10answers
264 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 ...
9
votes
2answers
503 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 ...
9
votes
3answers
2k 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 ...
8
votes
2answers
2k 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 ...
8
votes
1answer
9k views

How do you find the uncertainty of an 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 ...
8
votes
2answers
233 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 ...
8
votes
1answer
2k 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 ...
5
votes
6answers
913 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
1answer
2k 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 ...
5
votes
1answer
143 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 ...
5
votes
1answer
274 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 ...
5
votes
2answers
282 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. ...
5
votes
1answer
191 views

Advanced data analysis in Physics experiments

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or ...
5
votes
2answers
366 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
2answers
357 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
167 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 ...
4
votes
3answers
279 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
100 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 ...
4
votes
1answer
105 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
169 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
2answers
444 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 ...
4
votes
2answers
358 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
0answers
104 views

Statistical analysis of data in Physics

Analysis of data is integral in bridging the gap between theory and experiment. My question is about the two major methods of approaching the analysis - Bayesian and Frequentist. How much do the ...
3
votes
3answers
443 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 ...
3
votes
2answers
3k 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 ...
3
votes
3answers
377 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?
3
votes
4answers
3k 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
votes
2answers
187 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
61 views

Time of Measurement Vs Number of Measurements

Let's say that an experiment has to determine the number of cosmic muon at sea level. The appropriate equipment is ready to measure the counting rate. I can think of two ways Count for 10 minutes, ...
3
votes
1answer
40 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
62 views

Combining uncertainties - multiple measurements

I am trying to understand how to combine uncertainties when they are dependent and independent from each other. Using this formula : $$\delta z = \sqrt {\Biggl(\dfrac{\partial f}{\partial x} \delta ...
3
votes
1answer
87 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 ...
3
votes
2answers
743 views

Combining multiple theories with 5 $\sigma$ confidence level

Sadly I am not a physicist but I am interested in the topic. Please have mercy with me if you find my question trivial or dumb. Here it comes: As far I understand physicist express their certainty ...
3
votes
2answers
288 views

Relating the power to weather variables [closed]

Could you please help me in this problem? I have 3 independent variables, (T,H,t) , as inputs and one output P ( I have all data for these inputs and the output, done experimentally measured every ...
2
votes
4answers
189 views

What's the difference between $10\%$ of $10\text{ cm}$ and $1\text{ cm}$?

I overhead a physics professor at my university on the phone: I interviewed that student you sent me, but he didn't know the difference between increasing the length of a $10\text{ cm}$ rod by ...
2
votes
3answers
122 views

Physics Standard Deviation

I am a physics enthusiast and I have a question: Why is it meaningless to express the '$\pm$' (standard deviation) value as a percentage?
2
votes
3answers
82 views

Statistics software for basic undergrad lab

I'll have to perform some simple experiments, like measuring the period and damping of a pendulum, focal length of a lens, … As a result I will end up with some X, Y data points and need to calculate ...
2
votes
1answer
90 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
2
votes
1answer
301 views

Maxwell-Boltzmann velocity PDF to CDF [closed]

I asked on Math.SE and was advised to try here instead. I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
2
votes
1answer
518 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 ...
2
votes
1answer
414 views

Astronomical detection significance from magnitude error

At this website: http://heasarc.gsfc.nasa.gov/docs/swift/analysis/threads/uvot_thread_afterglows.html The passage at the bottom states that a V-band magnitude of 17.62, with an error $\pm$0.02 is a ...
2
votes
2answers
222 views

Average Neighbouring Impurity Separation in a Random 1D chain [closed]

I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...
2
votes
1answer
182 views

Experimental measurement of volumetric flow rate

The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
2
votes
1answer
102 views

Underlying physical basis of an exponential distribution

My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies ...
2
votes
2answers
91 views

Error in variance

I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
votes
2answers
111 views

What is the relation of the release time of fossil fuel emissions to climate change? [closed]

This question presupposes that The amount of fossil fuels on earth is limited Mankind will burn all of its fossil fuels eventually Based on these presuppositions, the total amount of CO2 released ...
2
votes
1answer
203 views

Coherency matrix of partially polarized light doesn't contain all information on polarization state?

The electric field of quasi-monochromatic, partially polarized light can be expressed by the following random process (Goodman, Statistical optics) ...
2
votes
2answers
204 views

Wave Function Statistical Interpretation vs Oscillation Interpretation

Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the ...
2
votes
1answer
201 views

How do you determine the degree of localization of a wavefunction?

Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
2
votes
0answers
48 views

Statistical Mechanics: Most probable orientation of grain particle in gas chamber?

I'm in an introductory statistical mechanics course, and we've been posed the following situation: Long-shaped dust particle (so imagine something like a grain of rice) is placed in a gas chamber (so ...