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12
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2answers
3k 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 ...
10
votes
2answers
720 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 ...
10
votes
3answers
4k 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 ...
10
votes
2answers
265 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 ...
9
votes
10answers
334 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
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
13k 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 ...
8
votes
1answer
290 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 ...
8
votes
2answers
243 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
2answers
223 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 ...
6
votes
0answers
159 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
0answers
133 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 ...
6
votes
0answers
183 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
1answer
3k 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
2answers
110 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 = ...
5
votes
1answer
384 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
438 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
2answers
1k 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
247 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
429 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. ...
4
votes
3answers
290 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
219 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
184 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
204 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
794 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
567 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
69 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
1answer
167 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 ...
4
votes
0answers
102 views

Is frequency or Bayesian interpretation used in quantum mechanics?

In quantum mechanics, we discussed about probability. There are two kinds of interpretations: frequency and Bayesian. Which one is actually used in quantum mechanics? My impression is, it doesn't ...
3
votes
3answers
685 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
529 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
5k 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
515 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
5k 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
1answer
706 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
307 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
99 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
2answers
125 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 ...
3
votes
1answer
21 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 ...
3
votes
1answer
103 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
147 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
157 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
878 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
292 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
5answers
256 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
4answers
211 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 ...
2
votes
2answers
172 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
86 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 ...