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2
votes
4answers
83 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
1
vote
0answers
28 views

Does a set of eigenvalues in QM correspond to a random variable in statistics? [duplicate]

In quantum mechanics the possible outcomes of a measurement of a quantity corresponding to a linear hermitian operator $A$ are only the eigenvalues $a_i$ of $A$ (see e.g. ...
2
votes
4answers
146 views

Is what statisticians call a “random variable” what physicists call an “observable” in QM? [duplicate]

I read at http://www.statlect.com/fundamentals-of-probability/random-variables that A random variable is a variable whose value depends on the outcome of a probabilistic experiment. Its value is ...
5
votes
4answers
775 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?
0
votes
2answers
46 views

Calculate the probability that a radioactive nucleus will have decayed after the passage of three half-lives

This is a problem given in my Physics Textbook and I've been trying to solve it for the past hour. It's not something exceptionally challenging, but more conceptual in nature. Not much, connections ...
0
votes
1answer
328 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: ...
1
vote
1answer
176 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 ...
3
votes
0answers
50 views

What is the physical meaning of the parameter of a Poisson distribution?

I have done a laboratory session at my university where I had to check that the disintegration of nucleii follows a Poisson distribution. $$P(n)=\frac{\lambda^n}{n!} e^{-\lambda}$$ Where $P(n)$ is ...
0
votes
1answer
48 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
3
votes
0answers
68 views

Remove measured distribution from another distribution [closed]

Take a particle beam as an ensemble of many particles. Assume two independent random variables $X_\beta$ and $\delta$ that add up to the horizontal position $X$ of a particle: $$ X = X_\beta + D_x ...
3
votes
2answers
65 views

What exactly is an arbitrary parameter?

I was reading the article Turning Points: A meeting with Enrico Fermi by Freeman Dyson (available e.g. here), and I had a question about Dyson's use of the term 'arbitrary parameter'. More ...
1
vote
1answer
518 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
2
votes
0answers
34 views

Comparing $X_\text{red}^2$ statistics for cosmological models

I'm evaluating a cosmological model which competes with ΛCDM. I have charted the $Χ_{red}^2$ and $R^2$ statistics for the sample of galaxies from McGaugh et al (2001) for my model and ΛCDM. Each ...
0
votes
1answer
15 views

Random partitioning of single-mode thermal light

While studying Fundamentals of Photonics by Saleh and Teich, I find it difficult to prove that the photon-number distribution of randomly partitioned single-mode thermal light retain its Bose-Einstein ...
5
votes
1answer
304 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 ...
0
votes
0answers
10 views

What is the distribution of a battery transmission?

I have an energy-harvesting battery attached to a node, transmitting data over Rayleigh flat fading channels. Energy in the battery is used, and simultaneously energy is harvested and stored. I want ...
0
votes
1answer
64 views

How should I interpret a Chi-Squared Result?

I've got a Model A with a reduced chi-square of 1.28. I've got a Model B with a reduced chi-square of 0.70. Which is a better model? The model closest to 1 or the model closest to zero? (Yes, I ...
1
vote
1answer
87 views

Can binary sequences generated from ergodic maps be chaotic?

Briefly, the way symbols are generated is: Consider a one-dimensional chaotic map $T: [0,1]→[0,1]$ and a time series $\{x_n\}_{n=1}^N$ generated with this map. Define a threshold $A$ and a ...
2
votes
1answer
55 views

Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form?

I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, ...
1
vote
0answers
52 views

How to estimate function from PDF and covariance? [closed]

I've added a picture of what I want to compute. In the nomenclature of the picture, I want to compute a realization of y(x) given the known distributions and constants. Let's say y(x), random ...
0
votes
0answers
21 views

Reduced Chi-Square - How to compare values?

I've got two models of velocity curves fitting a Low Surface Brightness (LSB) galaxy: one is MOND-like, the other ΛCDM. I've fit them both with Chi-Square minimization. I understand the winning ...
1
vote
2answers
110 views

Use of normal distribution in measurement error theory

When you study an experimental results you assume that normal distribution describe random error, specially in lab courses in K12. Is this true for every random component error treatment in physics? ...
1
vote
1answer
27 views

Residuals are normally distributed

I did not know whether to post this question in the Physics or Statistics section of StackExchange, but the question involves the application of statistics to the analysis of experimental results. I ...
1
vote
1answer
46 views

Error in total counts

I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t. Later on I take the total count rate. (Number of counts/time: $N/t$) I'm supposed to find ...
8
votes
2answers
354 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 ...
8
votes
3answers
321 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 ...
6
votes
1answer
214 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 ...
0
votes
0answers
33 views

Estimation of the autocorrelation for data on finite size interval

Let's consider we have a continuous random signal ${ t \in ] - \infty \,;\, + \infty [ \mapsto b (t)}$. We assume this signal to be stationary, so that when ensemble-averaged, one may introduce the ...
-1
votes
1answer
52 views

In double slit experiments of particles (quantum) which the result is interference pattern, How many particles reach the observing screen?

I mean, I know the particles that reach the screen are going both/neither/either of slits and interference with themselves but statically/percentage how many particles interact with slits, are there ...
0
votes
0answers
13 views

How to obtain a lower mass bound for a unstable (or stable) particle from Poisson statistics?

Imagine you have a particle (stable e.g. if some R-symmetry or similar does exits) heavy or not so heavy... Question: how to guess a lower (upper bound as well) with the aid of Poisson statistics, ...
4
votes
1answer
92 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 ...
0
votes
1answer
57 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 ...
12
votes
1answer
305 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
votes
0answers
17 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 ...
1
vote
0answers
32 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 ...
1
vote
0answers
58 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
votes
5answers
8k 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
186 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
40 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
votes
0answers
64 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
votes
2answers
5k 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
votes
2answers
982 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
votes
0answers
79 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 ...
4
votes
2answers
381 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
votes
0answers
31 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
votes
0answers
35 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 ...
5
votes
1answer
223 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 ...
3
votes
1answer
188 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
votes
3answers
1k 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
51 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