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4
votes
0answers
110 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 ...
2
votes
1answer
133 views

From where randomness comes from and why it exists? [closed]

I recently began to study statistics and probability and I have two questions: Where does randomness come from? What is the source of randomness? Why does the randomness exist? Is it possible to ...
1
vote
1answer
117 views

Measuring a fluctuating quantity: Instrument error vs. uncertainty, or both?

Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy ...
6
votes
0answers
173 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 ...
2
votes
5answers
257 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 ...
0
votes
1answer
63 views

What is the experimental uncertainty of an ensemble measurement? [duplicate]

Let's say you measure the time it takes for 10 oscillations of a mass undergoing simple harmonic motion to within ± 0.01s, what is the uncertainty of the period of one oscillation?
2
votes
1answer
91 views

Can I express the heat flow of a fluid in terms of estabilshed characteristics of the velocity distribution?

If $\rho$ is the mass density of a fluid and $A({\bf v})$ is an function of the velocity, which is distributed according to $f({\bf v})$, we have an averaging process $A\mapsto \langle A\rangle:=\int ...
1
vote
1answer
292 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 ...
0
votes
1answer
132 views

Calculating kWh from time series of kW

I have a time series of kW where each sample is measured at regular intervals (10 seconds). Could anyone explain to me how could I calculate the total power consumed (kWh) over an hour? Thanks
1
vote
0answers
35 views

What can I say about compatibility between predictions and results?

If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\ \omega_{b_1} = 0.0707 \pm ...
2
votes
1answer
2k 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 ...
1
vote
0answers
29 views

Quantity with approximate lognormal distribution

I am studying a quantity $x$ for which $\log( x)$ is nearly (although not exactly) lognormal. What would be the appropriate "typical" value: the mean $\langle x\rangle$ or rather ...
0
votes
0answers
30 views

Sum of independent errors [duplicate]

During a physics lab we stumbled upon a little problem. The measuring device was unstable, oscillating between two values. We were told to write down the average with the half-difference between the ...
1
vote
1answer
54 views

What is the correct way to handle significant figures when calculating compound uncertainties? [duplicate]

When processing experimental data, and calculating an uncertainty value in multiple steps, should intermediary uncertainties be used to a certain number of significant figures or kept to the full ...
9
votes
10answers
350 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
2answers
774 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 ...
0
votes
2answers
52 views

Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
1
vote
1answer
138 views

Error propagation of statistical error

I have a pulse profile (binned photon counts versus phase) of a star, and for each count rate I have its statistical error. I want to calculate the so-called pulsed-fraction ...
0
votes
2answers
123 views

Function for curved line in log-log-plot

I've done experiments on the thermo-viscoelasticity of liver tissue and the following results ...
2
votes
0answers
70 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 ...
3
votes
2answers
6k 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
1answer
162 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 ...
1
vote
0answers
55 views

Weighted average whenever a variance is 0? [closed]

So I have data for the number of times a certain event happens. Each column is a different event and each row is one trial. A sample of data would look like \begin{bmatrix} 1& 4& 7& ...
5
votes
1answer
258 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 ...
2
votes
2answers
181 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?
4
votes
1answer
282 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 ...
1
vote
0answers
87 views

What could be the distribution of an explosion energy of a mining-grade and seismic exploration explosives?

Seismic exploration involves the excitation of seismic waves using the industrially made explosive charges. What could be the distribution of explosion energy of such a charges? My guess is that it ...
1
vote
0answers
117 views

Canonical form representation of a Linear Gaussian CPD

I'd like to know how a linear Gaussian conditional probability distribution can be represented to a canonical form. For example, let X and Y be two sets of continuous variables, with |X| = n and |Y| ...
0
votes
1answer
69 views

Can a distribution with sharper energy maximum than the exp-function give an equivalent theory?

Because for many particles the distribution $\varrho\sim\mathrm e^{-\beta\ H}$ has an extremely sharp maximum, the expectation values of the canonical ensemble agrees with that of the microcanonical ...
1
vote
1answer
182 views

Paper in physics - calculations; rounding or not?

I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic ...
3
votes
1answer
195 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 ...
1
vote
2answers
315 views

Drude theory of electrical conductivity

I was just trying to calculate the electrical conductivity for a Fermi-Dirac distribution and a Maxwell-Boltzmann distribution, and I ended up with the same result: $$\sigma=\frac{ne^{2}\tau}{m}$$ ...
1
vote
0answers
305 views

Combining errors to calcuate the total error (standard deviations)

I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each ...
2
votes
0answers
151 views

Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
6
votes
0answers
141 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 ...
-1
votes
0answers
75 views

How to determine spatial color distribution? [closed]

Is there an easy way (i.e. free or open source tool) to determine the spatial color distribution (i.e "intensity") in a picture or in a region of interest of this picture? Let's say I used a laser or ...
2
votes
1answer
129 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 ...
1
vote
0answers
91 views

Fitting of data to a model

Imagine that I have some observable value predicted with a theory for some process to be: $1+a x + b x^2$ and observed value is 1.3 with an error 0.2; a and b are some numerical constants. I also have ...
2
votes
1answer
323 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
0answers
153 views

How long would it take for a container in vacuum to leak half of its air? [closed]

Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only ...
3
votes
1answer
107 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, ...
2
votes
2answers
180 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
1answer
413 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 ...
-1
votes
1answer
95 views

How many measurements should be done? [closed]

I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard deviation?
0
votes
2answers
362 views

Microsoft Excel not graphing $x = y^{1/2}$

The experiment was relating the period of one "bounce" when you hang a weight on a spring and let it bounce. I have this data here, one being mass and one being time. The time is an average of 5 ...
2
votes
1answer
172 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 ...
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 ...
1
vote
5answers
536 views

Are Uncertainties in Measurements Important?

In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...
0
votes
1answer
123 views

What is a long-tailed distribution for physicists?

What is the most common definition of long tailed distribution for physicists? I am looking for definition and examples. Examples should have arguments why the distribution is or is not long tailed. ...
0
votes
2answers
76 views

Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...