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9
votes
3answers
8k 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 ...
14
votes
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 ...
6
votes
2answers
224 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 = ...
4
votes
2answers
9k 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 ...
11
votes
2answers
18k 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
955 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 ...
2
votes
4answers
165 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 ...
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 ...
1
vote
1answer
98 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 ...
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 ...
4
votes
1answer
467 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
245 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 ...
5
votes
1answer
311 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
5answers
10k 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
213 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 ...
2
votes
0answers
327 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
1
vote
0answers
387 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 ...
5
votes
1answer
442 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
532 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
1answer
205 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 ...
3
votes
1answer
884 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 ...
1
vote
1answer
125 views

Variance of Nested Experimental Uncertainty

I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for ...