For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

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On the probability of the existence of a similar observable universe

Let's assume a standard ($\Lambda$CDM + some simple inflation model) cosmology in an infinite universe. Really it doesn't matter much what cosmology we take, just that we're considering an infinite ...
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1answer
55 views

Thermodynamics vs Kinetics

As a chemical reaction approaches equilibrium, one of forward or backward reactions dominate the other. According to thermodynamics, this is because the gibbs free energy change for one is negative. ...
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2answers
187 views

Entropy and Gibbs Free Energy

I've been struggling with the notion of entropy and gibbs free energy for almost three days now. Different sources on and off the internet say different things about entropy. Gibbs Free Energy is ...
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4answers
651 views

What is the difference between + and - signs in superpositions of quantum states?

What is the difference between states $$ \frac1{\sqrt{2}} |11\rangle+\frac1{\sqrt{2}} |00\rangle $$ and $$ \frac1{\sqrt{2}} |11\rangle- \frac1{\sqrt{2}} |00\rangle~? $$ They will all eventually ...
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66 views

What is negative probability? [duplicate]

I am going through Quantum Computing, and thought to clear the basics first. So, I read blogs on Quantum Mechanics. They mention about Negative Probability. Now, what is that, this is very new to me. ...
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35 views

Are the random variables in a delay embedded phase space uncorrelated and independent?

Consider a smooth manifold $M=R^d$ embedded in a higher dimensional space $R^D$ using Takens Attractor reconstruction where $D > 2d+1$. Let, the Random Variable $X \in R^d$ have a Gaussian pdf and ...
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1answer
87 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 ...
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16 views

Probabilistic interpretation of Hausdroff measure [closed]

My problem is to find/derive a pdf in terms of a parameter which closely resembles Hausdroff measure and the idea stems from the following concepts. Please correct me where I go wrong. Paper1 - ...
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1answer
299 views

Why are transition amplitudes more fundamental than probabilities in quantum mechanics? [duplicate]

I am reading Quantum Theory: Concepts and Methods by Asher Peres. Terminology used in the book: $P_{\mu m}$ are "transition probabilities". They are the squares of "transition amplitudes". That is, ...
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2answers
150 views

Probability of fluorescence: matching of binding energy and incoming radiation energy?

Assume an X-ray diffractometer equipped with a copper anode X-ray tube. When a sample containing cobalt, iron, or manganese is irradiated by copper's K$\alpha_1$ radiation, sample fluorescence becomes ...
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1answer
45 views

Empirical probability: what does it measure actually?

Empirical probability measures the probability of an event by thought experiment. But, by doing so, what information does it want to give? The experiment is done; so how can there be probability? The ...
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1answer
96 views

How to build a clock? [closed]

You have unreliable clocks that fire in the interval $(t,t+\delta)$ with probability density $f(t;\lambda)=\lambda\exp(-\lambda x)$. How will you build the best clock using these unreliable components ...
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205 views

Average kinetic energy of molecules hitting a surface

I am trying to prove that the average kinetic energy of gas molecules hitting a containers surface is $2k_{B}T$ instead of the average for the entire gas, which is $\frac{3}{2}k_{B}T$, where $k_{B}$ ...
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2answers
173 views

Quantum Bayesianism and contradictory preditions of two agents

In quantum Bayesianism (QBsim) interpretation, the wave function $| \psi \rangle$, or density operator $\hat{\rho} = | \psi \rangle \langle \psi |$, is not objective. It is instead interpreted as the ...
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0answers
75 views

What is the cause for the validity of Statistical Regularity?

My book writes: From experience it has been observed that the value of frequency ratio gradually approaches a definite constant number when the no. of trial becomes larger & larger. This ...
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1answer
448 views

In how many possible ways can a photon be emitted?

I am currently studying atomic physics, and I encountered the question above. I am posting this question because I can't afford to move on with even the tiniest bit of uncertainty in my understanding ...
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1answer
78 views

When everything follows strict laws in the universe, where does probability come from? [duplicate]

I am told that we can't predict whether we shall get a head or tail. We can only say that for an unbiased coin there is 50% probability for either. But coin is not case of Quantum Physics! I have ...
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0answers
101 views

What is a stochastic process in a physics context? [closed]

In my mind, a stochastic process is simply a "random" process, one where the outcome is informed by initial conditions but not in a deterministic way. Is this a correct definition? What are some ...
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2answers
238 views

How to calculate the tree-level probability amplitude for the electron-positron to muon-antimuon process?

Consider the following process: $e^+ + e^- \rightarrow \mu^+ + \mu^-$. I'm trying to calculate the probability amplitude of such a process in leading order. In leading order the amplitude is given ...
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3answers
976 views

How to work out the relation between the “mean relative speed” and the “mean speed”?

I'm a freshman and am taking the general physics course. I just learned intro thermodynamics. One problem that really puzzles me is the calculation of "collision mean-free path", where calculating the ...
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3answers
153 views

We don't know when a nucleus will decay. Then how can find its half life? [duplicate]

I mean how can we say that in 5730 years, 1/2 the no. of C14 nucleus will decay because in reality we don't know when a particular nucleus will decay
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2answers
209 views

Detailed balance condition for coupled Langevin equation

Suppose $a$ and $m$ are real variables and they satisfy the following two coupled Langevin equations: $$ \dot{a}=F_a(a,m)+\eta_a(t);\quad\dot{m}=F_m(a,m)+\eta_m(t); $$ where $\eta_a$ and $\eta_m$ are ...
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1answer
146 views

probability amplitude and path integrals [closed]

Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
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2answers
163 views

Why is time evolution of wavefunctions non-trivial?

(Note: This post focuses on a single simple example, however I'm asking about the error in general in my logic). Consider the infinite potential well "particle in a box" system described by ...
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4answers
62 views

Question about interpreting probabilities in QM [duplicate]

For the example of an infinite square well, $\psi(x)=0$ for $x$ outside the well/interval, and we are to interpret this as the particle cannot be found outside the well because ...
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1answer
135 views

Probability distribution of phase-space reconstructions

I am unable to find resources regarding the probability density and distribution of non-linear chaotic systems in phase space. For example, if a discrete one-dimensional system, say the logistic ...
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3answers
595 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
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1answer
51 views

X-ray diffraction analyisis: The angle of elastic x-ray scattering

What is the scattering angle distribution for x-rays (in the 8keV range) scattered elastically? I work with XRD analysis, which is fundamentally basede on these elastic scatterings of x-rays. I read ...
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2answers
162 views

Expectation value expression Quantum Mechanics

Whilst working on a project I kept stumbeling across two different expressions for the standard deviation $\Delta{X}^2 = <(X - <X>)^2 >$ and the other $\Delta{X}^2 = <X^2> - ...
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2answers
125 views

Second Law from Statistics

Hi all I hope you can help me with the statistical origins of the Second Law. I cannot find anything that mathematically proves that order from disorder is impossible only improbable Leading me to ...
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2answers
58 views

Entropy-A question. [closed]

If I have 100 coins then a macrostate is how many heads/tails I have, a micro state is the facing of each individual coin of the 100, but what then is a "configuration" in this example? It is a basic ...
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2answers
135 views

If the universe is spatially infinite, and if something (A) is possible, does that mean the thing (A) happens?

Assuming that the universe is spatially infinite, extending outwards in all directions without end, and is consistent with what we have thus far observed, and predict to find (and predict to be out ...
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3answers
136 views

Can you pre-determine the result of a coin toss?

The question is fairly simple. Consider the following parameters which are known to you: 1.) Mass of the coin 2.) The force applied on the coin 3.) The point where the force is applied on the coin ...
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0answers
152 views

Relaxation time approximation in Drude model apparant paradox

In the Drude model of the free electron gas to explain the conduction of a metal, the relaxation time approximation that the electron has a collision in an infinitesimal time interval $dt$ is ...
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3answers
1k views

Why does Law of Large Numbers work?

Often I see books and professors reasoning that, in order to make a good experiment, many measurements are necessary because then the average value of a quantity is closer to the expected value ...
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1answer
65 views

How was phase randomly changing in CHSH test (M. A. Rowe and others)?

Measuring phase of photon should always be random while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear experiment i ...
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1answer
393 views

If the universe is infinite, should there be a duplicate of me with probability 1? [duplicate]

I was just wondering: if the universe is really infinite, and there is a certain probability to find a life form just like me on another planet (for example $1.0 \cdot 10^{-150}$), is it therefore ...
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1answer
111 views

$\sigma$-additivity of Probability and Quantum Mechanics

$\sigma$-additivity - probability of a sum of countable number of pairly disjoint events equals a sum of probabilities of these events. (3. Axiom of Probability) For pairly disjoint sets $A_k$ ...
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64 views

Noise of a fiber optic gyro

I have not much experience with noise handling or calculations, furthermore in my researches couldn't find a similar problem, so here is my attempt: Having a fiber optic gyro that is rated with a ...
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1answer
33 views

To find the probability? [closed]

The mass of the earth is 5.975 X 10^27 g of average atomic weight 30.00 g. The fraction (by weight) of the earth that is gold has been estimated to be 3 X 10^-9. The atomic weight of gold is about ...
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41 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
2
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1answer
112 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
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97 views

Do doomsday arguments influence doomsday hypotheses?

The doomsday argument supposes that in the absence of any other knowledge, if we know the age of something now, we may assume that we are seeing it in the middle of its lifetime and then calculate our ...
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3answers
578 views

Why, in spin sums, we sum over final spin states and average over initial states?

I am reading Halzen's book about quarks and leptons and on page 120 he talks about spin sums. He says that in order to calculate the amplitude between unpolarized states we have to sum over FINAL ...
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2answers
181 views

Why the self-information is -log(p(m))?

Why is self-information given by $-\log(p(m))$? Shannon derived a measure of information content called the self-information or "surprisal" of a message $m$: $$I(m) = \log \left( ...
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1answer
220 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
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1answer
50 views

Probability to be in a particular state

If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle ...
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1answer
159 views

Was Max Born the first to notice a connection between quantum mechanics and randomness?

Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed? Today, quantum mechanics and ...
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45 views

Books on collision probability and collision processes

Are there any books specifically on collision processes between atoms and molecules and collision probability? I would like to get an overview of the factors that determine collision probability ...
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67 views

probability of sequence for given rate constants

lets consider a copolymer, $C_{r,s}^A$ containing r number of A monomers and s number of B monomers with A at the reactive end of the polymer. The equilibrium constant for A-A, A-B, B-A, and B-B bonds ...