Questions tagged [randomness]

Randomness covers questions having to do with the concept of randomness in physical processes and questions about determinism vs indeterminism or interpretations thereof. Question related to concepts of probability may also use this tag.

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Statistically stationary, periodic random process

As I understand in a statistically stationary process, the statistics are invariant under a shift in time. It is natural to assume that the statistics are periodic in a periodic random process. If ...
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Spectral unfolding for Aubry-Andre model

While I was studying on random matrix theory recently, I have tried to unfold the spectrum of Aubry-Andre model. If the amplitude $\lambda$ of quasiperiodic onsite potential is less than 2, then it is ...
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Does Wick theorem hold for ensembles of random unitary matrices?

Consider ensembles of random unitary matrices with weight function $w(\phi)$, which have partition functions of the form $$ Z= \int_{U(N)} w(U)dU = \int \prod_{i=1}^N \frac{d \phi_i}{2\pi } w(\phi_i)\...
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What is the probability that a random walk forms (almost) a circle?

Given is a random walk of a particle in 3d (such as an atom in a liquid). The particle proceeds randomly (in 3d), with an average straight displacement length a. Is there a way to get a probability ...
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Why can’t quantum randomness be understood as epistemic? [duplicate]

I often hear people say that quantum randomness is “true randomness”, but I don’t really understand it. Please bear with my question. Before the development of quantum physics, randomness is ...
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Is radioactive decay deterministic? [duplicate]

Suppose you know at time $t$ that there is some atomic nucleus that radioactively decays. If you were to magically roll back the universe to the exact same state and let it continue as per usual ...
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Is there any concept in physics, that could potentially in the future get rid of "randomness"? [duplicate]

This question was very interesting to a non physicists like me question (I am computer scientist and I work with "pure random" crypto hardware that uses quantum phenomena) Obviously string ...
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Is a coin toss pseudo-random or truly random? [duplicate]

I wonder if a coin toss is pseudo-random or truly random. Sure, you could say that a coin toss is pseudo-random because you don't know the speed of the coin or its rotation, but if you were to include ...
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How many flips does a tossed macroscopic coin need to go through until the coinflip's result becomes indeterministic?

A coinflip is a macroscopic event and is deterministic in nature. A coin-flipping machine that operates at the greatest physical precision possible would be able to predict the coinflip's result (...
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Source of randomness

Is the random nature of all macroscopic phenomena like for example, turbulence or chemical kinetics ultimately traceable to quantum randomness?
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Annealed and quenched free energies

For the systems with random fields and interactions, annealed and quenched free energies are defined: $$ F_a = -\theta\log\left(\overline{Z}\right),\quad F_q = -\theta\ \overline{\log(Z)}. $$ Here, ...
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How are single photons correlated inside the "coherence time" of the laser? (And how would this affect a random number generator?)

This review on quantum random number generation describes how random numbers can be generated from a simple optical setup. In one example setup they give: weak light travels through a beam splitter ...
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Are phase transitions in one-dimensional random-field Ising model possible?

Translationally invariant one-dimensional models, with interactions of finite range and a finite number of states at the site, don't allow phase transitions at positive temperatures. This fact is a ...
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How to randomly generate a POVM for a qubit?

We all know that a POVM $\Pi$ is a set of operator such that $$ \Pi = \left\{\Pi_k \quad s.t.\quad \Pi_k \geq 0 \quad \& \quad \sum_{k=1}^n \Pi_k = \mathbb{I}\right\} $$ Let us assume that we are ...
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Interpreting distance in random walk

I've recently started reading about the random walk, from different sources across the internet, and there is this small detail that I'm not being able to wrap my head around. Suppose we have, a ...
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Chaotic and Ordered Random Boolean Newtorks with a fixed in-degree k and a probability p

I'm working with Random Boolean Networks, I made a python program to show the dynamics of the networks. Before coding the program I study the theory and it says that the in-degree k and the ...
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Is there a relationship between quantum physics and chaos theory on a classical scale?

Im a complete physics lay person and I read somewhere that chaotic systems are subject to tiny differences in initial conditions and that the brain is a chaotic system. Does that mean our thoughts are ...
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Is weather a phenomenon impacted by quantum randomness?

Im trying to find phenomena that impact our everyday lives that are subject to quantum randomness. And I was wondering whether weather might be one of them. Can an electron behaving slightly ...
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Is there quantum randomness that significantly affects our macro world?

I was reading about the MWI and how there would be vastly different versions of "you" in the different branches. I'm just wondering, though, which quantum events lead to such different ...
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Is there a general equivalence of spectral correlations between hermitian and unitary random matrix ensembles?

It is common lore that the Gaussian Unitary Ensemble (GUE) and Circular Unitary Ensemble (CUE) have the same spectral correlations as the order $N$ of the matrix goes to infinity, see e.g. section 5.9 ...
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Multidimensional discretized Wiener measure for Langevin eq

How do I generalize the discretized Wiener measure in the case of the multidimensional Langevin equation: $$ dx^\omega=f^\omega(x,t) + \sum ^d_{\alpha=1} g^\omega_\alpha(x,t) dB^\alpha(t) \quad \omega=...
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Considering the deterministic nature of the macro/Newtonian world, how does branching in MWI cause so vastly different macro states?

Given that branching occurs at such a minute scale, how do we come up saying “in this world I’m having pizza today, in another curry” or something similar if changes at the quantum state are averaged ...
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6 votes
2 answers
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How is the randomness of single atom radioactive decay verified experimentally?

What experimental setups and statistical tests are used to empirically verify that the decay of a single atom cannot be predicted, it is truly random the decay of a single atom is not influenced by ...
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Second order brownian motion $\ddot{x}(t) = \xi(t)$

I'd like to solve for the pdf of position $$P(x,t) = \Big\langle \delta\Big(x-\int_0^t dt_1 \int_0^{t_1}dt_2 \xi(t_2)\Big)\Big\rangle $$ for the second order Brownian motion given by a Langevin-type ...
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How can one distinguish between a random process and a chaotic process? [duplicate]

Chaos is not a random process, although it may look like one. If I am given a set of observations, is it possible to determine if the observations are generated by a random process or if they are ...
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1 vote
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PDF for zero point of random function

Let us suppose a complex random function $\displaystyle \Psi (\mathbf{x})$ and its complex conjugate $\displaystyle \Psi ^{*}(\mathbf{x})$. We assume that these functions possess gaussian statistics, ...
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2 votes
4 answers
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Could an external being predict quantum uncertainty given all the information of our Universe? [duplicate]

I'll elaborate and be more specific. I understand that this is almost a metaphysical question but nonetheless I want to give it a try. Could an external being outside our Universe create 10 ...
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Why is entropy of gas reamains constant during adiabatic expansion?

In adiabatic compression, we add energy to the gas via piston and decrease volume. Now the increase in energy and decrease in volume will cause increase and decrease in entropy respectively, but it ...
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1 vote
1 answer
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What factors affect the rate of decay of a radioactive atom? [duplicate]

I saw a specific quote that made me question this : "Other atoms in the universe don't influence the rate, it's just an intrinsic property of each separate atom that it has some chance to decay.&...
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Mysterious path integral divergence after Hubbard-Stratonovich transformation

Let us consider common gaussian path integral over some complex random field $\displaystyle \Psi (\mathbf{r})$: \begin{equation*} N=\int D\Psi ^{*} D\Psi \ \exp\left( -\int d^{n} r\ \Psi ^{*}\hat{K} \...
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How much do quantum fluctuations affect our lives? [closed]

In other words, how deterministic is our daily lives given the probabilistic attributes of quantum mechanics? How much does the randomness of quantum mechanics affect our thoughts and our actions? To ...
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Could quantum world be deterministic even though there would be no hidden variables at play?

To my knowledge it is quite widely accepted in the scientific community that at the quantum level physics is not deterministic, only probabilistic. I know that there were some efforts to find some ...
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What is the probability distribution for the detection times of radioactive emissions from a radioactive sample?

Assume I have a radioactive sample composed of $N$ atoms of some type A. I know that if I measure at time t the number of atoms not already decayed, this number will be given by $$ N(t) = N_0 \exp^{-t/...
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Can you have an overall probabilistic many body quantum system with deterministic body mechanics but probabilistic interaction mechanics among them?

I try to understand if it is possible a quantum many body system in total to have a probabilistic time independent behavior (not stochastic which has a time-depended evolution) but with its elements (...
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Is consciousness likely to be a result of chaotic, or random processes? [closed]

Given that just about everything in the universe at a non quantum level is deterministic, what does this say about free will and consciousness? Are these likely to be a result of randomness at the ...
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1 vote
2 answers
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If there is a randomness to the polarization of photons (Bell's Theorem) why radio signals hit the reciever in the same state they left the emitter? [closed]

I have tried to understand Bell's Theorem (and I am still working on that) and I am probably missing something here, but a radio signal does not seem very random, rather the opposite. It seems very ...
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Is the Timing of Alpha Particle Radiation Perfectly Random?

Suppose one has a single atom of a radioactive isotope that radiates an Alpha particle. I'll accept that the timing of when that Alpha particle radiates is completely random, when the atom is ...
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Probabilities for quantum random number generators

Consider a quantum random number generator (QRNG) X, which generates integers at random. (Apparently, due to quantum statistical properties, this type of generation is truly at random, see e.g. "...
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Randomness in parallel universes [closed]

Suppose we have two completely identical universes (for instance in Tegmark's type III multiverse). In both of them, two identical men are sitting behind identical random number generators (RAN1 and ...
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Classical unpredictability

Consider, a box with $N$ particles each of mass $m$, arranged at time $t=0$ to be moving parallel to the $x$-direction, with mean velocity v and mean distance l. The particles are spheres of mean ...
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Feynman's random walk (6-3)

How does Feynman get to $D^2_{N-1}$? The expected value of $D^2_N$ for $N>1$ can be obtained from $D_{N−1}$. If, after $N−1$ steps, we have $D_{N−1}$, then after $N$ steps we have $D_N=D_{N−1}+1$ ...
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Why does a collection of radioactive atoms show predictable behaviour while a single one is highly random?

Well, we know that it is impossible to say exactly when a radioactive atom will go on decay. It is a random process. My question is why then a collection of them decays in a predictable nature (...
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3 votes
3 answers
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Fundamentally random physical phenomena

I read on Wikipedia: Quantum mechanics predicts that certain physical phenomena, such as the nuclear decay of atoms, are fundamentally random and cannot, in principle, be predicted. What does that ...
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How does quantum theory allow a rock to turn suddenly into a duck? [closed]

Quantum theory does not allow a rock to turn suddenly into a duck. It does not allow any other bizarre transformation to happen either. This idea is a myth perpetuated by people who misunderstand ...
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Applications of the Gaussian unitary ensemble

It is well known that the pair correlation function of the zeros of the Riemann zeta function reproduces the correlation function of the random matrices from the Gaussian unitary ensemble (GUE). ...
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Quantum: Is it possible to determine the past knowing the present?

Due to quantum randomicity, it's impossible to determine the future knowing the present. But is it possible to determine the past knowing the present? As far as I understand, it is impossible because ...
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Why do chaotic numbers improve evolutionary algorithms such as genetic algorithm?

I have implemented a genetic algorithm to solve a problem. In the process of genetic algorithm, instead of random numbers, I have used the chaotic numbers generated by the logistics map. The genetic ...
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45 votes
8 answers
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What is the reason that Quantum Mechanics is random?

We know quantum mechanics gives a random result when we observe a particle that's in a superposition, but why is it random? One of the explanations I've heard is that because light comes with those ...
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2 votes
3 answers
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What is a probabilistic physical theory?

What do we mean when we say that we have a probabilistic theory of some phenomenon? Of course, we know from experience that probabilistic theories "work", in the sense that they can (somehow)...
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Do physicists accept true randomness in nature? [duplicate]

I am not a physicist but I've started studying the subject and noticed that terms like "random", "randomness", "randomly" are widely used when talking about nature. For example, random movement of ...
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