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20
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5answers
188 views

Connections and applications of SLE in physics

In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
20
votes
2answers
109 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
19
votes
7answers
1k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is application of probability in QM fundamentally different than application of probability in other areas? Quantum mechanics applies probability according to the same probability theory that ...
14
votes
1answer
162 views

Monte Carlo integration over space of quantum states

I am currently facing the problem of calculating integrals that take the general form $\int_{R} P(\sigma)d\sigma$ where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
12
votes
2answers
216 views

Random Walk Randomly Reflected

Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will ...
11
votes
1answer
521 views

The measure problem in the anthropic principle

The anthropic principle is based upon Bayesian reasoning applied to the ensemble of universes, or parts thereof, conditioned upon the existence of conscious observers. That still leaves us with the ...
9
votes
1answer
694 views

Interpretation of the Random Schrödinger Equation

I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
8
votes
2answers
1k views

What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
8
votes
7answers
1k views

Mathematically possible vs physically probable outcomes

A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with ...
8
votes
5answers
622 views

Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
8
votes
1answer
245 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
8
votes
1answer
397 views

How to determine the probabilities for a cuboid die?

Imagine we take a cuboid with sides $a, b$ and $c$ and throw it like a usual die. Is there a way to determine the probabilities of the different outcomes $P_{ab}, P_{bc}$ and $P_{ac}$? With $ab$, ...
8
votes
4answers
3k views

Infinite universe - Jumping to pointless conclusions

I watched an episode of thee BBC Horizon series titled 'To infinity and beyond'. In this program a number of respected physicists and mathematicians were talking about the nature of infinity and an ...
8
votes
2answers
445 views

Why was quantum mechanics regarded as a non-deterministic theory?

It seems to be a wide impression that quantum mechanics is not deterministic, e.g. the world is quantum-mechanical and not deterministic. I have a basic question about quantum mechanics itself. A ...
8
votes
3answers
717 views

What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
8
votes
2answers
144 views

How to design a deliberately biased coin?

For demonstrating basic probability concepts, it would be nice to have a coin-like object that lands heads/tails not in 50/50% ratio, but biased in a way that can be revealed in a short experiment. ...
7
votes
4answers
343 views

Are probabilities really tangible physical real numbers?

Probabilities are usually considered to be a real number between 0 and 1. A real number has an infinite decimal expansion. Are probabilities really real numbers? Is the infinite decimal expansion ...
7
votes
3answers
971 views

Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone ...
7
votes
2answers
286 views

Interpretation: probability form probability amplitude (free particle)

If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
7
votes
3answers
301 views

Is “entanglement” unique to quantum systems?

My text shows (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. ...
7
votes
3answers
786 views

Determinism, classical probabilities, and/or quantum mechanics?

[I]f you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.] ...
6
votes
5answers
867 views

Differences between probability density and expectation value of position

The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. If wave function gives the probabilities of positions, why do we calculate ...
6
votes
6answers
4k views

Probability amplitude in Layman's Terms

I am basically a Computer Programmer, but Physics has always fascinated and often baffled me. I have tried to understand probability density in Quantum Mechanics for many many years. What I ...
6
votes
2answers
878 views

Amplitude of Probability amplitude. Which one is it?

QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$: $$P = \left|\psi\right|^2.$$ If I write down a wave function like this ...
6
votes
3answers
434 views

Could quantum mechanics work without the Born rule?

Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
6
votes
1answer
76 views

Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)

In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
6
votes
2answers
779 views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
6
votes
2answers
297 views

Mathematical probabilistic interepretation of probability amplitude

As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question: I'm looking at the possibility of using probability amplitude functions to ...
6
votes
1answer
114 views

Random walks on resistive network

I have been referring to a paper http://arxiv.org/abs/physics/0405135 to determine the effective resistance using random walks for an infinite square resistive lattice Though the author seems to ...
6
votes
1answer
127 views

Is there an equivalent of a Galton box for a converging probability?

This is a question about probability. The Galton box (or quincunx) uses the physical process of shot moving down a pin-board, to demonstrate central limit theorem, eg: So I am interested in events ...
6
votes
3answers
727 views

Born's Rule, What is the Reason?

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
5
votes
2answers
534 views

Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
5
votes
4answers
222 views

Does entropy alter the probability of independent events?

So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up: Given a fair coin that has been tossed 100 ...
5
votes
2answers
636 views

Why is quantum mechanics based on probability theory? [duplicate]

What makes us formulate quantum mechanics based on probability theory? Isn't the real quantum world based on unknown laws to us? Is it possible that results of an experiment will be measurable in ...
5
votes
5answers
6k views

Would one actually find their doppleganger in a “Googolplex Universe”?

Related: Infinite universe - Jumping to pointless conclusions I've recently become a fan of Numberphile, and today I happened to watch their video regarding Googol and Googolplex. In the video, ...
5
votes
2answers
605 views

What is the probability density function over time for a 1-D random walk on a line with boundaries?

If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution. \begin{align} ...
5
votes
3answers
248 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...
5
votes
2answers
162 views

What information is lost in the symmetrization necessary to derive the BBGKY hierarchy?

The book on Kinetic theory I'm reading derives the BBGKY hierarchy after introducing the reduced distribution functions $f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d ...
5
votes
1answer
495 views

't Hooft for laypersons

I have looked at some of 't Hooft's recent papers and, unfortunately, they are well beyond my current level of comprehension. The same holds for the discussions that took place on this website. (See, ...
5
votes
1answer
301 views

Boundary conditions from single-valuedness of spherical wavefunctions

This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharonov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
5
votes
1answer
116 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 ...
4
votes
3answers
356 views

Probability and probability amplitude

The equation: $$P = |A|^2$$ appears in many books and lectures, where $P$ is a "probability" and $A$ is an "amplitude" or "probability amplitude". What led physicists to believe that the square of ...
4
votes
3answers
924 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 ...
4
votes
3answers
154 views

Is there a phenomenon where physicists are only interested in the standard deviation of the quantity to be measured?

or a phenomenon where we can only measure the standard deviation ($\sigma_w$) of a variable $w$ and not the mean $\overline{w}$
4
votes
3answers
131 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 ...
4
votes
1answer
75 views

Convexity — reference request

I've been reading a few papers on generalized probabilistic theories, and have been struggling through proofs of some results that involve use of convexity and group theory, e.g. this paper on bit ...
4
votes
2answers
107 views

Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
4
votes
1answer
180 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 ...
4
votes
1answer
241 views

Probability in Quantum Mechanics

Do you need to take a probability/statistics course for Quantum Mechanics, or is the probability in quantum mechanics so rudimentary that you can just learn it along the way? I'm in doubt as to ...
4
votes
2answers
413 views

How do you come up with a POVM?

This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me. Say you have a physical quantity $E$ that can take values 1, 2, 3 ...