Correlation Definition and 338 Threads

Let's say we have a Dirac field ##\Psi## and a scalar field ##\varphi## and we want to compute this correlation function $$<0|T \Psi _\alpha (x) \Psi _\beta (y) \varphi (z_1) \varphi (z_2)|0>$$ $$= \frac {1}{i} \frac{\delta}{\delta \overline{\eta}_\alpha(x)} i \frac{\delta}{\delta \eta_\beta(y)}...

all the references I can find on the net to justifying a correlation treat it as a matter of judgment, and, quite correctly, that it depends on the application. But it seems to me that one could compare the fit to the data of a horizontal line (i.e. average y) with that of the linear regression...

I just read the policy for this forum "Earth" so i hope my next question will be approved, it is with the best intentions. My friends and i where having a discussion about CO2 and the correlation with the raising temperature, we know that CO2 is a greenhouse gas. About that, CO2 is a greenhouse...

Suppose we have two variables A and B. A has a truly random distribution over {0,1} with P(0)=P(1)=0.5 . B has the same distribution. Now suppose that A and B always show both a 1 or both a 0. This would be a strong correlation between A and B. Now could this be called 'a coincidence'? And if...

I am trying to estimate the distance of closest galaxy neighbor knowing the expression of number of neighbors into a volume ##\text{d}V##, the mean density ##n_\text{gal}## and the correlation function, i.e with this expression : ##\text{d}N=n_{\text{gal}}\,\text{d}V\,(1+\xi(r))## with...

Wooo! I am almost done with my stats class. I am having a reoccurring issue with finding the test statistic using a scatter plot and linear correlation coefficient. Internet Users (Per 100) Award Winners (Per 10 Million) 78.2 5.5 79.5...

Homework Statement [/B] I have the following questions as homeworks and I would like to get help. Question 1) Give the formal expression of the total number density of galaxies. Why is this expressoin problematic in practice? Question 2) In practice one uses a numerical value for the number...

I made three charts from several different sources plotting the luminosity and distance from Earth of 26 to 300 Stars. In each chart, there appears to be a correlation between a star's luminosity (in solar units) and its distance from Earth (or solar system, whichever you prefer) in light years...

Homework Statement I have a hipotetic rocket that have a power of 3000 watt, however its position don't change because the effect of a gravity of 10m/s^2 do the rocket remains like it would be resting. I need to determine the mass of the rocket. In a similar problem I have a rocket also in an...

If we make a measurement, does that mean that the outcome of the measurement gets correlated with the measured value?

I see no correlation between a dimensionless point and a line although it appears that math has made one. I'm just a philosopher so it's quite possible that I've got it all wrong. It seems as though any location along a line is always the same location. If a location has no size then it can't...

I'm trying to write a research paper in astronomy, and while I was brainstorming ideas, I came across supermassive stars and the abundance anomalies of proton-capture elements in globular clusters, such as the C-N, Na-O, Mg-Al and Na-F anticorrelations. I tried searching everywhere for an...

Suppose A is an ensemble of measurement events in the past. Suppose B is an ensemble of measurement events in the present. Suppose there is a correlation between A and B that stays the same over time. Suppose we can manipulate the outcomes of B (for example by choosing the orientation of the...

I have been reading about weak gravitational lensing and I am trying to calculate the dispersion ##\langle M_{ap}^2\rangle## of the aperture mass for a singular isothermal sphere acting as a lens for distant objects. I need some guidance on how to actually carry out the calculation of the power...

Sorry if this is a bad question, but would lower costs to produce electricity (e.g. hydroelectricity instead of solar) bring down the overall costs for us consumers? Also, if there is any reading material or website on this topic, that would be really great too! Thanks!

Homework Statement An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is Nu=0.53Gr^0.25 Pr^0.25 Where, Gr= (αp^2 d^3 (T_1-T_f )g)/μ^2 And Pr⁡〖= (C_p μ)/k〗 Show the above correlation can be simplified to h...

OK, so, I've forgotten more statistics than my students will ever know, and I'm not too proud to ask for help, because I'm just blanking out on this. I would appreciate it if someone could patiently follow along and let me know what I've got right or wrong please. My understanding of the...

Hello, I have two predictor variables: gender and class, and one response variable: survived. After converting the categorical variables into numeric variables using dummy variables, I found the correlation between gender_male and survived to be -0.54, and between class_1 and survived to be...

I'd like to know people's views on the possibility of Black Holes being 'Gateways' or 'Portals' to parallel universes.

For a fixed point in space, the first-order electric field correlation function may be given as (Possibly incorrectly, see my "second" post to this thread)! $$\langle\vec E^*(t)\vec E(t+\tau)\rangle = {\frac {1} {T}} \int_T\vec E^*(t)\vec E(t+\tau)dt~~~~~(1)$$ Where T is a very large time and *...

Can someone derive: ##\frac{Cov(Z+\Theta),\Theta)}{\sqrt{Var(Z+\Theta)Var(\Theta)}}=\frac{\sigma ^2}{\sqrt{1+\sigma ^2}}## My attempt: Numerator: ##Cov(X,Y)=E[(X-E(X))(Y-E(Y))]=E[(Z+\Theta-\theta)(\Theta-\mu)]## The denumerator is pretty simple: ##\sqrt{(1+\sigma ^2)\sigma ^2}##

In class while learning about electromagnetism, I was given the following two equations: U=-μ⋅B τ=μ×B where μ=IA First of all, what does μ stand for? How should I interpret the relationship between potential energy (U) and torque? Can someone explain this in terms of μ and B?

Hello everyone. I stumbled across an article in the social sciences that had a correlation coefficient of r=0.93. Being from a maths background and knowing nothing about things like social sciences, psychology, etc., is this r-value in these types of fields considered fairly strong, strong...

I was hoping to get some assistance in reproducing a calculation from https://arxiv.org/abs/0803.1292 (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.78.012304 for the published version). A certain four-spin correlation function for Kitaev's spin-1/2 model on the honeycomb lattice is...

In other words, it seems that if you have entanglement, then you have correlation (of measured properties). But is it true that if you have correlation, then you have quantum entanglement? Classically, correlation is between macro-events. But macro-events are made of micro-events. So is...

Hi I would be happy if anyone helped me understand what the physical meaning of n-particle correlation function in QFT is ?

Hello! I'm measuring the second order correlation function g(2) of quasi-thermal light, generated by focusing a 633 nm laser onto a rotating sandpaper-like surface at 45 deg. Part of the dispersed light is collected into a fiber and split with a fiber beam splitter. A simple HBT setup. g(2) is...

Hello! I am reading Peskin's book on QFT and I reached a part (in chapter 4) where he is analyzing the two-point correlation function for ##\phi^4## theory. At a point he wants to find the evolution in time of ##\phi##, under this Hamiltonian (which is basically the Klein-Gordon - ##H_0## - one...

Hi, I'm a new member in this forum. my question : How calculated the normalized error with two signals?

If variable X is positively correlated with variable Y, under what circumstances am I allowed to infer that X does not causally prevent Y with reasonable probability? I don't know much about statistics and I'm trying to motivate myself to learn by doing. For example...

Homework Statement Given correlation matrix $$M = \begin{bmatrix} 1 & .3 & .5 \\ .3 & 1 & .2 \\ .5 & .2 & 1 \\ \end{bmatrix}$$ And 3 independent standard normals $$N_1, N_2, N_3$$ using cholesky decomposition A) get the correlated standard normals B) and if...

I have 2 PERFECT data of the transmitter and receiver. From 2 data, I can calculate the delay estimation: Fs = 8e6; % sample rate ... for i = 1:2 [cc_correlation,lag] = xcorr(signal2(i), signal1); [cc_maximum, cc_time] = max(abs(cc_correlation)); cc_estimation...

A couple of questions today. First. I am running a panel data regression test. First I check the correlations between the independent variables and the dependent variable. these are the results. The D/(D+Em) is the dependent variable, and the independent are the 4 variables most adjacent...

Let's say that the correlation coefficient between X and Y were swapped so that the correlation coefficient between Y and X. If we were to compared the correlation coefficient between X and Y and Y and X. Based on my understanding of correlation coefficient, it doesn't matter if f X and Y were...

Suppose we have two truly random sources A and B that generate bits ('0' or '1') synchronously. If we measure the correlation between the respective bits generated, we find a random, ie no, correlation. Now suppose A and B are two detectors that register polarization-entangled photons passing...

Gauge symmetry is not a symmetry. It is a fake, a redundancy introduced by hand to help us keep track of massless particles in quantum field theory. All physical predictions must be gauge-independent...

I have 2 data files, which links are attached below: Transmitted data https://www.dropbox.com/s/0nmhw6mpgh7upmv/TX.dat?dl=0 Received data https://www.dropbox.com/s/xgyo6le3bcmd25r/RX.dat?dl=0 Those binary data are read by this MATLAB code: %% initial values: nsamps = inf; nstart = 0; %% input...

This is a chemically inspired problem, but the path is fully quantum mechanics and a bunch of integrals. How does one calculate fully quantum mechanical rate ($\kappa$) in the golden-rule approximation for two linear potential energy surfaces? Attempt: Miller (83) proposes...

From what I have understood about Pearson correlation coefficient I have created a visual illustration, I would like to know if this understanding looks correct. Say I have a sample with 5 data points:- x y 8 6 16 8 20 16 28 12 32 20 My goal is to...

I wasn't sure where to post this, I hope this was the right section. I've been struggling quite a bit with implementing an autocorrelation code into my current project. The autocorrelation as it is now, is increasing exponentially from 1 at the start of my MC run, and hitting 2 halfway through...

I have some difficulty understanding how to go about with this problem: I came up with several graphs, you can see them in the attached picture (they are up to ~g^4 order). I am not sure about the self-interaction diagrams, but I think they are considered in the connected graphs (they are not...

Hi all, in several vehicles, I measured the engine torque and speed and the engaged gear while it was driven for around 100km/h. I computed the average engine speed and torque of all the times the vehicle was run with each gear and also I computed the relative frequency of the gear used. So for...

Sorry if this is trivial - I'm arguing with someone on Facebook :sorry: who is claiming that r-squared values, or correlation coefficients represents "chance" or "probability". I've never heard of this. I just need a simple yes or no answer along with a short explanation why it is or isn't...

Hello everyone, we were discussing a project at work just yesterday (I work as a researcher in a medium-size biotech), and at some point the (in)famous 'correlation doesn't imply causation' sentence came up. I would like to know what you think, please. I apologise in advance, long post: the...

I am looking for a Nusselt number correlation that will work for a shell & tube heat exchanger in the Re < 3000 region, i.e. extremely laminar flow (for a lab experiment). I've been searching for a while now, but can only find empirical correlations for Re > 3000, and was thus hoping that...

Homework Statement Given ##v = {\left\{ {v}_{i} \right\}}_{i = 1}^{\infty}## and defining ## {v}_{n}^{\left( k \right)} = {v}_{n - k} ## (Shifting Operator). Prove that there exist ## \alpha > 0 ## such that $$ \sum_{k = - \infty}^{\infty} {2}^{- \left| k \right|} \left \langle {v}^{\left (...

Green functions are defined in mathematics as solutions of inhomogeneous differential equations with a dirac delta as the right hand side and are used for solving such equations with a generic right hand side. But in QFT, n-point correlation functions are also called Green functions. Why is...

I thought I understood the concept of a correlation function, but I having some doubts. What exactly does a correlation function quantify and furthermore, what is a correlation length. As far as I understand, a correlation between two variables ##X## and ##Y## quantifies how much the two...

The ##1##-point correlation function in any theory, free or interacting, can be made to vanish by a suitable rescaling of the field ##\phi##. I would like to understand this statement. With the above goal in mind, consider the following theory: $$\mathcal{L} =...

Given the theory $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m_{\phi}^{2}\phi^{2}+\partial_{\mu}\chi^{*}\partial^{\mu}\chi-m_{\chi}^{2}\chi^{*}\chi+\mathcal{L}_{\text{int}},\qquad \mathcal{L}_{\text{int}}=-g\phi\chi^{*}\chi,$$ the time-correlation function ##\langle \Omega |...