Interpretation Definition and 803 Threads

When a vector field representing a physical quantity (e.g. B) has ∇\cdotB = 0 what is then the physical interpretation of this? Some people have said that the field doesn't diverge away from anything, but as far as I can tell magnetic field can easily get weaker and weaker the further you go...

Where exactly do the probability distributions we observe come from under the many worlds interpretation? I know it has something to do with being the only stable configurations in Hilbert space but I don't understand why. This is my attempt to explain it in my own way, please tell me if it...

Homework Statement The problem along with its solution is attached as ProblemSolution.jpg. Homework Equations Δx = λ/sinθ (Eq. 1) Δp_x = (h/λ)(sinε) (Eq. 2) The Attempt at a Solution In Wikipedia, I found this article: http://en.wikipedia.org/wiki/Heisenberg's_microscope which uses...

Quantum field theory predicts a value for the cosmological constant that is 123 orders of magnitude larger than the observed value (if one assumes the Standard Model to be correct up to the Planck scale of 10^19 GeV)! To theoretically predict the value of the cosmological constant, one must, I...

Hello! I'm doing a modal analysis and I'm trying to extract modal parameters from my aqcuired data. I'm using the Pulse Reflex Software. I got to the point where the Software provides me with a MIF and a stability diagram and I am to choose the parameters. However, I am unsure how...

Hi, I would like to study SL(3,\mathbb{R}) a little. I was motivated to look into them a bit because of their volume-preserving nature. Now this group has n^2-1=9-1=8 generators and I found out through some reading that three of them are the generators for rotation (duh Judah, volume...

Hi all, I am working through Visser's notes http://msor.victoria.ac.nz/twiki/pub/Courses/MATH465_2012T1/WebHome/notes-464-2011.pdf section 3.5 onward. I am trying to differentiate between the torsion and the Riemann curvature tensor in a heuristic manner. It appears from "Geometric...

I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum. Consider a real (or complex, with + in the right places) scalar particle (a Klein-Gordon field). Now consider the propagator (or correlation function) G(x-y)=...

I noticed a youtube video, where Thomas Warren Campbell, a physicist and author of the book trilogy My big TOE the last standing for Theory of Everything and apparently he also works for NASA, deducts some very disturbing things from a certain double slit experiment. Here it is, I marked the...

From what I understand, a basis is essentially a subset of a vector space over a given field. Now what I'm not so sure of is the linearly independence part. If the basis has two linearly independent vectors, then than means they aren't collinear: rather, they wouldn't have the same slope...

When we calculate the average of anything: we add up (or integrate) the sum{ [all the things were taking the average of] * [the probability of getting that thing ]}. The thing about the average I'm that curious about is for example: the average height of 5 people turns out to be say 6...

http://dl.dropbox.com/u/33103477/Resistor.png For the first bit first I solved the equation \frac{dI}{dt}=\frac{U-RI}{L} I(t)=\frac{U-C_2e^{\frac{-t}{L}}}{R} Now I put in T(0)=0 to work out the constant and I got I(t)=\frac{U-Ue^{\frac{-t}{L}}}{R} Now here's the dodgy bit, I did...

Im really just searching for a general explanation! If you are solving a pretty standard left hand side differential equation, but a diracs delta function on the right hand side. I am abit confused about how to interpret this. If this is the case for the right hand side: r(t) = Diracs (t)...

http://dl.dropbox.com/u/33103477/Linear%20oscilator.png I am having trouble understand the question, what I have done its solve the equation using the substitution x=e^{rx} Then, I have the solution given by: x(t)=c_1 e^{t(\sqrt{\gamma^2 - \omega^2 })} + c_2e^{-t(\sqrt{\gamma^2 -...

I am a programmer by trade, so I am more adept at logic than mathematics. One thing that has always perplexed me about the Michelson-Morley experiment was how it is used to reach the conclusion that there is no ether. Just given basic logic, there is a third alternative that I have never seen...

We are starting to learn about spin in my introductory quantum mechanics course, and I was wondering if anyone could provide a physical interpretation of an electron's spin. I understand its a form of angular momentum which has nothing to do with the motion of the electron in space, but since an...

Wikipedia: "Reynolds Number is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces." What is meant by the inertial forces? I have a much better intuition of viscosity. But it seems to be like the Reynolds Number predicts turbulent flow for a...

Statistics question: I'm having trouble understanding my statistics professor's objection to this interpretation of confidence intervals. If you have some distribution with parameter x: X = Dist(x), and you perform a random experiment drawing N random variables from it, and derive from those...

I will try to keep things brief. I am trying to understand what is considered interpretation. Imagine we have a totally isolated and complex quantum system in a fixed initial state which we can prepare with essentially perfect fidelity. Suppose that this system is macroscopic in which small...

Can the covariant components of a vector, v, be thought of as v multiplied by a matrix of linearly independent vectors that span the vector space, and the contravariant components of the same vector, v, the vector v multiplied by the *inverse* of that same matrix? thinking about it like that...

Homework Statement A student takes a 30-question mathematics exam on which she got n questions correct and m questions incorrect and left k questions blank. If correct answers are worth 4 points, incorrect answers are worth -1 points, and blank answers are worth 0 points, write an equation to...

Hey, I had this question I thought i answered but now I'm questioning if the group operation is supposed to be addition and not multiplication. The question \varphi :\mathbb{Z}\to {{\mathbb{Z}}_{n}}\,\,\,\,\,where\,\,\varphi (a)=\text{Remainder}\left( \frac{a}{n} \right) When I...

I know, I know, it might be a little bit spam-y to post another poll, but since the option 'Other' was gaining so much attention, I decided to create a new poll with more options so that people could be more accurate in their description. Since I support the MWI, I will post a few links with...

I was wondering who/how many people in the forum subscribe to which interpretation, so I decided to make a poll :) Also anyone is welcome to post content about each interpretation to illuminate people who may not know the difference and/or definition of an interpretation.

Two individuals A and B are traveling through space at a velocity in the "x" direction at and are next to each other so they can synchronize their clocks. Since there is no other available reference they believe they are not moving. Both have a duplicate shape charge which as they are in the...

Hi, I am am currently taking a second course in geometry, the first part of the course concerns projective geometry, and I feel I'm not getting the picture. I would like to know what the motivation for the development of projective geometry is. What picture you guys have in your head of...

This is an extract from the lecture notes I took for the 'Foundations of QM' third year course. Copenhagen QM - classical-quantum division State: wavefunction ψ(x); (ψ,\varphi) = \int d^{3}r ψ^{*}(r)\varphi(r) Evolution: TDSE Observables (\hat{x},\hat{p},\hat{H}): A = A-dagger...

Interpretation of "dx" as the differential of x for Indefinite Integrals This question is concept-as-opposed-to-calculation based. I understand that when one sees the integral sign, followed by f(x)dx, that we can think of this as the indefinite integral, or antiderivative of f(x), with...

Hello, I have been following this forum for some time now, but this is the first time I participate. I would appreciate if you could give me a hand in understanding the results of a finite element analysis of an automotive component we have designed. The analysis results indicate that the...

There are tons of interpretations of quantum mechanics, but I'm unaware of any that are 'classical' as in being local, having realism and determinism. There is Bells famous work proving that that can't be true for certain aspects of quantum mechanics, but why aren't there any classical...

I was watching "The Fabric of the Cosmos: What is Space?" on pbs.com, and I couldn't help but wonder a few things after looking up some information about it. I find it funny that people have been using String Theory with only two dimensions (since they are supposed to keep adding dimensions...

hello forum, we all know that a rotation wheel, a rotating football, etc.. maintain their direction of motion with more stability than if they were not spinning... A bicycle wheel is suspended from one of end of its axie by a rope, and spun up by hand. The wheel's axle is then placed...

Hello, Before I ask, I'd just to say that I know this has been heavily discussed before, but I am asking for peoples' insight directly as this is for a report I'm currently working on, hence why I'm not just looking through old posts using the search option. So I'm sorry if this may be of an...

Let r = √(x^2+y^2+z^2) One can easily show that \nablar= \vec{r}/r. But I'm having a hard time understanding what this means geometrically - who can help? :)

Hi, I was at a party where there was a lucky draw. There were about 200 people and each of them had put a chit with their name on it, in a transparent bowl. There were 10 prizes. The announcer chose a person at random to pick a chit for each prize. For one of the prizes, the picker picked his...

can many world interpretation be valid for large scale collapses that brings out a single reality?

Given \triangle u = f(x,y,z) on a given body with vanishing neumann boundary conditions. I'm asked to interpret it in terms of heat and diffusion. Since heat/diffusion take the form u_t = k \triangle u, I am a little confused as I there is no time term here. I think the answer is that u...

Is there an interpretation of quantum mechanics, which could make a difference to future calculations and results? Maybe an interpretation which could rewrite and simplify the algebra? Or one which has new testible results which when correct would change the quantum mechanical equations to make...

Hi all, I'm trying to understand exactly what the physical meaning of conductivity/current is in relation to waves. if we have a wave traveling through a conductor, we find that it decays exponentially, i.e. e^{-\alpha z} where \alpha=imag(k)=\omega\sqrt{\frac{\epsilon\mu}{2}}...

Edward Nelson, a Princeton mathematician showed that quantum mechanics could be derived from the principle that elementary particles are subjected to a universal jiggling of an unspecified cause. As I understand the obstacle to use this mathematical model as a physical one, is that dynamics of...

I recently read an article entitled, "The Interpretation of Quantum Mechanics: Many Worlds or Many Words?" authored by Max Tegmark and it raised many questions on the matter as well as curiosity. In the article, Tegmark provides two tenable but diametrically opposite paradigms regarding physical...

Hello, I am a Bio informatician and encountered Likelihood while executing the Molecular data. I have used one software that is using the Hidden Markov Model in addition to the EM Algorithm and Viterbi algorithm. After calculations are done already, in addition to the output, it is giving me...

With Hobson's notation: H=(da/dt)/a dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2 If ((d2a/dt2)/a) is negative, (dH/dt) is certainly negative. But if ((d2a/dt2)/a) is positive, (dH/dt) can be positive or negative. What is your interpretation?

Hi all, I feel like there's a missing link in my understanding of brownian motion. I'm comfortable with the "method of http://fraden.brandeis.edu/courses/phys39/simulations/Uhlenbeck%20Brownian%20Motion%20Rev%20Mod%20Phys%201945.pdf" where the signal is written as a Fourier series, and with...

Homework Statement x,y, z are vectors in R^n. We have the equation: ax +by +cz, where a,b,c are constants such that a+b+c=1, and a,b,c>=0 What is the geometric interpretation of the equation? Homework Equations sv + tu, where u,v are vectors in R^n and s,t are constants such that...

dear expert, please guide me in interpretation of asme sec viii div 1 interpretation...the basic terms used as uw,ucs etc..what does these abbrevate..same like basic nomenclature used in this code.. regards, bali

I understand the basics of the mathematical descriptions of systems in superposition. But what I'm not clear about is whether such a system is actually in more than one state at the same time. Is this a matter of QM interpretation or is it simply moot b/c we can make no measurements that can...

Sorry for the confusing title! I have a question that I cannot wrap my mind around... Suppose the universe attains its state of maximum entopy (assuming maximum here also involves quantum effects such that in the end even the atoms disintegrate into photons and leptons). I understand that in...

Hi, I'm looking for a book that presents a pragmatic interpretation of QM that'd be appropriate for someone who's taken one semester of it.

Hello. This is my interpretation of what is currently known in cosmology, as regards the low entropy state of the early universe. If it is a poor interpretation, then I apologise, but in all fairness, I can only blame the industry professionals for not explaining the data clearly enough. I am...