Convention Definition and 177 Threads

Hi all, I have been figuring out relativity. I was just wondering how meaningful the simultaneity convention is, how meaningful it is for say something a million light years away to be on our plane of simultaneity. I'm guessing not very, we must really wait for light to get to use to have...

Hi For an operator A we have Aψn = anψn ; the matrix elements of the operator A are given by Amn= anδmn My question is : is this an abuse of Einstein summation convention or is that convention not used in QM ? Thanks

(I admit this might be better in the mechanical engineering forum, but let me ask, and the moderator can decide) What is a "convention?" For example, in elasticity, we have a stress tensor. If a coordinate axis is in one direction, positive, we state the the convention is that the stress is...

I have a number of questions about some S.R. basics. The answer to one question may affect the next, so I will try to focus on one question at a time. The question here is about the possible range of “simultaneity conventions.” We place an observer at location A. This observer releases a photon...

According to Wikipedia, the definition of the Riemann Tensor can be taken as ##R^{\rho}_{\sigma \mu \nu} = dx^{\rho}[\nabla_{\mu},\nabla_{\nu}]\partial_{\sigma}##. Note that I dropped the Lie Bracket term and used the commutator since I'm looking at calculating this w.r.t. the basis. I...

Hi If i have a vector r = ( x1 , x2 , x3) then i can write r2 as xixi where the i is summed over because it occurs twice. Now is xixi the same as xi2 ? I have come across an example where they are used as equivalent but i am confused because xi2 seems to be the square of just one component of r...

Here is the circuit... Here is my work so far in cadence (I haven't put in values for other components in because the moment I saw the dot convention I started trying to figure that out). Where I'm at -There apparently isn't a way in Cadence Virtuoso (the program my class uses) to change the...

Hello: I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments. For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached? Beam...

Hi, I've read a number of posts here on PF about Einstein's clock synchronization convention. In the context of SR we know the transformation law between inertial frame's coordinates is actually the Lorentz one. The invariant speed for Lorentz transformation is c (actually it coincides with...

If I understand correctly, the concept of electric and magnetic fields originated with Faraday and was developed by reconceptualizing forces acting at-a-distance. For example, the electric field concept was developed by looking at the force on a test charge in the presence of a source charge...

Hi, I just have a quick question when I was working through a linear algebra homework problem. We are given a matrix A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix} and are asked to compute e^{A} . In earlier parts of the question, we prove the identities A = V \Lambda V^{-1} and e^{A}...

If the source is at ##(t,0)## in ##S## and the receiver is at ##(t',0)## in ##S'## which moves at ##\beta_x## w.r.t. ##S##, then by considering two crests at ##(0,0)## and ##(T_s, 0)## in the source frame ##S## and transforming these events into ##S'## we can derive that ##\lambda_{r} =...

Below is my attempted solution: $$\epsilon_{ij \ell} \, \epsilon_{km \ell} \, \epsilon_{ijm} \, a_k$$ $$\Rightarrow (\delta_{ik} \, \delta_{jm} - \delta_{im} \, \delta_{jk}) \epsilon_{ijm} \, a_k$$ $$\Rightarrow \delta_{ik} \, \delta_{jm} \, \epsilon_{ijm} \, a_k - \delta_{im} \, \delta_{jk}...

Attempted Solution: $$a_i \, b_j \, c_k \, \epsilon_{ij \ell} \, \epsilon_{3k \ell}$$ $$a_i\, b_j\, c_k\, (\delta_{i3} \, \delta_{jk} - \, \delta_{ik}\, \delta_{j3})$$ Beyond this, though, I am quite lost. I know I am very close to the answer, but seeing this many terms can become fairly...

Just to clarify, I'm aware of the two equivalent expressions of the first law ##\Delta U = Q + W## and ##\Delta U = Q - W## when applied to a certain system, though my question is primarily about ##Q## - for which, as far as I am aware, the convention is almost universally that ##Q > 0## if heat...

Hi, There are three clocks - Clock A, Clock B, and Clock C. The distance, D, between each clock is 6 light-second. The clocks are situated in a frame of reference which is moving toward the right at speed of 0.5c where 'c' is taken to be 300000000 m/s. Please look here...

Einstein's synchrony convention (ESC) defines the one-way speed of light as equal to the roundtrip speed IN A VACUUM, at least, the discussions and papers I read on it (even Einstein's 1905 paper) always seem to set the context as in space (a near vacuum) or in a (theoretical) vacuum. I'm...

I got another basic question: should the summation in einstein notation start from first occurance of index or in beginning of equation? For eampledoes this equation ##R_{\alpha \beta }={R^{\rho }}_{\alpha \rho \beta }=\partial _{\rho }{\Gamma ^{\rho }}_{\beta\alpha }-\partial _{\beta }{\Gamma...

Sorry for the silly question! If we start of with the relationship $$\int_{x_{1}}^{x_{2}} F dx = KE_{2} - KE_{1}$$ and then state that at position x1 the velocity (and hence also kinetic energy) of the particle is 0, and at x2 its velocity is v, is it sloppy or valid to write the integral...

Precursor : Sign conventions regarding Work by the system/on the system may even vary among Physics textbooks and among Chemistry textbooks and as a rule of thumb it is better to clearly mark out the convention used by the text being referred to specifically and remain consistent with it...

Hello, there are a couple things about magnetism that I do not understand. 1. Why didn't we define the magnetic field to be in the directions of the force? This isn't really a technical question, I am just more curious about why it is this way. The way I was thinking of it, the math seems to...

This is about the history of electromagnetism. I already know about the convention that defined which electric charge is the "positive" one, which ended up making the electron a negative particle. But what about the "positive" direction of the magnetic field? Does anybody here know how it was...

Hello all, I understand there are four d'Alembert (fictitious) (non-inertial) forces: 1. Coriolis 2. Centrifugal 3. Linear 4. Angular acceleration. But then I think about the Gyroscopic Effect (I understand how it arises, so that is not the issue). I am wondering if one can "classify" these...

How do physicists call a tensor of ## V^* \otimes V^* \otimes V##, (1,2) or (2,1)? And which part do they call contravariant and which covariant? I'm just not sure, whether the mathematical definition of funktors apply to the usances in physics. (LUP - tensor)

Homework Statement So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure you I read them all and that only left me more confused. So here are my questions: Homework Equations 3. The Attempt at a Solution [/B] ->...

Is (Tii)2 equivalent to (∑i = 1nTii)2? That is, when you encounter parentheses with Einstein summation, you perform the summation first and then apply any mathematical operations indicated by the parentheses? The solutions manual gives a solution to a problem I've been working out seems to...

Hi. I'm reading a paper "Transmission of light through a single rectangular hole in a real metal" and the author refers to the incident light shown below as "p-polarized" without further specification. Note that ax > ay. Is there any convention in regarding a certain polarization as...

Homework Statement I know that by definition Γijkei=∂ej/∂xk implies that Γmjk=em ⋅ ∂ej/∂xk (e are basis vectors, xk is component of basis vector). Can I write it in the following form? Γjjk=ej ⋅ ∂ej/∂xk Why or why not? Homework EquationsThe Attempt at a Solution

Homework Statement Assume that you want to the derivative of a vector V with respect to a component Zk, the derivative is then ∂ViZi/∂Zk=Zi∂Vi/∂Zk+Vi∂Zi/∂Zk = Zi∂Vi/∂Zk+ViΓmikZm Now why is it that I can change m to i and i to j in ViΓmikZm?

Homework Statement A carriage is mounted on a spring, as shown in the diagram. The bottom of the spring is fixed to the ground. The carriage (loaded with its passenger) has a mass of 150kg. The carriage can only move vertically. The natural length of the spring is 10m and its spring...

Homework Statement I needed help to undestand some concepts in Ray Optics for my assignment. The topics which U am concerned are: Part 1: Mirror Equation, Refraction at singly curved surface, lens maker's equation, combination of thin lenses in contact. Part 2: Magnification Power of simple...

I Google and find all of the following are used: Modulus square of the wavefunction Modulus squared of the wavefunction Square modulus of the wavefunction Squared modulus of the wavefunction Which is correct? Or are these all correct? Or does it depend from... what? I'm confused, need help.

Here the voltage is negative so the current is negative. does it matter if I traverse the circuit through the other direction?

Homework Statement Is there a power factor convention when it comes to the angles of a given current and voltage? In one class I learned that PF = cos(θ_V - θ_I) but in another the professor claims (I still think he is wrong) the convention for that class is PF=cos(θ_I - θ_V). Here is a...

Homework Statement Cartesian sign convetion for microscope,compound microscope and telescope. Homework Equations distances in the direction of incident ray are negative and thsoe along it are positive. all distances are measured from pole of lens or mirror. The Attempt at a Solution 1.FOR...

Homework Statement Homework Equations KVL and KCL The Attempt at a Solution I am very confused by the dot convention and how it works when writing your loop equations... I can't find any good videos or explanations online and I am completely lost with this dot convention. So I understand...

Homework Statement I don't understand why the fixed end moment at AE is 10KNm ( clockwise) . Homework EquationsThe Attempt at a Solution Forger about the sign convention here , i have the resultant moment = 10KNm , which ic clockwise , why in the 2nd picture ( SFD and BMD part) , the moment...

Homework Statement The question asks us to write down the matrix represented by the following summation. 2. Homework Equations The question summation... $$\sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k}$$ The Attempt at a Solution $$ \sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k} =...

I thought this was an easy enough question but then I managed to obtain arguments both for and agaisnt it and confused myself. Is there a clear demonstrable answer to this question in relativistic field theory? Is spatial and temporal orientation a convention?

If the zeta function intersects the critical line when the real part is 1/2, then it will intersect some other line when some other real part is used. Isn't the Riemann Hypothesis just based on a particular convention for the critical line?

Homework Statement In this question , we can see that in teh second picture , the 12.86kNm is in clockwise direction at the right of span BC . Homework EquationsThe Attempt at a Solution In meachnic of materials , i learned that when the beam curve upwards ( U shape) , then it has positive...

To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that ##1+2*3 = 3*3 = 9##? Would it be the same or would it be completely different?

Has there ever been an attempt to organize a PF meeting or convention? Personally, I think that would be a great thing for everyone to be able to meet the people they talk to here, if they don't already know them. Obviously, though, there are some immediate issues such as the worldwide PF...

I have a question on convention regarding the universal law of gravitation formula. Sometimes the distance is represented with the lowercase r and sometimes with the uppercase R. Why is it listed two different ways? I am thinking that r is the total distance and R is the radial distance, no...

It seems to me that convergence rounds away the possibility of there being a smallest constituent part of reality. For instance, adding 1/2 + 1/4 + 1/8 . . . etc. would never become 1, since there would always be an infinitely small fraction that made the second half unreachable relative to the...

Homework Statement Particle A has a mass of 1kg and velocity 2x10^8m/s to the right and collides with a stationary particle B that has a mass of 4kg. after the collision, particle A moves to the left with a velocity(v) and particle B moves to the right with a velocity of 1x10^7 m/s. calcuate...

Homework Statement I doubt that is the following notes (in the first picture), correct or not? Because i couldn't find any proof in the other book... Homework EquationsThe Attempt at a Solution Can I say that consider σ positive to right and τ positive downward, orientation (θ) clockwise as...

Homework Statement I don't understand why the sign of moment of beam at left (clockwise) and moment at the right of beam (anticlockwise) are considered as positive... Why we can't assume the clockwise moment as positive and anticlockwise moment as negative? Homework EquationsThe Attempt at a...

Homework Statement http://nptel.ac.in/courses/112107146/22[/B] in the notes, the author define upward shear force as positive (LHS) , he take downward shear force as positive as positive (RHS)? Homework EquationsThe Attempt at a Solution why the author didnt fix downward shear force as...