Questions tagged [conventions]

A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.

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$d$-dimensional Einstein equations

I am reading this paper https://arxiv.org/abs/2002.02577. On page 13, it is written that the $d$-dimensional Einstein equations are $$G_{\mu\nu}+\frac{(d-1)(d-2)}{6}\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}...
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Where does the infinity in the definition of electric potential lie?

Electric potential at a point is defined as the amount of work done in bringing a test charge from infinity to that point..my question is that if we don't know where this point of infinity lies then ...
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How does the transformation of 4-derivative into a 4-momentum actually happen in a derivative coupling?

Consider a derivative coupling with $$\mathcal{L}_{int} = \lambda \phi_1 (\partial_\mu \phi_2) (\partial_\mu \phi_3),\tag{7.101}$$ and a scalar field $$ \phi(x) = \int \frac{d^4p}{(2\pi)^3} \frac{1}{\...
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Is force always the negative change in potential energy with respect to position?

For example, In the non-inertial rotating reference frame of a turntable that has a tether ball pole rotating on top of it, the ball at the end instantly starts rotating and then eventually moves up ...
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Discrepancy in Legendre function for angular momentum [closed]

On wikipedia: https://en.wikipedia.org/wiki/Associated_Legendre_polynomials It is clear that the formula to solve for the eigenfunctions of $\hat{L}^2$ are the spherical harmonics where: $$ Y_{l, m} ...
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Is this a typo in Peskin's QFT?

In ''An intro to QFT (2018)'' chapter 3, Peskin does the following: Let me introduce some notation first, let $v^s_k=\begin{pmatrix}\;\;\,\sqrt{k\cdot\sigma}\,\xi^{-s}\\-\sqrt{k\cdot\bar{\sigma}}\,\...
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Is there a rhyme or reason behind constant symbols? [closed]

Why are fundamental constants like $c$ (speed of light constant) and $h$ (Planck constant) in lowercase, but other constants like $G$ (Gravitational constant) and $R$ (Gas constant) capitalized?
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What is the heat needed for an isothermal expansion of gas and why do physics and chemistry yield different answers?

One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a temperature $T$. The face of the piston opens into the atmosphere. What is the heat supplied in the ...
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Why do we have to include sign while calculating image position due to refraction by a lens? [closed]

When we calculate image position due to reflection by a curved mirror or due to refraction by a lens, we have to include the sign of the object's position. However, while deriving the equations that ...
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The order of Pauli matrices

Is there any special reason why Pauli matrices are: $\sigma _1=\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right)$, $\sigma _2=\left( \begin{array}{cc} 0 & -i \\ i & 0 \...
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Why is the vector of angular momentum perpendicular to the plane of rotation?

I just don't understand this. I have read about the right hand rule, but I am finding it hard to take it on faith, and would like to have some proof. Also, try not to make your explanation too ...
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How did J.J. Thompson decide that the electron was negative charge? [duplicate]

I read Ben Franklin had it wrong by stating "current is the flow of positive charge". Right from the start Ben Franklin could have easily decided to say that current is the flow of negative charge. ...
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What are the accepted abbreviations for Million Years and Billion Years?

I'm putting together some charts and the time axis in one shows billions of years, the time axis in another shows millions of years. I've seen in various publications $my$ and $myr$ (also $ma$) for ...
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Phasor Notation Convention - Which Projection to Consider?

In the following video (not necessary to watch)... https://www.youtube.com/watch?v=K_vWYEjgVRg&list=PLdnqjKaksr8pXF2SpDyyD7ouAVlz96_Ra&index=23 ...the creator takes the projection of the ...
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1answer
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Notation for vector time derivatives

So I am self-studying mechanics using Marion and, as many books, it uses the notation of the dot over the function to express a time derivative, as in $$x = x(t)$$ $$\dot{x}= \frac{dx}{dt}(t) $$ The ...
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Confusion regarding a few sign conventions in appyling faraday's law to inductive circuits

In the mit ocw lecture by Prof. Lewin on EMI, He quotes a few statements from here to couple of seconds of the lecture. I am confused why the sign of $L\frac{dI}{dt}$ changes, when we go around and ...
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Thumb rule and right hand rule

Thumb rule and right hand rule are for conventional current or electron flow ( for finding N, S in wire and winding)? In a real experiment for finding true N , S what should I do?
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Negative sign in Faraday's Law

With Faraday's law, is it standard convention to leave off the negative sign? Or are answers with negative EMF acceptable (generally speaking)?
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Reference Point for Potential Energy

The title is quite misleading, sorry for that i couldn't think of any other title. Energy is a certain quantity whose value is constant anywhere in space. There are different forms of energy such as ...
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Why is torque $r \times F$ instead of the reverse?

As we all know $\tau = r \times F$. But why wouldn't we write $\tau = F \times r$? As it's vector product, these two expressions are actually opposite of each other. Mathematically $$r \times F = -F \...
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Ordering of Tensor indices: a specific example

As an example of construcing tensors out of the product of other tensors I found the following example. $$T_{i}{}^j{}_{kl}=A_i{}^jB_{kl}+C_m{}^{mj}D_{ikl}$$ But I am a bit confused about the ...
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If velocity in forward and backward directions is positive and negative respectively, then what is it in left and right directions? [closed]

I have defined velocity in forward direction to be positive and negative in the backward direction. So what is the velocity if the body is moving right or left?
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Why do (kilo)watt-hours double-count units per time?

A watt is defined as 1 joule per second and is therefore a measurement of energy transfer over a period of time. A kilowatt-hour is a measurement of energy equal to one kilowatt sustained over a ...
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How can we apply lens makers formula to combination of lenses?

Like in lens makers formula the material must have same material on both sides but that doesnt happen when lenses are touching each other. So how can we neglect that connection and use formula as if ...
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What is wrong with this calculation of work done by an agent bringing a unit mass from infinity into a gravitational field? [duplicate]

Let us assume that a gravitational field is created by a mass $M$. An agent is bringing a unit mass from $\infty$ to distance $r < \infty$, both measured from mass $M$. The agent is always forcing ...
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Why does electric potential decreases along the direction of electric field?

I've been reading about Equipotential Surfaces and I came across this statement which I'm not able to understand conceptually. Does it's mathematical proof has something related to $\mathrm d V = -E.\...
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Why isn’t there a $\cos(\theta)$ in the work-energy theorem? [duplicate]

please don’t use any calculus in your answers I was reading the derivation of the work energy theorem in my textbook and it goes like this: $$W = Fs\Rightarrow W_{net} = mas$$ Since $v^2 - u^2 = 2as ...
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Why is the gravitational potential energy defined as negative? [duplicate]

It is said that since work is done by the gravitational potential itself , so at a finite distance the gravitational potential energy of the body is negative. Could someone explain why?
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Why is this integral giving wrong sign? [duplicate]

I’m trying to calculate the change in the potential(potential difference) between two points in the field of a point charge $q$. Now I calculated it taking two different cases. CASE-1 positive test ...
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25 views

Problem with Cartesian sign convention for geometrical optics [duplicate]

This confuses me a lot. We use the convention in the derivation of thin lens formula and mirror formula. In derivation in place of u (object distance) we write -u. Since we have written it this way, ...
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1answer
88 views

Why are these quantization forms different?

I'm confused about the form of the quantized electromagnetic field. Sometimes, one writes the quantized electric field as $$\hat E = \vec E_0(\hat a + \hat a^†)$$ , which can been seen the website ...
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How can electric flux be negative?

If electric flux is the number of field lines, then how can it be negative?
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1answer
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Does the quadratic mass term $\phi^2$ belong to the free Lagrangian or is it an interaction term?

$$L = -\frac{1}{2}\partial_\mu\phi\partial^\mu\phi - \frac{m^2}{2}\phi^2.$$ Why is the $\phi^2$ term in the scalar Lagrangian not considered a self-interaction?
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Sign of work against an electrostatic field

I think I'm slightly confused with the signs. The work needed in order to bring point charges $q_i$ from infinity to a distance $r$ from some shape of charge $Q(r)$ with a varying charge (because we ...
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Can we assume a force to already be negative before knowing the value of it? [closed]

Let me make my question clear by the following example:- Let’s take a case of an individual who is in an elevator accelerating downward with some acceleration ‘ a ‘ such that ‘a’ < g . Let’s take ...
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1answer
35 views

Regarding sign of energy stored in springs

A block of mass $m$ is at natural length initially.It is attached to two springs having spring constant $k1$ and $k2$. It is attached in such a way that when one elongates ,the other compresses.Using ...
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Regarding the signs in the Clebsch-Gordan coefficients

Let's take, for example, the $\frac{1}{2}$ $\frac{1}{2}$ spin case. We have, for $J = 1, M = 0$ $$|1,0\rangle=\frac{1}{\sqrt{2}}(|-1 / 2,1 / 2\rangle+|1 / 2,-1 / 2\rangle),$$ and, if we follow the ...
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Euler beam equation sign confusion

Euler beam equation is defined as follows: $$M=-EI{\frac {d^{2}w}{dx^{2}}}$$ There is a negative sign, so if the second derivative of the deflection is negative, the moment is positive. When the ...
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Can an affine first-order polynomial system be chaotic?

While studying chaos theory, one of the basic principles presented to me was that chaos only occurs in deterministic nonlinear systems. This pointed me to learn more about the differences between ...
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Which way of integrating the quaternion representation of orientation is correct?

I am wondering how to integrate a measurement of angular velocity into an orientation quaternion. Suppose I have measurements of the rotation rate about the three principal axes of a body. I would ...
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4answers
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If Gravitational potential energy increase with height then why it is 0 at infinity?

Due to MGH relation, if we increase height then potential energy increases. Then why it is zero at infinity?
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1answer
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Sign of effective action of bosonic string?

I've been looking at David Tong's Lectures on String Theory. He states that the low-energy effective action of the bosonic string is given by $$S=\frac{1}{2k_0^2}\int d^{26}X\sqrt{-G}e^{-2\Phi}\Big(\...
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1answer
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Time-like coordinate vs space-like coordinates in GR

I know the definition of space-like and time-like coordinates in simple geometric, basically, we got: $$ds^2=dt^2-dx^2-dy^2-dz^2$$ so the coordinate with a positive contribution to the $ds^2$ is the ...
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What's the justification for the sign in the formula for work?

In case of electric potential at a point (P) the derivation says that it is equal to the external work done to bring a unit positive charge from infinity to point P without acceleration i.e with ...
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Sign Problem When Dealing With Quadratic Air Resistance and Gravity [closed]

While dealing with an object falling vertically, and subject to quadratic air resistance, an equation of motion that is often presented is \begin{equation*} m\dot{v} =mg-cv^{2} \end{equation*} In ...
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1answer
114 views

Gauss' Law in 2D?

At first I thought it was $$∮E.dl=Q/ϵ.$$ So i've read through some sources here and on the internet and most of them said that $$∮E.dl=2πq.$$ But I'm confused. Can anyone explain where does the $...
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1answer
29 views

Why is the work term negative in the 1st law of thermodynamics using constant pressure specific heat?

From the first law, we have that $$dq = c_v dT+pd\alpha\tag{1},$$ that is, the total energy (by unit mass, where $\alpha$ is the specific volume) equals the variation in internal energy plus the work ...
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1answer
26 views

Sign convention for Maxwell's model of viscoelastic material

Maxwell's equation for viscoelastic body is $\dot{\varepsilon}(t)=\frac{\dot{\sigma}}{E}(t)+\frac{\sigma}{\eta}(t)$, where $\varepsilon=\frac{dl}{l}$ is strain and $\sigma$ is stress. I am a little ...
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3answers
61 views

Conservative Force and Energy [closed]

When a charge is moved from infinity to $r$, its electric potential energy is equal to the negative work done by the field. In this argument, is it also true that there is positive work done by the ...
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Regarding number of degrees of freedom of a dynamical system (as well as it's relation to number of equations of motion)

I would like to know why in the context of vibrating systems, we define degrees of freedom in terms of number of independent coordinates (by coordinates I mean the numbers which specify the components ...

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