# 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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### 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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### 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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### 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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### 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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### Complex notation convention for time variation

In describing plane wave EM variation, some textbooks use the complex notation $\exp(i\omega t)$, while others use $\exp(-i\omega t)$. Is there a motivation for chosing one or the other convention, ...
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### Tensor ordering in index lowering operation

If we take two vectors and want to contract them with the metric tensor to find some frame invariant quantity: $$A^a B^b g_{ab}=\vec A\cdot \vec B$$ is there a convention on where the metric tensor ...
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### Mathematical convention when using spatial indices: numerical $(1,2,3)$ versus Cartesian $(x,y,z)$ [closed]

When writing a document I find that I am switching back and forth between indicial notation for spatial coordinates. I would like to get your thoughts on the following examples accompanied with ...
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### Is the labelling of $g_{\mu\nu}$ as “the metric” and $g^{\mu\nu}$ as “the inverse metric” arbitrary?

I understand the up and down indices change the way in which the metric transforms under basis changes, that's not what I'm getting at. My question is that since the metric is specifically an ...
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### Not understanding the minus sign in the torque equation for a simple pendulum

The pic above is from Introduction to mechanics by Kleppner. In the torque equation they justified the minus sign because the torque has a clockwise sense. This makes sense to me if I pick the y axis ...
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### Determining Signs when Deriving Voltage

In my intro E&M class, we were given an example problem to determine the voltage within a cylindrical capacitor as a function of radius. A diagram of such a cylindrical capacitor is below. The ...
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### $(\psi_L^\dagger \psi_R)^\dagger \neq (\psi_R^\dagger \psi_L)^\dagger$ ? What is the transpose for spinors?

The dirac mass term in terms of Weyl spinors is $$\psi_L^\dagger \psi_R + \psi_R^\dagger \psi_L.$$ My understanding is that both terms are necessary to form a hermitian term. Naively, if you take ...
$$W=-\int_\infty^\textbf{r}\textbf{F}\cdot\textbf{dl} =-Q\int_\infty^\textbf{r}\textbf{E}\cdot\textbf{dl} = Q(V(\textbf{r})-V(\infty)) =QV(\textbf{r})$$ I'm trying to understand how this definition ...
In Lagrangian mechanics, it is possible to multiply the Lagrangian by a constant $a$. Let's assume I take $a=-1$. Then, the Hamiltonian will have its sign changed as well. And it will represent the ...