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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61
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11answers
44k views

Why is the charge naming convention wrong?

I recently came to know about the Conventional Current vs. Electron Flow issue. Doing some search I found that the reason for this is that Benjamin Franklin made a mistake when naming positive and ...
41
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2answers
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Difference between $\Delta$, $d$ and $\delta$

I have read the thread regarding 'the difference between the operators $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In Mathematics, $\...
60
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2answers
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What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole?

The metrology world is currently in the middle of overhauling the definitions of the SI units to reflect the recent technological advances that enable us to get much more precise values for the ...
31
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2answers
3k views

Symbols of derivatives

What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
10
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2answers
4k views

Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\...
14
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1answer
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What is a base unit in the new SI, and why is the ampere one of them?

One question that comes up pretty much always in introductory electromagnetism courses is Why the base unit of electrical measurements is the ampere and not the coulomb, and the usual answer is that ...
11
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3answers
104k views

Thermodynamics - Sign convention

I use the sign convention: Heat absorbed by the system = $q+$ (positive) Heat evolved by the system = $q-$ (negative) Work done on the system = $w +$ (positive) Work done by the system = $w -$ (...
3
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2answers
362 views

How is the “normalisation” of non-normalizable states chosen?

This question is about non-normalisable states in quantum mechanics, e.g. the eigenstates of the position operator $|x\rangle$ which are defined by the eigenvalue equation $$\tag{1} \hat{X}|x\rangle =...
9
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3answers
2k views

Staggered Indices ($\Lambda^\mu{}_\nu$ vs. $\Lambda_\mu{}^\nu$) on Lorentz Transformations

I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of $\Lambda^\mu{}_\nu$ as ...
40
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2answers
1k views

Identification of particles and anti-particles

The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and ...
9
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2answers
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Why do we still not have an exact (constants-based) definition for a kilogram?

I read that there is an effort to define a kilogram in terms that can exactly be reproduced in a lab. Why has it taken so long to get this done? It would seem this should be fairly important. Edit: ...
32
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2answers
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Square bracket notation for dimensions and units: usage and conventions

One of the most useful tools in dimensional analysis is the use of square brackets around some physical quantity $q$ to denote its dimension as $$[q].$$ However, the precise meaning of this symbol ...
30
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7answers
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Why is gravitational potential energy negative, and what does that mean?

I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by ...
14
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5answers
1k views

Near Earth vs Newtonian gravitational potential

Newton's Law of Universal Gravitation tells us that the potential energy of object in a gravitational field is $$U ~=~ -\frac{GMm}{r}.\tag{1}$$ The experimentally verified near-Earth gravitational ...
4
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5answers
14k views

Sign convention in optics

Why is the sign convention used in the derivation of the lens formula and yet used again when it is applied in numerical problems? Won't the whole idea of sign convention be eliminated if it is used ...
4
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2answers
21k views

Work done against gravity [closed]

The work done against gravity is $mgh$, well at least that's what my textbook says. I have a question: I can apply a force say 50N, so total work done = $mgh + mah$. Where $ma$ = Force. But the truth ...
11
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1answer
15k views

Who (and Why) started the “electrons are negative, protons are positive” convention? [duplicate]

For some reason everyone labels electrons using a minus sign and protons using a positive sign, even though the opposite seems more intuitive: Who started the convention that electrons should be "...
3
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3answers
2k views

Square bracket notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
11
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2answers
1k views

What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
3
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4answers
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Potential energy sign conventions

Almost every book on physics that I read have some weird and non-clear explanations regarding the potential energy. Ok, I do understand that if we integrate a force over some path, we'll get a ...
9
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2answers
3k views

Why is the work done on a charge calculated from infinity?

Why is the work done on a charge calculated from infinity to a point? Why not from one particular point to other?
7
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3answers
593 views

In electromagnetism, why does nature prefer the right-hand rule over the left-hand rule? [duplicate]

At school I learnt the Right-hand rule to remember the resulting direction of different phenomena, such as geometrical cross products, mechanical torque, or the direction a screw will move when ...
4
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2answers
692 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
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3answers
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Convention of tensor indices

Let $g_{ij}$ be the diagonal Minkowski metric tensor diag$(g) = (1,-1,-1,-1)$, then $g^{ij}$ is defined to be $(g^{-1})^{ij}$, hence $$g_{ik}g^{kj} = g_i^{\ \ j} = \text{diag}(1,1,1,1)=\delta_i^{\ \ j}...
85
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6answers
14k views

Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?

I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although ...
7
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6answers
14k views

Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
8
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2answers
2k views

Why is there a minus sign in this wave equation derivation?

My book on quantum mechanics suggests a derivation of the wave equation $$\left(\Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \psi(\bar{r},t) = 0$$ from the photon energy-impulse ...
12
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3answers
10k views

Why is a conservative force defined as the negative gradient of a potential?

I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to ...
6
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2answers
3k views

Fourier transform standard practice for physics

I'm very confused about the definition of the inverse Fourier transform between time and frequency spaces. In many places, including Wikipedia, the Fourier transform pairs are defined by: \begin{...
4
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5answers
10k views

Sign of Work and potential energy in electrostatics

Conceptual question: Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive. I'm kind of rusty with my mechanics, ...
2
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2answers
655 views

Point charge potential (sign problem)

I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right ...
2
votes
3answers
281 views

Why does time in Minkowski's space have the opposite sign of the space coordinates?

I've looked up here and on Griffths' didatic Introduction to Electrodynamics, but, still, am struggling to understand why time has the opposite sign of the space coordinates. Any insights are welcome.
2
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3answers
209 views

Direction of $d\mathbf{l}$

A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point. My attempt: From Gauss'...
9
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1answer
3k views

Is 4-volume element a scalar or a pseudoscalar in special relativity?

In general relativity 4-volume element $\mathrm{d}^4 x = \mathrm{d} x^0\mathrm{d} x^1 \mathrm{d} x^2\mathrm{d} x^3$ is clearly a pseudoscalar (or scalar density) of weight 1 since it transforms as $\...
5
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3answers
5k views

Sign convention for mirror and lens formulas

I have just started learning optics at school and my teacher derived the lens and mirror formulas. While doing so, she applied the sign convention for $u$, $v$ and $f$ and arrived at the final ...
2
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3answers
6k views

Which one true in First law of thermodynamics: $Q = \Delta U \pm W = \Delta U \pm p\Delta V$ or $\Delta U= \Delta Q + \Delta W $?

Which one true in First law of thermodynamics: $Q = \Delta U \pm W = \Delta U \pm p\Delta V$? (where $\Delta U$ is change of internal energy, $W$ work made by system and $Q=cm\Delta T $ heat made by ...
2
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1answer
345 views

On Landau-Lifshitz's derivation of four-momentum

I'm studying the ninth section of The Classical Theory of Fields by Landau & Lifshitz, where they introduce four-momentum through the principle of least action. I can understand the derivation ...
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2answers
587 views

Derivation of plane wave from inner product of position ket and momentum ket

In textbooks it seems to be taken for granted that $$\langle \mathbf{r}|\mathbf{k}\rangle ~=~ \frac{1}{\sqrt{\Omega}}\exp(i\mathbf{k}\cdot\mathbf{r}).$$ I'm sure it's obvious but is there a ...
1
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2answers
349 views

Majorana Flip Relations

In the Supergravity book of Freedman et.al, which uses the signature $(+,-,\dots,-)$, we have defined the charge conjugation matrix for general Clifford Algebra as $(C\Gamma^{(r)})^T = -t_rC \Gamma^{(...
-1
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2answers
367 views

Electric Potential produced by Hollow Sphere

Let there be a hollow sphere (Throughout the question we will ignore the thickness of the sphere) which is positively uniformly charged,q of radius, R. Suppose there to be a test positive charge, q' ...
20
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4answers
35k views

Why is the potential energy equal to the negative integral of a force?

Why is the potential energy equals to the negative integral of a force? I am really confused with this negative sign. For example, why there is a negative sign in the gravitational potential energy ...
13
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6answers
38k views

Why the electric potential of Earth is zero?

For a localized charge distribution the potential is set to zero far away from the charge distribution (at infinity) Now, when grounding a conductor, i.e. connecting it to Earth, it is said that we ...
7
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3answers
2k views

Why does the density matrix $\rho$ obey a wrong-signed Heisenberg equation of motion?

The density matrix is defined as $$ \rho_\psi ~:=~ \frac{\lvert\psi(t)\rangle \langle \psi(t)\vert}{ \langle \psi(t) |\psi(t)\rangle }$$ in the Schrödinger picture. $\rho_\psi$ is obviously a time ...
7
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3answers
1k views

What is the meaning of the double complex integral notation used in physics?

In Altland and Simons' condensed matter book, complex Gaussian integrals are introduced. Defining $z = x + i y$ and $\bar{z} = x - i y$, the complex integral over $z$ is $$\int d(\bar{z}, z) = \int_{-\...
11
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3answers
1k views

Performing Wick Rotation to get Euclidean action of a scalar field $\Psi$

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-time Lagrangian $$ \mathcal{L}_M ~=~ \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi. $$ The Minkowski action is $$...
8
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3answers
6k views

Is the adjoint representation of $SU(2)$ the same as the triplet representation?

Is the triplet representation of $SU(2)$ the same as its adjoint representation? Where the convention for the adjoint representation used is the one used in particle physics, where the structure ...
4
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3answers
24k views

What is the point of the reduced Planck's constant $\hbar$ (h-bar)? - Why don't we just have Planck's Constant $h$?

I know that $\hbar$ is $h / 2\pi$ - and that $h$ is the Planck Constant ($6.62606957 × 10^{-34}\:\rm J\:s$). But why don't we just use $h$ - is it that $\hbar$ is used in angular momentum calculations?...
3
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1answer
665 views

Why is not ${(\Lambda^T)^\mu}_\nu = {\Lambda_\nu}^\mu$?

I am following lecture notes on SR. The author writes that the following is equivalent: $$\Lambda^T\eta\Lambda = \eta \iff \eta_{\mu \nu} {\Lambda^\mu}_\rho{\Lambda^\nu}_\sigma = \eta_{\rho \sigma}. \...
5
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2answers
1k views

What is the most natural value of Heaviside step function at zero argument?

In many physical applications, the Heaviside step fuction is defined as $$H(x) = \left\{\begin{eqnarray} 1, \quad x>0 \\ 0, \quad x<0 \end{eqnarray}\right.$$ The value $H(0)$ is left undefined. ...
2
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2answers
770 views

Is the sign in the Schrodinger equation physical?

I always have trouble remembering the sign in factors like $\exp(\pm ik\cdot x)$ (I'll use mostly minus signature here) that arise in field theory. My mnemonic is to remember that the Schrodinger ...

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