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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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Number of Isotopes created with decay <-> Chain Yield

The chain yield (or fission yield) states how many isotopes with a certain mass $A$ are created with the decay of $^{235}$U. But how do we know the fractions of specific Isotopes that are created ...
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Why is the MKS unit of time the same as the CGS unit? [on hold]

There are many system of units used in physics. In the CGS, the units are, length : centimetre mass : gram time : second And in the MKS system the units are, length : metre mass : kilogram time : ...
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Dimension of Lie algebra and Lie group generators

In physics, we define the Lie group generators as the basis of Lie algebra. E.g. for $SO(3)$, whose generators are $$J=\begin{pmatrix} 0 & 0 & 0\\ 0 & 0 & i\\ 0 & -i & 0 \end{...
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Why does the integration over momentum has normalization constant of volume?

If I Fourier transform a wave function in position space, integration carries no normalization constant: $$\displaystyle{\phi(k) \equiv \langle k|\psi\rangle = \sum\limits_x \langle k|x\rangle\langle ...
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5answers
196 views

Why isn't there a minus sign in Ohm's law, $V = IR$?

Suppose current runs through a resistor from left to right, and we define the left-to-right direction as positive. Then from left to right, the potential decreases. So $V,$ the voltage across the ...
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1answer
47 views

Sign ambiguity when going from position to momentum space evaluating Feynman diagrams

When calculating a simple diagram I came across an ambiguity in the conservation of momentum, i.e. it seems to me that the particle could come out of the process with opposite momentum with respect to ...
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4answers
157 views

Why does the chain yield in nuclear fission sum up to 200%?

The table of nuclides states the fission yield, or chain yield $Y$, the percentage of decays of $^{235}$U that lead to an isotope with mass number $A$. Why do they sum up to 200%? Wikipedia just ...
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Why $\kappa = 8 \pi G$ in $D$ dimensional spacetimes?

Probably another question without an answer! ;-) In most books/papers I saw on General Relativity, everybody writes $\kappa = 8 \pi G_D$ in the right part of Einstein's equation, even for spacetimes ...
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Explanation of the sign of Clebsch-Gordan coefficients

These are the Clebsch-Gordan coefficients when the orbital and spin-angular momenta of a single spin 1/2 particle are added. I'm not able to understand the explanation. What I can understand is that: ...
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2answers
59 views

How to define signs for angular velocity, acceleration and torques?

I get confused how to define signs of angular velocity, acceleration and torques in the cases like the following. We have a disk with radius $r$ and center of mass at point $CM$ shifted $d$ from the ...
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60 views

Sign mistake in the energy momentum tensor of the Klein-Gordon Equation

Recently I understood that the energy momentum tensor can be calculated by: \begin{equation} T_{\mu \nu}=\frac{2}{\sqrt{-g}}\frac{\delta S_m}{\delta g^{\mu \nu}}.\tag{1} \end{equation} So consider ...
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Why an elementary work is written $\delta W$ instead of $dW$? [duplicate]

Why an elementary work is written $\delta W$ instead of $dW$? For example, it's often written $$\delta W=F\cdot dr$$ if $dr$ is the elementary displacement. Why don't we write as usual $dW=F\cdot dr$?
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4answers
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Understanding the difference between timelike and spacelike separations

From Woodhouse's General Relativity: If $A$ is the origin and $B$ is a nearby event with coordinates $dt, dx, dy, dz$, then, $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$ is the same in all local inertial ...
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60 views

Is there a difference of sign conventions of Dirac Index between mathematics and physics?

In section 12.6.2 of Nakahara, on a four dimensional manifold, the index of a twisted Dirac operator is given by $$\mathrm{Ind}(D\!\!\!\!/_{A})=\frac{-1}{8\pi^{2}}\int_{M}\mathrm{Tr}(F\wedge F)+\frac{...
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1answer
41 views

How did Coulomb arrive at value of electron charge?

Charge of one electron is known to be as $1.6$ x $10^{-19}$ C or alternative 1 Coulomb contains charge of $6.24$ x $10^{18}$ electrons. I am just wondering if these numbers are arbitrarily chosen or ...
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2answers
50 views

What does a double parenthesis in a quoted value ─ like e.g. 157(3)(3) ─ mean?

Sometimes, in journal articles, the author writes a number followed by two parenthesis. For example, $157(3)(3)$, where it seems that the first parenthesis shows uncertainty in the last digit (here, $...
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1answer
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Defining potential of the ground

In electronics, it is customary to define the potential of ground (thinking the Earth as a large conductor) as zero. Is this consistent with the fact that the Earth has a net electric charge that is ...
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2answers
45 views

Potential energy is zero at infinite distance

We set the electrical potential energy to be zero in infinite distance to calculate potential energy at a distance $r$. But how is it possible from infinite distance to end up with finite distance? ...
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1answer
34 views

Sign convention in optic problems

Note: The convention used in our physics textbook and the mentioned question is Cartesion Convention Today in our physics test, we were given the following question:- A mirror has focal length 20 cm ...
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4answers
100 views

Why $g$ is not negative in potential energy $= mgh$ formula

For eg. A boy of mass 55 kg runs up a staircase of 50 steps in 10s. If the height of each step is 10 cm, find his power. My question is here why are we not taking g as negative as boy is moving up ...
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5answers
103 views

Why is torque defined as $r × F$ and not $F × r$?

Is it merely due to popular convention or does it supply any special clarification regarding other physical quantities?
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2answers
130 views

Does the death of Kilogram ($kg$) affect us in any means in our day to day life? [closed]

Recently, the sleek cylinder of platinum-iridium metal has been discarded and the kilogram is set to be redefined along with ampere for electricity and Kelvin for temperature. Hereafter the Kilogram ...
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3answers
141 views

Relative potential energy vs Absolute potential energy

I have seen in many textbooks and sources which say that we can't experimentally measure potential energy but we can measure differences in potential energy. $$\Delta U_g=-W_g$$ Choosing zero ...
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4answers
112 views

Why does this line integral give the wrong sign?

I've been trying to find the error in this approach to calculate the work of a uniform gravitational field on an object falling to the ground in the $-y$ direction. $$\begin{align} W &= \int_{i}^{...
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2answers
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How to get the UT1 directly? or How to get the UT1-UTC

I have a question to consult you. Even though I know the relationship between time scales like UT1, UTC, TAI, and TT, I do not know which one is the key point for the computation. That is, from which ...
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2answers
114 views

Einstein GR and metric signature

Let us take the einstein Equation $R_{\mu\nu} -\frac{1}{2}g_{\mu\nu}R = T_{\mu\nu}$. I'm just ignoring all the constants. For a perfect fluid, $$T_{\mu\nu} = (\rho + P)u_{\mu}u_{\nu} - Pg_{\mu\nu}.$$ ...
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1answer
47 views

Solution to Klein-Gordon equation: real field condition and other questions

Sorry for the lengthy question, pretty much the whole text is the standard derivation of the solution of the KG equation which I included to illustrate my doubts, and some questions are at the end. ...
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1answer
326 views

What is the meaning of the negative sign in $\Delta s^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 - (c\Delta t)^2$?

In the equation of the spacetime interval formula $\Delta s^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 - (c\Delta t)^2$ is there meaning for the minus sign before the $(c\Delta t)^2$ or is it just a ...
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1answer
24 views

Weyl basis gamma matrix identity

In finding the scattering amplitude matrix $|\mathcal{M}|^2$, I see the solutions get a way nicer calculation by using that (using Peskin & Schroeder notation): $$(\bar v \gamma^\mu u)^*= \bar u\...
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Why is gauge theory gravity (GTG) not very widely used?

I plan on learning geometric algebra soon and while researching the subject I came across gauge theory gravity (GTG). The Wikipedia page says that it isn't very widely adopted and I was wondering the ...
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Will the SI units need redefining ever again?

Up until recently, there were obvious problems with the SI definitions of fundamental units, like bits rubbing off the kilogram prototypes (or mercury vapour absorption), and the water used for the ...
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45 views

Derivation of the adjoint of Dirac equation

My goal is to deduce the adjoint of Dirac equation: $$ \overline \psi (i\gamma^\mu \partial_\mu+m)=0 \tag{1} $$ My process: I started with Dirac equation $(i\gamma^\mu \partial_\mu-m)\psi=0$. ...
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1answer
67 views

What will happen to the International Prototype Kilogram? [closed]

The kilogram has been redefined in a way that does not refer to the International Prototype Kilogram. That kind of makes the International Prototype Kilogram useless. So what will happen to it? Can I ...
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1answer
69 views

Is spacetime defined mathematically without using $c$ speed?

Is there a mathematical definition of spacetime that does not use $c$ speed as a conversion factor or involve the spacetime interval? If not why?
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3answers
66 views

Confusion over use of contravariant notation in Noether's theorem and Lagrangian filed theory

The variational principle clearly gives $$\frac{\partial \rho}{\partial t} + \overrightarrow{\nabla}\cdot \mathbf{J} = 0.$$ So the sign is positive. However in my lecture notes it is claimed that ...
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3answers
65 views

How to specify the orientation of an area vector?

We all know that the area of a triangle having consecutive sides as $\vec { a }$ and $\vec { b }$ is $\frac { 1 } { 2 } | \vec { a } \times \vec { b } |$, but what is the direction of that area vector?...
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2answers
94 views

Positive work along path [closed]

Consider I have a simple formula for the work along some path (in 1 dimension): $$W~=~\int_{x_0}^{x_1}\vec{F}\cdot d\vec{x}.$$ If I now move from left to right ($x_1 > x_0$) along the axis (...
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4answers
109 views

Why do we assume that Earth and infinity are at same potential?

In many standard texts I have seen the approach of taking any point connected with Earth in a circuit as 0 potential. Obviously, there is nothing special with 0 as long as we are concerned with ...
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3answers
39 views

Sign of work in adiabatic expansion

I know that in an adiabatic expansion, $W = -U.$ My question is, is the work positive or negative? I'm confused on the difference between work done "by" the system and work done "on" the system.
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1answer
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Dot convention inductors in series: what is going on

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 I read them all and that only left me more confused. So here are my ...
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3answers
84 views

What determines the voltage in a battery?

This diagram problem has got me thinking about what determines the voltage in a battery. At school, we were taught this method of giving a value of voltage to points in a circuit. However, I do not ...
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1answer
64 views

Pion decay constant: How to know which convention to follow?

As summarized by Wikipedia, different sources use different choices for the (pion) decay constant. This means that the numerical value can vary between $$ \sqrt 2\ f_\pi \quad\leftrightarrow\quad f_\...
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1answer
35 views

Operator $A$ only act on the neighboured state or operator but not the entire expression?

In state vector formalism $A|\psi(x)><u(x)|=(A|\psi(x)>)<u(x)|$, where $A$ only act on $|\psi(x)>$ However, in terms of wave formalism, suppose $A$ is the well known $\frac{d}{dx}$. ...
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2answers
71 views

Defining generalized momentum in terms of kinetic energy versus a Lagrangian

Reputable authors (e.g., Bergmann, Wells, Susskind) define generalized momentum using the Lagrangian $L$ as $$p_{i}\equiv\frac{\partial L}{\partial\dot{q}^{i}}.\tag{1}$$ Joos and Freeman define ...
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Is there any consensus on what is meant by Lagrange's equations of the first kind?

Is there any consensus on what is meant by Lagrange's equations of the first kind? Joos and Freeman define them as follows: Coordinates are given in terms of a rectangular Cartesian coordinate ...
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5answers
289 views

Why is there a physical preference to real numbers?

In quantum mechanics, operators can only be observables if the eigenfunctions they operate on have real eigenvalues. If they are complex, I am told that, surely, some observable of a physical system ...
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2answers
48 views

Potenial difference from electric field and line integral

I am really confused about the relation of potential difference and the electric field. The relation between potential and electric field is $$V_{ab} \equiv V_a - V_b = -\int_{b}^a{\vec{E}\cdot\vec{...
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74 views

Convention Special Relativity

I am a little confused about the factor $c$ in different conventions of special relativity I know that $$ds^2=c^2dt^2-dx^2-dy^2-dz^2.$$ This can be interpreted in two different ways: Either we define ...
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1answer
59 views

How is the division of physical quantities into base quantities and derived quantities a matter of convention?

Several physics textbooks and even the SI-The International System of Units Brochure(8th-edition) says that, ''The division of quantities into base quantities and derived quantities is a matter of ...
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71 views

Most used convention about Christoffel symbols

Just a simple question: what is the most used form for Christoffel symbols, (1) or (2), see below: (1) $$\Gamma_{ij}^{k} = g^{kl}\Gamma_{lij}$$ and then, we have: $$\Gamma_{lij}=\Gamma_{lji}$$ (2) $...