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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Expression for Potential energy of a hanging mass
If the acceleration due to gravity is $g$ and a mass $m$ is hanging from a fixed support with a thread of length $l$, then it's potential energy ($U$) is given by:
$$U = -mgl;$$
This was stated by my ...
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Contradiction in Thermodynamic Work and Mechanical work [duplicate]
The first law states that $ \Delta U = Q - W $ where W is the work the system does on the outside. If there is no heat added, the change in energy is equal to the work done. If the work is negative, i....
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Help understanding quote on theory and knowledge in Gravitation (Misner, Wheeler, & Thorne, 2017)
I came across an interesting discussion at the start of chapter 3 of MWT Gravitation. It reads:
Here and elsewhere in science, as stressed not least by Henri Poincare, that view is out of date which ...
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Understanding sign convection for entropy change
I recently solved a problem where I had to study the change of entropy for a lake that is freezing. It started off as being plain water at $0$ degrees, that then freezes to some negative temperature.
...
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Landau/Lifshitz Particle Disintegration
In Landau/Lifshitz "Mechanics", 3e., there is a problem which asks the reader to find the relation between the angles $\theta_1,\theta_2$ in the lab frame when a particle disintegrates into ...
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What does $\overset{\circ}{=}$ mean in the context of thermodynamics? [closed]
Few days ago I started thermodynamics and whilst talking about systems and its type of walls the professor, a part from this one, showed some diagrams including this equal sign. He was talking about ...
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Sign convention for the Lagrangian of a free massive point particle in general relativity
As far as I understand, the Lagrangian of a massive free particle in the context of general relativity is the following:
$$L=-mc\sqrt{g_{\mu\nu}\dfrac{dx^\mu}{dt}\dfrac{dx^\nu}{dt}}.$$
But is this the ...
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The energy-momentum tensor of a scalar field
In Carroll's Introduction to General Relativity: Spacetime and Geometry, I am going to express the components of the energy-momentum tensor of scalar field in three-
vector notation, using the ...
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Why can $ϕ(p)$ be Fourier expanded to $ψ(x)$ in quantum mechanics? [closed]
I know the Fourier transform is $$
F(\omega)=\int_{-\infty}^{\infty} f(x) e^{-i \omega x} \,d x
$$
$$
f(x)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i \omega x} \,d \omega,
$$
but in ...
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Significant figures in simple calculations
I have the resistivity of a material $\rho = 7.4 \times 10^{-7}$ $\Omega\cdot$m and I want to compute its conductivity $\sigma = 1/\rho$.
Straight forward calculation gives (up to 3 decimals) $\sigma =...
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The Plus/Minus sign on Forces in a Cartesian coordinate system
I have been struggling with Forces in a Cartesian Coordinate System and whether to understand what signs to put on to solve simple problems in the view of mathematics.
Let's make a simple one ...
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Clarification on thermodynamics and mechanics
This is a follow-up question to an answer https://physics.stackexchange.com/a/746974/377012 on this topic. In that answer, what does $W$ refer to? Is it the work done ON the system, by forces OTHER ...
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Reference point of potential in case of a battery
When we define electric potential of a charge,we need to take a charged body as a reference and then we bring the test charge to calculate the electric potential. Now,electric potential energy is ...
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Minus sign in Force potential relation, a convention?
The usual defination of force in terms of potential energy is
$$\vec F=-\nabla U$$
This definition leads to
$$K_1+P_1=K_2+P_2\rightarrow \Delta K + \Delta P =0$$
Where $K$ and $P$ are kinetic and ...
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Sign ambiguity of two diagrams in Mahan's book
In Mahan's book 'Many-particle Physics' 3rd Ed., Eq. (3.213) on page 135 gives a sign rule for Matsubara Green's functions $$(-1)^{m+F}$$ where $F$ is the number of fermion loops and $m$ is the order, ...
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Work Done By vs Work Done On
Assuming right to be positive, in this question, is the work done by the boy positive or negative? I would think it is negative because the force that the boy exerts is towards the left while the ...
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Sign conventions pressure volume work
In the first law of thermodynamics, using the convention that work is done on the system by the surroundings,
$dU=Q+W$.
Usually it is written that pressure volume work is $W=-pdV$, where $p$ is ...
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Combinatorics in $\lambda \phi^4$ theory and critical exponents
I am trying to understand critical phenomena from the perspective of Statistical Mechanics.
The interacting term in the $\lambda \phi^4$ scalar theory is usually (but not always) multiplied by $\frac{...
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Why do we indicate current to be flowing against electrons in a electric circuit ? If it is a convention thenwhy do we draw it along studying it? [duplicate]
I believe that electric current is a kind of force (even when we consider it to be opposite to the flow of electrons). If it is so then what is the nature of this force ? And also tell me if there are ...
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Does change in metric signature affect the result of loop integrals in momentum space?
I was wondering whether the change in metric signature affect the standard results of loop integrals. Suppose a rank-4 tensor integral's result is known, does changing the metric signature for the ...
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System in thermal equilibrium with reservoir
Let's say I was trying to build Statistical Mechanics from scratch. I had studied the microcanonical ensemble and made the following definitions:
$$\frac{\partial S}{\partial E} = \frac{1}{T},$$
$$\...
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Embedding diagram in west coast signature
Assume you have a metric in (+,-,-,-) signature,
$$d s^2=e^{2 \Phi(r)} d t^2-\frac{d r^2}{1-\frac{b(r)}{r}}-r^2 d \Omega^2.$$
To embed it, we take $t=$Constant, $\theta=\pi/2$ slice,
$$d s^2=-\frac{d ...
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What is the significance of a reference point in calculating the potential?
The gravitational potential is given as $$U(r)=-\frac{GMm}{R}$$ where $G$ is the universal gravitational constant $M$ is the mass of the earth and $m$ is the mass of an arbitrary object and $R$ is the ...
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Confusion about the signs we use in Faraday's law for emf
While reading griffiths, I came accross the definition of emf, which is given by
$$ \epsilon = -\int_a^b \vec{E} \cdot d\vec{l} = \oint \vec{f} \cdot d \vec{l} $$
Here we use $\vec{E} + \vec{f} = 0$ ...
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Sign of reversible work done
Consider a piston such that it is in mechanical equilibrium with its surroundings. If I pull the piston (reversible work) then the work done by me would be positive. If I push the piston, again work ...
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Why does Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ is frequently written with a factor of $i$?
The tensor Dirac bilinear $\bar{\psi}\sigma^{\mu\nu}\psi$ has the matrix tensor $\sigma^{\mu\nu}=\frac{i}{2}\left[\gamma^\mu,\gamma^\nu\right]$.
I can understand that the factor of $\frac{1}{2}$ is a ...
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Lorentz Transformation - Intuitive way to determine when to use Inverse transformation
Any intuitive way to decide when to use Lorentz transformation and when to use its inverse relation?
For example: A particle is moving with respect to me with speed of 0.99C. If question is : What ...
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Correct way to reference to a percentage value's category/label
When a percentage is written as, for example: 20% of sold products were of product A and 80% product B. What is the correct concept / word to use to describe "product A"? Is it units?
As ...
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Minus sign for incoming antifermions
In his Diagrammatica, The Path to Feynman Diagrams (Cambridge University Press, 1994; §4.5 "Quantum Electrodynamics", p. 88), M. Veltman reports the following Feynman rule for incoming ...
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Jackson's Electrodynamics: Green's function prefactor
In Ch. 6 of Jackson's Classical Electrodynamics 3rd ed., the Helmholtz equation Green's function is written as satisfying the following inhomogeneous equation (Eqn. 6.36):
$$ (\nabla^2 + k^2)G(\mathbf{...
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Generators in the fundamental representation of $SU(2)$ are $\sigma_i/2$. Why? [duplicate]
In physics, the generators of the fundamental representation of $SU(2)$ are taken to be $\sigma_i/2$ instead of $\sigma_i$ where $\sigma_i$ denotes the $i$th Pauli matrix. This is because, as I ...
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What happens if we define the gravitational potential zero point at a finite distance? [duplicate]
Two questions.
Can we, and if so how do we define the gravitational potential of a mass (say the sun) to be zero at a finite distance (say 1 light year)?
How does this change the gravitational force ...
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How can negative potential energy cause mass decrease?
The mass of a hydrogen is less than its constituent parts(proton/electron). The explanation given for this is the following: Youtube
For hydrogen, $m = m_{components} + m_{extra}$ where we can write $...
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Does the Lagrangian have to have units of energy?
I've read that the standard formulation of the lagrangian is $L = T-V$ which has energy units (Joules).
But when I read a bit about electromagnetism and relativity I've seen that the lagrangian is ...
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Why isn't frame of reference called reference point? [closed]
A frame of reference is the perspective you have on a happenstance. But isn't it a viewpoint or point of view? As in, a literal point, from which something is observed?
If so, why is it called a frame ...
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Order of fields in scattering amplitude
Given the lagrangian
$$\mathcal L=-\dfrac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D_{\mu}\phi)^*(D^{\mu}\phi)-M^2|\phi|^2+\bar\psi(i\gamma^{\mu}D_{\mu}-m)\psi.$$
I tried to compute some first order scattering ...
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The sign of the QED vertex in Feynman rules
I am confused with the sign of the QED vertex. It seems that in different books, the signs are different.
In Chapter 7 of Griffiths' book, the vertex is of the form $-iq\gamma^\mu$ (the particle (...
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How is the index notation for the electromagnetic potentials defined?
I don't understand, how the $\vec{A}$ potential is defined in the covariant formulation of the Maxwell-Equations.
I am using the metric $(+,-,-,-)$.
The electric field (SI-Units) is defined as:
$$
\...
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Common choice in FLRW between dimensionless of scale factor (and coordinates of r lenght dimension) or the contrary
I have an old cosmology book in which the scale factor is expressed in the Roberston-Walker metric as:
$\mathrm{d} s^2=c^2 \mathrm{~d} t^2-R(t)^2 \mathrm{~d} l^2$
with: $\mathrm{d} l^2=\dfrac{\mathrm{...
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Is the Lorentz boost boosting me or the frame?
I am starting to dive deeper into Special Relativity, but something that always confuses me is whether the Lorentz boost is the increase in my own velocity to catch up with moving objects or the ...
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I know $E=- dV/dr$, but while solving a question professor took $\vec E$=dV/d$\vec s$. But I think minus should also be in the vector equation [closed]
$E= - dV/dr$ and the magnitude of all the vector quantities are putted in this equation. But while solving a numerical, the professor used vector signs over all the vector quantities and removed the ...
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Klein-Gordon inner product for annihilation operator
This answer https://physics.stackexchange.com/a/404321 over here gives the Klein-Gordon inner product for the annihilation operator as $a(k) = (\psi, \phi)$ where $\psi$ is a plane wave.
However, ...
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On the metric signature and the energy-momentum tensor [duplicate]
Given a Lagrangian $$\mathscr{L} = -\frac{1}{2}\partial_\mu \phi \partial^\mu \phi - V(\phi),\tag{1}$$ is the metric always with signature $(-, +, +, +)$? It seems to me that This post Sign Convention ...
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How to distinguish outgoing and incoming photon in Feynman Diagrams?
So, the feynman rules for QED claims that:
For an incoming photon, we add a $\epsilon^{\mu}(k)$ factor,
For an outgoing photon, we add a $\epsilon^v(k')^*$ factor.
But i am not sure how do we ...
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Direction of Area Vector of a simple 2D figure
For a two-dimensional plate placed in the $xy$-plane, while calculating the electric flux, should we consider direction of the area vector along $\hat{k}$ or $-\hat{k}$?
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Why do we call high terminal the positive side?
I want to confirm if I understand something correctly.
We call the "high potential terminal" the positive side (cathode).
Though, electrons move from negative to positive. Logically, ...
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When to convert $x/y$ units in physics questions?
I've searched the internet for this question but found no answer. Sometimes when I plot graphs where the units are not SI units, the units are converted during gradient calculation, and sometimes the ...
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The sign of the energy released by an explosion
On a simple system with no external force, we can calculate the energy released by an explosion as the difference of the sum of the kinetic energy before and after.
With kinetic energy $K_i$ (initial) ...
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Why do we use a unit positive charge while calculating the electric potential? Can't we use unit negative charge?
Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge?...
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Sign of Lagrangian constraint function in rotations
How can I foolproof decide the correct sign of the constraint function in Lagrangian mechanics, particularly in rotations?
In a simple example, lets consider a cylinder rotating around its main axis ...
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