Questions tagged [definition]
The definition tag is used in situations where the question is either about how some term or concept is defined or where the validity of an answer depends on a subtle definition of some term or concept used in the question.
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How can parallel rays meet at infinity?
I found that in every book (till my 12th) it is written that, in concave mirror, when object is at focus, then reflected rays will be parallel and they meet at infinity to form a real image.
But, as ...
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What exactly is Landau Damping?
I would like to understand what exactly happens when Landau damping takes place. I have seen the mathematics of it. But I am not sure If I truly understand what happens when we are talking about ...
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What is the meaning of the word 'momentum' in quantum physics? (Especially in the problem that I will describe below.)
In undergraduate quantum physics class that I am taking in this semester, I had to solve a problem about quantum Zeno effect. The problem describes the thought experiment which is trying to determine ...
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Work done on a frictionless surface
Imagine that we apply a force $F$ on a frictionless surface to move a body by a distance $d$. (The body starts at rest and is stopped after moving a distance $d$.)
Is the work done $F d$?
But from ...
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Symmetry condition for continuous coordinate transformations
Considering a continuous coordinate transformation defined as
$q_i(\epsilon,t)=q_i(t)+\epsilon\eta_i(t)$ and a Lagrangian $L(q_i,\dot{q_i},t)$. The symmetry condition for a system described by these ...
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Landau Vol. 2: On four-vectors
In Chapter 1, section 6 of The Classical Theory of Fields by Landau and Liftshitz, I didn't understand the following:
"Under purely spatial rotations (i.e. transformations not affecting the time ...
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Definitions of dielectric constant and relative permittivity? How do they differ?
It's all about the definition, as in how they both are defined.
My book defines dielectric constant as the proportionality constant
$$K=\frac{\sigma}{\sigma-\sigma_p}$$
where $\sigma$ is the surface ...
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Are chaotic systems examples of complex systems?
I am struggling to find a proper source or reference where examples of complex systems which are chaotic are given. Based on my understanding, complex systems consist of interacting components, each ...
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Positional is not equivalent to conservative in dimensions greater than one
I've just started writing dynamical systems and I was trying to find an example to show that if we are in a $2$ or $3$ dimensional real space "positional do not implies conservative".
In ...
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How do 'locally Euclidean' and 'Lorentzian' requirements in manifolds reconcile?
In GR, we define our manifolds to be locally Euclidean. However, we also demand that our metric tensor have a Lorentzian signature. Since the metric tensor is a measure of curvature, doesn't the first ...
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What is Dirac indices?
In Maggiore A Modern Introduction to Quantum Field Theory Eq. 4.31
$$\{\Psi_a(\vec x,t),\Psi_b(\vec x,t)\}=\delta^{(3)}(\vec x-\vec y))
\delta_{ab}$$
where "$a,b=1,2,3,4$ are the Dirac ...
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Why isn't the magnetic field defined by the magnetic force on a particle moving through it?
A magnetic field describes the influence a charge (in motion) experiences. In other words, it is essentially a vector field that describes the force that a particle will feel at a given location. ...
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What is $v_{\infty}$?
So, you can calculate the trajectory of a celestial projectile by using this equation:
$$e=\frac{rv_{\infty}}{\mu},$$
where $\mu$ is the central body's Gravitational Parameter, so it is definable by $\...
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Momentum in Lagrangian mechanics
In the context of translation symmetry for lagrangian mechanics i was given this statement:
For a mechanical system $\frac{∂L}{∂\dot{q}_i}=p_i$ is the momentum.
I have no idea where this comes from.
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What is momentum?
Momentum tells you the mass of the object and how fast it is going right? So if I have a 2 kg ball moving at 2 m/s, then the ball has 4 kg⋅m/s of momentum. My question is why do we multiply mass and ...
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What is the interpretation of non-uniqueness of field expansion in flat spacetime?
Scalar field expansion in terms of plane wave modes is given by
$$\phi(x)=\int\frac{d^3{\vec p}}{\sqrt{(2\pi)^{3}2\omega_{\vec p}}}\left(a_{\vec p}e^{-ip\cdot x}+a_p^\dagger e^{+ip\cdot x}\right)$$ ...
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Interpretation of adiabatic assumption in quantum mechanics
This thought just occurred to me. I recall from my quantum mechanics courses that adiabatic transformation is defined as a process in which a band-gap is kept open while the process is carried in a ...
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What does it mean to be "gauging" a symmetry?
I read this and other similar questions, but they all address the problem of gauging a global symmetry (implying that one could also gauge a local one).
This confused me a lot: in my mind gauge and ...
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What is a dynamical symmetry?
What does the term dynamical symmetry refer to? Does it refer to the symmetry of the equation of motion? How is the symmetry of the equation of motion different from the form-variance of the equation ...
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What is quiver momentum in plasma physics?
In plasma physics texts discussing dynamics of individual charged particles under electromagnetic fields, the term "quiver momentum" is frequently used, but I haven't seen a clear definition ...
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Why is Fermi energy equal to chemical potential at absolute zero temperature
The probability that an orbital at energy $\epsilon$ will be occupied in an ideal electron gas at thermal equilibrium is given by
$$f(\epsilon)=\frac{1}{exp[(\epsilon-\mu)/k_bT]+1}$$
in kittel's book ...
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Electrodynamics and relativistic electrodynamics
It is always said that Maxwell equations from classical electrodynamics are itself relativistic but I often encounter the term "relativistic electrodynamics". What is the difference between ...
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What is meant by "inertial forces", in contrast to the "resultant force"?
For example, in the Wikipedia page on Reynolds number it is said:
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid..
In explanations of the Reynolds number, it is ...
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Dirac's radiated field definition
In Dirac's 'Classical theory of radiating electrons', submitted in 1938, the electromagnetic radiated field is defined as:
$$F_\text{rad}^{\mu\nu}=F_\text{ret}^{\mu\nu}-F_\text{adv}^{\mu\nu}$$
Where $...
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What is mechano-sportive behaviour? [closed]
I am researching about the behaviour of wood and I was reading a paper where the term "mechano-sportive" was mentioned, I tried googling it but could not find anything useful.
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Definition of "particle" in QM and QFT
To sum up;
In Classical Physics, particles can be defined as
... particles (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties ...
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What is a mode in quantum optics?
I am studying quantum optics and it is often cited the word "mode", in particular there are spatial and temporal modes.
I really don't know what they are. I know the general definition of ...
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Is the dimension of a Lie group equal to the dimension of the corresponding Lie algebra?
I have gotten myself quite confused with dimensions and ranks of Lie group and Lie algebras. As far as I understand:
_The $\bf{rank}$ of a Lie algebra is its number of Casimir operators (linearly ...
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What is astrophysical fluid?
I am reading a book about astrophysical fluid dynamics, some basic fluid equations are mentioned, but is there any difference between astrophysics case and general case? Is there any definition about ...
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Static spacetime and Schwarzschild solution
The Schwarzschild spacetime $(\cal{M},g)$, for which the metric is a solution for the Einstein field equation in vacuum,
$$g=-\Big(1-\frac{2m}{r}\Big)dt^2+\Big(1-\frac{2m}{r}\Big)^{-1}dr^2+r^2d\Omega^...
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When we talk about the Higgs mechanism, is it a quantum effect?
I have heard assertions that in QFT, the Higgs mechanism and Yukawa Couplings are calculated "at tree level" making the effects only classical in nature, not quantum. What does this mean, ...
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Why do centrifugal force and centripetal acceleration have opposite signs?
I know that rotating body has centripetal acceleration that is directed to the center of rotation.
$$a_{cp}=-\frac{v^2}{R}$$
(Lets imagine that body is located at 12 o'clock and that Ox axis is ...
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A stone tied with string, rotated in circle. Is this type of motion is rotational or circular? [closed]
I've confusion in this question because circular motion is defined for point masses while rotational motion is for rigid bodies.
And also of if we consider a particle of that stone, it seems that it's ...
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What $r_0 $ in the nucleus radius equation?
I'm doing some self-study and I'm attempting to calculate the energies needed to overcome the Coulomb barrier. I stumbled upon $R = r_0A^{1/3}$ for the radius of nuclei. I've been looking around ...
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Meaning of 'Local' density in Liouville's theorem
Liouville's theorem is commonly stated as
$$\frac{d\rho}{dt} = \frac{\partial{\rho}}{\partial{t}} + [\rho, H]$$
Where, $H$ is Hamiltonian of the system, $\rho$ is the density, $[...]$ is the usual ...
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The definition of Quasi-static process?
A quasi-static process is often defined as a process "that occurs infinitely slowly such that equilibrium holds at all times."(Harvard, Matthew Schwartz, statistical mechanics Spring 2019). ...
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Connection between different kinds of "Lagrangian"
Being a physic student I first heard the term: "Lagrangian" during a course about Lagrangian mechanics; at that time this term was defined to me in the following way:
For a classic, non ...
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Definition: How can you tell if a coordinate system is "generalized coordinates" or not?
I'm trying to remember this stuff and using only Wikipedia and not textbooks which is probably part of the confusion.
But what is the precise definition of a "generalized" as opposed to a &...
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What properties of MOND differ from Newtonian gravity?
I know of the following properties that set modified Newtonian dynamics (MOND) apart from Newtonian gravity:
There is a $1/r$ dependence instead of a $1/r^2$ dependence, at large distances/low ...
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Difference between current density and current
I'm a little confused, I can't understand intuitively what current density is. From the formula looks obvious:
$j=\frac{I}{A}$
it is the current per area. Very similar to the "everyday life ...
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Equations homogeneous in $X$ and $y$
Arfken and Weber in their mathematical methods for physicists edition 6 on page 334 talk about equations homogeneous in $X$ and $y$ and tells they are homogeneous if the combined powers of $X$ and $y$ ...
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What is a simple example illustrating the concept of "commensurate" and "incommensurate" order in condensed matter physics?
In a wide range of contexts in condensed matter physics, e.g this paper, the concepts of commensurate and incommensurate orders are invoked to describe particular ordered phases. I think I have some ...
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Is this the most general form for a gauge transformation?
From my understanding, a gauge transformation in QFT is a local transformation in the fields under which the action is invariant. I usually write it, for a theory with scalars, fermions, and vector ...
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What is the sign of the metric determinant?
I read that for the Levi-Civita symbol $\tilde{\epsilon}_{ijk}$, people somtimes define another version of the symbol with upper indices:
$$\tilde{\epsilon}^{ijk}=\text{sgn} (g) \tilde{\epsilon}_{ijk} ...
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The "wrong" definitions of "Algebra" and "Lie Algebra"
I am reading Robert Mann's "An Introduction to Particle Physics and the Standard Model" and a review from Amazon (with 12 upvotes) concerns me:
...The definition of algebra on page 54 is ...
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If a molecule is a collection of atoms why we can't call a molecule matter and vice versa? [closed]
if a molecule is a collection of atoms why we cant call a molecule matter and matter a molecule?
what is the difference between the two?
in school we are taught that matter is made up of molecules and ...
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Can someone please explain the difference between an electric charge and electric current? [closed]
Well I understand the definition my question was that we measure charge by calculating 6.24 *10 powers 28 in one second then what is electricity if it is the rate of flow of charge is,t it's the same ...
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Definition of an equation to be Lorentz invariant
What is the precise mathematical definition of an equation to be Lorentz invariant? Is it the same as being invariant under the maps $x \mapsto \Lambda x$, with $\Lambda$ being a given Lorentz ...
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Is electron a matter?
I know electrons are subatomic particles which make up atoms, the building blocks of matter. But is electron a matter itself? Moreover, are atoms or quantum particles matter too considering their ...
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What is Relative and Absolute? [closed]
I was studying about relative motion, and randomly thought about What actually is a Relative Term or a Absolute Term. So far in the school book it is written that, Quantities that depends on a ...
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