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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26 views

Is there a formalization of the butterfly effect?

According to my understanding, the butterfly effect says, very informally, that even a tiny perturbation in a physical system can lead to significant alterations in future states of the physical ...
1 vote
1 answer
1k views

Dew point and frost point: definition, calculation and the en.wikipedia.org disambiguation

Good day! I found the definition of dew point and frost point somewhat odd on wikipedia. At the first line you see The dew point is the temperature to which air must be cooled to become saturated ...
1 vote
3 answers
103 views

What are relativistic particles? [duplicate]

What are relativistic particles? I got it in a question of mechanics. So, what is it about a particle that makes it "relativistic"?
3 votes
1 answer
569 views

Are monochromaticity and coherence in the context of lasers two sides of the same coin?

We know that monochromatic lasers produce monochromatic light, i.e., all photons have the same wavelength $\lambda$ (ideally). Coherence, on the other hand, states that the phases of photons are in ...
2 votes
2 answers
193 views

Can the composition law of a group be defined only when considering a representation or realisation of the Group?

When we talk about, lets say, the Lorentz group, we define the action of the Lorentz transformation $\varLambda$ on \begin{alignat}{1} x^{\mu} & \in\mathbb{R}^{1,3},\\ x^{\mu} & \rightarrow x'^...
1 vote
1 answer
206 views

How exactly IS Newton’s second law verified experimentally?

In R. Shankar’s “Fundamentals of Physics : Vol 1” while discussing Newton’s Second Law of Motion, Prof. Shankar raises the question : how do we know Newton is right? I quote from the book : Take ...
2 votes
1 answer
69 views

The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as $$ Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
4 votes
3 answers
595 views

Why isn't work a state function?

I've heard the example, that work is path dependent. But whether I climb a mountain directly or in serpentines, in the end it's the same amount of work, with the one difference that it takes me longer ...
2 votes
1 answer
78 views

Equivalent definitions of Wick ordering

Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
2 votes
1 answer
62 views

In what sense is $\int (u \cdot \nabla) u \cdot u dx$ an energy flux?

Due to the nature of this question I have have cross-listed it on mathSE. Let $u$ be either a solution to either the Euler equations or Navier-Stokes equations over a domain $\Omega$. In fluid ...
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0 answers
50 views

What is the name of the transformation from one harmonic oscillator basis to another centered elsewhere?

If I have a harmonic oscillator basis centered at $x=2$, how do I rewrite it in terms of the harmonic oscillator basis centered at $x=0$? To be more specific: If $|\Psi_n\rangle$ is the $n$th ...
1 vote
4 answers
189 views

Kinetic Energy equation: Is $K=\frac12mv^2$ a Definition, or a derived Theorem?

I am trying to understand classical physics as a mathematical model. I will first specify the trail of thoughts that led up to this question. (Please correct me if anything is wrong with the reasoning ...
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0 answers
27 views

Why is Wigner-Seitz cell considered primitive?

During the lecture I listened, as well as in the internet, in Wikipedia for example, unit cell was defined as the parallelepiped spanned by the translation vectors. Primitive cell was defined as the ...
13 votes
1 answer
961 views

Is 4-momentum a vector or a 1-form?

This is a follow-on to https://physics.stackexchange.com/a/576885/117014. If we should not consider a vector and its "canonically" dual 1-form to represent the same object, then it seems ...
2 votes
0 answers
48 views

Is there any difference between Wick time order and Dyson time order?

Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
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2 answers
453 views

What are internal and external estimates of error?

I have n measurements for a quantity, and I need to calculate the internal and external estimates of error. I know what standard error is and how it is calculated, but have no clue regarding internal ...
0 votes
1 answer
598 views

What does gauge pressure indicate in fluid flow?

In flow measurement, suppose we find gauge pressure difference between any two sections. Does this pressure is total pressure difference, I mean potential, kinetic and pressure head difference or only ...
0 votes
1 answer
100 views

Mathematical meaning of a position eigenbra $\langle x_0 |$

Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$. For $f\in L^...
-2 votes
2 answers
92 views

Why can the Ampere not be defined as the flow of $n$ Coulomb in $n$ seconds?

1 Ampere is defined as the flow of 1 Coulomb of charge in one second. However, I do not understand why it cannot be defined as the flow of n Coulomb of charge in n seconds. This definition is ...
13 votes
4 answers
20k views

Explanation of homogeneity of space and time by giving examples?

While reading Landau and Lifshitz, I came across these three terms:- homogeneity of space. homogeneity of time. isotropy of space. it would be of great help to me if someone could explain it by ...
0 votes
1 answer
69 views

Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow

I am learning about the renormalization group and I am getting confused on some terminology. For the massless $\phi^4$ theory the Callan-Symanzik equation is: $$\big[ M \frac{\partial}{\partial M} + \...
0 votes
1 answer
39 views

Definition of quenched data set/disoprder in the context of spin glass

I cannot come across a good definition of what "quenched" means in the context of spin glass problems. I see such use as "quenched connectivity", "quenched data set", &...
0 votes
1 answer
67 views

Clarification regarding the meaning of Universal Time UT1

I've been reading the book "From Sundials to Atomic Clocks: Understanding Time and Frequency" by James Jespersen and Jane Fitz-Randolph which is available at https://www.nist.gov/system/...
-3 votes
0 answers
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What is gradient? What's the difference between gradient and divergence? [migrated]

I don't really get what's the difference between them. What does each thing physically and mathematically signify? Aren't both things just a dot product with the del operator?
6 votes
2 answers
585 views

Why is angular momentum defined so?

We know angular momentum is defined as $mvr$. In the context of Lagrangians and Noether's theorem, this definition pops up as the conserved quantity due to rotational symmetry of the system. Is there ...
3 votes
1 answer
69 views

Relating the different "notions of charges" in field theory

Thinking back to my lectures of QFT/Classical field theory, I am getting confused about the different things called charges: First of all, we have the notion of Noether charge, i.e. the integral of ...
5 votes
2 answers
3k views

What does it mean when a degeneracy is lifted?

I would like to ask what is the meaning of degeneracy been lifted? For example when the Schrodinger equation is subjected to magnetic field, there is a $m\ell$ degeneracy is lifted while $\ell$ ...
1 vote
1 answer
443 views

Definition for internal energy of an ideal gas

We know that the internal energy for an ideal gas depends only on its temperature. What confused me was the correct defination of the internal energy for the ideal gas. Is it: $dU = nC_vdT$ OR $U ...
1 vote
0 answers
46 views

Definition of angular velocity in rotational motion of a non-rigid body? [closed]

Consider a particle in rotational motion with radius r and angular velocity w both varying with time, what is the relationship between the displacement u and w of the particle? $w=\frac{\partial u}{\...
1 vote
4 answers
1k views

What is the precise definition of a 4-vector?

In Minkowski space, I know that there are some vectors such as the ordinary velocity that are not proper 4-vectors. But what is the exact definition of a 4-vector? For any fixed numbers, say 1,2,3,4, ...
-1 votes
2 answers
72 views

What exactly is kinetic energy? [duplicate]

What exactly is kinetic energy? I know that kinetic energy is the energy that an object obtains by the virtue of its motion, but I need an exact answer. So, potential energy, like there are three main ...
0 votes
1 answer
765 views

Minkowski vs. Lorentz metric

Can anyone help me to understand the difference between Minkowski and Lorentzian metric? They appear to me to be the very same: $$\langle x,y\rangle=-x_1\cdot y_1+x_2\cdot y_2+\ldots+x_n\cdot y_n.$$ ...
5 votes
4 answers
806 views

Contracting the metric tensor with its inverse yields Kronecker delta

It's probably straightforward, but I would like to see the proof of the identity: $$g_{\mu\nu}g^{\nu\alpha}=\delta^\alpha_\mu.$$ In the book 'Spacetime and Geometry' by Carroll, this identity is the ...
0 votes
0 answers
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Inconsistent definitions of Entropy [duplicate]

On the wikipedia page "Entropy", entropy is defined as $S=k_B \ln\Omega$, where $\Omega$ is "the number of microstates whose energy equals the system's energy". This is what I had ...
0 votes
2 answers
113 views

In physics, what is the difference between a fact and a definition?

For example, I came across this statement: "It is a fact that the components of force are derivatives of potential energy, but it is not a definition." What does this statement mean? I ...
4 votes
2 answers
2k views

First integral of relativistic Euler-Lagrange equations

Consider a pseudo-Riemannian ($4$-dimensional) manifold $M$ with a pseudometric $g_{ab}$. The Lagrangian of a free particle in $M$ (in analogy to the flat case) is $$\mathcal L=\frac{1}{2}g_{ab}\frac{...
2 votes
1 answer
448 views

Definition of contrast-to-noise ratio?

I have been looking at definitions of the contrast-to-noise ratio. As indicated in numerous sources (e.g. here (page 12)), the contrast to noise ratio between two signals $A$ and $B$ is: $$ CNR=\frac{...
4 votes
3 answers
897 views

What is capacitance, in general?

In circuit analysis software capacitance can be measured between any two nodes of a circuit or of a multiterminal device. In practical terms we take $C_{ij}$, the capacitance between $i$ and $j$ as ...
0 votes
1 answer
74 views

What actually is Boyer-Lindquist coordinates?

I want to know the difference between spherical and Boyer-Lindquist coordinates. Don't they both use $r, \theta, \phi$ parameters? I've searched books and sources on the internet and there's none that ...
1 vote
1 answer
62 views

Fierz idendity (supersymmetry)

So basically I have two Fierz identities involving spinors: $$\psi^a \psi^b = -\frac{1}{2} \epsilon^{ab} \psi \psi$$ And $$\overline{\psi}^{\dot{a}} \overline{\psi}^{\dot{b}} = \frac{1}{2} \epsilon^{\...
1 vote
1 answer
56 views

Difference between stationary states, collision states, scattering states, and bound states

A few weeks ago, I was presented one-dimensional systems in my QM class, and of course one-dimensional potentials too. Nonetheless, I'm still a bit unclear about the terminology my professor uses. ...
1 vote
2 answers
3k views

Differences between eigenstates, bound states and stationary states [closed]

I am not very clear about the differences between eigenstates, bound states and stationary states.
0 votes
1 answer
47 views

Cosmology - Anthropic Principle [closed]

What do cosmologists actually mean by Anthropic Principle? What are the differences between weak and strong Anthropic Principle?
2 votes
4 answers
778 views

What exactly does it mean for a unit to be dimensionless?

For instance, why are moles and decibels considered dimensionless, but kg and meters aren't? Or, in other words, what exactly is a "dimension" in this context? Is just about the system of ...
4 votes
2 answers
5k views

What is $R$-symmetry with supersymmetric theory?

What is $R$-charge and $R$-symmetry? In usual context, $\mathcal{N}=2$ supersymmetry has $U(1)$ $R$-symmetry. I don't understand what this means. Could you explain to me with more examples? $R$-...
1 vote
2 answers
235 views

Coulomb Gauge misunderstanding

If we have $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ and we make the following gauge transformations: $$\vec A(\vec r,t)'= \vec A(\vec r,t) + \nabla f(\vec r,t)$$ $$\phi(\vec r,t)'=\phi(\vec r,t) - \...
3 votes
6 answers
1k views

Relationship between bel and decibel

Bel is a unit of $log_{10}$ of ratio of two quantities. 1 Bel = $\log_{10}\frac{P_1}{P_2}$ On Wikipedia it says: 1 decibel = $\frac{1}{10}$ bel According to this definition then, 1dB = $\frac{1}{10}$ $...
1 vote
2 answers
201 views

Are dual bases and the Hodge dual "entirely distinct" uses of the word "dual", as per MTW?

NB: Basis one-forms and contravariant basis vectors (which, following Menzel, I am calling reciprocal) are the same thing. See, for example, the Mathematical Appendix to Gravitation and Inertia, by ...
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0 answers
51 views

Matter vs antimatter asymmetry per particle [duplicate]

What is called matter and what is called antimatter is just a convention, isn't it? For example, suppose we call the bottom, the charm and the down quark antimatter and we call the strange, top, and ...
2 votes
1 answer
110 views

Definition of generalized force in Lagrangian formalism

In some texts (e.g. Taylor's Classical Mechanics), the generalized force is defined to be (I'll simplify to one particle in one dimension for ease of notation): $Q \equiv \frac{\partial{L}}{\partial{q}...

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