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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2
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4answers
198 views

Why is escape velocity independent of direction of projection?

However, for any body projected with a velocity less then the escape velocity, the final maximum height will vary with variation in angle of projection. But why is this not the case in case of ...
2
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1answer
79 views

Is there any special significance of force field in physics?

What is the formal definition of force field? Which is more fundamental force or field? Do field exist in nature (as force do i think as per section 12-1 of Feynman lecture volume 1, and page 8,9 of ...
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1answer
43 views

Is there a “standard” Newton?

Basic SI units have definitions through experiments that seems to imply a pretty obvious setup. Is there a standard experiment for calibrating Newtons? The definition is the force needed to cause a ...
2
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1answer
45 views

States of classical general relativity

In Classical Mechanics a state of a system is either a pair $(q,p)$ or $(q,\dot{q})$ depending if we formulate the theory on the tangent or cotangent bundle of the configuration space. The evolution ...
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0answers
79 views

What is the difference between acoustic photon and acoustic phonon?

In the book Biomedical Photonics Handbook, 3 Volume Set edited by Tuan Vo-Dinh, it is written : Brillouin Scattering is caused by the interaction of the photon with the acoustic phonon. As the result ...
4
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5answers
381 views

Could someone explain what is a potential?

In many part of physics, me talk about potential (electrical potential, gravitation potential, elastic potential...). All those definition looks very different, and I would like to know how all those ...
6
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1answer
125 views

GR with Torsion: Definition of contorsion

I start doing some computations in manifolds with non vanishing torsion and things are getting a bit confused, basically because of notations and definitions. I understand that in presence of non ...
2
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1answer
69 views

Definition of equilibrium for thermodynamics and statistical mechanics

Is the definition of equilibrium for thermodynamics and statistical mechanics the same? From my understanding, a system is in thermodynamic equilibrium if its macroscopic variables are not changing. ...
6
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2answers
281 views

Is this actually the rigorous definition of the path integral in Quantum Mechanics?

Let a quantum system with a single degree of freedom be given. We want to define the path integral so that we get the representation for the propagator as $$\langle q' |e^{-iHT}|q\rangle=\int_{x(a)=...
2
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1answer
89 views

Time Travel, CTC and Causal Loop

What is the difference between a closed timelike curve and a causal loop? If someone is travelling in a closed timelike curve, are they also in a causal loop?
2
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4answers
148 views

Thermodynamics second law variational statement query

In thermodynamics as I understand entropy is a state function. A state function is a property whose value does not depend on the path taken to reach that specific value. In contrast, functions that ...
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0answers
84 views

Superstate vs superposition

Is superstate the phase space of a superposition that includes subsets? It seems like superstate is not used as a word that often, and usually seems to be a synonym for superposition. Can anyone give ...
6
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2answers
194 views

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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2answers
56 views

Strange super script notation $^{(4)}R$ in the textbook Numerical Relativity

In Numerical Relativity by Thomas W. Baumgarte and Stuart L. Shapiro. There are bunch of superscript $(4)$ over $T,\Gamma, R$ i.e. $^{(4)}\Gamma^a_{bc}$ _ $^{(4)}R_{abcd}$ _ $^{(4)}R$ ... (...
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1answer
29 views

Meaning of flux 2-integral

Can someone please explain the meaning of flux 2-integral in this sentence: Mass is evaluated as a flux 2-integral at the asymptotic infinity. For asymptotic infinity, I believe it is as ...
2
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2answers
144 views

How to arrive at the thermodynamic definition of entropy?

My question is, how do we say that, $$dS=\dfrac{dQ}{{T}} ~?$$ How do we relate heat and temperature to entropy? Why is the temperature in the denominator? Can we replace heat by work? How does ...
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2answers
90 views

Quantum Mechanics Defining a field

I am currently in a basic class where I am being taught some concepts of QM.. We were taught today some field theory but we were not given the definition of field in QM. I looked around but my book ...
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1answer
304 views

A new definition of mass using Planck constant

Tonight in a italian television news channel well known internationally I have heard that almost certainly the definition of mass that we currently know will be obtained by means of the constant ...
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0answers
68 views

Extensors in mathematics and in physics [closed]

Could someone explain in a simple but accurate manner what extensors are as mathematical entities and how they are used? How do extensors essentially differ from tensors? Are there or could there be ...
1
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1answer
154 views

Ladder operators vs creation/annihilation operators

I am trying to figure out the difference between the ladder operators (for harmonic oscillator) $a^\dagger$, $a$ and the creating/annihilation operators $c^\dagger$, $c$. Are they the same? I have ...
5
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1answer
164 views

What is the general mathematical definition of wave?

What is the general mathematical definition of wave?
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1answer
58 views

What is the general mathematical definition of periodic motion?

What is the general mathematical definition of periodic motion? My answer : Can you say that each function is in the form $ \overrightarrow{r} (t)= \overrightarrow{r} (t+T)$. it is right?
-1
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1answer
161 views

What is the difference between space-like four-momentum and time-like four-momentum? [closed]

I was reading a wiki page on Tachyon, came across these terms? What i need is bit of a mathematical description to understand these terms?
0
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1answer
76 views

Are there timelike 3D surfaces in special relativity

I am reading Scharf's 'finite QED' and I am puzzled at the beginning. He first introduces Minkowski space with $(+,-,-,-)$ signature, and here is a definition I find difficult: A three-...
2
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1answer
241 views

Definition of one-particle irreducible diagrams

Text books often defines one-Particle Irreducible diagram (1PI diagram) as a connected diagram which does not fall into two pieces if you cut one internal line. Is this internal line the full ...
2
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3answers
100 views

Is there a traditionally accepted threshold probability at which highly unlikely becomes impossible? [closed]

Many events which by any practical definition are impossible have extremely low but nonzero probability of occurrence. For instance, the positions of oxygen molecules in a room are basically random ...
-1
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1answer
70 views

Why is velocity mathematically describes as a division? [duplicate]

I want to know why, in kinematics, is velocity described as $v = \frac{\Delta x}{\Delta t}$, and why it is not described as any other expression (like a multiplication), why does a division is the one ...
2
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2answers
262 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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0answers
72 views

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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1answer
150 views

D'Alembert Operator

In which book or where can I find the derivation of the d'Alembert operator? \begin{equation} \Box \psi= \frac{1}{\sqrt{-g}}\partial_\mu \left( \sqrt{-g}\partial^\mu \psi \right) \end{equation}
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3answers
127 views

Why speed = distance/time? [duplicate]

Is it merely an arbitrarily chosen definition that we created in order to quantitatively measure the speed of an object or is it some other way around. I want to know what's the reason behind such a ...
0
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4answers
140 views

Why is Work equal to Force * distance? [duplicate]

I totally get the mathematical part, but I cannot imagine how this works. I apply a force to a ball. Why does the distance over which it moves matter to me? Sure, if I calculate the kinetic Energy of ...
1
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1answer
61 views

What is the physical meaning of static and velocity pressure?

According to Bernouli's equation, the static pressure inside a pipe with streamline and steady flow decreases with fluid's velocity. One explanation to rationalise this phenomenon is because velocity ...
0
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1answer
87 views

What is the difference between a quadrivector and a 4-vector? [closed]

What is the difference between a quadrivector and a 4-vector? Why is the square of a 4-vector equal to $t^2+x^2+y^2+z^2$ while the square of a quadrivector is equal to $t^2-x^2-y^2-z^2$? Aren't they ...
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2answers
147 views

Definition of the spherical harmonics do not agree

I Griffiths' Introduction to quantum mechanics, the spherical harmonics are defined as $$Y_l^m(\theta,\phi) = \epsilon\sqrt{\frac{2l+1}{4\pi} \frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi} P_l^m(\cos \theta)$$ ...
0
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1answer
249 views

How might I write an operational definition for Vertical and/or Horizontal? [closed]

I really don't want to have to rely on a forum website to tell me how I can solve my physics homework, but I honestly have no idea where to begin. Can any of you guys explain how I might logically ...
0
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1answer
153 views

What is a fuzzy space?

Can someone give a down-to-earth explanation of what is a fuzzy space? (As known from M-theory and noncommutative geometry)
2
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1answer
51 views

How do we quantify this kind of information in Quantum Mechanics?

Let a quantum system be given with Hilbert space $\mathscr{H}$. Suppose it is described by the quantum state $\rho$, i.e., a density matrix. We can define the Von-Neumman entropy as $$S(\rho)=-\...
0
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3answers
199 views

Meaning and significance of the Levi-Civita symbol

I am recently reading Sean Carroll's Spacetime and Geometry: An introduction to General relativity. I am much of a beginner but am really curios to learn about GR. In the first chapter, after ...
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0answers
34 views

What exactly is a nonequilibrium quantum state?

How do we define a quantum equilibrium and nonequilibrium state? And how are these two different from each other?
2
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2answers
74 views

Definition of velocity in classical mechanics

Let $(r_1,r_2,r_3)$ be the coordinates of a particle $r$ in the coordinate system $\phi$. Let $\{\hat{e_1},\hat{e_2},\hat{e_3}\}$ be the coordinate basis of $\phi$. Why do we define the velocity $v$ ...
10
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5answers
817 views

Paradox in the definition of work [duplicate]

I'm trying to understand the Oberth effect and came across this paragraph that seems crazy to me: when the rocket moves, its thrust acts through the distance it moves. Force multiplied by distance ...
6
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1answer
460 views

Generalized divergence of tensor in GR

Although I've forgotten the proof (and cannot find it in, say, Carroll's book), the following formula holds for the covariant divergence in general relativity: $$\nabla_{\mu} A^{\mu} = \frac{1}{\sqrt{...
3
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4answers
104 views

Velocity definition in quantum mechanics?

What is the definition of velocity in quantum mechanics? is it an operator?
0
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1answer
119 views

What is the (quantum) definition of thermal equilibrium?

What is the necessary condition for a quantum system to be in thermal equilibrium? The quantum systems I have in mind are a bunch of cold atoms, of photons in a cavity. Does a system need to obey a ...
2
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1answer
152 views

What does existence mean in physics? [closed]

I would like to understand what we mean when we say, within a conversation about physics, that some structure or some phenomenon exists. I tried searching a couple of online physics dictionaries ...
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1answer
76 views

What is the real definition of density? [closed]

What does density really mean? Everyone just provides me with the equation of finding density whenever I ask this question.
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1answer
86 views

Is there any moon without its planet?

Is there any planet without its star? Is there any moon or any planet wandering in outer space without a definite orbit? (The name moon or planet used here serves only for size and spherical shape ...
1
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1answer
80 views

Definitions of $\vec{B}$ and $\vec{H}$

From here, I have got the definition of $\vec{H}$. However even in wikipedia and other sites, I cannot find a definition for $\vec{B}$ which shows its similarity with $\vec{H}$. Similarity: I know ...
24
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9answers
6k views

Why does work depend on distance?

So the formula for work is$$ \left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right] \,. $$ I'm trying to get an understanding of how this represents energy. ...