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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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0answers
21 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. ...
5
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2answers
99 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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4answers
80 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 ...
0
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0answers
31 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 ...
-1
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2answers
141 views

Isn't definition of potential energy a vague definition? [duplicate]

Why do we define potential energy? If we know the essence of defining work then isn't defining potential energy useless?
5
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2answers
89 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 ...
1
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2answers
53 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
28 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
113 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
84 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 ...
1
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1answer
96 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 ...
1
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0answers
60 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
61 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
145 views

What is the general mathematical definition of wave?

What is the general mathematical definition of wave?
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1answer
55 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
votes
1answer
64 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
votes
1answer
58 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-...
1
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1answer
60 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 ...
3
votes
3answers
93 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
votes
1answer
63 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 ...
1
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2answers
63 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
43 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 ...
-1
votes
1answer
58 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}
1
vote
3answers
122 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
98 views

Why is Work equal to Force * distance?

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
vote
1answer
31 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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0answers
11 views

Quantum synchronization description used in paper

In the paper "Steady-state spin synchronization through the collective motion of trapped ions" it states the following: "Steady-state synchronization of atomic dipoles forms the foundation for ultra-...
0
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1answer
77 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 ...
1
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2answers
103 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
votes
1answer
72 views

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

WARNING: PLEASE DO NOT GIVE ME A DEFINITION, JUST TELL ME HOW I CAN DO THIS. 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 ...
0
votes
1answer
74 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
votes
1answer
45 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
votes
3answers
65 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
29 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
59 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
773 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 ...
5
votes
1answer
307 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{...
0
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0answers
38 views

Difference between ideal gas and perfect gas?

I tried seaching it in the internet but I didn't understand anything. I know the definition of ideal gas. But I don't understand what perfect gas is. Can you help me, please?
3
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4answers
79 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
46 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 ...
1
vote
1answer
90 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 ...
-3
votes
1answer
64 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
72 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
vote
1answer
78 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
5k 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. ...
0
votes
2answers
90 views

What is a 'spacelike surface' in relativity?

I am studying Noether's theorem in field theory and I am not understanding what spacelike-surfaces mean. I will reproduce the bit of the argument below that contains the term "spacelike-sufaces" in ...
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2answers
315 views

If an object moves at constant speed, does it necessarily have constant velocity? [closed]

If an object moves at constant speed, does it necessarily have constant velocity?
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2answers
55 views

What exactly is meant by magnetic poles?

If I have a magnet, which of the following is really called magnetic pole and why?: $(1)$ Half of the volume of the magnet - north pole, other half volume - south pole. $(2)$ Area at one end of the ...
0
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3answers
121 views

Exergy, entropy and energy quality

I'm teaching a class on the subject of "energy quality". I'm supposed to tell them that energy quality is a measure of how easily (effective I guess) the type of energy can be converted to different ...
2
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2answers
63 views

What are chromoelectric and chromomagnetic fields?

Are they the normal elctric and magnetic fields from Maxwell fields? Or are they just the corresponding components from $G_{\mu\nu}^a$ (the gluon fields), say chromoelectric fields are simply $G_{0i}^...