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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24
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3answers
11k views

Why are they called “cyclic” coordinates?

In Lagrangian formalism, when $\frac{\partial L}{\partial q} = 0$, the coordinate $q$ is called cyclic and a corresponding conserved quantity exists. But why is it called cyclic?
12
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3answers
1k views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of micro-...
8
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1answer
541 views

Introduction to Gauge Symmetries: Good, Bad or Ugly?

I'm trying to come up with a good (as in intuitive and not 'too wrong') definition of a gauge symmetry. This is what I have right now: A dynamical symmetry is a (differentiable) group of ...
2
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4answers
37k views

Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: http://inside.mines.edu/~fsarazin/...
16
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5answers
5k views

In what sense can a complex number be a scalar?

A definition of a scalar like A scalar is a one-component quantity that is invariant under rotations of the coordinate system (see http://mathworld.wolfram.com/Scalar.html) seems to exclude ...
10
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3answers
2k views

What is a photon? [duplicate]

I'm trying to get a definitive and clear answer to the question of what a photon actually is. Textbooks seem to give quite vague explanations, all starting with Einstein's idea that a quanta is a form ...
7
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3answers
3k views

What's the difference between “boundary value problems” and “initial value problems”?

Mathematically speaking, is there any essential difference between initial value problems and boundary value problems? The specification of the values of a function $f$ and the "velocities" $\frac{\...
5
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1answer
677 views

What does it actually mean “to define a field” in QFT?

First of all: how does one define one operator in a Hilbert space? This is just a mathematics question and the answer is simple: we have a Hilbert space at hand $\mathcal{H}$, then we define a ...
4
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4answers
3k views

Physical meaning of Impedance

So I have been thinking about the way impedance is defined for electrical systems, and the way it is derived. Even after looking through some websites, I cannot seem to grasp something, which every ...
5
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2answers
2k views

Potential functions

Can someone please explain what a potential is? Example. velocity potential in ideal flows, acoustic potential (gradient of which gives the particle velocity in a sound wave). Whenever I see potential ...
3
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4answers
5k views

Why is moment of inertia dependent on $r^2$ and not on $r$? (physical reason)

Moment of inertia is the mass equivalent in rotational dynamics. I know, by mathematical arguments, moment of inertia of a particle is $$ I = \text{mass} \cdot r^2.$$ But what is the physical reason? ...
18
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3answers
2k views

Ambiguity in the definition of entropy

The entropy $S$ of a system is defined as $$S = k\ln \Omega.$$ What precisely is $\Omega$? It refers to "the number of microstates" of the system, but is this the number of all accessible microstates ...
6
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4answers
1k views

Physicists definition of vectors based on transformation laws

First of all I want to make clear that although I've already asked a related question here, my point in this new question is a little different. On the former question I've considered vector fields on ...
5
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3answers
515 views

Bounded operator - definition?

As mentioned also in Bounded and Unbounded Operator, an operator $A$ is said to be bounded, if $$\|Af\|\leq k \|f\|,$$ where the constant $k$ does not depend on the choice of $f$ (let us consider a ...
4
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2answers
44k views

Difference between angular frequency and angular velocity?

What is the difference between angular frequency and angular velocity? I think one is used for SHM and the other for circular motion? Also can both be used for centreptal accelartion? I think angular ...
31
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3answers
2k views

Is there any truth to interpreting definition of a second as corresponding to oscillations?

As far as I understand the definition of a second, the Cs-133 atom has two hyperfine ground states (which I don't really understand what they are but it's not really important), with a specific energy ...
14
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2answers
648 views

What accounts for the discrepancies in my calculations of year lengths?

A common exercise in many introductory astronomy texts is to use the lengths of various kinds days to calculate the approximate length of the corresponding year. For example, ratio $k$ of the length ...
13
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2answers
3k views

Why is the length of the Kelvin unit of temperature equal to that of the Celsius unit? [duplicate]

The Celsius unit is arbitrarily defined, based on the boiling and freezing point of water. Is it a coincidence, then, that the SI unit of temperature Kelvin, which is used in all natural equations, ...
13
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2answers
2k views

What is a coherent state?

In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?
11
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3answers
20k views

273 + degree Celsius = Kelvin. Why 273?

Temperature conversion: $$273 + \text{degree Celsius} = \text{Kelvin}$$ Actually why is that $273$? How does one come up with this? My teacher mentioned Gann's law (not sure if this is the one) but ...
8
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3answers
1k views

Is a “shift in the meaning” of Accuracy and Precision occurring?

Accuracy and precision are among the most fundamental concepts in experimental physics, and, I always believed, completely unambiguous. Recently I found that the Wikipedia article on Accuracy and ...
8
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5answers
708 views

Definition of entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
7
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3answers
698 views

Can temperature be defined as propensity to transmit thermal energy?

I was recently surprised to learn that defining temperature isn't easy. For a long time, it was defined operationally: how much does a thermometer expand. Also surprising, temperature isn't a ...
7
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3answers
6k views

What is the difference between UT0, UT1 and GMT time?

Every reference I find says that they are "essentially" the same, which we all know really means that they are not the same, but different only by a some small amount that someone else other than me ...
7
votes
4answers
526 views

Is there a fundamental reason not to define the work vice-versa

My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as: $$W=\int_\Omega \underline{\underline{\sigma}}:\mathrm{d}\underline{\...
6
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4answers
257 views

Is $\mathbf{F}=m\mathbf{a}$ a vector field or just a vector?

I've heard both yes and no. Is $\mathbf{F}=m\mathbf{a}$ a vector field or just a vector? I think it's ambiguous, it's always written without an argument. For sake of clarity: I use the notation $\...
6
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3answers
981 views

What is a Theory of Everything (TOE)?

I see many learned contribution about the role of a Theory of Everything (TOE), what it might do or not do, what kind of answer it might provide, and what not. But I do not know what a TOE is, how I ...
6
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4answers
802 views

Can we rigorously define force?

I'm looking to get rigorous definitions on which to base the important quantities in classical mechanics. To me a "rigorous" physical definition is an operational definition -- that is one in which ...
5
votes
2answers
4k views

what is meant by “crossover phenomena”?

In many articles I read the term "crossover phenomena" and a lot of methodology discussed according to it, with little or no description about what is meant by it. Sometimes there is a connection to ...
4
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1answer
811 views

Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
2
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2answers
3k views

Can we define tension in a string as the reactive force produced in a string being pulled at both ends?

In my textbook, the definition of tension was given that Tension is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate ...
7
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3answers
444 views

Is this statement about the impact of the fine-structure constant accurate?

I'm trying to describe a few physics concepts for non-physicists, and one of the things that came up was the fine-structure constant in the context of multiverse theory. I want to make sure my ...
6
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2answers
3k views

What are global and local gauge invariance defined as they are?

I'm sorry for the triviality of my questions. Why is $\bar{\psi} = e^{i \theta}\bar{\psi}$, where $\theta$ is a real number, used as the global gauge transformation? Why $e^{i \theta}$; what's the ...
6
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2answers
1k views

What is the definition of soliton?

What is the definition of soliton? I've encountered this name in different situations like when the topic discussed is about QFT, fluid dynamics or optics, but I cannot find a general definition. I've ...
5
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2answers
5k views

Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
5
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1answer
2k views

What is the difference between kinetic momentum $p=mv$ and canonical momentum?

What is the difference, if any, between kinetic momentum $p=mv$ and canonical momentum? Why is canonical momentum important (specifically to classical field theory)?
5
votes
1answer
669 views

Why are states that are separable but not simply separable considered to be unentangled?

For pure states $|\psi\rangle$, entanglement is straightforward. Given two Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, a pure state $|\psi\rangle \in \mathcal{H}_A \otimes \mathcal{H}_B$ is a ...
4
votes
1answer
499 views

What is the difference between thermodynamic free energies and the Landau free energy?

How and why is the Landau free energy any different from thermodynamic free energies? It is written on page 140 of Nigel Goldenfeld's book Lectures on Phase Transitions and The Renormalization Group ...
4
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1answer
531 views

Precise definition of jet energy scale and jet energy resolution

Is it correct to say that jet energy scale is only related to Monte Carlo simulations? I can't seem to find a pedagogical introduction about these things that states it properly.
3
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2answers
2k views

The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
3
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0answers
560 views

How is Infinitesimal coordinate transformation related to Lie derivatives?

I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment: The effect of an ...
2
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1answer
1k views

Situation of Stable, Neutral and Unstable Equilibrium

Recently, I was reading about stability of equilibrium. I came across the definitions for different types of equilibrium. Neutral Equilibrium: The kind of equilibrium of a body so placed that when ...
1
vote
1answer
276 views

Technically, what is a spacetime singularity? [duplicate]

In popular science books and articles, one often finds that the BigBang is a singularity of spacetime, and it is expected to be solved by a successful theory of Quantum gravity. Technically what is a ...
8
votes
4answers
876 views

On the definition of work

Work is defined as $$W = \vec{F}\cdot\vec{s}$$ But what what exactly is $\vec{s}$? Is it the displacement of the body on which the force is being applied? Or is it the displacement of the point of ...
7
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2answers
13k views

What is a Null Geodesic? [duplicate]

What is a Null Geodesic? My textbook only explains it as the Minkowski metric which equals to zero, but I'd appreciate a more detailed explanation.
7
votes
5answers
42k views

What is basically the difference between static pressure and dynamic pressure?

What is basically the difference between static pressure and dynamic pressure? While studying Bernoulli's theorem, I came before these terms. The law says: When the fluid flows through a small area,...
6
votes
1answer
863 views

Definition of mean free time in the Drude model

In the Drude model they derive a formule for the conductivity of a conductor. I wonder though how the main free time $\tau$ is defined in this formula. Wikipedia says that it is "the average time ...
5
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2answers
2k views

What is the gamma five matrix $\gamma_5$?

This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = \eta_{\mu\nu}\gamma^{\mu}...
4
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2answers
528 views

Torsion tensor: definition

The definition of torsion tensor is the following: $$ \mathbf{T}(\mathbf{X},\mathbf{Y})=\nabla_{\mathbf{X}}\mathbf{Y}-\nabla_{\mathbf{Y}}\mathbf{X} -\left[\mathbf{X},\mathbf{Y}\right]. $$ In an ...
4
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3answers
1k views

Is a theory the same as a hypothesis? [duplicate]

“Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it.” Excerpt from Stephen Hawking, A Brief History of Time, iBooks. So does that mean ...