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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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What are quasi-regular singularities?

The book EXACT SPACE-TIMESIN EINSTEIN’SGENERAL RELATIVITY by Podolsky and Griffiths has a section on Taub-Nut space-time metrics and there is defines the singularity made in the Taub metric as quasi-...
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24 views

Definition of closed, compact manifold and topological spaces [migrated]

This is a very basic question but I seem not to get a "simple" definition anywhere that is at the same time rigorous and clear. I probably understand basic definitions of topology, topological spaces, ...
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0answers
33 views

Covariant, Contravariant & Invariant [closed]

What are the difference between "Covariant" and "Invariant"? What does "contravariant" mean?
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2answers
2k 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, ...
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18 views

Hodograph transformation

What is hodograph transformation? Can you explain it in a readily understandable manner?
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3answers
66 views

How do we define “mass” in the context of particle physics and relativity?

In laypersons terminology, mass is defined as the amount of matter. However, consider the following: The $W$ and $Z$ bosons have mass. An antiparticle has the same mass as its corresponding particle. ...
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1answer
81 views

How can tempered distributions be paths?

I'm reading the Appendix A of Glimm and Jaffe book "Quantum Physics: a functional integral point of view", and there is something that I'm missing In section A.4 the authors talk in a very general ...
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0answers
49 views

Scattering amplitudes vs correlators

What are the practical differences between correlators and scattering amplitudes in quantum field theory? On a very practical level: scattering amplitudes describe the evolution of an IN state into ...
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1answer
59 views

Questions about an inertial frame

Can someone explain to me what I put in bold? Inertial frame definition: When the coordinate axes are stationary with respect to the mean position of the "fixed" stars or if they move with uniform ...
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1answer
43 views

Is this understanding of potential energy correct?

I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due ...
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1answer
42 views

Discretization of path integral and linear interpolations

Consider the evaluation by discretization of the path integral $$\int e^{iS[x(t)]}\mathfrak{D}x(t),\quad S[x(t)]=\int_{t}^{t'}\left[\frac{m}{2}\dot{x}(\tau)^2-V(x(\tau))\right]d\tau.$$ One ...
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21 views

Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
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1answer
62 views

Exact meaning of 'degree'

I wish to know if there is an exact meaning of degree in physics/math/chemistry. It is used in many cases and it is not clear to me which requirements must have an unit of measurements for carrying ...
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0answers
18 views

Question reg. reasoning of deterministic reversible cyclical laws - The Theoretical Minimum

I recently started reading "The Theoretical Minimum: What you need to know to start doing Physics". In the first chapter, the authors define the "Minus-First law", and state that reversible ".. laws ...
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8 views

What to say when making conclusions from experiment that tests a hypothesis?

I recall from inferential statistics, when performing a hypothesis test, that one either “fails to reject the hypothesis” or one “rejects the hypothesis” based on the outcome of the hypothesis test. ...
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1answer
56 views

Definition of “tidal forces”

May anyone give me definition of tidal forces? Topic is related to force between two celestial bodies which are tidally locked. I have never heard for such force. Here is quotation which is intriguing ...
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2answers
55 views

Different definitions of the EMF of a device - None of them applies to devices in a circuit

Wikipedia gives two formal definitions of the electromotive force: One in case of a closed loop, in which case the the EMF is supposed to be the path integral of the electric field (and all other ...
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1answer
104 views

Are there 2 laws of motion or only 1?

It seems clear that Newton's first law is a special case of his second. Although perhaps people might argue that it emphasizes the centrality of inertial frames. But is the third law also just a ...
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2answers
109 views

Is there a difference between a Hermitian operator and an observable?

My poorly written lecture notes say that any Hermitian operator does have a complete set of orthogonal eigenstates with real corresponding eigenvalues and is therefore an observable. In the article ...
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3answers
190 views

Definition of Newton's first law [duplicate]

I have always had a doubt in the definition of the Newton's first law. In general, it is stated in a form like: An object at rest remains at rest, or if in motion, remains in motion at a constant ...
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2answers
54 views

Is time a mathematical entity or there is any demostration of its existence? [duplicate]

I an having trouble trying to understand time as a physical entity. We can demonstrate the existence of air, the source of infection, electromagnetism, voltage, amperage, among many other physical ...
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1answer
172 views

Understanding pressure of gas in thermodynamics using 2D model

I am trying to understand why the pressure for adiabatic process is given for an ideal gas as the following. $$ p = - \frac{\partial E}{\partial V} (V, X_1, ..., X_k) $$ where $p$ is pressure, $E$ ...
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2answers
104 views

Why does electrical resistivity have units of $\Omega \cdot \mathrm{m}$ rather than $\Omega \cdot \mathrm{m}^3 ?$

Electrical resistivity has units of $\Omega \cdot \mathrm{m} .$ However, since resistivity can be described as the resistance of a unit cube, shouldn't the units therefore be $\Omega \cdot \mathrm{m}^...
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45 views

Can displacement be negative after calculation?

Regardless of the positive or negative, doesn't the number determine the total displacement and not the sign in front of the numbers?
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16 views

What is the definition of a bipolaron and a dipolaron?

I wondered about the exact definition of a bipolaron? In particular, if I have an oxygen vacancy in a metal oxide and the 2 excess electrons (when forming a neutral oxygen vacancy) localise on the 2 ...
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2answers
89 views

Value of a discontinuous function at the discontinuity

Although this is a maths related question, it is important that the answer physically makes sense, so I'm posting it here. (Btw. the problem is related to stochastic thermodynamics, and I'm using ...
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3answers
41 views

Does the set of the degenerated eigenfunctions of hamiltonian forms a subspace?

I have read in a book that the set $\{ \Psi_{n}^{(\nu)} \in \mathcal{H} | \ \ \hat{H}\Psi_{n}^{(\nu)} = E_{n}\Psi_{n}^{(\nu)} \}$ (that is, the set of all eigenfunctions of the hamiltonian with the ...
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2answers
38 views

What is the definition of beam energy in particle physics?

For example, the proton beams in the LHC collider have 7 TeV energy. Does this mean that the individual protons in the beam have 7 TeV energy or that the energy of all the protons in the beam add up ...
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0answers
21 views

Confusions regarding macrostates and thermodynamic probability

I often came across completely different definitions of a macrostate, or at least they feel different. One of the definitions were supported by an example which I would like to state here: Suppose N=...
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0answers
48 views

Is Universal Law of Gravitation a 'law'? [duplicate]

My textbook mentions that the universal law of gravitation cannot be proved. If so, then why is it called a 'law' and not a 'hypothesis'?
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1answer
27 views

Magnetic flux density compard to other definition of flux

With regards to flux i have always assumed it was defined as $$(1) Something/m^2s$$ For instance $Luminosity/(4\pi r^2)$ Is an example of radiation flux. Why then is faradys law often cited as the ...
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3answers
108 views

Deep meaning of work integral formula [duplicate]

I want to understand very deeply the meaning of the work integral formula: $$ \int m\frac{d\bar{v}}{dt}d\bar{l} \, .$$ It is not enough for me to know that it was defined in this way, I want to know ...
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1answer
59 views

Why is the kinetic energy a fixpoint of the Legendre transformation?

Question: Why is (from an intuitive standpoint) the kinetic energy $T$ a fixpoint of the Legendre transformation, i.e. $\frac{\partial T}{\partial \dot q}\dot q-T = T$ for any general coordinate $q$? ...
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1answer
24 views

A question on the strong interaction and charm number

I know that the particle $P_c(4380)^+$, has quark content $\bar{c}cuud$. Furthermore I know that the reaction $K^-+P_c(4380)^+\rightarrow K^-+J/\psi+p$, is strong and the quark content on the left ...
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1answer
39 views

Why 2nd-order derivatives of $G$ are discontinuous in 2nd-order phase transition?

In most undergraduate books, it is said that for second order phase transition Gibbs free energy and its first order derivatives are continuous at transition temperature. But the second order ...
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2answers
116 views

Precise definition of the Hilbert space in QM?

In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
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0answers
31 views

Inner product axioms and Special Relativity

In Linear Algebra, an inner product is a function $(\cdot,\cdot): V \rightarrow F$ , where $V$ is a vector space over the field $F$. This function satisfies the usual three axioms (Conjugate symmetry, ...
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0answers
26 views

The Lagrangian and inertial reference frames [duplicate]

From my understanding, my instructor told me that in order to use the Lagrangian, defined as $$L \equiv T - V,$$ to find the equations of motion via the Euler-Lagrange equations, the generalized ...
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1answer
19 views

Luminostiy, Flux, Intensity definitions and meaning

I am taking astrophysics course and we are constantly talking about Luminosity,Brightness,Intensity,Flux etc. I thought that I understand the idea properly but I see now that I dont. Intensity is the ...
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1answer
60 views

Definition of Vector

In a book on General Relativity that I am reading, it defines a vector as an object or array of numbers that transforms like a vector (under rotations). I understand that under rotation $\theta$, a ...
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1answer
1k views

Why is the ratio of two extensive quantities always intensive?

Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
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1answer
46 views

What is the difference between linear and plane polarization?

What is the difference between linear and plane polarization?
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42 views

How to prove Caratheodory's Concept of temperature

Lenker T D . Caratheodory's concept of temperature[J]. Synthese, 1979 This is a discussion in the article: let $S_i$ be the state space of the thermodynamic system $\sum i = 1, 2, 3$, and assume ...
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3answers
36 views

Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
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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 ...
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68 views

What is the formal definition of energy in physics? [duplicate]

What is the formal definition of energy in physics? My question is what is the definition of energy in physics in general ? Moreover is energy a naturally occurring quantity or is a term defined in ...
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2answers
89 views

Field momentum of Klein-Gordon Lagrangian

Given the Lagrangian $L$ of the field $\phi$ the field momentum $\Pi$ reads: $$L_{KG}=-\frac{1}{2}\partial^\mu\phi\partial_\mu\phi-\frac{1}{2}m^2\phi^2$$ $$\Pi=\frac{\partial L}{\partial(\partial_\...
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2answers
91 views

Are $2$ and $1/2$ universal constants? [closed]

For example, if the equation for energy were: $$E = mc^{2.713397972993}$$ clearly $2.713397972993$ would be a universal constant. And in the Einstein field equation: $$R_{\mu \nu} - \tfrac{1}{2}R \...
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1answer
54 views

How do I know that I am observing a quasar?

When I find a faint object on the sky that looks like a star or a far away galaxy how do I know that it really is a quasar? I guess that I could first compare the apparent magnitude (how bright it ...
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5answers
179 views

Difference between voltage, electrical potential and potential difference

I am having hard time to visualize these two concepts in my mind seriously. First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from ...