# Tag Info

56

Velocity is a vector. Speed is its magnitude. Position is a vector. Length (or distance) is its magnitude. A vector points in a direction in space. A negative vector (or more precisely "the negative of a vector") simply points the opposite way. If I drive from my home to my workplace (and then defining my positive direction in that way), then my velocity ...

44

The division is conventionally made at the boundary between where stars end their lives as white dwarf stars and where more massive stars will end their lives in core collapse supernovae. The boundary is set both empirically, by observations of white dwarfs in star clusters, where their initial masses can be estimated, and also using theoretical models. ...

35

There is a consistent definition, but it involves a couple of arbitrary thresholds, so I doubt you'd consider it rigorous. The construction $X \gg Y$ means that the ratio $\frac{Y}{X}$ is small enough that subleading terms in the series expansion for $f\bigl(\frac{Y}{X}\bigr) - f(0)$ can be neglected, where $f$ is some relevant function involved in the ...

26

Our physics prof once put it informally that way: A state is a set of variables describing a system which does not include anything about its history. The set of variables (position, velocity vector) describes the state of a point mass in classical mechanics, while the path how the point mass got from point $A$ to point $B$ is not a state.

23

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...

22

The definition of a state of a system, in physics, strongly depends on the area of physics one is dealing with and it comes as one of the initial definitions once such underlying theory has to be set up. In particular one has: classical mechanics: a state of a system is a point $m\in TQ$ (or equivalently $T^*Q)$ in the tangent bundle of the configuration ...

13

A c-number basically means 'classical' number, which is basically any quantity which is not a quantum operator which acts on elements of the Hilbert space of states of a quantum system. It is meant to distinguish from q-numbers, or 'quantum' numbers, which are quantum operators. See http://wikipedia.org/wiki/C-number and the reference therein.

11

Informally speaking, a complete description of a physical system is referred to as its state. Completeness of the state of a system means that it provides all the possible information about the system, i.e. everything that can be possibly known about the system has to be contained in the specification of its state. Every physical theory is ultimately based ...

11

Different people have different definitions of dynamical phase transition. At present, a widely accepted one is by Heyl et al. See their original paper Dynamical Quantum Phase Transitions in the Transverse Field Ising Model. Basically, it means some quantity (e.g., the fidelity) as a function of time is non-analytical at some critical times. See the cusps ...

9

Your question is not specific to inflation, and really applies to any case where a bosonic quantum field behaves semiclassically due to macroscopically large occupation numbers. One very simple example of this is the Stark effect in quantum mechanics, where a Hyrodgen atom is placed in a uniform electric field. The atom is treated as a quantum mechanical ...

8

A resonance (in the particle physics or related physics sense) and an unstable particle is exactly the same thing. The object has some complex mass and the imaginary part determines the decay width (and decay rate). But these two terms describe different aspects of the same thing. "A particle" refers to the object, the particle species (in your URL's case, ...

8

In a very mathematical sense, more often than not a mode refers to an eigenvector of a linear equation. Consider the coupled springs problem $$\frac{d}{dt^2} \left[ \begin{array}{cc} x_1 \\ x_2 \end{array} \right] =\left[ \begin{array}{cc} - 2 \omega_0^2 & \omega_0^2 \\ \omega_0^2 & - \omega_0^2 \end{array} \right] \left[ \begin{array}{cc} x_1 \\ x_2 ... 8 Of course the name implies that time is involved somehow. People talk about dynamical thermal and quantum phase transitions and in one case you will rapidly change temperature, while in the other state defining parameter (say pressure or field etc.). We will consider thermal PT. Now what does it mean rapidly? Let us consider 2-d order phase transition as ... 8 Roughly, an additive quantum number is the log of a corresponding multiplicative quantum number. Mathematically, this comes from the difference between the representations of a group and a Lie algebra; in the former, the natural operation is multiplication and in the latter it is addition. Many quantum numbers we care about come from continuous symmetry ... 8 A Hilbert space \cal H is complete which means that every Cauchy sequence of vectors admits a limit in the space itself. Under this hypothesis there exist Hilbert bases also known as complete orthonormal systems of vectors in \cal H. A set of vectors \{\psi_i\}_{i\in I}\subset \cal H is called an orthonormal system if \langle \psi_i |\psi_j \rangle ... 7 From the math point of view, you cannot have “negative velocity” in itself, only “negative velocity in a given direction”. The velocity is a 3-dimension vector, there is no such thing as a positive or negative 3D vector. However, if you consider the velocity in direction \mathrm{x}, where \hat{\mathbf{e}}_{\mathrm{x}} is some ... 7 Kinetic energy of two free particles is additive: the total energy is just the sum of the individual energies:$$ K=K_1+K_2 $$Another example is charge: the charge of a multiparticle system is the sum of the individual charges. Parity is multiplicative: the parity of a two-particle system is the product of the parities of the inidividual particles:$$ ...

6

Hertz should be understood to mean "periodic events per second". I your case the events are the display of frames, so yes, you would be perfectly justified in using $\mathrm{Hz}$. That said, as several commenters have already mentioned, the unit "Hertz" does not specify what kind of periodic behavior is being counted. So the author(s) or speaker must make ...

6

To fill out Mew's comment further: A slit is a gap wide enough for the electron to pass through True, but for the purposes of a clear discussion of double slit interference, we need the following further quality: a slit should be such that there is much less than a wavelength difference between the pathlength of all paths through the putative "slit" to ...

6

I agree with your definition of locality (probably not surprising :)). Causality I would say is the statement that an event in the future should not affect an event in the past. We can formulate this in classical physics terms. Causality is necessary in order for there to be a well defined initial value problem: I should be able to choose an initial time ...

6

It isn't necessary to introduce the effective potential in orbital mechanics but it is really useful. Let's say we have a particle moving in a central gravitational potential. Newton's laws give you a vector equation of motion $$m \ddot{\vec{x}} = - \nabla U$$ where $U = - G M m /r$. In a general coordinate system this is a ...

6

Revolving around the sun is equivalent to free fall around the sun, so the revolution allows you not to 'feel' the sun's gravity. The rotation of the earth is something that can be measured: (i) a centrifugal force which is a small offset on gravity, and (ii) causes the coriolis force. Both these are small effects, so can often be ignored for laboratory ...

6

The term c-number is used informally in the way Meer Ashwinkumar describes. As far as I know, it doesn't have a widely promulgated formal definition. However, there is a formal definition for c-number that agrees with the way the term is used in many cases, including the case you're asking about. As you may know, you can think of the operator formalism for ...

6

In relativity (both special and general) one of the key quantities is the proper length given by: $$ds^2 = g_{\alpha\beta}dx^\alpha dx^\beta \tag{1}$$ where $g_{\alpha\beta}$ is the metric tensor. The physical significance of this is that if we have a small displacement in spacetime $(dx^0, dx^1, dx^2, dx^3)$ then $ds$ is the total distance moved. You ...

6

For any operator $\hat A$ an eigenstate $|\psi\rangle$ is one for which: $$\hat A|\psi\rangle=\lambda |\psi\rangle$$ Where $\lambda$ is a constant, and is called the eigenvalue of that state. If $\hat A$ is an observable, then $\lambda$ will be real. A stationary state is an eigenstate of the Hamiltionain $\hat H$ (the energy operator). It is called ...

6

The effective in effective action has nothing to do with the effective in effective field theory. An effective field theory is a low-energy theory (described by some action $S_{eff}$ and cut-off $\Lambda_{eff}$) of some given higher energy theory (with action $S$ and cut-off $\Lambda\gg\Lambda_{eff}$). The effective action $\Gamma$, which is sometimes ...

6

Like Wikipedia says: "Moment is a combination of a physical quantity and a distance." This 'physical quantity' could be various things. To take the examples you mention: Moment of momentum (commonly known as angular momentum) is expressed as $\vec{L}=\vec{r}\times m\vec{v}$, and is a measure for the rotational momentum of an object around some axis. Moment ...

5

The Osher paper does define what a weak solution is. We seek a solution $w$ of $x$ and $t$ such that $$\partial_t w + \partial_x f(w) = 0$$ for a known function $f$ (the flux function), given initial conditions $$w(x,0) = w_0(x)$$ for known $w_0$, for $-\infty < x < \infty$ and $0 < t < \infty$. A weak solution is a bounded measurable ...

5

I was taught that the Standard Model was a misnomer; that it ought to be called the Standard Theory. I'm inclined to agree, though theories and models are both indispensable in science. Ultimately, the purpose of a model is provide local understanding of a particular phenomena. A model: Typically considers only fields, objects or quantities relevant to a ...

5

A theory is a set of statements that is developed through a process of continued abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. A model, on the other hand, is a purposeful representation of reality. As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) ...

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