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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 ...


34

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 ...


17

The definition of a wave is not that it is the oscillation of a medium. Waves are called waves because they are solutions to a wave equation, which is, for a generic "excitation" $A(t,x)$ depending on the time $t$ and some spatial coordinate $x\in\mathbb{R}^n$, of the general form $$ \frac{\partial^2 A}{\partial t^2} = c^2\Delta A$$ where $\Delta$ is the ...


12

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.


10

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 ...


10

In addition to the other answers, back in the olden days they were thought of as oscillations in the ether. As a result of the Michelson-Morley experiment back in 1887, physicists began to think that there was no ether. But the term didn't change.


8

Suppose we have two Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$. A quantum state on $\mathcal{H}_A$ is a normalized, positive trace-class operator $\rho\in\mathcal{S}_1(\mathcal{H}_A)$. If $\mathcal{H}_A$ is finite dimensinal (i.e. $\mathbb{C}^n$), then a quantum state is just a positive semi-definite matrix with unit trace on this Hilbert space. ...


8

Electrostatic refers to the case where the fields are not time dependent. In that case the Maxwell's equations reduce to: $$\nabla \cdot E =\frac{\rho}{\epsilon_o} \\ \nabla \times E = 0 \implies E=-\nabla \phi \\ \text{then,} \nabla \cdot \nabla \phi = \nabla^2 \phi = -\frac{\rho}{\epsilon_o} $$ The solution to the last equation is: $$ \phi = ...


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 ...


7

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, ...


7

A paper came out this week pointing to them having a banal (if amusing) origin: they are from two 27 year old microwave ovens. When people get impatient and open the door before the timer runs down, a short burst from the ovens' magnetron is released, which appears as a peryton if the telescope is pointed in the right direction. Figure 7. shows the perytons ...


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

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 ...


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

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 ...


5

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 ...


5

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 \begin{equation} m \ddot{\vec{x}} = - \nabla U \end{equation} where $U = - G M m /r$. In a general coordinate system this is a ...


5

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 ...


5

I think the answer is no. It generally precedes some approximation method with a bounded error, but there are so many approximations methods in physics -- some rigorous, some nonrigorous -- that it's way too presumptuous to give it a rigorous definition. Generally, it means one of several things: If $a\ll b$, expanding in powers of $\frac{a}{b}$ is ...


5

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 ...


5

I have a feeling this has been answered before, but basically it is because H and He dominate the elemental abundances in the universe. When we look at what else there is we are guided by the elements we can ascertain are present in the photospheres of stars. It just so happens that the most prominent sgnatures are those due to atomic and ionic absorption ...


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) ...


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

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

There is no rule, and it depends on the context. If you're worried about things being very big, then zero is an OK value to have, and you'd count it as a finite quantity. In other situations, however, you are concerned about whether a quantity $q$ is exactly zero, or whether it is only a finite-precision approximation of it. Thus, you might say that "$q$ ...


5

Multiplying by $e^{i\theta}$ is a rotation of $\theta$ in the complex plane. Physically it changes the phase of a plane wave by an angle $\theta$. This is a global symmetry because we arbitrarily choose a reference point for measuring the phase of plane waves. If we change the phase of all plane waves by an equal amount then this is equivalent to just moving ...


5

Either. It's context dependent. Chemists generally mean the whole atoms, nuclear physicists usually mean the nucleus, and people not in those categories could mean either. And there are exception to all those rules or thumb. And the distinctions is important when people start throwing masses around because the mass of an electron is almost on the same ...



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