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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 ...


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

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 ...


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 ...


3

Well, if you're wondering if people won't know what it is, or if you should be calling it something fancier: no. This and closely related notions are common language among physicists, much like "mass" and "force" are common language. A "right-handed triple" is a collection of three vectors in a particular order such that they obey the right-hand rule. A ...


3

It means that when the neutrinos hit electrons, the electrons are moving preferentially in the same directions that the neutrinos were moving. So when we are building a water Cherenkov detector for solar neutrinos, the Cherenkov signal will be coming from the direction of the sun. This is very advantageous to suppress background and because of the daily and ...


3

The object for which you need to find the electric field is a uniformly charged sphere. Uniformly charged means that at every point on the sphere the charge density is same. Suppose someone blind-folded you and then he rotated the sphere in some arbitrary fashion about the origin(assuming your sphere has origin as the center). Then he takes off the blind ...


3

It has to be an error. Rayleigh-Jeans theory fails at high frequency, but it's a good approximation for low frequency. Infrared catastrophe has nothing to do with the black body radiation problem. Only at high frequencies it was evident that Rayleigh-Jeans model failed. In the following plot you can see how at low frequencies (where infrared belongs), the ...


3

I know this is an old thread, but I had to figure this out for a problem on my physics homework. What helped me to understand this is to think about 2 objects on a spinning disk, one being close to the center of the disk and one being close to the outside of the disk. Angular (rotation) speed deals strictly with the angle. How long does each object take to ...


2

In 1969 Adler [https://inspirehep.net/record/55000] and, Bell & Jackiw [https://inspirehep.net/record/54998] showed that in the UV divergent triangle Feynman diagram made up of one axial and two vector currents, only the vector current is conserved, whereas the conservation law of the axial current is broken. Hence the names ABJ or chiral anomaly. ...


2

This is simply about words. A process can cause a change. For example: A (reversible) adiabatic process can cause a (reversible) temperature change.


1

Based on a quick read of the Wikipedia article on the kinetic theory of gases, it looks like you would need statistical mechanics to derive any of the results in the kinetic theory of gases. For example, the Maxwell distribution of velocities is typically derived using the canonical ensemble. However, the equilibrium velocity distribution is not a dynamical ...


1

A vector is a scalar with direction. So Time can be a vector, but what it means depends on the context. In 1D it has only 2 directions, positive and negative with zero being positive. In 2D it can be an angle between รท/-Pi radians. And so on. Time can be a single dimension attached to the familiar 3 Euclidian spacial dimensions and in this case it is ...


1

In the second law of Newton appears the acceleration $a$. It refers to a generic acceleration due to any phenomenon. $g$ has the same role of $a$, but it refers specifically to the acceleration of gravity (free fall particular case) on the Earth. Usually we approximate $g$ to be constant $\left(9.81\, \mathrm{m}/\mathrm{s}^2\right)$, but in the real case the ...


1

Newton devised a very good law of gravity (until Einstein came along) where the force between the two bodies is scaled by a very small number usually written as a capital G. It's a general law that applies to any two bodies. But if you plug in the mass of the earth, the mass of a test ball, and the distance between the center of earth and the test ball, then ...


1

The "unique" here is, IMO, not a good, evocative word. A better one would be preferred direction or privileged direction. Another way of looking at this is all directions are equivalent. A further confusing subtlety is that there is also something else that the author is assuming without telling you. There are no privileged directions for a problems with ...


1

I think one of the main reasons that you have velocity is to isolate a particular direction of movement from your forward speed. If you travel North north east, you can extract the speed at which you move eastwards by calculating your eastwards velocity (possibly 1/3 of your speed travelling NNE). Negative velocities probably arrived as a consequence of ...


1

WetSavannaAnimal's answer covers the geometry of the slits necessary to produce a clear pattern. Which properties does it have to have to be a slit and prevent an electron from passing through? These factors decide what material to use for the barrier/boundary of the slits: it's electron-stopping power primarily, which depends on the energy of the ...


1

Both operations are equivalent, up to a local phase in the second mode. In particular, if you shift the second basis vector's phase by $i$, then you will turn $H$ into $A$. In a beam splitter this is perfectly natural, because the phases of the output modes are not particularly well defined, and you can always model the difference between the two operations ...


1

A gauge field transforms in the adjoint of the gauge group, but not in the adjoint (or any other) representation of the group of gauge transformations. In detail: Let $G$ be the gauge group, and $\mathcal{G} = \{g : \mathcal{M} \to \mathcal{G} \vert g \text{ smooth}\}$ the group of all gauge transformations. A gauge field $A$ is a connection form on a ...



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