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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 ...

0

Current density is defined as electrical charge per unit time for a certain cross-section. Since a cross-section is a two-dimensional entity, it has to be $A / m^2$. In some cases it can be simplified to $A / m$.

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The one-particle density can be viewed as the localization probability of a particle in the system, with integration over all the state vectors except that of the single particle of interest. For example, suppose you are interested in the positions $\mathbf{x}_i$ of $N$ electrons in a many-electron system in which the $i$-th electron is in spin state ...

4

A null geodesic is a geodesic (that is: with respect to length extremal line in a manifold), whose tangent vector is a light-like vector everywhere on the geodesic (that is $x(s)$ is a geodesic and $g_{\mu\nu} \frac{dx^\mu}{ds}\frac{dx^\nu}{ds} = 0$ for all $s$, where $s$ is an affine parameter along the curve). The null geodesics are exactly the paths that ...

7

A null geodesic is the path that a massless particle, such as a photon, follows. That's why it's called null, it's interval (it's "distance" in 4 D spacetime) is equal to zero and it does not have a proper time associated with it. When they are drawn on a spacetime diagram, they are the edges of the light cones, as in the picture below, the lines at 45 ...

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From the definition of temperature from statistical physics and thermodynamics we have: $$P=T{\partial S(E,V,N) \over \partial V} |_{E,N}$$ where P is the pressure, T is the temperature, E is the energy of the system. So the temperature will have a negative value if 1)The derivative of entropy over volume change is negative, or 2)The absolute temperature ...

1

Your sources were probably trying to keep you from getting confused when they threw in a minus sign later. Typically you deal with a positive scalar pressure which doesn't have a direction. But like if you're doing a fluid mechanics problem and you've just calculated one pressure and you've got other areas of interest, say the other side of a divider, and ...

0

A conservative force is one where $$\nabla \times F = 0$$

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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

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 ...

0

Consider, lets say, a wire of cross sectional area $A$, with charges (each of the same magnitude, $q$) flowing through it. If you consider a section of the wire of some length $x$, the volume of this region would be $Ax$. Because $n$ is the no of charges per unit volume, the charge in this region would simply be $q(nAx)$ ($nAx$ is the number of charged ...

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Current is defined as the rate at which charge flows through a given surface: $$I=\frac{\mathrm{d}Q}{\mathrm{d}t}$$ and in a circuit this surface is any cross-sectional area (perpendicular to the flow). You can often simplify that to charge through a cross-section per unit time and write $I=\frac{Q}{t}$ Answer to the comment: Another but equivalent way ...

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It's the amount of charge flowing through a surface per unit time.

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I think you are confused between gravitational CONSTANT g, and gravitational acceleration a which can be thought of as a VARIABLE. Gravitation acceleration g is around 9.81m/s^2 near sea level. But as you go higher the gravitational acceleration is no longer g, but another number, let's say a. a is a more generic gravitational acceleration that is not ...

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If $\vec{F}$ is a conservative force field, then it satisfies the property $$\tag{1} \vec{\nabla} \times \vec{F} = 0,$$ and it can be written as $$\tag{2} \vec{F} = \vec{\nabla}V,$$ for a scalar function $V$ (which corresponds to potential function in physics). Note that, when you put $(2)$ into $(1)$ it becomes a "curl of a gradient" and is ...

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Using the anti-simmetry of the two first indices of the Riemann tensor and the fact that $x^a y_a = x_a y^a$.

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