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6

The sort of trick involved in removing the $|P\rangle$ on both sides to get the conjugate imaginary equation $$\langle P|\xi|P\rangle = \langle P|a|P\rangle \tag1 $$ is quite common but it is indeed nontrivial to grasp the first time. In essence, you leverage the fact that in an equation of the form $$ ⟨\psi|\hat A|\phi⟩=⟨\psi|\hat B|\phi⟩\tag2 ...


5

Yes! Any beam that is blocked by an object will basically make a shadow. For example, the IceCube detector can see the moon's cosmic ray shadow.


4

We use the term mass, when we mean the mass of a weight, and we use the term weight, when we mean the weight of a mass. :-) The important thing to remember is, that the mass is the same everywhere, while the weight varies with the local gravity. So if you are referring to the constant mass of an object, you use mass expressed in kg. If, however, you mean ...


3

Hints: The action is $$\tag{A} S[y]:=\int_0^1 \! dt ~L(y,\dot{y}), \qquad L(y,\dot{y})~:=~\frac{m}{2}\dot{y}^2 -mgy, $$ with Dirichlet boundary conditions $$\tag{B} y(0)~=~0 \quad\text{and}\quad y(1)~=~-\frac{g}{2}. $$ Calculate explicitly the composed function $$\tag{C} s(\epsilon)~:=~ S[y_{\epsilon}] , $$ where $$\tag{D} ...


2

For example, acoustic shadow (http://en.wikipedia.org/wiki/Acoustic_shadow ).


2

If you care about the inertia you use "mass". When you are considering the force of gravity you use "weight". So when you do calculations about the force in the cables due to acceleration of an elevator car you need to know both it's mass and it's weight... The (calibrated) object you place on a scale is called a "weight" - because that is the property you ...


1

Yes, the term "shadow" can refer also to something or (dare I say) someone that is dark, shady, inconspicuous, etc. One can also use it as a verb; to shadow someone is to follow them closely. Like "I'm having the new guy shadow me for a while until he learns how to do everything".


1

1. No, there is no "shift in meaning". "Accuracy", "precision", and "trueness" is a technical term for measurement not physics. And there is no such thing as a "measurement community" because measurement occurs everywhere. As such, "accuracy", "precision", and "trueness" are heavily overloaded technical terms used in varying fields like maths, computer ...


1

SIS-100/ SIS-300 is an accelerator under construction for FAIR (Facility for Antiproton and Ion Research) in Darmstadt, Germany. see - http://cern.ch/AccelConf/e08/papers/mopc100.pdf I believe, but am not sure, that the -100 and -300 refers to the magnetic rigidity (i.e. Magnetic field * bending radius) of the accelerators, which determines the maximum ...


1

The SIS accelerators are heavy ion accelerators, and the German for heavy ion accelerator is SchwerIonenSynchrotron (my capitalisation), hence the abbreviation SIS. There is more info in this article.


1

Yes, for example a Crookes tube shows an electron shadow. The area I live (Chester, UK) is in a rain shadow.


1

Continuity equations are an embodiment of local conservation laws, and they both reflect the fact that there is no 'quantity teleportation'. That said, the local transport of a quantity is perfectly possible within local conservation laws and it is precisely this that the continuity equation models. Your distinction between global and local conservation ...


1

In the equation (i.e. mathematically), where do you see the differences between continuity equations and conservation laws? The continuity equation is not sufficient to derive conservation of something. For example, continuity equation for fluid flow in non-relativistic theory is $$ \partial_t \rho + \nabla \cdot (\rho \mathbf v) = 0 $$ wherer $\rho$ ...


1

The web site you link is using the expression: $$ \rho_c = \frac{3}{8\pi G \theta^2} $$ where $\theta$ is the Hubble time and is equal to $1/H$. So your second equation should be: $$ \rho_c = \frac{3}{8\pi G \theta^2} = \frac{3}{8\pi G \left(1/H\right)^2} = \frac{3H^2}{8\pi G} $$


1

The best way to understand the nature of intensive and extensive quantities in thermodynamics is like this: Take a system of your interest. Make it into two portions (one large portion and the other a small portion) by using a partition, for example. Then see the property of interest of the two samples. Density of the two portions will be the same as the ...


1

Here's a point of view from thermodynamics that might be useful. Typically, the intensive quantities (in the form they're usually defined) arise as derivatives of the total (internal) energy $U$ by some particular extensive quantity. Thus: Temperature $T=\frac{\partial U}{\partial S}$, the derivative with respect to the entropy Pressure $P=-\frac{\partial ...


1

I know that air pressure and temperature are inversely proportional. You should not know that. This is the source of your misunderstanding. The ideal gas law, $PV=nRT$, can be rewritten as $P=\frac R m \rho T$, where $m$ is the average mass of a molecule in the gas and $\rho$ is the density of the gas. The first term on the right is a constant for a ...



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