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If one of the rules to be a planet is that it needs to clear ALL objects from their orbit, does this also make Neptune a non-planet? This is a somewhat common misconception of the meaning of the term "clearing the neighborhood". None of the planets could be called "planets" if clearing ALL objects from the vicinity of the orbit was what that term meant. ...

8

Neptune actually is the dominant gravitational force in the region of the Kuiper belt in which Pluto resides. In fact, if you look at the image below, the belt is being cleared out by Neptune: In fact, there is a class of objects, suitably named the plutinos, that have been captured by Neptune. Solar system models have actually shown that Neptune was ...

6

The bound state is defined such that the probability density average will be finite at some particular space region when time passes. While for unbounded states, as time passes, the probability density will tends to zero. See Landau Quantum Mechanics section 10. This can be understand as this, if the state is bounded, i.e. it is exist only within some ...

5

The first bullet would be read "$A$ dot $B$" or "The dot product of $A$ and $B$" The second bullet would be read "$A$ cross $B$" or "The cross product of $A$ and $B$"

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The $\Delta$ is a quartet of particles with isospin 3/2: $$\Delta^-, \Delta^0, \Delta^+, \Delta^{++}$$ I would expect the anti-$\Delta$ to be written $\bar\Delta$, with the four isospin projections $$\bar\Delta^{--}, \bar\Delta^-, \bar\Delta^0, \bar\Delta^+$$ In this case the antiparticle of the $\Delta^+$ would be the $\bar\Delta^-$. If you'd like a ...

4

The question of mass has arguably been one of the two most important issues in physics (the other being the electromagnetism). Physics has tried to uncover the true nature of mass for hundreds of years, to no avail so far. Not surprisingly, its description is somewhat circular: “In physics, mass is a property of a physical body which determines the body's ...

4

Usually there's a great deal of overlap between the definitions of the momenta you've listed, so your confusion is understandable, but nonetheless there are cases (that I know of at least) where the distinction is more clearly enunciated: Momentum as known in Newtonian mechanics: The momentum is a vector quantity (its vectorial superposition for many ...

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We can't see in the heads of committee members, but to understand the tradition of "what for what" in Nobel prizes, I think it is instructive to see the chain of Nobel prizes awarded for developments connected to nuclear magnetic resonance (NMR). Here's a list. There were three prizes in Physics during 1943-1952, two prizes in Chemistry during 1991-2002 ...

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If you want to restrict the question to numerical quantities that have physical units, sometimes they are called "dimensionful quantities" in contrast to "dimensionless quantities" that have no units, see p. 6 of Introduction to Classical Mechanics by David Morin for an example of such usage.

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"To clear an orbit" has a specific meaning which may not entirely intuitive. "Clearing an orbit" specifically does not mean emptying an orbit of all other bodies. It means the planet gravitationally dominates other bodies at approximately the same distance to the sun. Now you can wonder perhaps whether Neptune dominates Pluto or Pluto dominates Neptune. ...

4

The concept of inertia is indeed useful in two ways. I think your notion of it as a technical promotion of the everyday word "sloth" (without the baggage given it by the Roman Catholic translation of the "deadly sin" Ἀκηδία) as extremely close to the mark. In physics the notion of "inertia" has two, very alike uses: The first is practical, through a weak ...

3

Since states which are not eigenstates of the Hamiltonian are also not eigenstates of the time evolution, it does not make sense to talk about "bound states" for these states, as they are continually changing into other states. For energy eigenstates, it makes sense to speak of "a bound state", since that state will stay the same forever unless acted upon.

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So I've done some further research into this question and the result I found is quite surprising. There truly is no set definition. Some cosmologists will tell you (as John Rennie mentioned) to avoid using the term "Big Bang" unless you absolutely have to. However, that is a luxury not afforded to all cosmologists. The more surprising thing is that among ...

3

Historical background I am posting an answer as it may be of interest to know the historical facts about the first law of motion. These can also represent a solid base on which to build an eventual answer to the opinions presented in the other posts. Aristotle interpreted the everyday-life experience of his time, which is absolutely valid also today: if ...

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This graphic on Things Made Thinkable uses the $\bar\Delta^-$ notation, which corroborates rob's prediction.

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Apparently it's a historical quirk. Characterizing spectral lines as principle, sharp, or diffuse dates back to the 1870s with the works of George Liveing and Sir James Dewar. Living and Dewar also noted that these lines appear in series. Arno Bergmann discovered a fourth series in 1907, which he labeled as the fundamental series. If Arnold Somerfeld had ...

2

Hopping and tunneling are often used as synonyms, but they are really very different terms with a fundamentally different basis. Tunneling is an inherently quantum-mechanical feature which means that a particle wave-function tends to overlap into it's energetically disallowed area which leads to a non-zero probability of finding it "where it should not be". ...

2

Bound states are usually understood to be square-integrable energy eigenstates; that is, wavefunctions $\psi(x)$ which satisfy $$\int_{-\infty}^\infty|\psi(x)|^2\text dx<\infty \quad\text{and}\quad \hat H \psi=E\psi.$$ This is typically used in comparison to continuum states, which will (formally) obey the eigenvalue equation $\hat H\psi=E\psi$, but ...

1

First of all, you wrote the equation for $U$ wrong; it should be $r$ instead of $r^2$ in the denominator. However, that typo isn't what the problem is. The problem is that you've overlooked the word "magnitude" in the question. If a negative number is changed to be a different negative number that's closer to zero, then the magnitude of the number has ...

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Strictly speaking the prefix semi means half, but it's often used in the sense of partial. A good example of this would be semiconductor. So semileptonic just means partially leptonic.

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To my mind, the Big Bang doesn’t refer to a distinct event but to a cosmogonic theory as a whole, that “predicts” ( should we say “retrodicts”?) many different events of the deep past. For example, there is such established term as “Big Bang nucleosynthesis” that describes an epoch several seconds past the Beginning of Time. The Beginning of Time in the ...

1

An internal symmetry only involves transformations on the fields of a theory, and must act the same independent of the point in spacetime. For example, consider a Lagrangian, $$\mathcal{L} = \partial_\mu \psi^\star \partial^\mu \psi - V(|\psi|^2)$$ for some potential $V$, and complex field $\psi$. The theory has an internal symmetry, namely one which ...

1

I think your confusion (like mine) is simply over technical English usage. As you rightly state "vectors look like passive elements on which the group matrices act, and do not contain the structure of the group". To my mind, a representation of a group is a triple $(\mathfrak{G},\,V,\,\rho:\mathfrak{G}\to GL(V))$: the group $\mathfrak{G}$ being ...

1

In mathematics, complex numbers and rotation are intimately related. After rotation $\theta$ in the complex plane, the number $1$ becomes $e^{i\theta}=\cos\theta + i\sin\theta$. Although $e^{i(2n\pi)} = 1 = \cos(0) + i\sin(0)$, you actually moved by $\theta$ and not by $0$. If you rotated something by $\pi$, you could say the angle is now $-\pi$ - but you ...

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So I think $\partial_\mu F$ should also be 4 vectors, each being the directional derivative along a coordinate axis. It's a single covector, not a vector and not a collection of vectors. A gradient of a scalar field is a classic example of how we obtain a covector. In index notation, a free index such as your $\mu$ is interpreted as having the potential ...

1

Other answers being good, i'll add 2 more cents here. Inertia as quoted in question (btw, this is nice, to see actual historical sources), is (defined as) the tendency of matter to continue in its current state, unless changed. This is inertia, the term "force of inertia" is just another way to state the same thing but using Newton's second law, $F=ma$, so ...

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Now that I have a better understanding of what you're asking, I think a good candidate would be "quantity value", also known as the "value of a quantity", from p. 28 of the International Vocabulary of Metrology, Basic and General Concepts and Associated Terms (VIM) by the Joint Committee for Guides in Metrology, online in pdf form here. I found this linked ...

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