# Tag Info

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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 ...

30

Which year? The sidereal year? The tropical year? The anomalistic year? The calendar year (and whose calendar)? The sidereal year is the average amount of time it takes the Earth to make one complete orbit about the Sun with respect to the fixed stars. The tropical year is the amount of average amount of time between successive spring equinoxes. The ...

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 ...

15

A fermion is any particle, elementary or composite, that obeys Fermi-Dirac (as opposed to Bose-Einstein) statistics relating to how identical particles behave when you swap two of them. Due to an important but complicated result, this is taken to amount to having half-integer spin. A lepton is one type of elementary particle with spin 1/2. The only leptons ...

13

What is “special” and what is “general” in Relativity? The "special" in special relativity refers to the fact that it is not a universal theory. Predictions made by special relativity only apply under certain special circumstances. Those special circumstances are where gravitation is not present or can essentially be ignored. Initially I thought in ...

13

If I saw the word "amp" written as such in a paper in my field (astrophysics) it would strike me as a bit informal. I would expect to see the full "ampere" written. That said, it is rare to actually write out the full name of a unit; usually it follows a number and is given its standard abbreviation. When abbreviated to e.g. "$5\ \mathrm{A}$", I would ...

11

Technically, apparently, your teacher is correct. BIPM and NIST In the official brochure from the Bureau international des poids et mesures (BIPM, the keepers of SI units) in §5.1 Unit symbols we find: It is not permissible to use abbreviations for unit symbols or unit names, such as sec (for either s or second), sq. mm (for either mm2 or ...

11

SR: Flat Space-time (Minkowski metric), no gravity, Lorentz coordinates transformations (usually $\Lambda \in SO^+(3,1)$, the proper orthochronous Lorentz group). Acceleration is allowed, but you usually want to work with inertial frames. GR: Curved Space-time (non trivial and dynamic metric tensor), theory of gravitation, generic coordinates ...

11

First, you have system with some energy, named $U$ by physicists. You think you have all the information you need to characterize the system but then some guy comes near and says: "Whoa, that's bad, the volume of your system can change." You say: "No problem, we just add here $pV$. Our new energy is $H=U+pV$." "But hey," they say, "your temperature can ...

10

Short answer: Gibbs free energy $G = U + PV - TS$ combines internal energy $U$, pressure $P$, volume $V$, temperature $T$, and entropy $S$ into a single quantity that measures spontaneity. With that, I mean that processes that lower the Gibbs free energy of your system will spontaneously occur, and equilibrium is reached when the Gibbs free energy reaches ...

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.

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A fermion is any particle characterized by Fermi–Dirac statistics and obeying the Pauli exclusion principle. So for example quarks are fermions, as are Helium-3 atoms. A fermion does not have to be an elementary particle. I'm not even sure that it has to be spin $\tfrac{1}{2}$, though I can't think of any fermions that aren't. A lepton is a spin ...

9

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. ...

9

Below follows a handful of excerpts from the book Introduction to the Classical Theory of Particles and Fields (2007) by B. Kosyakov. Controversial/misleading/wrong statements are marked in $\color{Red}{\rm red}$. We agree with OP that the statements marked in $\color{Red}{\rm red}$ are opposite standard terminology/conventions. Some (not all) correct ...

9

The "shift in the meaning" refers to some attempts to reinterpret the terminology that were made by a metrological document, ISO 5725, in 2008. That may be described as a bureaucratic effort by a few officials – really bureaucrats of a sort – and as far as I know, the "shift in the meaning" hasn't penetrated to the community of professionals. The people ...

8

The Big Bang was originally defined as the zero time limit of the FLRW metric, so it's a mathematical construct and not primarily something physical. We have chosen to apply it to the zero time limit of the universe because we thought the FLRW metric was a good description of the universe, but then inflation gatecrashed the party and spoiled the fun. So if ...

8

Special relativity is physics in a $3+1$ dimensional Lorentzian spacetime, with the additional requirement that the spacetime is flat, which determines spacetime completely. General relativity is physics in a $3+1$ dimensional Lorentzian spacetime, with no additional geometric requirement. An equation for the metric is required to determine the spacetime, ...

8

OK I don't understand anything.when I placed my mobile phone on the ground, its accelerometer shows nine point something m/s^2. So is that the value of its acceleration? That is the value of the phone's proper acceleration. From the Wikipedia article "Proper acceleration": proper acceleration is the physical acceleration (i.e., measurable ...

7

what does memorylessness mean? Essentially, it means that the length of a rod and the rate of a clock depend on their current state only. The alternative would require that, e.g., two otherwise identical clocks at rest with respect to each other may run at different rates if their histories differed.

7

Sanaris's answer is a great, succinct list of what each term in the free energy expression stands for: I'm going to concentrate on the $T\,S$ term (which you likely find the most mysterious) and hopefully give a little more physical intuition. Let's also think of a chemical or other reaction, so that we can concretely talk about a system changing and thus ...

7

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 $B$"

7

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 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 $$⟨\psi|\hat A|\phi⟩=⟨\psi|\hat B|\phi⟩\tag2 ... 6 We use the term mass, when we mean the mass of a weight, and we use the term weight, when we mean the weight of a mass. :-) The important thing to remember is, that the mass is the same everywhere, while the weight varies with the local gravity. So if you are referring to the constant mass of an object, you use mass expressed in kg. If, however, you mean ... 6 The bound state is defined such that the probability density average will be finite at some particular space region when time passes. While for unbounded states, as time passes, the probability density will tends to zero. See Landau Quantum Mechanics section 10. This can be understand as this, if the state is bounded, i.e. it is exist only within some ... 6 The more common names for what you are talking about are the abbreviated action$$S_0[q] := \int p \mathrm{d}q$$versus the action$$ S[q] := \int_{t_1}^{t_2}L(q,\dot q,t)\mathrm{d}t$$Both are used in different formulations of classical mechanics, and deliver a different "flavor" of solutions. On both one can do variations calculus and obtains the ... 6 Microscopically, i.e. in the quantum theory the scattering with radiation is a collision of particles with photons such as$$ e^- + \gamma \to e^- + \gamma$$The momentum vectors of the particles above are$$ \vec p_1+\vec p_2= \vec p_3 + \vec p_4 where the identity holds due to momentum conservation. But in general $\vec p_1\neq \vec p_3$ and $\vec ... 6 I took a quick look at pages 59 and 60 of "Gravitation", section 2.6 "Gradients and Directional Derivatives", to see if there's anything there we can use to clarify this issue. In this section, the gradient of$f$is$\mathbf df$, the directional derivative along the vector$\mathbf v$is$\partial_{\mathbf v}f\$ and the following relationship holds: ...

6

"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. ...

6

In the sense of "Copenhagen Interpretation", what exactly is an interpretation? What purpose does an interpretation serve? I would describe interpretations of quantum mechanics as part of the philosophy of physics. Here is a well-known quote by Bertrand Russell: "As soon as definite knowledge concerning any subject becomes possible, this subject ceases ...

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