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55

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 ...


23

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...


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 ...


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.


9

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 ...


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

The current mathematical formulation of Quantum Mechanics is based on the theory of Operator Algebras. The fundamental Axiom is that a mechanical system is described by a C*-algebra and the set of states is given by (a restriction of) the state space of the said C*-algebra. Hilbert spaces come into play from the representation theory of C*-algebras. Given a ...


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

"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

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 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

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

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 ...


6

In normal usage, a gauge is a particular choice, or specification, of vector and scalar potentials $\mathbf A$ and $\phi$ which will generate a given set of physical force fields $\mathbf E$ and $\mathbf B$. More specifically, a physical situation is specified by the electric and magnetic fields, $\mathbf E$ and $\mathbf B$. A set of potentials $\mathbf A$ ...


6

Why are states rays? (Answer to OP's 1. and 2.) One of the fundamental tenets of quantum mechanics is that states of a physical system correspond (not necessarily uniquely - this is what projective spaces in QM are all about!) to vectors in a Hilbert space $\mathcal{H}$, and that the Born rule gives the probability for a system in state $\lvert \psi ...


6

A paper came out this week pointing to them having a banal (if amusing) origin: they are from two 27 year old microwave ovens. When people get impatient and open the door before the timer runs down, a short burst from the ovens' magnetron is released, which appears as a peryton if the telescope is pointed in the right direction. Figure 7. shows the perytons ...


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 ...


6

A resonance (in the particle physics or related physics sense) and an unstable particle is exactly the same thing. The object has some complex mass and the imaginary part determines the decay width (and decay rate). But these two terms describe different aspects of the same thing. "A particle" refers to the object, the particle species (in your URL's case, ...



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