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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 ...


12

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

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. RG: Curved Space-time (non trivial and dynamic metric tensor), theory of gravitation, generic coordinates ...


9

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 ...


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

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 ...


6

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, ...


5

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 ...


4

It is a "crank and slider" or "slider-crank" mechanism.


4

The Standard Model includes 12 elementary known as fermions that respect the Pauli exclusion principle. They include six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino) (ref) All leptons are fermions, but not all fermions are leptons.


4

The word 'Physics' comes from the Greek Word for 'Nature' (written as 'φύση'). From Google: 'etymology of physics' physics - ˈfɪzɪks noun: physics the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, ...


4

The other answers are correct. I would like to add to them with an example. Take a spring, with spring constank $k$, with a mass, $m$, at one end and fixed to a large immovable object at the other. Let the only force acting on the mass be due to the spring and the difference from the equilibrium position to be $x$, which can be positive and negative. This ...


3

We say "superposition" when we talk about the adding of the amplitudes of two waves. Typically it is called "interference" when this adding results in an different waveform (for example, regions with no signal - like the fringes in Young's slits experiment). However really all interference is superposition, and all superposition is a form of interference.


3

In special relativity the laws of physics are covariant under Poincaré transformation, whereas in general relativity the laws of physics are generally covariant, meaning that they take the same form under any smooth co-ordinate transformation. The Lorentz transformations are a special case of general transformations which is why we call them special and ...


3

The equation you gave is indeed the definition of matrix multiplication, applied to a $d\times d$ matrix and a $d\times 1$ matrix. But the underlying concept is something more. The thing about vectors is that they exist, in some sense, independent of the numbers used to represent them. For example, an ordinary 3D displacement vector represents a physical ...


2

Both $h$ and $\tilde{h}$ are usually called weights. Their sum, $\Delta=h+\tilde{h}$ is the (scaling) dimension of the operator, while the difference, $s=h-\tilde{h}$ is called the spin. This is due to their association with scale transformations (dilatations) and rotations, respectively. To see this, note that the dilatation operator is given by ...


2

Torque is not a force. You can say there is a torque caused by normal forces, but there is no special name for that. A normal force comes from acting with a force on an object resting next to a surface. The surface prevents the object from moving through it by producing a reaction force that is necessarily normal (perpendicular) to the surface (parallel ...


2

In the simplest sense of it, the Free Energy is the heat of the system minus the compulsory heat loss due to entropy. So, in short, it is the amount of "energy" left over in the system, after we consider losses due to entropy. So basically some amount of heat is wasted, and the remaining amount is useful. And this remaining amount is the Gibbs Free Energy. ...


2

There are two forces inluencing the spontaneity of a reaction: (1)The tendency of a system to attain a state of minimum energy and maximum orderedness, or stability. (2)The tendency of a system to attain a state of maximum energy and minimum orderedness , or entropy. If a system attains maximum stability, it attains mininum entropy; and if it attains ...


2

If you have different Hilbert spaces, you cannot say it is the same operator on them, since operators are defined on the Hilbert space. The momentum operator is a tricky one for many systems, and rigor requires the discussion of concepts like rigged Hilbert spaces. A nice introductory discussion of this is "Mathematical surprises and Dirac's formalism in ...


2

A fermion is just a particle of half-integer spin. Being a lepton for a particle is a matter of definition of global symmetries of the theory. This means that a lepton can in principle be both a fermion or a boson, although all known leptons are fermions (electron, muon, tau and their neutrinos). One example of bosonic lepton is the weak triplet Higgs ...


2

An electromagnet is an electromagnet. i.e.: a (insulated) wire wrapped around an iron core that produces an electromagnetic field when current is passed through it. A solonoid uses an electromagnet to perform a mechanical function.


2

The sling is not what makes it a trebuchet instead of a catapult. Catapults get energy from tension (usually torsion) and the arm hits a stop near the top of its arc to release the projectile. Trebuchets get their energy from gravity. The arm is off-center on an axle with the longer "launch" end (with or without a sling) holding the projectile and the ...


2

Interference is an effect of superposition. If you add two waves of close amplitudes, the interference picture will be the strongest. If one of the waves is of a much smaller amplitude, the resulting wave will be that of the highest amplitude, practically with no interference effect.


2

A multi-body problem consisting of $N$ objects requires $N$ coupled differential equations that need to be solved simultaneously (if you want to find the objects trajectories in time with known initial positions) When you solve $x + 2y = 3 \text{and} x + y = 2$, this is what is known as mathematical analysis. The exact solution can be found: $$x = 1, y = ...


2

The eigenvalue is something physicists should be familiar with. For some matrix, $A$, multiplied by some vector $\mathbf x$, we get $$ A\mathbf x=\lambda\mathbf x \tag{1} $$ where $\lambda$ is the eigenvalue, a characteristic of $A$ on $\mathbf x$. An eigenfunction is related to Equation (1). Given an operator (a differential operator in the case of quantum ...


1

This is a usual term about solving differential equations. By "analytic" (or mathematical analysis), we mean finding an algebraic expression like $y=f(t)$ which satisfy the desired differential equation. But sometimes we solve the equation only at some special points. The latter method is called "numerical". Since the Newton's law (and other principal ...


1

In quantum chemistry two-center integrals refer to exchange or coulomb integrals involving 1-electron atomic wave functions (orbitals) centered on two different atoms in a molecule. Say the coulomb repulsion between an electron described by an orbital belonging to atom A and another electron described by orbital belonging to atom B is given in a simplified ...


1

The statement that special relativity is valid locally is equivalent to general relativity. This was indeed Einstein's initial logic. He realised that every point in spacetime has a local inertial frame. In other words a falling man feels no gravity - gravity is a fictitious force based entirely on your reference frame! Originally special relativity was ...


1

"The Fabric of the Cosmos-Space, Time, and the Texture of Reality" by Brian Greene is the book which I read first to get introduced with GR and SR. Here is the brief passage to explain the general difference: In an empty unchanging universe-no stars, no planets, no anything at all-there is no gravity. And without gravity, spacetime is not warped-it ...



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