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28

This is actually a very tricky question, mathematically. Physicists may think this question to be trivial. But it takes me one hour in a math summer school to explain the notion of gapped Hamiltonian. To see why it is tricky, let us consider the following statements. Any physical system have a finite number of degrees of freedom (assuming the universe is ...


24

Pluto is now classified as a dwarf planet. The main difference between a planet and a dwarf planet has to do with the requirement that a planet clear out the material in and near its orbit. Planets do this, dwarf planets do not. The reclassification was triggered by the discovery of many additional object (the Edgeworth-Kuiper Belt) out beyond the orbit ...


23

Depends on what you mean by 'central force'. If your central force is of the form ${\vec F} = f(r){\hat r}$ (the force points radially inward/outward and its magnitude depends only on the distance from the center), then it is easy to show that $\phi = - \int dr f(r)$ is a potential field for the force and generates the force. This is usually what I see ...


19

Using the distance between the Sun and the Earth, at least for distances within the Solar system, just gives a better feel for the scales involved. You can't really imagine a distance of, say, 1000000000 kilometers -- or at least I can't. (I deliberately didn't include commas in that number, to illustrate the point.) But using a concrete physical distance ...


18

Officially, no -- but there is a weak case to be made that the Moon orbits the Sun rather than the Earth. If you trace the Moon's path in a Sun-centric frame of reference, that path is completely convex. Quoting this Wikipedia article: Unlike most other moons in the Solar System, the trajectory of the Moon is very similar to that of its planet. The ...


16

A second-order tensor can be represented by a matrix, just as a first-order tensor can be represented by an array. But there is more to the tensor than just its arrangement of components; we also need to include how the array transforms upon a change of basis. So tensor is an n-dimensional array satisfying a particular transformation law. So, yes, a ...


16

The main distinction you want to make is between the Green function and the kernel. (I prefer the terminology "Green function" without the 's. Imagine a different name, say, Feynman. People would definitely say the Feynman function, not the Feynman's function. But I digress...) Start with a differential operator, call it $L$. E.g., in the case of ...


16

The constellations are the 88 internationally recognized stellar groupings in the sky that toghether cover the entire celestial sphere. They typcially correspond to a recognziable pattern and many are named from mythology. However, in modern usage, a specified constellation tecnically referres to the entire region of the sky, not just the recognizable star ...


15

It is important to remember that words like this get used in spit-balling sessions and then stick. You have to think of a couple of guy sitting by a black board, coffee in hand saying something like OK, OK! SO that doesn't work. But what if we assume these things come in three flavors and ... It's just a word made up on the spot. That said, I think ...


15

One Celsius (or Kelvin) degree as a temperature difference was defined as 1/100 of the temperature difference between the freezing point of water and boiling point of water. We call these points 0 °C and 100 °C, respectively. The number 100 arose because we're used to numbers that are powers of ten because we use the base-ten system. The Celsius degree is ...


14

Charge is a fundamental conserved property of particles. It is, if you like, a measure of how much a particle interacts with electromagnetic fields. A particle with charge can produce and be affected by electromagnetic fields. This is what we mean when we say a particle has charge. Its a simple quantised way to measure the coupling strength of particles with ...


13

As there wasn't a formal definition of a planet until recently, there still isn't one for a moon. But, a few guidelines: It should be in an orbit which is cleared of other objects, that is, not a bunch of objects in the same or very similar orbit. The typical minimum size for consideration is around a km. There is a smaller class known as moonlets that are ...


13

The mass, strictly the inertial mass, relates the acceleration of a body to the applied force via Newton's law: $$ F = ma $$ So if you apply a force of 1 Newton to a mass of 1kg it will accelerate at 1m/s$^2$. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. The weight is the force a body exerts when ...


12

Matrices are often first introduced to students to represent linear transformations taking vectors from $\mathbb{R}^n$ and mapping them to vectors in $\mathbb{R}^m$. A given linear transformation may be represented by infinitely many different matrices depending on the basis vectors chosen for $\mathbb{R}^n$ and $\mathbb{R}^m$, and a well-defined ...


11

Potential is a special case of a more general construction in differential geometry. Let's start abstractly and we'll get to the potentials again at the end. Differential forms The framework of differential forms provides a basis for integration on arbitrary manifold. Differential $p$-forms are totally antisymmetric covariant $p$-tensors. What's special ...


11

What I've been telling the students in the intro mechanics class I TA is that each force corresponds to some amount of work. The individual contributions of work add up to the net (or total) work, just as the individual forces add up to the net force. So, for instance, when you lift a box up from the floor to a table, there are two forces acting on that ...


11

It's because the Kelvin scale was and still is defined so that as a measure of temperature difference, one kelvin exactly coincides with one Celsius degree. So the temperature in kelvins was defined as the temperature in Celsius degrees minus $A$ where $A=273.15$ °C is the temperature of the absolute zero, without any additional multiplicative factor. When ...


10

I don't think the situation you mentioned is possible. You're describing two planets, each of which being in each others L3 points (a lagrangian point is a point in an orbit with special gravitational properties, where an object will remain somewhat stationary relative to the body whose orbit it's in). Even our comparatively tiny spacecraft which sit in ...


10

Indeed most examples of unambiguously labeling chiral states fall back on having another pre-labeled chiral object on hand. For a long time it seemed as though "left" and "right" were entirely interchangeable labels. This symmetry is known as parity. However it turns out there is a way to distinguish left from right in a fundamental way; parity is not ...


9

In general, quantum numbers are labels of irreducible representations of the relevant symmetry group, not primarily eigenvalues of an otherwise simply defined operator. But for every label that has a meaningful numerical value in every irreducible representation, one can define a Hermitian operator having it as an eigenvalue, simply by defining it as the ...


8

In general usage, "sound" refers to our perception of the vibrations of particles (atoms, molecules) in some medium, typically air or water, though sound waves can travel through any medium. Vibrations are produced whenever objects cause the particles in the medium to oscillate, e.g. clapping your hands together, beating a drum, or yelling. Sound can ...


8

I found a general, qualitative answer in David Blackstock's book Physical Acoustics, on page 46: Impedance is often described as the ratio of a "push" variable $q_p$ (such as voltage or pressure) to a corresponding "flow" variable $q_f$ (such as current or particle velocity). I also received a nice answer to this question on another Q&A site ...


8

Physics studies many other things than just atoms, electrons, and molecules. (For example, it also studies light, gravitational and electromagnetic waves, black holes, expansion of the Universe, heat, other elementary particles such as W/Z gauge bosons or Higgs bosons, and lots of other things.) Or to say the least, it studies other aspects of matter than ...


8

The kilogram is defined by a prototype (the "International Prototype Kilogram", IPK) -- basically, a kilogram is by definition the mass of a metal cylinder sitting in a vault in Paris. People have made a bunch of other metal blocks with almost exactly the same mass (as near as they could get), called "sister copies". To measure a mass extremely accurately in ...


8

Yes of course, According to physics the Mass and Weight are different from each other. Following is their main difference, Mass: Mass is the amount of matter contained in a body. Mass of the body is the constant quantity and does not change with the change of position or location. Weight: Weight is the force by which the earth attracts a body toward ...


7

To name an simple example, a 1D simple gravity pendulum with Lagrangian $$L(\theta,\dot{\theta}) = \frac{m}{2}\ell^2 \dot{\theta}^2 + mg\ell\cos(\theta)$$ has one degree of freedom (d.o.f.), $\theta$, although its solution $\theta=\theta(t)$ has two integration constants. Here, $\theta$ is the angle of the pendulum; $\dot{\theta}$ is the (angular) ...


7

If a system S is composed of two subsystems A and B, then a state of S is a vector $$|\Psi\rangle \in H_A\otimes H_B$$ Tracing over the "B degrees of freedom" allows you to define the reduced density matrix $\rho_A$ The entanglement entropy is defined as$$-Tr(\rho_Aln\rho_A)$$ I believe that the entanglement spectrum just refers to the spectrum of ...



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