0
votes
1answer
114 views

How to discover the $F = m\cdot a$ equation from scratch? [duplicate]

Is there a paper or a book that conceptually 'discover' the Newton's famous formula? I've been thinking about this equation, and I really don't know it for sure. Did Newton empirically noticed that ...
3
votes
0answers
550 views

LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} ...
2
votes
0answers
81 views

How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
6
votes
2answers
122 views

Why is the Hubbard model written down so late?

It is just the tight binding model plus on-site interaction. What prevented people from arriving at the Hubbard model?
2
votes
2answers
295 views

What would be walking speed in low gravity?

In $1g$ the average adult human walks 4-5 km in an hour. How fast would such a human walk in a low gravity environment such as on the Moon $(0.17g)$ or Titan $(0.14g)$? Let's ignore the effects of ...
3
votes
0answers
171 views

Derivation of the Noether current

(c.f Di Francesco et al, Conformal Field Theory, pp40-41) I am trying to derive eqn (2.142) or $\delta S = \int d^d x \partial_{\mu}j^{\mu}_a \omega_a$ in the book CFT by Di Francesco et al. I have ...
1
vote
2answers
454 views

Why are carbon nanotubes are so difficult to create?

I have heard that the future of the techonolgy are the carbon nanotubes due to their resistance and conductivity, but why are they so difficult to create?
1
vote
1answer
245 views

Work done in pulling a rope from a boat

A boy sitting on a boat pulls on a rope with a constant force $F$ over a duration of time $t$. The other end of the rope is either tied to a bridge or to another freely floating boat of equal mass. ...
7
votes
1answer
295 views

E&M and geometry - a historical perspective

Recently, I was contemplating the beautiful formulation of electromagnetism (specifically Maxwell's equations) in terms of differential forms: $$F=\mathrm{d} A\implies \mathrm{d}F=0 ...
1
vote
0answers
37 views

Association of financial phenomena/indications with the conservation laws of Black Scholes equation

For a while I've been doing research on methods of obtaining conservation laws via the symmetries of differential equations (DEs). I'm presently doing research on identifying financial ...
14
votes
6answers
1k views

Why must a singularity form inside a black hole? [duplicate]

What is the exact reason that normal matter can not exist within an event horizon? I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less ...
1
vote
0answers
45 views

Dipole charge attractions while one of them is turning around other [closed]

There is a electric dipole which is fixed. So angular momentum isn't conserved. And there is charge $Q$ which has initial velocity $u$. My question is: What is the tangential velocity of the charge ...
2
votes
1answer
62 views

What's the critical temperature of the XY model on a triangular lattice

I've been looking deeply into many bibliographic references without finding the answer. I would be interested in knowing the numerical value of the critical 2d XY spin model on triangular lattice. ...
2
votes
1answer
276 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
58
votes
8answers
7k views

Will a blanket warm you if you are underwater?

Suppose a man falls into very cold water and gets their foot stuck under a heavy rock. Fortunately, his head is above water and someone is able to call for help. The paramedics want to keep him warm ...
0
votes
1answer
441 views

Electromagnetic radiation and black body radiation

I was taught today that the Electromagnetic wave Theory is unable to explain black body radiation. The example that was given to me: When a metal is heated, it emits different frequencies of light as ...
3
votes
2answers
87 views

What is different in representation?

I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear ...
2
votes
1answer
315 views

Lagrangian depends on second derivative of field

In case of the gauge-fixed Faddeev-Popov Lagrangian: $$ \mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu ...
0
votes
1answer
61 views

About $\chi^2_\text{adjusted}$ [closed]

I am reading "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by J. R.Taylor", and I read the following formula in an exercise: ...
7
votes
3answers
726 views

Why is salt so hard to remove from water?

Water molecules and various salt molecules are very different. However, it seems very difficult to separate the two. Once a salt is dissolved in water, an energy or chemical intensive method (like ...
2
votes
2answers
150 views

Can a point source be located more accurately out-of-focus or in-focus?

Let's say I am taking a picture, and I know a priori that the image is of a single ideal point source of light at infinity. With a perfect imaging system in focus, the image shows an Airy disk. I ...
2
votes
1answer
57 views

what if the time is zero in one reference frame

Consider measuring the length of an object in another frame of reference. Of course this should happen at the same instance in the frame of reference the measurement takes place in. but using Lorentz ...
5
votes
2answers
911 views

What is the difference between surface plasmon and surface plasmon polariton?

I'm trying to understand this reading article linked below and I still don't know how to explain this simply, without need to derive everything mathematically. Can someone just write here how do SP's ...
8
votes
5answers
9k views

Black and white matters. But why and how?

I know black conducts heat while white reflects it. But they are colors after all. If a metal is painted black, it conducts more heat or at a rapid speed than it would do before it was coated. But, ...
4
votes
0answers
58 views

Is there a general H-theorem?

In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum ...
0
votes
0answers
105 views

Contact resistance copper-silver

I need to determine the contact resistance of a copper silver interface. The copper wire was soldered to the substrate using an IR-Laser. I was wondering if I can treat the entire system as a series ...
2
votes
0answers
24 views

Why do I have spin splitting at 5 and 7 at the quantum hall effect?

I just learned something about the quantum hall effect, and was wondering about the spin splitting at a filling factor of 5 and 7, i.e. I have nearly equal sized plateaus for the filling factor of 2, ...
7
votes
0answers
187 views

Role of physics in the zeta function $\zeta$ and the Riemann hypothesis

Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the ...
1
vote
0answers
35 views

regarding vertex function and proton scattering

I am currently going through electromagnetic form factor. I came across the fact that since the proton is not an elementary particle its scattering(elastic) with electron can be modeled using general ...
0
votes
2answers
229 views

If magnets exert greater force on heavier objects, why is it possible to separate magnets from very heavy objects?

I was thinking of the question "Do magnets exert more force on heavier (more massive) objects?" I would think the answer is "yes", because for example if you have a magnet and 2 paperclips, they will ...
2
votes
2answers
131 views

Non-additivity of energy (thermodynamics)

In page 15, Chapter 1 (Laws of Thermodynamics) of the book "An Introduction to the Study of Stellar Structure" by Nobel laureate S. Chandrasekhar, it is mentioned (in context of total energy of two ...
1
vote
0answers
172 views

Numeric value of the electrons drift velocity in superconductors

Somebody knows the numeric value of electrons drift velocity in superconductors? How this value depends from the used superconductor material? What's about the current? Since the electrical resistance ...
3
votes
1answer
66 views

Frequency-averaged (gray) radiative transfer

The equation for radiative transfer is $$ \omega \cdot \nabla I = \kappa(B - I) $$ where $I$ is the intensity of radiation, $\omega$ is the ray direction, $\kappa$ the absorption coefficient, $B$ the ...
2
votes
4answers
147 views

How units were defined?

I was wondering how we humans can be sure that one meter is one meter and that one second is one second. Nowadays, except for the Kilogram, all other units are well defined using highly accurate ...
1
vote
0answers
51 views

Why is more angular momentum required to stabilize the orientation of a heavier bullet?

It's often stated that "heavier" bullets require more "spin" to stabilize vs. "lighter" ones. My question is whether this is really a matter of mass. I'm assuming that the destabilizing ...
2
votes
0answers
147 views

Capillary action column height in a tube fitted inside another tube?

I was thinking about how would capillary action change in a tube (classic example) and in a tube fitted inside another tube (considering water as the liquid involved). Height of liquid column: ...
2
votes
1answer
224 views

Determinant of ray transfer matrix

Quick question on the wikipedia entry for the ray transfer matrix, which is defined : where $x$ is the distance of a point from the optical axis and $\theta$ the angle that the beam profile at that ...
1
vote
1answer
48 views

Effects of firing shells on the Earth's angular momentum

During a certain war, millions of shells were fired by country A towards the west, and even more shells were fired back by country B towards the east. The average momentum of each bullet were the same ...
0
votes
1answer
83 views

Ideal gas and inelastic collisions

Why is it necessary that all inter-molecular collisions in an ideal gas be elastic? My understanding is that a gas behaves ideally so long as the potential energy arising from inter-molecular ...
1
vote
0answers
289 views

A question on an exercise from Gravitation by Misner, Thorne and Wheeler

My question is on problem 4.1 of Gravitation. In a generic case of electric field and magnetic field(i.e not $E=0$ or $B=0$ or $E$ and $B$ perpendicular), define the direction $\hat{n}$ unit vector , ...
2
votes
2answers
140 views

Energy definition in special relativity

I'm going through the early homework assignments for my special relativity course and I've got myself a little confused about energy. I've got a basic understanding of what the 4-momentum is, having ...
2
votes
1answer
64 views

Converting Point Gradients to Rotational Representation

I'm a PhD student in an unrelated field. It's been a very long time since I've done physics, and I've run into a problem in my research which I think is actually a physics problem. Basically, I have ...
4
votes
1answer
198 views

Expressing an adjoint representation Wilson line in terms of the fundamental representation

I'm working out some calculations with Wilson lines, defined as path-ordered exponential integrals of a gauge field: $$U = \mathcal{P}\exp\biggl(ig\int_{-\infty}^{\infty}\mathrm{d}x^\mu T^c ...
3
votes
0answers
39 views

Existence and uniqueness of solutions to $\nabla^a T_{ab}$ in general (or special) relativity

The equation in the title of this question can be a relativistic analogue of the Navier-Stokes equation (in the sense that, in the low-velocity limit, it reduces to Euler's equation when $T_{ab}$ is ...
13
votes
1answer
272 views

Gravitational collapse of a photon cloud

The Schwarzschild solution shows that a spherically symmetric, static fluid will undergo gravitational collapse if too much mass-energy is concentrated together (i.e. if the fluid's radius is less ...
3
votes
2answers
3k views

Why does a mirror reverse polarization of circularly polarised light?

A glass mirror (with metal backing layer) will reverse the polarisation of circularly polarised light upon reflection. A polished piece of metal will also reverse the polarisation of circularly ...
1
vote
1answer
136 views

Specific Internal Energy Decreases with Increasing Pressure?

I was looking at "Properties of Compressed Liquid Water" (Table A-5) in Fundamentals of Engineering Thermodynamics by Moran. Table A-5 shows that the specific internal energy $u$ of compressed liquid ...
0
votes
1answer
650 views

Leg Press & Actual Lifted Weight [duplicate]

I was doing leg press at the gym today and was curious how much weight I actually lift when I do the exercise as compared to when I do a squat. Suppose I load $w_L$ onto the machine, which has an ...
9
votes
3answers
2k views

Why is the second the SI base unit for time?

Specifically, during the moves towards Le Système international d'unités in the 18th and 19th centuries, why didn't anyone attempt to move us away from the definition of there being 24 hours in a day? ...
3
votes
3answers
872 views

Why does water not evaporate in below 0 degrees?

I have learnt that, most objects still have energy in their atoms until the temperature reaches absolute zero. In other words, everything has energy around us. Now, that in mind if I go to antartica, ...

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