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I recently watched a lecture on dispersive medium. I understand that if you disregard the idea that a string is ideal, you must add a stiffness factor into the wave equation. From that you can derive the equation $$ω/k = v\sqrt{1 + αk^2}$$ where $v$ is the speed of propagation. As a result, it is obvious that the speed...
How does Fig. 26-3 (shown below) correspond to the following paragraph from this Feynman lecture? Finally, we give a very crude view of what actually happens, how the whole thing really works, from what we now believe is the correct, quantum-dynamically accurate viewpoint, but of course only qualitatively described. I...
I am a bit confused as to how we calculate Full-Width-Half-maxiumums (FWHM) of a function. Consider a function as $$f(x) = {\frac{\sin(ax/2)^2}{(ax/2)^2}} \cos(bx/2)^2 $$ where b>>a. It looks something like this: How would I deduce the FWHM of both the envelope as well as the FWHM of the enclosed fringe of such a fun...
In plank position, the body is not moving, but it still burns calories. Work is defined as force multiplied by distance ($Fd$). There is force, but no distance, so the energy should be $0$ ($F \times 0 = 0$), as anything multiplied by $0$ is $0$. Someone please explain how planking burns any calories.
If that is not the case, can someone please help me out in understanding the movement of the pulleys which is leading to a different ratio of acceleration?
Forgive me if what I’m asking is too naive for this site. I'm a math student who is recently studying electrodynamics and gauge theory myself. While I'm aware of the fact that QED can be realized as a $U(1)$ gauge theory, I don't know if I have a valid understanding of this statement. Let $A$ denote the electromagnetic...
Why do we have to inflate our tires to a set psi every once in a while? When we drive, does the tire loses air? Is it because of the difference in pressure? Would a properly installed new tire lose pressure over time? Or do we have to pump air due to poor installation?
They say celestial objects like Earth make a curve on spacetime due to their heavy mass. Well what about any object just above Earth? They do poses mass then they make a curve in spacetime. So, isn't Earth passing through the Spacetime of that object? Which means Spacetime is being holed by Earth. So is Spacetime multi...
I was doing some questions and reading a things in thermodynamics, when was asked to calc the Tension variation of a dependured wire when we varies the temperature, maintaining the length constant. In the end, i founded (and it was right) that $$\delta F = -YA \alpha \delta\theta$$ Where Y is the young module A is the ...
I just heard someone mention that photons take 40 thousand years to travel from the centre of the Sun to its surface which is roughly 700,000 kilometres. How is that possible if the speed of light/photons is 300,000 km/second?
Suppose we have a compact submanifold $K$ of $\mathbb{R}^3$ with uniformly distributed charge. Neglecting multiplicative constants, the electric potential $\Phi(\vec{x}) = \int_{K} \frac{dK}{|x - k|}$. (The type of integral depends on the dimension of $K$). For a small voltage level $R$, it is understood that the equi...
We have many theories that advocate the particle nature of light. But have we ever observed photons physically? If so: what do they look like? How big are they? If not: why not? Is it because they move at the speed of light?
What I do not understand is while balancing the torque, why the $\sigma_{11}$ is added to the product of $dx_{1}$ and the derivative of $\sigma_{11}$?
Are magnetic field and magnetic flux the same? I am confused because texts books are using these two terms interchangeably.
I know that while integrating dot product to two vector quantities along a line integral, the limits of the integration implicitly takes care of the direction in which we integrate from here and here. But would this be true in case of cross products? Would the limits of the line integral of a cross product implicitly t...
We know that the Schrödinger equation is $\hat H|\Psi\rangle=E|\Psi\rangle$. If we write the hamiltonian $\hat H$ as $\frac{\hat{p}^2}{2m}+V(x)$ and then use $\hat p=-i\hbar\partial _x $ we can write this equation in position basis as: $$\left [\nabla^2+\frac{2m}{\hbar^2}(E-V(x))\right ]\Psi(x)=0 \tag{1}$$ Now we can r...
I don't understand this diagram... the projection is meant to be a shadow, right? So shouldn't the shadow of the radial vector as shown in the circle on the y-axis, be the entire y-axis (since the radius is the same, everywhere)? Why is the projection shown to be smaller than the radius? For instance, let the origin b...
Shortsightedness is due to reduced focal length and long sightedness is due to increased focal length.howcan the focal length of eye lens change overtime?
I am now reading Weinberg quantum field theory volume 1. But the notations are almost impossible to read for me. I completed Griffiths elementary particles book and Srednicki quantum field theory. So I need some advanced book on standard model.
Why do flow of electrons generate current? whenever an electrons flows through a wire it generates electricity why does it actually happen?
Suppose something existed faster than light will we be able to perceive it? And even if we encounter it wouldn't seem to travel with speed of light?
In the page 74 of Batchelor's fluid mechanics book, it is given that Differentiation following the motion of the fluid It will be evident that in a steady flow field a material element of fluid may nevertheless experience acceleration through moving to a position where $\mathbf{u}$ has a different value. The derivativ...
In what way are the Casimir energy and Helmholtz free energy related / do they differ? In QFT one can compute the Helmholtz free energy as the vacuum expectation value of the zero point function. This seems to capture the same information as the Casimir energy.
In the derivation of pressure variation with depth in a fluid, we consider a hypothetical cylinder (or any convenient shape) and make a fbd for that shape. In the fbd , the forces included are $mg$ (where $m$ is the mass of the cylinder) The pressure difference force on the cross sections and finally we equalise them....
Here the Rate of change in Kinetic energy is not equal to the the power. Please explain
In the Feynman Lectures, he lays out how in special relativity, the mass is adjusted by a factor of $\sqrt{1 - v^2 / c^2}$ and then writes: For those who want to learn just enough about it so they can solve problems, that is all there is to the theory of relativity – it just changes Newton’s law by introducing a corre...
I am wondering what is an average intermolecular distance in liquid water (say under normal pressure and room temperature). I need just order of magnitude. A reference would be helpful.
The definition of "hedgehog" or instanton event here is "a space-time event where the skyrmion number Q changes by $\pm1$ is called a hedgehog" (ref.1 & 2). A nice figure illustrates such an instanton event is found in ref.3, where the initial configuration has non-zero skyrmion number, and the final configuration afte...
Considering the standard evolution for a generic quantum state $\psi(t)$, setting $\hbar=1$ we have: $$| \psi(t) \rangle = U |\psi(0) \rangle \hspace{5em} \text{where}\hspace{1em} U=\exp[-iH(t-t_0)] $$ it is known that in the basis of the eigenvectors it can be written as: $$| \psi(t) \rangle =\sum_{n}c_n \exp[-iE_n(t...
I have been stuck for hours now on this thing. While going through my thermodynamic lectures, I came across this: 'The entropy change for the system for an adiabatic irreversible process is always positive while that of the surroundings doesn't change.' Will someone please explain how that is true. PS: I'm not quite us...
So, I broke down the meaning of this equation and have got stuck at one point. I have not done rotational mechanics and have started with centre of mass newly .Getting a bit confused here with this new equation. Let us say say we have a bar if length L , Now take a small segment dx in it. We know mass per unit length ...
I mean this formula: $$\varepsilon ={\frac {h\nu }{2}}+{\frac {h\nu }{e^{h\nu /kT}-1}}$$ Is there full derivation somewhere?
Me and the boys can't explain the following construction: A capacitor with a hole in both plates is charged and an electron is accelerated in it. So the electrons potential energy should be converted in kinetic energy. Once the electron leaves the capacitor we ony use magnets to redirect the electron via the lorentzfor...
If $\hat{S}_{1}=i \int d^{d} x \mathcal{L}_{I}$ and $$ \begin{aligned} V\left(x_{1}, x_{2}, \ldots, x_{n}\right) & \equiv \int\left[\prod_{j=1}^{n} \frac{d k_{j}}{(2 \pi)^{d}}\right] e^{i k_{\mu}^{j} x_{j}^{\mu}} \exp \left(-\frac{i}{2} \sum_{i<j=1}^{n} k_{\mu}^{i} k_{\nu}^{j} \Theta^{\mu \nu}\right) \\ & \times(2 \pi)...
I am reading the book "Gravity in a nutshell" in which the author talks about rotation in a plane and different frames, one rotated with respect to the other. The rotated frame is denoted with a prime. We are trying to find the matrix relating the differences of coordinates in both frame. It is strange, he finds $$\be...
When looking at solutions of the Dirac equation people tend to give solutions as $$\psi^{(1)} = e^{\frac{-imc^2t}{\hbar}}\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix},\psi^{(2)} = e^{\frac{-imc^2t}{\hbar}}\begin{pmatrix}0\\1\\0\\0\\\end{pmatrix},\psi^{(3)} = e^{\frac{imc^2t}{\hbar}}\begin{pmatrix}0\\0\\1\\0\\\end{pmatrix},\...
In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed V. Pulleys A and B are fixed. What will be the velocity of Mass M? The answer is $\frac V {\cos\theta}$. I've seen the solution of this problem in many websites, and I understand the method. But my pr...
In 'Non-abelian Bosonization in Two Dimensions', Witten argues that the Poisson brackets of the currents that generate the $G\times G$ symmetry of the WZW model give rise to a Kac-Moody algebra upon canonical quantization. The Poisson brackets are calculated on page 465 to be \begin{equation} \begin{aligned} \left[X,...
The $\mathcal N = 1$ algebra \begin{equation} \{Q_\alpha,\overline Q_\beta\} = -2P_\mu\Gamma^\mu_{\alpha\beta} \end{equation} is in a frame where $k_1 = k_0$ \begin{equation} \{Q_\alpha, Q_\beta^\dagger\} = 2k^0(1 + 2S_0)_{\alpha\beta} \end{equation} or in $\bf s$ basis, \begin{equation} \{Q_{s_0',s_1'},Q^\dagger_{s_0...
AFAIK the photons inside a star essentially perform a random walk until they leave. Considering these factors: closer to the core the curvature of the sphere that seperates "closer to the core" from "further from the core" is higher, so initially a step in the random walk will be more likely to increase the distance f...
Many people with long hair tie their hair to ponytail-style: Closely observing the movement of their hair when they are running, I have noticed that the ponytail oscillates only horizontally, that is, in "left-right direction". Never I have seen movement in vertical "up-down" direction or the third direction (away-and...
1.What is the radius vector of a material point? 2.How is it related to the coordinates of a material point? Do I understand correctly, that the radius vector of some point $A$ is a vector drawn from the origin of a fixed coordinate system of some $O$ to some point $A$? How to answer the second question?
In the book Relativity, Gravitation and Cosmology by Ta-Pei Cheng, page 106-7, the Eddington-Finkelstein coordinate system is described as a coordinate system set up using a photon falling radially towards the gravitational source at the origin as the observer. It was then said that the null geodesic $ds^2=0$ in the E...
A small disc and a thin uniform rod of length $l$, whose mass is $\eta$ times greater than the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity $\vec{v}$, after which it elastically collides with the end of the rod. Find...
I have a question about canceling forces that my teacher gave me. I have sketched out the image in the question below. The grey bar on the mechanism below is anchored and the joints are shown in black. Will the forces provided by the springs on the mechanism cancel? If a 20N weight is placed on the hook, can it be move...
The Schwarzschild spacetime is described by $$ds^2=-(1-\frac{r^*}{r})c^2dt^2+(1-\frac{r^*}{r})^{-1}dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2,$$ where $r^*$ is the Schwarzschild radius. The advanced Eddington-Finkelstein (EF) coordinate system is a transformation of the Schwarschild coordinates $(t,r,\theta,\phi)$ wher...
If an observer moves in an accelerated frame in flat spacetime, the vacuum looks like a thermal distribution of particles to that observer. This is the Unruh effect. Is it a special relativistic (SR) effect or a general relativistic (GR) effect? On one hand, it's flat spacetime which seems that SR is enough. But then ...
The differential form of internal energy is the following $$dE = TdS - PdV + \mu dN$$ But I naively think that this is inconsistent. Because when I do the following calculation I found it different. $$E = W + Q$$ $$dE = dQ + dW$$ $$dE = TdS - PdV - VdP$$ So where does the other term come from? Furthermore how the last ...
Tipping the magnetisation $\vec{M}$ with a $\vec{B}_1$ field for the time $\tau$, results in a tip angle of $\alpha = \omega \tau$ where $\omega$ is the frequency of the $\vec{B}_1$ field. I think I am mixing up, something but I am not sure what. Where is the condition, that $\omega = \omega_0$ for tipping $\vec{M}$ in...
The car shown above with mass M is turning to the left with an uniform angular speed W on a circular path with radius R. When the angular speed is increased to a critical value C, one of the normal forces vanishes. If W is increased beyond C, the car will roll over, explain why. I did some calculations and found C = s...
So when we covered the derivation of a simple pendulum we , and from what ive found on the web, defined our free parameter as $q=L\theta$ and arrive at the Hamiltonian for a Harmonic oscillator. But we were also told that this is an arbitrary choice and that any other available parameter would work, such as momentum. ...
A projectile is fired horizontally from the top of a mountain of height 'h' at a very high velocity. The projectile almost completes one revolution around the earth and crash lands at the bottom of the mountain (coming from the opposite side after circling the earth). I know that if it was fired at the orbital velocity...
So i was reading the book "Basic Laws of electromagnetism" by I.E. Irodov and he states: $$\oint \mathbf{j}\cdot d\mathbf{s}=0$$ for a steady state/direct current (where $\mathbf{j}$ is the current density vector and $d\mathbf{s}$ is the area vector), since $-dq/dt= 0$ for a steady state current. But then he goes on to...
I have a soda bottle (consider no leaks) at room temperature and 55 psi. Oxygen is saturated in the water inside. After removing the cap, what law or formula can I use to estimate the time oxygen dissolved will take to un-dissolve and reach the saturation point at room temperature/pressure?
Let $X=x\partial_{t}+t\partial_{x}$ and $Y=y\partial_{t}+t\partial_{y}$ be Killing vectors on Minkowski $(-,+,+,+)$. It can be shown that $[X,Y]$ is also Killing. I get the following: \begin{equation} [X,Y]=(x-y)\partial_{t}+x\partial_{y}. \end{equation} What isometry is this Killing associated with?
I have a doubt about the formula of the kinetic energy of the rototranslatory motion \begin{align} K = \frac{1}{2}MV_{cm}^2 + \frac{1}{2}I_{cm} \omega^2, \end{align} does it come from Koenig's first theorem or from another proof? And if so, when should I use Koenig's theorem?
Quoting Feynman from Chapter 2 of his book Six Easy Pieces (emphasis mine): Suppose that we have two unlikes that attract each other, a plus and a minus, and that they stick very close together. Suppose that we have another charge some distance away. Would if feel any attraction? It would feel practically none. ... On...
The Phenomenon The lecture I am watching contained this figure: It is supposed to show two particles colliding in $S$ and $S'$ frames. I wanted to check the vectors on this slide using lecture notes, but I failed. Context Below I outline the context of which this problem above appears. 4-velocity basics Relying on le...
Is it possible to use laser cooling to cool Ethanol in it's gas phase? I've seen research on IR diode cooling when you reverse the electrodes but laser cooling was/has always been limited to atoms and a handful of diatomic molecules. If you where to design a laser trap for ethanol, what would the Maxwell speed distribu...
I am looking for a good book on the historical development of quantum mechanics. I have come across quite a few, but do not know which to read. I have a graduate background in physics, and so I am hoping for a (at least somewhat) technical review. Not a text book, but not a pop science level read. I have come across th...
Consider a Stern Gerlach devise. If the spin of the Ag atom makes an angle of say 30 grades according the magnet's up direction would Ag come out in the up or down ray on the plate behind? I consider it (Ag spin) to be in superposition of up and down spin and so there is probability to end in either rays. What Energy (...
At the start of chapter 5 of Mark Srednicki's lecture notes on quantum field theory we define an operator that creates a particle that is "localised in momentum space near $\mathbf {k_1}$, and localised in position space near the origin": $$a_1^\dagger\equiv\int d^3k\text{ }f_1(\mathbf k)a^\dagger(\mathbf k) \tag{5.6},...
I recently heard a talk at my university about the search for a renormalizable theory of quantum gravity. I then asked myself the following question: Isn't the reason that we need to regularize and renormalize our theories related to the fact that the usual quantum field theories are not suitable/applicable for the who...
Prove that the force exerted on a sphere of radius $r$ by a light source of intensity $I$ is not affected even if the sphere is not perfectly absorbing. Question 11,Photoelectric effect and wave-particle duality, Concepts of physics Volume-2 by Dr.HC Verma The derivation for the force exerted on a perfectly reflect...
I'm studying Rotational Kinetic Energy of an Object and the section reads: Each particle of mass mi in the object has kinetic energy, Ki: $$ K_{i} = \frac{1}{2}m_{i}v_{i}^2 $$ We can sum the kinetic energy of each particle together to get the total rotational kinetic energy, $ K_{rot} $, of the object: \begin{aligned} ...
I've found a very intricate task, that I have found no answer for on the internet: A meteorite (m = 75000kg, velocity = 13000km/h, c = 800J/(kgK)) crashes into an asteroid (m = 600000kg, velocity = 0km/h, c = 230J/(kg/K)). The crash is inelastic. How much do they heat up, if their temperatures before crash are the s...
I don’t understand why parallel wires with current running in the same direction attract. Wire 1 on the left, per the right hand rule, should cause wire 2 to experience a leftwards force. Wire 2 on the right, should cause wire 1 to experience a leftwards force as well. Shouldn’t they both be going to the left, never r...
In classical electromagnetics, static electric and magnetic fields in a given volume in a vacuum are completely determined by measuring the fields on the surface that bounds the volume. The fields at the surface can be probed by measuring both the force and torque on a spinning charge. Does a similar situation hold f...
I drop a test-particle in the Schwarzschild geometry, at an initial radial coordinate $r_0 > a \equiv 2 G M$ ($a$ is the Schwarzschild "radius"), with initial velocity $v_0 < 1$ relative to the local stationary observer (I'm using units such that $c \equiv 1$). To simplify the analysis, the initial velocity is perpend...
The famous picture taken by Event Horizon Telescope (EHT) showed a dark disk in surrounded by luminous bodies. Astrophysicists claimed it is a black hole. But how sure are we that this is actually a black hole? Could it just be a planet? Do we have evidence to believe it's a black hole?
I'm currently beginning to study QM and came across this interpretation of the expectation value in Griffiths: Quote: "It emphatically does not mean that if you measure the position of one particle over and over again, $\int x \left|\psi\right|^2dx$ is the average of the results you'll get." Now,by searching on the w...
The eigenstates of the particle in a 1D finite square well Hamiltonian: \begin{align} H = \frac{\hat{p}^2}{2m} + V(x) \end{align} \begin{align} V(x) = \begin{cases} -V_0 & \text{if } |x| < a \\ 0 & \text{otherwise} \end{cases} \end{align} belong to eigenvalues given by the following exp...
It is noticed that when a disk or something of that sort is rotated really fast and a small bead is put on it that bead flies almost radially outwards. Here's my problem: If there were no friction at all then from an inertial frame of reference the ball would be absolutely stationary. Ok that's fine. But in the prac...
This question is inspired by the (now looking at it, improper use of, my bad) comments section here in Physics SE. I'm not sure I could explain better than our short discussion does below: No, the sun is not extremely dense. The conditions at the center of the sun are quite extreme in terms of pressure and temperature...
I am not sure what to be looking for when observing the secondary maxima of a multiple slit interference. What does it mean when secondary maxima occurs (n-2) evenly spaced positions between the principal maxima?
I understand that there are differential equations that model the pendulum. I also know that, the period of the pendulum is given by $2\pi/\omega$. However, in the case of the simple pendulum, angular velocity, $\omega$ is changing. How should I approach this problem if I want to find the period?
Also, does this phenomenon apply only to lasers, or also to other EM beams? I wonder if the answer is related to the fact that diffraction limit(s) are proportional to wavelengths...
I'm following the derivation for the Field of a moving point charge, from Griffiths' Introduction to Electrodynamics. Particularly, on page 458 the author states that I find this familiar except for the $\frac{1}{2}$ that vanished from the first line. I know the 2nd line comes from a triple product but I can't see why...
I am reading a quantum optics paper on superradiance and subradiance. In building their Hamiltonian, the authors define an operator $ J_\pm(t)=\sum^N_{n=1}\sigma^{(n)}_\pm \exp{\left(\pm i \delta \omega_n t \right)} \tag{1},$ and say that $\sigma^{(n)}_\pm = \sigma^{(n)}_x \pm i\sigma^{(n)}_y \tag{2},$ with "$\sigma^{(...
Could someone give me a proof to justify that pressure is a state function? Thanks in advance.
For a problem I have been working on, I faced some difficulties in understanding some parts. The problem is as follows: A body of finite mass is originally at temperature $T_2$, higher than that of a heat reservoir at a temperature $T_1$. An engine operates in infinitesimal cycles between the body and the reservoir unt...
For QFT in Minkowski space, the usual story is that particles lie in irreps of the Poincare group. Wigner's classification labels particles by their momentum and by their transformation properties under the little group, which comprises the Poincare transformations that leave the momentum unchanged. How is this discuss...
I've read that, according to the Equivalence Principle, no experiment can distinguish between uniform acceleration and gravity. If one is in the classically-described elevator with a basin full of water on the Earth, Coriolis forces will cause the draining water to circulate around the drain. No such phenomenon will ...
I seems strange to me that I could not easily find information on "when quantum entanglement ends?", "What causes quantum entanglement to end?". Google search finds explanations of what quantum entanglement is, wiki article gives a lot of info, definition of entanglement: Quantum entanglement is a physical phenomenon ...
My Background: A senior Undergraduate Student With no Idea of Field Theory Whatsoever. I am looking for a very general and natural answer to my question. I noticed that Symmetry is not something nature abides by. In layman's terms, the planet revolves in an elliptical orbit and not circular orbit. And It's hard to expl...
With rainy season starting, I have been thinking about traction and have a question: Question: If two identical vehicles, one of mass $m$ and the other of mass $2m$ are starting from rest with equal acceleration, which vehicle's wheels are more likely to slip assuming no deformation of the tire? I have been wondering a...
First I prove that: $$[\hat L, \hat H] = 0$$ with $$\hat H = \frac{\hat{p}^2}{2m}+\hat V(\hat r)$$ Then, with $\hat V(\hat r,\hat p)$ as a vector: $$ [\hat L^2, \hat V(\hat r ,\hat p )] = -2i\hbar (i\hbar \hat V - \hat V \times \hat L) $$ I know that: $$ [\hat x_i,\hat p_j]=i\hbar \delta_{ij} $$ $$ [\hat L_i,\hat x_j]...
Hello, I dont understand the red part. Shouldn't it have minus instead? Sorry for lack of formatting, I only have a phone.
In a circular motion the acceleration is always perpendicular to the velocity. But is the converse true? If yes then is there any rigorous mathematical proof behind it? This caused a confusion when I learnt about the Lorentz Force and every source I referred quoted that 'As this force is perpendicular to the velocity, ...
In the Thomson tube experiment, after the electrons have been accelerated, they enter a glass tube filled with a gas at low pressure. The tube is put between two coils that form a Helmholtz-coil. The electrons are deviated to a circular path due to the magnetic field of the coils. In the gas, ionisation impact occurs b...
In the hydrostatic case with no viscosity, we can write the gradient of the pressure inside a container of water within the gravitational field as $$ \nabla P = g \rho$$ Moving close to a wall vertical wall, We encounter a normal force which should reduce our pressure, however, due to the isotropic nature of pressure, ...
So the question consists of two parts- The random motion of the particles is equivalent the amount of heat energy. The velocity of collective motion does not result in heat energy. For example take the case of wind. The particles are collectively moving with some velocity (wind velocity) but there isn't any heat energ...
Lets say some amount of ice is given to some amount of water in a copper container ( I will not give the exact values because you can choose them at your wish).The ice is at a temperature and the water and copper container is at some temperature. We will assume that it is separated from the out side environment. The qu...
With static electricity it's clear that free electrons would go to the ground. But I have significant doubts that an accumulator battery will discharge if one of it's electrodes is connected to the ground. What I mean by ground is soil in this message, e.g. the surface of the Earth. Would an accumulator battery dischar...
Can light be converted to radio waves by reducing the frequency of electromagnetic waves? If so how do you do it? And how much energy, approximately in percentage, would be lost during the conversion?
In string theory, a string is a one-dimensional space that can be closed on itself as a circle (closed string) or open as a linear interval (open string), but does a string have one real dimension or does it mean one complex dimension?
We know how unique water is and this question is based on a recent discovery that water can exist in two different liquid states. The density of the two states vary by almost 20 %. Can someone explain me how a single fluid is being converted into two fluids of different densities at the atomic scale? Also why are the s...
Valence band electrons in semiconductor may jump to conduction band if appropriate energy is applied in form of (I found the point from Samares' answer in this link and it also makes sense): Thermal energy Photon energy Electric field According to this link, "Red photons of light carry about 1.8 electron volts (eV) o...
I am currently a senior high school student taking IB and I chose to write an extended essay in physics. The essay is about the diffusion of a gas with the research questions: "How does the diffusion of a gas vary with distance from its origin?" "What factors affect the variation?" I was already able to gather data for...
Let us consider a relativistic point particle action $$ \begin{equation} S= -mc\int \sqrt{-\frac{dz^\mu}{d\sigma}\frac{dz_\mu}{d\sigma}} d\sigma \end{equation} $$ for some arbitrary curve parameter $\sigma$ and we use the mostly plus metric. My aim is to find the total energy through Noether's theorem by considering $\...