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Let's say we have a particle of given mass 'm' and given charge 'q'. This particle enters a region of magnetic field which varies as $$\ B = (k)\sin(wt)...(1)$$ where k and w are fixed constants and t is time. The velocity of the particle, say V, is perpendicular to the magnetic field. At t = 0 the particle enters the ...
When we walk on the ground, we push the ground backward and hence the ground pushes us forward and we change our position. The effect of our force on the Earth is very minute (literally negligible) because it's massive !! Also we know that each point of an spinning ball has tangential velocities as shown below. Now im...
If I have a ring threaded onto a fixed rough vertical rod, and it is in equilibrium, in which direction does the normal force point? Why? Isn't there contact with the rod from all directions? Here's the question for clarity: Also, am I correct in saying the friction force goes vertically upwards, opposing the directio...
When you have a solution to a time-dependent Schrodinger Equation, $$\Psi(x,t)=\exp\left({-\frac{i\hbar^2k_0^2t}{2m}}\right)\sin(k_0x), \tag{1}$$ and want to know the distribution of momentum at time t, you can decompose the sin function into $$\sin(k_0x)=\frac{\exp(ik_0x)-\exp(-ik_0x)}{2i}, \tag{2}$$ and say each is a...
After spinning around the atomic mass equation for calculating neutron separation energies, I have run into somewhat of a conundrum. It appears that the mass of the simplest of the examples, hydrogen is not correctly produced, yet I cannot put my finger on what is the reason for this. Let me elaborate: the atomic mass ...
Do you know the Pauli exclusion principle?-'No two particles could be in the same quantum state at once'. Well can you use that principle to explain why electrons stay in shells and electrons in separate shells can never get closer than a certain length to electrons in another shell. I learned somewhere that what the P...
I am trying to calculate the redshift drift where its written as $$\frac{dz}{dt} = (1+z)H_0 - H \tag{1}$$ We also know that $$1+z = a(t_o) / a(t_e) \tag{2}$$ and $$H_0 = \frac{\dot{a}(t_0)}{a(t_0)}$$ $$H = \frac{\dot{a}(t_e)}{a(t_e)}$$
I understand that Wigner functions are quantum-mechanical phase-space distribution functions (quasi-distribution to be more specific). For spin-1/2 particles the Wigner function is a $4\times 4$ matrix. However the Fermi-Dirac distribution function is a scalar quantity. One can write up a relativistic form of FD distri...
I am attempting to measure the fluorescence timing distribution (how much light is emitted over time from initial excitation) of a substance and I would like to use a solid calibrated sample (some material that has a very well known fluorescence timing distribution, not in solution) to make sure that my experimental se...
In many references including Wikipedia, electric flux and magnetic flux is written as $\Phi_{E}$ and $\Phi_{B}$, respectively. But they are not vectors (even then, they have to be bold) nor units. I think they should be written as $\it{\Phi}_{E}$ and $\it{\Phi}_{B}$. Shouldn’t they?
Let's consider a system of $N$ point particles. Let's also assume that acceleration of each particle is a function of positions of all the particles. I assume that for such a system we can prove that the motion of the system is described by Lagrangian equations of motion. How exactly can it be done? ADDED I do not ask ...
This question is related to this other question. I first consider an atom in a cat's superposition. It obeys the Schrödinger equation. The idea would be to make it weakly interfere with a thermal bath and let it begin to decohere. At the end it would be in the hot thermal bath. It would follow a Brownian motion and as ...
Suppose $p$ is the momentum operator, we know that the matrix element of $p$ in the $q$-basis reads $\langle q'\|p\|q''\rangle=-i\hbar\frac{\partial}{\partial q'}\delta(q'-q'')=i\hbar\frac{\partial}{\partial q''}\delta(q'-q'')$. Now consider the eigenequation $p\|p'\rangle=p'\|p'\rangle$. If we start with the LHS and inser...
Please explain, at atomic level, What is happening inside a string when a tension force is created?
Taking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames? Is the atmosphere attached to an inertial or non-inertial reference frame? Are there any visible effects this might cause when we view it? If an object mo...
I wonder if there is a concept similar to the one of BEC but arising from Quantum Field Theory instead that from the usual one developed in non-relativistic many-body Quantum Mechanics. In non-relativistic many-body QM the particles undergo condensation by occupying the single-particle ground state (if the system is no...
I know that net force on a charge decreases by a factor of K(dielectric constant of medium ) but I wanna know that whether The force on one charge due to other charge has changed Or This decrease of force is due to force exerted by the medium and force between the two charges still remain the same. ( I mean that force...
I was told that when a wave of visible light is reflected (or refracted) then the incident ray, the normal to the reflective surface (or interface of two optical media) and the reflected and refracted ray are coplanar, if we assume the rectilinear propagation of light (the geometric optics approximation). But I do not ...
A quantum-mechanical "density" matrix is Hermitian (self-adjoint), positive definite, having trace 1. In terms of its four ordered eigenvalues ($\lambda_1 \geq \lambda_2 \geq \lambda_3 \geq \lambda_4$, $\Sigma_{i=1}^4 \lambda_i=1$), the (Verstraete–Audenaert–de Moor) requirement that a generic (15-dimensional) "two-qu...
I just had to teach something that I myself have never learned, concerning recessional velocity of galaxies. Awkward! The question was: "A line in a hydrogen spectrum has a wavelength of 486.1nm when observed in the lab, the same line is observed at 492.3nm from a distant galaxy. Determine the recession velocity of the...
Been reading up on intersystem crossing and have gotten rather confused by: a photon possesses an angular momentum of $h/2\pi$ so it can couple to an electron spin and in principle induce any plausible spin transition between two spin states This suggests to me that in a system with two coupled electron spins, the ab...
I tried to imagine what would happen to a theoretical astronaut in the following thought experiment. The astronaut floats in space with the velocity of zero. He/she has a 10kg object and a wall 2 meters away (it floats in one place too). The wall and the object both have a(n) elasticity (coefficient of restitution) of ...
In hadron-hadron collisions, scattering events can be classified into diffractive and non-diffractive events. I don't clearly understand the definition of this two adjectives and I don't understand if this classification is alternative with respect to the elastic vs inelastic classification or not. I mean: can an event...
The operator product expansion systematically expands QFT interactions in terms of a sum of local operators. Is the leading twist of this expansion identifiable with collinear factorisation and, if so, how is this reconciled with the fact that the input Parton densities are quantum field theoretically defined in terms ...
A string of length $L$ fixed at $x=0$ and $x=L$ and released at time time $t=0$, the transverse displacement at a position $x$ along the string is given by: $y(x,0)=Ax(L-x)$ Assuming that the string is released from rest, write down an expression for $y(x, t)$, the transverse displacement profile of the string at an ar...
It is written in the book(Concept in Thermal Physics by Blundell) that A system will appear to choose a macroscopic configuration that maximizes the number of microstates of the system. And this statement is based on the following assumption: Each one of the possible microstates of a system is equally likely to occur ...
I'm reading Nielsen and Chuang, and I'm trying to understand what we actually mean when we talk about observables and their relationship to measurements. I'm more of a mathematician than a physicist, and I think there are intuition disconnects when it comes to the intuition/meaning behind these concepts. When I think a...
I ride a velomobile which is a fared tricycle . The trike is a recumbent to enhance aerodynamics so my knees are over the front axle which supports two front wheels and my head partially lies above the rear driving wheel. A very long chain runs from my feet which are upfront to the sprocket on the driving wheel. My qu...
Why it makes no sense is because centre of mass (COM) is a place where the mass of the whole body is present. Why can't we think like this: "When the semicircular wire is stretched and made to a straight wire the COM will be at the centre, right?". But COM of semicircular wire is $2R/\pi$ from the centre. If we think i...
Pomeranchuk effect poses a paradox of order by disorder phase-transition. The liquid Helium-3 is in a liquid form close to absolute temperature. For high enough pressure, as you increase the temperature, it becomes Solid and stays as a solid for a range of temperatures. This effect is attributed to the fact that in the...
In this case, since the z-coordinate is zero, $\sum_{i} q_i z_i = 0$. This was the answer I found when I googled it it. But I have a doubt about it. Every charge has an electric field around it, does this electric field come into z axis and play a role in centre of charge in Z plane? I know that this question is weird ...
I'm taking an introductory thermodynamics course, and according to my professor, the heat capacity of an ideal gas is $\frac{3}{2}R \approx$ 12.5. Since ideal gases don't have any attraction between molecules, every bit of energy put into the system goes towards increasing the Kinetic energy of molecules. Since average...
It is said that Coulomb's 'inverse-square' law (and Gauss's Law) are empirical facts. I'm wondering how do we know that Coulomb's law is inverse-square, and what are the possible consequences if it's not an inverse-square law. Suppose I write out the 'generalized' Coulomb's law for a point charge of the form: $$ \vec{E...
I am currently studying precession, and have a question regarding the angular velocity of precession. Let's simply use a spinning top in this case. I understand that it is given by the formula $$ \omega_P=\frac{r Mg}{I\omega}\, . $$ The proof and derivation makes sense to me; however, I don't quite understand the conce...
How would I derive the Electric Field on a square surface, which has continuous distribution of charge, given that I know the surface charge density is a function of two variables $\sigma(x,y)$, where $x$ and $y$ are positions on the square surface. My understanding is that the potential is given as $$\phi(r)=\frac{q}{...
When I was reading Joao Penedones's TASI Lecture on AdS/CFT, it says in (104): $$ \lim_{z\rightarrow 0}\int \frac{d^dx}{z^{d-1}}\frac{z^\Delta}{(z^2+(x-y_1)^2)^\Delta}\partial \frac{z^\Delta}{(z^2+(x-y_2)^2)^\Delta}=\frac1{(y_1-y_2)^{2\Delta}} $$ up to some finite normalization constants which can be found on the notes...
I stumbled upon the following question: Given the Hamiltonian of a spin-$1/2$ particle $$\hat{H}=\epsilon\begin{pmatrix} 0 & -e^{i\pi/4}\\ -e^{-i\pi/4} & 0 \end{pmatrix} = \frac{2\epsilon}{\hbar} \vec{S} \cdot \frac{\hat{y}-\hat{x}}{\sqrt{2}}$$ what is the rotation transformation that diagonalizes $\hat{H}$? Find th...
I've seen the explanation before that holes are basically electron deficiencies in an atom and that the hole "moves around" by electrons from surrounding atoms shuffling to fill that spot which is a very spatial way of viewing what a hole is. However, when I think about the band structure picture, the excitation of an ...
The photoelectric work function is the minimum photon energy required to liberate an electron from a substance. However, what are the properties of a material that affect its photoelectric work function? In other words, what causes the photoelectric work function to differ from one material to another?
I would like to check whether my analogy is right and ask some related questions. So, I am studying Thermodynamics right now and there are many calculus techniques are used for the thermodynamic relations between various state functions. One example is $ dH = \left(\frac{\partial{H}}{\partial{T}}\right)_{P}dT + \left(\...
I'm trying to buy a car that really feels fun to drive, and the one I test drove doesn't feel all that fun despite having high horsepower, torque, and acceleration. I'm trying to find a mathematical method for observing the car's push-you-back-in-your-seat factor. It's not just acceleration. http://www.city-data.com/fo...
$\hat{L_z}$ has the eigenvalue m$\hbar$ for a given eigenfunction with non-zero $m_l$ values. This is the component/projection of the angular momentum vector on the $z$ axis. Can i say that the $\hat{L_z}$ operator is a projection operator?
I have been given the following function to model the behaviour of a simple physical pendulum: $$\theta(t) = \theta_o e^{-\frac{t}{\tau}} \cos\left(2\pi \frac{t}{T} + \alpha\right)$$ Where $\alpha$ is a constant, $T$ is the pendulum's period, and $\tau$ is a time constant of decay. I only understand $\tau$ to be a fric...
I was given the $\mathbb{R^2}$ metric in polar coordinates, as follows: $$ ds^2=dr^2+r^2d\theta^2 $$ In this context we denote $e_1=\partial_r=(\cos(\theta), \sin(\theta))$, $e_2=\partial_{\theta}=(-r\sin(\theta), r\cos(\theta))$. Also, here we call $z^1=r$, $z^2=\theta$. We can also define: $$\frac{\partial e_{i}}{\pa...
The RKKY effective action applies 2nd order perturbation theory to the interaction of magnetic moments $\vec I_n$ with conduction electrons $$H_{eS}= \frac12 \frac{J}{V} \sum_{k,k'} \vec I_n e^{i(k-k')r_n}c_{k\alpha}^\dagger \vec \sigma_{\alpha\beta} c_{k'\beta}$$ where $H_0 = \sum \epsilon_k c_{k\alpha}^\dagger c_{k\a...
Boiling point is defined by wikipedia as: The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. -- My question My question is what exactly are we referring to as "pressure surrounding the liquid" with...
I came up with this thought experiment that seems to exemplify a paradox. In this paradox, one clock is ticking unevenly for one observer and evenly for another. Essentially, the clocks record a “tick” each time the light reaches a mirror. There is a light clock in the standard arrangement perpendicular to the motion ...
Suppose you have a beam of $s$-polarized light that reflects off of some medium. Is the reflected beam also $s$-polarized? What about with $p$-polarization? I'm assuming those nice properties of media (whatever they are) that one assumes in typical undergrad E&M and optics courses.
The differential cross-section of Rayleigh scattering is inversely proportional to the fourth power of wavelength of the radiation incident on the scatterers. More precisely, $$\frac{d\sigma}{d\Omega}=\frac{8\pi}{3}\bigg(\frac{e^2}{4\pi\epsilon_0mc^2}\bigg)^2\frac{(1+\cos^2\theta)}{\lambda^{4}}$$ where $\theta$ is scat...
This was a question that my fluid mechanics teacher ask today in class, I find the number of total molecules, and then my teacher says that we could search the size of one $\rm H_2O$ molecule, then I assume that the molecules are arranged in a hexagon shape, like a honey bee cell, then I found how many hexagons are in ...
Electrons have a definite spin but I read somewhere that when an electron gets subjected certain types of electromagnetic waves they can switch their spin direction... Is that true?(wouldn't that violate the pauli exclusion principle?) If so can you pls explain to me why they do that when they get subject to em radiati...
For an atom Griffiths says $$ \mathbf{p}=\alpha \mathbf{E} $$ The constant of proportionality $\alpha$ is called atomic polarizability. And $\mathbf{E}$ is the external applied field Then he goes on to give an equation of polarisation for a linear molecule like $\require{mhchem}\ce{CO2}$ as When the field is at some...
Say we have a particle in an infinite square well where $V= \infty$ if $x<0$ or $x>a$. Then, suppose the well expanded to $V= \infty$ if $x<0$ or $x>2a$. While the wave function is momentarily undisturbed, to find the probability of new possible states of the particle, we compute $$c_n = \int_0^a \sqrt{\frac{2}{2a}}sin...
It is more on theoretical-math-physics stuff side, it is not crucial for practical application (the practical context of this question is "video projection"), just curiosity and liked to hear somebody's take on what I see as inconsistency within photometry related definitions. This year I have been faced twice with foo...
you know how when you spin a gyroscope it supernaturally stays up even if you bend it over and its parallel to the ground? Well that was unbelievable so I did some math to see why this works. I tried to use conservation of energy but it didn't get me the result that I wanted. Heres my reasoning- The gyro starts of with...
If $\hat p:\mathcal H\to\mathcal H_p\subseteq\mathcal H$ is a projection operator, and if $\hat u$ is unitary, then it's easy/trivial to show that $\hat u \hat p \hat u^{-1}$ is also a projector. But if we interpret unitary $\hat u$ as a rotation in $\mathcal H$, then it seems (at least to me) intuitive that $\hat u\ha...
The energy of electromagnetic waves is said to be dependent on frequency. Is the energy of a sound wave also dependent on frequency?
The divergence a 2D vector Field $\mathbf{F}(x,y) = F_x(x,y)\, \hat{i} + F_y(x,y)\, \hat{j}$ is defined as $$\mathrm{div}\,\mathbf{F} = \bigg( \dfrac{\partial F_x}{\partial x} + \dfrac{\partial F_y}{\partial y}\bigg).$$ This can be calculated IF a function $\mathbf{F}(x,y)$ is given. How do I compute the divergence if...
It is well-known fact that the appearance of superconducting state in superconductor relates to the existence of the pole in two-particle Green function. Does exist a similar fact for Bose condensation? I mean the following: one can compute a Green function of interacting Bose gas and see that a singularity of this fun...
Can anyone show me a proof that the torque on an arbitrary shaped object having a dipole moment $\vec{P}$ in a uniform electric field $\vec{E}$ is given by $\mathbf{N}=\mathbf{p} \times \mathbf{E}$. I couldn't find it in my textbook or on the internet.
Teflon's melting point is 327 degrees Celsius, whereas a regular gas stove easily reaches temperatures above this. So why doesn't the Teflon coating in cookware melt while cooking?
We detect an object with the help of light. When photons hit the retina our eyes find the presence of the source of the light (object), the source being the original source of detected light or reflected light's source. But how the exact position of the source (object) is detected? Photons just reach our eyes, but how ...
Suppose I have some material in solid-state (say), I cut it into two parts. Take the first cut it into two parts, take the first cut it into two parts, and then repeat this again and again. There will be a point when the substance loses its solid property. I'm interested in this point. I realize we don't have to go unt...
I was watching a video on a typical black hole formation from a neutron star and it suggested that the event horizon appears instantaneously at the surface of the star even as the stellar matter inside starts to converge into a singularity. I have also read that the information that gets encoded on an event horizon is ...
If I shine an electron beam in a sample and it returns, for an example, an X-ray wavelength compatible with both $K_\alpha$ of copper and $L_\alpha$ of hafnium. How can I tell the difference between these elements? Edit: Using Moseley Law here I get copper for $K_\alpha$ and hafnium for $L_\alpha$ for an wavelength of ...
According to some (e.g. Haroche and Raimond in Exploring the quantum: atoms, cavities and photons), the quantum world consists (mainly) of spins and harmonic oscillators. For harmonic oscillators (i.e. bosons), it is well known that they can be appropriately described in $(x,p)$ phase space, which satisfies a 'symplect...
In other words, is it assumed that the fluid density is constant after expansion and through the time development of an expanding universe?
It's some time that I notice some sign issues in my calculations of quantum field theory and I started to think that the origin should be addressed to my choice $(\hat{p}_\alpha)\doteq -i\hbar\partial_\alpha$ instead of the $(\hat{p}_\alpha)\doteq i\hbar\partial_\alpha$, but many other things just didn't come right. S...
Do velocity and displacement always have the same direction? I know this seems like a silly question to ask, but I'm having a hard time coming up with any counter examples, and I'm not able to prove the statement either. I can think of plenty of examples where acceleration has a different direction than that of velocit...
Let us say we have a particle in a superposition of spin-up and spin-down at time $t_1$. The particle is measured as spin-up at time $t_2$ by an observer. At the current time, $t_3$ all traces of measurement is erased and lost by later interactions and fluctuations, the universe (including observer) is in exactly the s...
The axion photon coupling is given by the expression $ g_{a\gamma\gamma}= \frac{\alpha}{2\pi f_a}(\frac{E}{N}-\frac{2}{3}\frac{4m_d+m_u}{m_d+m_u}) $, where $f_a$ PQ symmetry breaking scale, $E$ and $N$ are the electromagnetic and color anomaly coefficient. My question : why the color anomaly ($N$) is included in the f...
A garden hose on the ground, water with enough speed flows out at its end. In the beginning, the hose is bent. Assuming only the force caused by bending and the friction force on the ground act on the hose, will the hose eventually become a straight hose? Assume that the hose is very soft. picture source Does the hydr...
Background: The quantum fisher information can be used to lower bound the variance, when estimating a parameter $\Theta$. This estimation can be decomposed into three steps. The initial state $\rho_0$ The encoding process, discribed by a CPTP map $M_\Theta$ The Messurement $\{E_m\}$ discribed by a POVM The QFI allrea...
Given the Robertson-Walker metric for a scalar field $\phi(t)$, how can we obtain the equation of motion for this scalar field? I took the contravariant derivative of the scalar field is which is nothing more thant the gradient of that same field and then I applied the covariant derivative to that quantity, since th...
The equations of motion that describe the above situation is given by: $$ m \ddot{x_1} = -2kx_1 + kx_2 $$ $$ m \ddot{x_2} = -2kx_2 + kx_1 $$ Now I want to work out the potential energy of this system. How would I use the equation: $$ V(x) = - \int F(x) \hspace{.1cm} dx$$ to calculate the potential energy? My attempt i...
Point electric dipoles are usually introduced as two charges $\pm q$ at a distance $d$, then taking the simultaneous limit $d \to 0$ and $q \to \infty$ keeping the product $qd = p$ constant. In this way, we obtain a meaningful electric quantity, the dipole moment $\vec{p}$. Next, it is shown that the electric field pro...
Can electrical current flow both ways at the same time in the same wire? If so, what are the drawbacks or complications of it?
I started to develop a VSEPR application. My question is that what is the accuracy of a VSEPR computation and what variants does it have?
I know that as a car accelerates on earth, for the car-earth system angular momentum is conserved. Attached is a nice animation for simplistic proposes. https://www.animations.physics.unsw.edu.au/jw/momentum.html However, the front wheel experiences a torque due to friction. The front non-driving wheel also has angular...
This might seem like a very simple problem, but it's stumping a few of us (myself obviously included). We have been tasked with showing the mechanical energy of a particle is dissipated under the influence of a drag force, the force is defined as being made up of a conservative and a drag component. $$F(x)=-U'(x)-k\|\do...
Is there any relevance of it? E.g. some problems are easier to solve without quantization and correspondence makes it a valid solution. This isn't about the quantization of gravity. It is much more general.
The 'impedance of free space is written like this, too, as the absolute value of the $E$-field over the absolute value of the $H$-field. What does the ratio of the strengths of the two fields of an electromagnetic wave have to do with the impeding of their propagation through space? Also, the impedance of a wave throug...
Question: Fundamentally, is the existence of negative temperatures a consequence of (a) the violation of entropy postulates, (b) inequilibrium, or (c) finite number of configurations? Context: In my statistical mechanics class, we first began by claiming the existence of a function $S$, called entropy that contains al...
I was studying YDSE. It was a topic where a glass slab was inserted just after a slit. Does lateral Shifting takes place? If it takes place then why does the ray go straight as shown in image below? I got no clue about it on the internet therefore, came to SE. For reference please consider the given image.
I've seen in a lot of movies and animations of bubbles forming when something moves underwater (e.g., fish swimming). Is it theoretically possible (under any temperature, pressure circumstance possible in oceans) that bubbles could form miles underwater, just because of mere movement?
I was running some calculations of ideal gas molecules in a box for $O_2$ molecules at $T=300K$ and $V = 100 cc$, and I saw that $v = 445 m/s$. My question is, why don't we hear sonic booms all the time when we are outside on a nice day? Is it because gas molecules are constantly colliding? Even if we have a box of gas...
We have two similar buckets of equal weight submerged in water, the first up and the second down. Calculation of the weight of each bucket (Can the weight of the water inside each bucket be considered an additional weight, or can it be considered in one case without the other) Are the forces applied to each bucket th...
Conservation of momentum is valid when $F_{\rm external}=0$ and $F_{\rm internal}$ not equal to zero. According to Newton's 2nd law of motion $F=dp/dt$, so if there is a force acting there will be a change in momenta and vice-versa. If there is a force (internal) acting there should be a change in momenta, but in conse...
It is stated that the equation leading to Stokes law describes an equilibrium state, such as the upwards force is equal to the downward force: $$ 6\pi r\eta v = \frac43\pi r^3 (d_1 - d_2)g $$ Now $v$ is velocity, and velocity at equilibrium is $0$, and this is the breaking point of my understanding. What is the nuance ...
I want to understand constraints of unitarity in quantum field theory. There is quite folklore statement: gravity with a Weyl tensor square term is non-unitary How to understand this? (I think that it is quite simple, because we rarely prove unitarity and it directly follows from action) How to modify theory to obtai...
I have great difficulties to understand the article "On the Form of the Highest Progressive and Standing Waves in Deep Water", which is available freely on Jstor. This article deals with the largest possible steepness, $(H/\lambda)_{max}$, of a stable progressive wave in deep water. Stokes had shown in 1880 that waves ...
In classical field theory (for a single field $\psi$) the dynamical variables are defined to be functions of the fields $\psi$, $\pi$, $\partial_{x_{i}}\psi$ and maybe $\mathbf{r}$, where $\pi$ is the conjugated field to $\psi$. For $F=\int\mathcal{F}\,d\mathbf{r}$ and $G=\int\mathcal{G}\,d\mathbf{r}$, where F and G ar...
I have been trying to derive the dispersion relation for the low energy Hamiltonian described in Ref. 1. The relevant equations are (1a) through (1d). I will re-write the equations here to save time: $$H_0 = \nu_F\left(\tau\sigma_x p_x + \sigma_y p_y\right)+\frac{m}{2}\sigma_z$$ $$H_{SOC} = \tau s_z\left(\lambda_c\sigm...
If I understand correctly, the radius of the M87 event horizon is approximately 19 billion km. I used an escape velocity calculator as a sanity check, entering 1.28E40 kg and 1.9E10 km and the calculator yielded an escape velocity of 299,879 km/sec. I used the same tool to calculate the escape velocity for the ISCO, wh...
Let's assume an electrically conductive object made of metal is static and does not move. Then let's apply an outer electric field. Clearly, a constant DC field would not induce any currents and magnetic field in the conductive object. However, a changing AC field would induce a current and therefore a changing magneti...
In paper Topological Gravity as the Early Phase of Our Universe there's statement: Hamiltonian of gravity would vanish by time reparameterization invariance. How to derive such result?
I have the following problem: Suppose that, as a function of x, an electric field has an x component $E_x=6x^2y$ where the electric field is measured in volts per meter and the distances are measured in meters. Find the potential difference between the origin and the point x=3 on the x axis. I have done the following: ...
I have been studying the effects of massive gravitons on the emblackening factor $f(r)$; i.e., given a Reissner-Nordstrom AdS geometry $$ds^2=L^2 \left(\frac{dr^2}{f(r)r^2}+\frac{-f(r)dt^2+dx^2+dy^2}{r^2} \right)\quad(\textrm{Eqn. } 1) $$ and $$A(r)=\mu\left(1-\frac{r}{r_0}\right)dt\quad(\textrm{Eqn. } 2) $$ how does ...
The generalized uncertainty principle can be derived and shown to be this which is fine and rigorous. $\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2} + \dfrac{1}{4} \vert \langle \{ \Delta A, \Delta B \} \rangle \vert^{2}$ On the right hand si...
This question is about how small the interstellar density is (less than 1 atom per cubic centimeter). But although the interstellar density is very low, matter tends to extremely aggregate in certain clusters within and through the whole universe (we call them e.g. galaxies, solar systems and planets). Of course this i...

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