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In a paper about the splitting of the space-time [for reference "THE STRUCTURE OF SPACE–TIME: RELATIVITY GROUPS" (International Journal of Geometric Methods in Modern Physics Vol. 3, No. 3 (2006) 591–603)], it identifies the reference frame with a $(1,1)$-tensor field $R\in\mathcal{T}^1_1(M)$, $M$ is the space-time, an... |
As per the Big Bang model of Cosmology roughly 13.8 billion years ago a singularity exploded exponentially to eventually become the present universe.
At the present time (basically current time-slice) we have all the space which according to the said model was crunched into a singularity. My question is whether two dis... |
As stated here,
In purely viscous materials, strain lags stress by a 90 degree phase.
How can we derive this statement? Is it experimental? If not, which is its proof and what is the physical cause of this lag between stress and strain?
|
During calculation of the Q-value in beta decay, is the mass of the electrons of the reactants (and product) atom included during calculation of Q-value?
|
So, I was reading the chapter of small oscillations in Landau and Lifshitz's book of Mechanics. We assume solutions of the equations of motion that are in the form of $X_a=Ae^{iω_at}$ where $A$ is an complex constant. We need real and positive solutions (normal frequency) to the characteristic equation in order to end ... |
In the book Introduction to Many-Body Physics by Piers Coleman, it states on page 12 that
... the particle field and its complex conjugate are
conjugate variables.
In other words, the particle field $\psi(x)$ and its complex conjugate $\psi^\dagger(x)$ obey the canonical commutation relation $ [\psi(x), \psi^\dagger... |
The amplitude of a spherical wave can be shown to be $$A \propto \frac{1}{r},$$
where $A$ is the amplitude and $r$ is the distance from the (isotropic) source. This seems to imply that $A$ tends to infinity very close to the wave source.
However, if we were studying sound waves which have this form, I know that the (pr... |
Suppose we have a depolarizing channel operation
$$E(\rho)=\frac{p}{2}\textbf{1}+(1-p)\rho$$
acting on a Spin$\frac{1}{2}$ density matrix of the form $\rho=\frac{1}{2}(\textbf{1}+\textbf{s}\cdot\textbf{$\sigma$})$. I have found the Kraus operators to be:
$$E_1=\sqrt{\left(1-\frac{3}{4}p\right)}\textbf{1}, E_2=\frac{\sq... |
Imagine Alice falling into a black hole with a Schrodinger's cat experiment setup.
after passing the event horizon towards the singularity she performs an observation to see if the cat is dead or alive. Bob floats just above the event horizon of the black hole. Will he ever know what was the result of the observation d... |
We have a air over oil lubrication system. The air compressor is putting 45 psi of air thru 1/4" id stainless tubing mixed with oil for the lubrication of motor bearings. The system is located outside along some duct work which is up to 300 deg F. We have one issue. Whenever it rains, we get high flow alarms on the sys... |
Why is the mass of the proton such a precise value?
A proton is composed of 3 net valence quarks and what is often described as "binding energy" or "a zillion gluons and quarks and anti-quarks self annihilating and popping into existence". The quarks are only about 1% of the mass but the mystery to me is understanding ... |
How do we prove that del operator is invariant under any kind of change of coordinates, specifically under galilean transformations? I am getting an extra term containing the relative velocity of two frames in denominator, componentwise.
Invariance of divergence can be under stood since it is a scalar field. But how do... |
Is there any deeper motivation behind the fact that all elementary fermions have the same exact amount of spin angular momentum ($\frac{\sqrt3}{2}\hbar$ total or $\frac12\hbar$ projected) or is it really just an axiom of quantum theory? Because sometimes spin is described in terms of the transformation properties of t... |
This is part (b) of Schwartz's Problem 14.3 in his Quantum Field Theory and the Standard Model textbook.
Suppose that we have a real scalar field operator $\hat{\Phi}(x^0,\mathbf{x})$ with conjugate momentum field $\hat{\Pi}(x^0,\mathbf{x}) := \partial_0 \hat{\Phi}(x^0,\mathbf{x})$. These operators satisfy the equal-ti... |
Consider this lagrangian:
$$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2} (\partial_{\mu}\phi_{2})^2 + \dfrac{m^2}{2}(\phi_{1}^2 + \phi_{2}^2) + \dfrac{g}{4!}(\phi_{1}^4 + \phi_{2}^4) + \dfrac{h}{4}\phi_{1}^2\phi_{2}^2 $$
It has symmetries: $ \phi_{1,2} \longleftrightarrow -\phi_{1,2} $ and $ \p... |
I would like to know if there is a difference produced by the added spin of a black hole to its gravitational space-time distortion.
I am considering the distortion of space-time from a point far enough for this distortion to be “stable”.
|
I am trying to prove the continuity equation for a charged particle moving with some speed v. So, I start with the charge density and current density as,
\begin{align}
\rho(x,t) & = q\delta(x-vt) \\
J(x,t) & = q v \delta(x-vt)
\end{align}
It seems that one would have to take a derivative of the delta function to prove ... |
Could someone point to the math that explains this?
“For example, at 10 percent of the speed of light an object’s mass is only 0.5 percent more than normal, while at 90 percent of the speed of light it would be more than twice its normal mass.”
Excerpt From: Stephen Hawking. “A Brief History of Time: From Big Bang to... |
I have been doing personal study in Classical Mechanics and reading Newton's Laws. While thinking about them I had a question I haven't been able to answer. It comes from the interactions of Newton's 1st and 3rd laws.
First law
In an inertial frame of reference, an object either remains at rest or
continues to move at... |
I am reviewing the Landsat 1 satellite, specifically its Multispectral Scanner (MSS) imaging system. The system had the following specifications
Sensor type: opto-mechanical
*Spatial Resolution: 68 m X 83 m (commonly resampled to 57 m, or 60 m)
Spectral Range: 0.5 – 1.1 µm
Number of Bands: 4, 5 (Landsat 3 only)
Tempora... |
In Riemann geometry one can formally solve the parallel transport equation
$$ \dot{v}^\mu + \Gamma^\mu_{\rho\sigma} \, u^\rho \, v^\sigma = 0 $$
of a vector $v$ along a curve with unit tangent vector $u^\mu = \dot{x}^\mu$ using the path-ordered exponential
$$ P^\mu_\nu(s,0) = \left( \text{P exp} - \int_0^s ds \, \Gamma... |
Cosmologists from the BOSS and eBoss surveys construct 3-D maps of correlated galaxy positions, measure their redshifts and use the comoving BAO feature as a standard ruler. With these data, how do they proceed to evaluate cosmic distances and infer the expansion history of the universe?
|
I know that stiffer EoS gives bigger stars and stars with bigger maximum masses. The problem is that I'm computing the maximum spin-frecueny of a neutron star for two EoS, and I'm getting higher $\Omega_{max}$ for the softer one. For me this is counterintuitive. Is this true?
|
I was studying the electric field behavior at one point with respect to a uniformly charged disk, and while analyzing examples, this specific one caused me doubts.
The example talks about a disk fixed at the origin of the xy plane, and its charge density being $> 0$ for $0$ $\leq$ r $\leq$ $B/2$ and $<0$ for $B/2 \leq ... |
In Bose-Einstein statistics, two identical bosons can be in one of the following three states with respect to some orthonormal single particle states $|A\rangle$ and $|B\rangle$:
(1) $|A\rangle |A\rangle$
(2) $|B\rangle |B\rangle$
(3) $1/\sqrt{2}(|A\rangle|B\rangle + |B\rangle|A\rangle)$
Now, (3) is a linear superposit... |
I am reading through Luttinger's "Theory of Thermal Transport Coefficients". In equation (1.14), the charge-density operator is defined as
$$\rho(\mathbf r) = e\sum_j \delta(\mathbf r-\mathbf r_j).$$ In equation (1.16), the current-density operator is subsequently defined as $$\mathbf j(\mathbf r) = \frac{e}{2}\sum_j \... |
I was reviewing some basic concepts in physics. I was reading a concept that says “the force needed to push/pull an object on an inclined plane (suppose friction is zero) is
$$F= m\,g\,\sin(\theta)$$
My question is, if we exert the force on that object with that amount of force, wouldn’t we end up preventing the object... |
What do black holes spin relative to?In other words, what is black hole spin measured in relation to?
Spinning black holes are different from non-spinning black holes. For instance, they have smaller event horizons. But what are the spins of black holes measured relative to?
Let's first look at an example with commo... |
The Coulomb force between charged particles is inversely proportional to the square of the distance. Yet, why don't we observe the infinite force when the distance approaches zero? Say we can bring two positively charged glass rods and make them touch each other. We don't observe a very large amount of repelling force.... |
I know that Noether's theorem relates conservation laws with symmetries, and I read that to find CPT violation, Lorentz invariance symmetry needs to be broken.
This implies that if a symmetry is broken, it's associated conservation law becomes an approximate conservation law.
If this is the case, spontaneous symmetry b... |
Is it possible that time is not a 'time-like' dimension, but a proper spatial dimension just like the others but we only have access to a 3D cross-section of it?
I did some research about the internet if there is some discussion about this but I haven't found anything related. I am sure that people have already thought... |
There was a problem in my book that read- A magnet is pointing towards geographic north at a place where the horizontal component of the Earth's magnetic field is 40 microtesla. Magnetic dipole moment of the bar is 60 Am^2 and the torque acting on it is 1.2 x 10^-3 Nm. What's the declination at this place?
Now, the an... |
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("the ring of observables") of the weakly coupled B-model topological string on a Calabi-Yau threefold $X$ is identified with the ordinary Dolbeault cohomology ring of $X$.
My trouble:
I'm reading the famous Witten'... |
If multiple bosons can occupy the same state, does that mean you can put an infinite number of them in a fixed container at zero temperature without pressure.
|
I was doing a question on transformers and found this really confusing question:
A 100% efficient transformer converts a 240V input voltage to a 12V
output voltage. The output power of the transformer can be a maximum
of 20W. The output is connected to two 0.30A bulbs in parallel. One of
the bulbs fails. How does the ... |
Are polarization-entangled photons correlated spatially?
That is, if I took a pair of entangled photons and looked at their spatial modes with two cameras (one for each photon), would I expect to see correlations between their spatial modes? Does this change depending on if the photons are generated colinearly or not c... |
So far I have learned about topological quantum material, my understanding is that topological order in a quantum material is the way the eigenvectors of the Hamiltonian of the system aligned. So if I am right, I need to know how this topological vector space differs from the eigenvector space of Hamiltonian which desc... |
I am looking at a problem where a woman has travelled down a simple waterslide and into a pool, then hurt her knee by striking the floor of the pool. I need to figure out how deep the pool needed to be for her to not hurt herself.
She is 165 cm tall, weighs 83 kg and can be assumed to have a foot to crotch length of ab... |
After I woke up this morning while sitting at our table I looked at a plastic bottle of cola lying on the floor. Please, don't think it's a mess out here. It just lay there. I put it nicely back on the table but not before I gave the bottle a push.
The water (which is what the zero-energy-cola is in essence made up of)... |
I recently found the derivation of the Lorentz factor here. It shows the ratio of time in different inertial frames to be equal to the Lorentz factor.
I'm now trying to understand how this ratio relates to the equation
$_{rel}≡$.
|
Cheers to everyone. I' ve got a serious doubt about the following: consider the annihilation operator $\hat a$. For practical reasons, I sometimes find useful redefining it in the following way : $\hat a' =\hat a e^{i \phi}$, with $\phi \in \mathbb R$. If I add a new global phase to each eigenstate of $\hat a^\dagger \... |
I have read some literature to know that Raman intensity corresponds to the inelastic scattering of light with ion vibrations, and the positions of Raman peak correspond to the energy of phonon.
My question is on the large crystals such as large graphene, in which the phonon modes have wave number k. I found in many li... |
We can write a the covariant form of a perturbed Minkowski background to second order as
$$ g_{\mu \nu} = \eta_{\mu \nu} + \kappa h^{(1)}_{\mu \nu} + \kappa^2h^{(2)}_{\mu \nu}$$
where $\kappa$ is just used to track the order of terms.
Now, I understand that the contravariant form at second order is,
$$ g^{\mu \nu} = ... |
I am trying to make an electromagnet and most online resources suggest soft iron core is used as the material. What is the composition or the engineering name for this soft iron?
|
This question is about a derivation in section 5.2.1 of the book Quantum Computation and Quantum Information by Nielsen & Chuang. More specifically the derivation of the equation (5.27). This equation gives a probability of obtaining value $m$ such that $\mid m-b\mid > e$, or in symbols:
$$p(\mid m-b\mid > e) = \sum_{-... |
In most text books of statistical physics, temperature is defined as :
$$T=\left(\frac{\partial E}{\partial S}\right)_V$$
where $V$ stands for any external variable(s) the system's Hamiltonian depends on.
However, it is often suggested that the temperature is also the average kinetic energy per degree of freedom as in ... |
The Hamiltonian from the Hubbard model for the double well potential $V(x) = V_0 \frac{x^2 - q^2}{q^2}$ is given by
\begin{equation}
H = -J(a_L^\dagger a_R + a_R^\dagger a_L) + \frac{U}{2} (a_L^\dagger a_L^\dagger a_L a_L + a_R^\dagger a_R^\dagger a_R a_R)
\end{equation}
corresponding to the left side and right side r... |
How is coefficient of static friction and coefficient of kinetic friction is calculated in real life without knowing the frictional force?
|
even though it's the electrons that move from negative terminal of the battery and gets move along the external circuit and finally enters the positive terminal of the battery and due to battery force move again to its negative part, so what should i consider, can anyone clear it ?
|
We've a potential given as:
$V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$.
We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$,... |
I guess when I'm moving my hands around, the electrostatic potential stored in the chemicals in my body is converted to motion of my arms?
But what about momentum conservation? I think the brain sends Electrical signals to my arm, which probably further use the potential energy stored in my muscles' chemicals to make m... |
Let's recapitulate and state both the Maxwell's demon and the official most-widely accepted solution to the paradox, namely Landauer's principle:
The Maxwell demon paradox:
A demon just by observing But Never Touching -hence no energy is transferred- the molecules of two chamber of gas separated by a door, opening and... |
I have come across a text which, without proof or detailed explanation, states that the rate of change in internal energy $U$ of a system with constant volume $V$ is given by
\begin{equation}
\frac{\partial U}{\partial t} = \frac{\partial}{\partial t} \left( \rho V C T \right),
\end{equation}
where $\rho$ is density, $... |
I was calculating the spin-orbital correction in the fine structure of Hydrogen, but then bumped into an irritating problem.
In the process of calculation, I must calculate $\langle n,l,j,m_j|\frac{\overrightarrow{S}\cdot\overrightarrow{L}}{r^3}|n,l,j,m_j\rangle $. In all of the textbooks and posts I read, they simply ... |
I have a debate with my friend. Suppose that an apple with weight of 10N fell from 1m high. We want to apply the 1st law of thermodynamics for this situation.
My friend thinks that $W$ should be considered as work done by the apple to the Earth, and thus $W=-10J$. Meanwhile the kinetic energy of the apple increased by ... |
If $M$ is a smooth manifold and $X(t)$ is a parameterized curve on it, then at each point $X(t)$, we can define a tangent vector that lies in $T_{X(t)}M$. All these tangent vectors together form a tangent (to that curve) vector field $v_X$. Why this is called the "velocity" is intuitively clear to me.
But I'm really st... |
What happens when one connect a 110V appliance to a 220V supply, and vice
versa? Please explain in detail.
Is there any way to safely connect such an appliance to a
220V supply without causing any damage?
|
Do coefficient of static friction depend upon the objects if same surface is taken or will it be constant for any object ?
|
Can someone explain why the moment of inertia of this circular current carrying ring about its diameter is $\frac12 mr^2$?
|
When we consider a solid cylinder rolling down an incline we consider IAOR to be center of rotation but when the same cylinder is dragged across a rough horizontal surface by a horizontal force that acts at COM, the point of contact with floor becomes the IAOR. Why is this?
|
I read about the principle of least time. However, I think, for light to follow this principle, light would have to remember its past path before deciding where to go for its future path. Why I think that:
Suppose I shine a torch in the air medium, directed toward the water medium. I shine it at point A. It hits the su... |
In order to prevent the chain from slipping, the friction on the part of the chain kept on the table should be equal to the weight of the hanging part of the chain. Why is that so?
|
Say there a child, that stands on the edge of an AT REST merry go round. When they jump off, the child has a linear velocity, and the merry go round begins to turns.
They say there is no net torque on the merry go round/child system and angular momentum is conserved.
I understand the torque applied to the merry go roun... |
Above is the picture of the path taken by an electron in a conductor which is connected to a circuit. It was drawn by my teacher. Now, I know that the direction of flow of electron is opposite to that of the Electric field. But as you can see in the picture, he told the class that this is the path taken by an electron... |
Let's imagine an electromagnetic wave that points every direction (i.e., from $\theta = 0$ to $\theta = 2\pi$). For simplicity let's consider only the electric field vectors. The wave goes through a polariser. Setting $\theta$ to be the angle from the vertical line (parallel to the polarising direction) the magnitude o... |
I am trying to do the dimensional analysis of power using two different ways
Using $P = \frac{dW}{dt}$
$\frac{[W]}{[t]} = L^2\cdot T^{-3}\cdot M$
since $W$ is in joule
Using the power formula $P = VI$
I get to $[P] = [V]\cdot I$ and $[P] = [L]\cdot [T]^{-1}\cdot I$ and I am stuck here, how can I get to the first re... |
If we know that a photon scatters an electron should it be tried as an indirect detector to say a deflector at one slit which can help to deduce the 'which path' information as only an electron that passes through a 'deflector free' slit can be recorded on the screen?If the vertical laser deflector is moved towards or ... |
I encountered a statement that "while Lorentz invariance is apparent in the Lagrangian formulation, it is not so in the Hamiltonian formulation of a classical field." I do not completely understand this statement, though I thought this statement was essentially pointing to the two questions I asked.
|
let's define 'a measurement device' as a system which is highly sensitive to the eigenstate of an observable. The sensitivity is quantified let's say by how irreversible and grand the small changes in the eigenstate result in the large scale, classical system's future. A wavefunction collapses when it interacts with s... |
Using $M87^*$ data from EHT observation (mass, temp of the surrounding accreting disk) and approximating area of EH by euclidean geometry $4\pi r^2)$, error comes around of order one or two.
One gets following result:
$T_{M87^*}\approx0K$ and since surrounding temperature is $6\times10^9K$ therefore by Boltzmann formul... |
Next problem shows a rigid rod with mass 'm' and length 'L', rotation only occurs on the Z axis in the $\hat{k}$ direction. Angular momentum can be easily calculated by using equation:
$H_{G/O} = I_{zz}\dot{\theta}$
Result is shown on figure in RED color
$H_{G/O} = \frac{mL^{2}}{12}\dot{\theta}\hat{k}$
But I am looking... |
In his article "The Universe as a Whole" 1, physicist Dennis Sciama said
We therefore face a crisis in theoretical physics. Either classical general relativity breaks down, or effectively negative energy densities can exist, or causality breaks down, or singularities exist in nature
Igor D Novikov developed his Self-... |
We all know that the sun generates its energy from nuclear fusion in the core. The electromagnetic radiation produced slowly travels upwards, while constantly being absorbed and re-emitted by the charged ions, until it reaches the photosphere, where it can basically travel freely (because there are less charged ions), ... |
I was going through this video about lightning and I couldn't understand some points .
1: What caused the water molecules in ice crystals to be arranged in that specific pattern i.e. having positive charges at its boundary and negative in the inner region ?
2: Also WHY do the crystals break (which created or may have... |
Recently I have done some simulations with a linear system that behaves similarly to the wave equation. Now I have a bit of trouble understanding when interaction is possible in linear theories, especially in the context of quantum mechanics. If we, for instance, consider a linear theory like the maxwell equations we h... |
As a concrete example, in section 1.3 Equilibrium Statistical Physics by Plischke and Bergersen we can read
The simplest example is the internal energy $E(S,V)$ for a $PVT$ system. The second law for reversible processes reads
$$dE = TdS - PdV = \delta Q - \delta W.$$
My question is not about this expression in parti... |
Helium-4 has a normal-superfluid phase transition which corresponds to the lambda line in the P-T diagram. The heat capacity at constant pressure $C_p$ shows a discontinuity when the lambda line is crossed. From universal scaling, the susceptibility associated with the order parameter has a divergence at the critical t... |
Schwartz's QFT equation (3.43) reads
$$ \mathcal{L} = - \frac{1}{4} (\partial_\mu A_\nu - \partial_\nu A_\mu)^2 - A_\mu J_\mu. \tag{3.43}$$
Does the contraction of $\mu$ on the last term carry over to the first term? In particular, is it the same as saying:
$$ \mathcal{L} = - \frac{1}{4} (\partial_t A_\nu + \partial_x ... |
Shouldn't the current passing through a resistor be lesser than that which passes through a circuit?
My understanding is that since Current = Charges/Time. If there exists a resistance to the flow of charges, then that must mean the charges slow down, meaning that more time is required to pass through a point. So, the ... |
I have heard people say that the heat equation isn't invertible because it smooths out irregularities that can not be recovered by backwards time evolution. But is this so? I will now argue that it can be inverted assuming that its Fourier modes decay quickly enough.
For a function $f(t, x)$, the heat equation is
$$ \f... |
My understanding is that since Current = Charges/Time. If there exists a resistance to the flow of charges, then that must mean the charges slow down, meaning that more time is required to pass through a point. So, the current should then decrease. But, since this opposition to the flow of charges doesn't exist in the ... |
I have a question that is bothering me, Lets assume that I have a parallel plates capacitor with distance $d$ between them. Now connect it to DC voltage source $V$.
according to equation $$V=\frac{Q}{C}$$ $$C\approx\frac{1}{d}$$ by getting the plates smaller I will decrese $Q$ because $V$ is constant in this case (I a... |
Consider a quantum system that is governed by a Hamiltonian with explicit time dependence $H(t)$.
Is it always legitimate to perform a Wick rotation $t \rightarrow -i\tau$, and calculate the time-dependent ground state with imaginary-time Schrodinger equation?
If not, what are the sufficient and necessary conditions to... |
A supervisor of mine claims that the following formula holds
$$
U = \rho V C T,
$$
where $U$ is internal energy, $\rho$ is density, $V$ is volume, $C$ is specific heat capacity and $T$ is temperature. I have tried to find this formula in the literature, but all I can find is the well known equation
$$
dU = \rho V C dT.... |
So I was thinking of using a barometric sensor to measure the compression of air in a tube in order to measure water level in a tank (Basic diagram below).
So based on the equation $ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $, I assumed that temperature remains constant (realistically it doesn't, but I will account f... |
Having 2 liquids I wonder which of the two is more viscous.
I'm not looking at precise values, but something like roughly "twice as viscous".
Without lab instruments, only using kitchen elements, is there a way to estimate roughly the difference in viscosity of 2 liquids?
|
There is a horizontal bar of length $10 \mathbb{m}$ and mass $1 \mathbb{kg}$ that is held up (somehow) in the earths gravitational field. A ball of mass $0.1 \mathbb{kg}$ inelastically collides vertically into the center of the bar from below. The system rises $1 \mathbb{m}$ before dropping. Now the ball inelastically... |
this the reaction formula:$H^2_1 + H^3_1 ->He^4_2 + n^1_0$ (idk how to put the numbers in the left)
and I have the released energy of one reaction $E_r=2,8.10^{-12}J$, How to calculate the released energy if the mass of $H_1^2$ is $1g$ and the mass of $H^3_1$ is $2g$?
$N_A=6,02 . 10^{23}$
so I have to calculate the num... |
For a positive constant $C$, the double well potential $V(x) = -C|x| $ exists between two infinitely high potential walls at $x=a$ and $x=-a$.
I wish to use the WKB approximation to obtain an equation determining the energy eigenvalues for $E<0$. From this eigenvalue equation, I should be able to determine the minimum ... |
I've spent the last couple of hours trying to derive the Lorentz Transformation from Maxwell's Equations. What I ended up with is $$L_{\nu}^{-1}=\left(\begin{array}{ll}
\frac{1}{\sqrt{1-v^{2}}} & \frac{-v}{\sqrt{1-v^{2}}} \\
\frac{-v}{\sqrt{1-v^{2}}} & \frac{1}{\sqrt{1-v^{2}}}
\end{array}\right)$$
Which matches exactly... |
There is a T-Shirt with this equation on it:
It says: And God said ... and the universe was ...
It looks like something related to General Relativity but I don't know what is it? Could you help me? Why the universe was ...?
|
The following is taken from Kittel's solid state physics.
An electron moving in a one-dimensional lattice of lattice constant $a$, suffers a periodic potential $U(x)$ where $U(x+a)=U(x)$. The periodicity of $U(x)$ implies $$U(x)=\sum_G U_Ge^{iGx}.$$ where $G=G_n=2\pi m/a$, the reciprocal lattice vectors. Due to periodi... |
I'm a bit confused with how the foucault pendulum works.
EDIT for clarity:
The Foucault pendulum shows an effect which is commonly described as follows: the plane of oscillation of the pendulum seems to rotate from the perspective of the person observing, who is on the same frame of reference as the Earth, due to the E... |
Assuming your object is symmetric, is there a way to tell whether it is positioned at A'' or A' purely by recording its movement from A to either location?
(I'm experiencing polystyrene beads being pulled out of a microscope's focal plane in an optical-tweezing experiment and wish to know which direction they are being... |
I've read that the Rindler horizon cuts off access to fundamental quantum fields and leads to a mixing of positive and negative frequencies via the Bogoliubov transformations. But here is where I have questions. How does this mixing happen? Does every horizon mix quantum fields?
|
Does the frequency of a tuning fork depend on the strength by which it is struck?
If yes, then how was the actual frequency(stated on the tuning fork) calculated? Was there a defined or average human strength
I found some resources at this site itself to understand this but it was still confusing
|
There is a construction of symmetry protected topological (SPT) states which roughly goes as follows. We start with a $d$-dimensional system with symmetry $\mathbb{Z}_2 \times G$ in the phase where the $\mathbb{Z}_2$ is spontaneously broken. To the $\mathbb{Z}_2$ domain walls, we attach a $d-1$ dimensional $G$-SPT, and... |
I guess this answer may depend on rimfire or centerfire ammo, but I was wondering if it'd be theoretically possible to shake a container of ammo enough to get one bullet to hit and ignite the primer in another bullet?
If it was, I'd think that transporting bulk/bagged ammo would be somewhat more dangerous but I'm guess... |
In the fifth edition of Optics Hecht shows that a superposition of wavefunctions (functions that satisfy the wave equation) is a solution to the wave equation. No problem there. He then claims
What this means is that when two separate waves arrive at the same place in space wherein they overlap, they will simply add t... |
I'm having trouble solving this problem:
By applying a harmonic force, acting on the end of a free bar of length $L$, a standing wave is formed due to multiple reflections:
Where are the nodes of the tensile stresses in it? What will be the amplitude of the driving force $F_o$, if the amplitude of the tensile stresse... |
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