Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Are wormholes evidence for traversal of a higher dimension? Warning, pop science coming.. please correct what I’m getting wrong. Einstein’s equations of relativity showed the potential for existence of wormholes that can connect different points in space time. I understand the mechanisms for their practical implement... | I guess so. At least according to the illustrations/analogies of folding paper. However there is nothing in Einstein's equations that require an existence of a higher dimension unlike in string theory. But if wormholes are proven to exist, then yes this could prove the possibility of higher dimensions since there is no... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/586941",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 2
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Why is pressure different at different points in the same level when the water is flowing? In fig.a below, water is to flow out from the yellow tank. But the flow is stopped because of the mercury in the green manometer. So the water is stationary. In this situation, the pressure at both the points A and B will be the ... | The Bernoulli equation (which ignores the effect of friction) expresses conservation of energy density. Changes in pressure are included to account for the work done by pressure between the two points under consideration. If the cross section decreases, the velocity must increase. The pressure does work in increasing t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587035",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Permissible Electrostatic Potential Let us consider a $1D$ real function $V(x)$. When is this a classical electrostatic potential?
My take on the problem:
*
*$V(x)$ must be differentiable everywhere. In fact, we should be able to differentiate it $n$ times.
*$V(x)$ should vanish at $\pm \infty$.
I think these are n... | I think that most conditions can be seen from the Poisson equation:
$$
\frac{d^2 V(x)}{dx^2} = -\rho(x).
$$
Thus, it should be differentiable everywhere except a few singular points. One often bypasses this issue by using generalized functions (delta-function and Heaviside step function).
However, there is no requireme... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Generalized Pauli matrices I wanna know the generalized form of Pauli matrices, for example for $3\times 3$. And do they satisfy all of the properties of Pauli $2\times 2$ matrices?
I wrote $3\times 3$ but I couldn’t write all Hermitian $3\times 3$ matrices with those.
| As @Charlie asks, the Pauli matrices have several properties, which generalize in different manners. They certainly, together with the identity, provide a complete basis for 2×2 matrices, but they are also hermitian. If Hermiticity is important to you, you generalize them as in the link provided, that is along the Gel... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587360",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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} |
Is $U^\dagger(R)\hat{H}U(R)=\hat{H}$ always true? Consider a Rotation transformation on momentum state,
$$U^\dagger(R)\hat{\mathbf{p}}U(R)=R\hat{\mathbf{p}}$$
Now the question is whether,
$$U^\dagger(R)\hat{H}U(R)=\hat{H}\,?$$
Here, $\hat{H}$ is the Hamiltonian of a free particle. Is it always true? Is there any counte... | There is a dot product in fact $\mathbf p^2 = \mathbf p^{\dagger} \mathbf p$. So one may do the following:
$$
U^{\dagger} \mathbf p^{\dagger} \mathbf p \ U =
U^{\dagger} \mathbf p^{\dagger} U U^{\dagger} \mathbf p \ U = (U^{\dagger} \mathbf p \ U)^{\dagger} U^{\dagger} \mathbf p \ U = (R \mathbf p)^{\dagger} R \ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587489",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Curl of electric field is not zero in the case of a steady current in a loop Say we got conducting circular loop connected to a battery . The electric field inside the loop obeys equation $\vec{J}=\sigma \vec{E}$.
Since the current flows in a circumferential way around the loop the electric field will be circumferenti... | Note that the curl of the electric field is not necessary to be zero in all cases. It's only valid for electrostatics.
Maxwell's equation here is valid through out the electrodynamics which given by :
$$\nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}$$
$$\nabla\times\mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}$$
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587705",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Interpretation of normal modes from the mathematical formula In the topic of small oscillations, the system below has a normal mode described by:
$$n_{1} = \frac{x1+x2}{2}.$$
This normal mode is represented as the symmetric mode:
In that case, the center of mass moves as a simple harmonic oscillator. However, the pic... | You should notice that the other normal coordinate is implied to be fixed at zero while you consider the motion along the normal coordinate $n_1$.
The normal coordinates of two particles (or blocks in this case) can generally be written as
\begin{align}
n_1 =& a_{11} x_1 + a_{12} x_2, \\
n_2 =& a_{21} x_1 + a_{22} x_2.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587871",
"timestamp": "2023-03-29T00:00:00",
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How we feel (perceive) exact size of object through our eyes? Light after getting reflected from objects gets focused on retina by our lens. The images formed on retina is small, which is then sensed by our brain and depending on distance we feel size of that object.
If an object is at particular distance from us, the ... | One eye perceives the angular size of an object. With two eyes we can get an estimate of the distance to the object. In combination these can let us estimate the actual size. Our estimate of size will often be dependent on the context in which the object is observed.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587964",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Heating cup in microwave? I heated my milk cup in the microwave today and noticed that the cup was hot but not the handle. Even if I heat it too much , cups handle temperature remains the same. How is that possible?
| Like Bob has mentioned, the container doesn’t absorb the microwave. The reason for this lies in quantum mechanics according to which the energy levels of atoms are quantised. This means the atom can’t have any arbitrary energy and can only absorb energy corresponding to the difference of the allowed energy levels (see ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/588033",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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What causes pressure in a liquid? Say there is a mass inside a liquid. What causes the force on its upside downwards and the force on its downside upwards? It seems logical that the downward force is due to the weight of the fluid above it, is it similar with the upward force? Just collision of liquid particles?
| Consider a vessel of any shape.
At any 2 or more points is the vessel that are coplanar,
no matter what the shape of the vessel, the pressure will be equal.
Just collision of liquid particles?
If an object is immersed in the liquid, pressure will act on all directions on it from the liquid's particles.
The net pressur... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/588150",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What conditions are necessary to guarantee uniform circular motion? Suppose an object is subjected to a force of constant magnitude, which is always directed to the origin. And suppose we know the initial position of the object relative to the origin, and the initial velocity of the object, can we determine if the obj... |
But can we go the other way around and deduce the equation of motion as I described above? Perhaps by solving the differential equation
$$m \ddot{\mathbf r} = - \lVert \mathbf F \rVert \frac{\mathbf{r}}{\lVert \mathbf r \rVert}$$
where $||\mathbf F||$ is constant
This would not be the correct equation of motion.
You ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/588485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does an observer outside an accelerating body rationalize the effects of pseudo force? Consider this following thought experiment: There are two tracks, one with a line of cameras and another on which a car with transparent sides moves (*). Now, imagine attaching a pendulum to the roof of the car, as the car accele... | I think the best answer here is that, from the perspective of the inertial observer, there just isn't anything to explain, as long as you've accepted Newton's laws. The pendulum bob is doing exactly what Newton's first law predicts it will do: maintaining its momentum in the absence of any forces on it.
The need for ex... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/588619",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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In the entropy formula, how do we know which one is a valid microstate for a particular macrostate? Consider a very long vertical cylinder containing air in thermodynamic equilibrium. Observe that the air column is necessarily bottom heavy. The macrostate is described in part by a pressure gradient that is due to gravi... | Remember that macro state parameters are derivable from the distribution of micro states. Concretely, macro state parameters like pressure, density etc are averages over micro states of like velocity, number density etc.
It is not true that for a gas in a gravitational field, the uniform density micro state does not c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/588734",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is a reflected wave on a string of the same form as of the incident Griffiths says that if a incident sinusoidal wave on a string gets reflected, it's form will be sinusoidal as well.
Why is it so? Does it hold for all wave forms in any medium?
| You already understand how a string can sustain and propagate sinusoidal waves in both directions. Having a reflector at one end is a boundary condition, one that is compatible with the string's motions. Since the string allows propagation both ways the boundary condition representing the model of the reflecting wall c... | {
"language": "en",
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Why don't we use the concept of axis of mass in place of center of mass? Being a high school student, I read the concept of center of mass and it was written in my book that
When a spinning ball is projected with some velocity , then all the points on the ball have complicated paths except the center of that ball whic... | If the sphere is fully symmetric, then you can't define "the" axis of mass, because ANY axis of the sphere would be equally good, so it's not a well-defined quantity. Only the center is well defined.
In general, in 3D Newtonian physics, an object actually has three "axis of mass," expressed by the Inertia Tensor. This ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/589219",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 10,
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Can quantum measurements be the origin of thermodynamic arrow of time? We can practically consider that the microscopic interactions are symmetric with respect to time(as we can neglect weak force for many cases which is the only interaction that can violate $T$ symmetry). So I thought that the asymmetry might be due t... | No, because "measurements" and "wave function collapse" are not part of the system modeled by QM; they're interpretations. As such, no physical phenomena can be effects of them.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/589435",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How is a free theory defined? In field theory, I've seen a free theory described as
*
*A field with the specific Lagrangian density ${\cal L}=|\partial\phi|^2+m^2\phi^2$
*A field whose equation of motion yields a linear set of solutions
*A field with non-interacting i.e. free normal modes
The first seems too speci... | By defining the action of a free moving object.
By free I mean it is not confined in a potential but I'm sure someone will argue self action. I mean we need a point mass or something which carries charge which implies a field. Moving charge implies work done. Which implies force which implies accelration which implies ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/589587",
"timestamp": "2023-03-29T00:00:00",
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How is torque transmitted between inclined surfaces? In the picture below, in a), a body K1 is pivotably attached to a bearing. My question is about the torque that results from a force exerted onto a surface of the body K1.
A first force F1 applied orthogonally onto the surface should result in a torque M1 in clockwis... | Don't wrap yourself around in pretzels. Even for planar cases, assume they are defined in 3D (with z-axis out of plane) and use the cross product to define torque
$$ \vec{\tau} = \vec{r} \times \vec{F} $$
which expands to
$$ \pmatrix{ 0 \\ 0 \\ \tau_z} = \begin{bmatrix} 0 & -z & y \\ z & 0 & -x \\ -y & x & 0 \end{bmatr... | {
"language": "en",
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A simplified version of the Fizeau experiment for measuring the speed of light? Long ago in high school I saw a short film in which as I recall the apparatus was just a spinning paper plate (with holes along its edge) with a light source -- I don't recall a spinning mirror or a half-silvered mirror -- and the entire ex... | Fizeau used a folded light path that was very long, and mirrors to bounce the beam back and forth, and a very high-speed motor running the slotted disc. There is no way to spin a paper plate fast enough in a classroom to perform the fizeau experiment with a classroom-sized baseline for the light beam.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/589781",
"timestamp": "2023-03-29T00:00:00",
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Why does a capacitor act as a frequency filter? What is it about a capacitor which allows it to filter frequencies?
I understand the construction of a high-pass RC filter, and the mathematics behind it, but I'm struggling to find an explanation of the physics behind the phenomenon.
In my mind I can picture the broad sp... | FWIW, I think of it as the capacitor having lower impedance at higher frequencies. As the frequency component of a signal gets higher, the capacitor in the RC filter diagram above looks more and more like a piece of wire, thus allowing more of the signal amplitude to be developed across the resistor. At low frequencies... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590006",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Why is the electrostatic force felt in straight lines? When two positive charges are kept close, they get repelled in the direction of a line joining both the charges. Why is it so?
Also, why is the repulsion in a straight path?
In both the cases, the potential energy of the charge which gets repelled decreases. What... | Just to elaborate on the symmetry argument - Let's suppose in your first diagram you are observing the two charges from the side and we assume, as you have done, that the repulsion direction is vertical and to the right. If we now observe the two charges from the top looking down, we are presented with the exact same s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590107",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 8,
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What are the best resources for Crystallography? I am undertaking a module in nanosurfaces and I was unaware that I would require some knowledge in Crystallography. The information that I must know regarding this area are Miller indices, Symmetries, Bracket conventions, so that I can answer some example questions such ... | I personally used The basics of crystallography and diffraction by C. Hammond in conjunction with my material science class and the book did a more than outstanding job in explaining the basic concepts that you would like to know.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590293",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Confusion about the dimension of a Hilbert Space in Quantum Mechanics In Quantum Mechanics, the quantum state of the physical system lives in an infinite-dimensional Hilbert space and can be written in terms of two different bases, the position basis (uncountably infinite) and the energy basis (countably infinite). App... | I am a mathematician and not a physicist, so I don't know the physical context and other physicists here are very welcome to correct my answer if it is wrong.
I think your confusion comes from the unfourtantate terminology of "basis" in the context of Hillbert spaces. There are two different concepts both happen to be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is Penrose's CCC consistent with Penrose's singularity theorem? According to Penrose's Conformal Cyclic Cosmology (CCC), there were universes prior to ours, prior to the singularity of our universe.
But how is this claim compatible with his famous singularity theorem, according to which spacetime geodesics cannot be ex... | My reading of the paper is that there is a singularity, in the sense of the singularity theorems, at the beginning of each cycle, but it's physically irrelevant because physics is precisely scale invariant there. The FLRW metric in terms of conformal time is $ds^2 = a(η)^2 (dη^2 - d\mathbf Σ^2)$, where the "coordinate"... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590844",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Argument on why spin correlation functions in Ising model decay exponentially with a correlation length? I'm reading Quantum Field Theory in Strongly Correlated Electronic Systems, Nagaosa.
Consider 1D Ising model,
$$H=J_z\sum_i S^z_iS^z_{i+1}.$$
on page 3, it says
The groud stae is 2-fold degenerate because the Hamil... | Let me write the Hamiltonian
$$
H = -J \sum_i S_i^z S_{i+1}^z.
$$
This choice will avoid some annoying (and irrelevant) signs.
One way to formulate the statement in the OP precisely is as follows.
Consider the variables $\delta_i=S_i^zS_{i+1}^z$. Since $\delta_i=1$ when the spins at $i$ and $i+1$ agree and $\delta_i=-1... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Meaning of complex conjugate in $T$-symmetry I have a question about the meaning of complex conjugation in time reversal symmetry in quantum mechanics.
$T$-symmetry in classical mechanics is defined simply by the substitution $t \to -t$. If I have an external magnetic field it is not enough and I have to substitute $ \... | Time reversal operator $T$, when acting on $i$, must result in $TiT^{-1} = -i$. This comes from the fact that $TxT^{-1} = x, TpT^{-1} = -p$, and commutation relation $[x, p] = i\hbar$.
Combine this fact with linearity of time reversal operator, we conclude that $T$ is antiunitary operator, and can be decomposed in the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the equivalent to $\Box A^\alpha =- \mu_0 J^\alpha$ using differential forms? The set of equations $$\Box A^\alpha = -\mu_0 J^\alpha$$
can be found in section 12.3.5 of Griffiths's book. From what I understand, the real-valued functions on both side of the equations are the coefficients of some $1$-forms with r... | Maxwell's equations can expressed in the language of differential forms.
In terms of tensors, Maxwell's equations can be written as
$$
\nabla_{\nu}F^{\mu\nu} = \mu_0J^{\mu}\,, \nabla_{[\alpha}F_{\mu\nu]} = 0
$$
where $F_{\mu\nu}$ is the Faraday tensor.
In terms of differential forms, these equations are written as
$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Understanding of electric potential's integration form I already known that the potential difference when a charge moves from A to B is
But I still have confusions about what does the infinitesimal of vector $s$ refers. I mean when you change the movement of the charge from B to A, the $\Delta V$ should be opposite nu... | you appear to have accounted for the change in direction twice. You need to first recall why reversing the limits change the signs in good old integration of functions in the cartesian plane. Although we simply put the minus sign, the reasoning behind it is that the new or infinitesimal change in x is negative of what... | {
"language": "en",
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Generalised Lorentz force expression from Classical Mechanics by Goldstein I am reading chapter 7 in the 3rd edition of Goldstein's Classical mechanics textbook and the expression for the Lorentz force is confusing me. I cannot scan it so I am just going to write it out verbatim and formulate my question afterwards. He... | TL;DR: The total derivative term
$$\frac{dA_\mu}{d\tau}~=~\gamma\frac{dA_\mu}{dt}
~=~\gamma\left(\vec{v}\cdot\vec{\nabla} A_\mu+ \frac{\partial A_\mu}{\partial t}\right)$$
in eq. (7.68) is correct. It should not be a partial derivative.
Before trying to read the relativistic formulation in section 7.6, I would strongly... | {
"language": "en",
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Shouldn't We modify the field in force equation $\mathbf{F}=q\mathbf{E}$? Consider charge particle $q$ in electric field $\mathbf{E}$. The force on the charge is given by
$$\mathbf{F}=q\mathbf{E}$$
Now we know that charge $q$ will also produce an electric field. Due to this field, the field already present in the space... | In the absence of particle acceleration the only way I know to alter the force on the particle is by proximity to a (neutral) conductor which would induce asymmetric surface charge on the conductor of the opposite polarity to the particle's.
The quantitative calculations are beyond intro physics. I'll let others delve... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Effect of motion on ball in a moving cart I know that in case of cart moving with an acceleration we are supposed to apply the concept of pseudo acceleration to judge the motion of ball in frame of the cart.
Now , consider the case where cart is moving with constant velocity. What will be the trajectory of the ball? ... | I think your terminology is confusing you - the correct term is pseudo-force, not pseudo-acceleration.
Introducing a horizontal pseudo-force in the reference frame of an accelerating cart allows us to pretend that objects that are stationary in the reference frame of the cart are in equilibrium, even though we know the... | {
"language": "en",
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Is Loop quantum cosmology replacing the Big Bang singularity with a big bounce? Am I correct in understanding that in the cosmological version of Loop quantum gravity, namely Loop quantum cosmology, the universe in all models starts with a big bounce? Are there other models, for example, the pre-big bang condition with... | Loop Quantum Cosmology is a finite, Symmetry reduced model of LQG, which for a layman means it arose from Loop Quantum Gravity. It predicts a Quantum bridge between the Expansion and the Contraction of the Cosmological branches. So, instead of having Big Bang, you have a Big Bounce. Loop Quantum Cosmology aims to descr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Confusion on repeated index for Einstein Summation The rule for Einstein notation is that the same dummy index cannot be repeated twice. However suppose I want to compute Christoeffel symbols:
$$
\Gamma^{\alpha}_{\beta\gamma} = \frac{1}{2}g^{\alpha\sigma}(\partial_\beta g_{\gamma\sigma}+\partial_{\gamma}g_{\sigma\beta}... | The Einstein summation rule is true for tensor-equations. Once you assume a form for the metric (diagonality), the equation you get is no longer a true tensor-equation (it is only true in some coordinate-systems). This is the reason why you need to write the summation by-hand from this point on.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/592468",
"timestamp": "2023-03-29T00:00:00",
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A tilted disk rolling on the floor First of all, an image to describe the situation we have:
Background
A uniform disc is rolling without slipping on a flat surface. The disc itself is also in circular motion about the point $O$. I have tried this with a roll of cellotape so the situation itself seems plausible. Wha... | This problem is in Introduction to Classical Mechanics by David Morin as problem 9.23.
Let the rate of precession of the coin be $\Omega$. Let the moments of inertia be $I = \frac 14 mr^2 $ and $I_3 = \frac 12 mr^2$ respectively. In this situation, it is most convenient to find $\mathbf{L}$ about the center of the coin... | {
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Matsubara sum with log term How do I compute the Matsubara sum
$$\sum_n \log\left(-i\omega_n +\frac{k^2}{2m}+\mu\right)?$$
If I have sums like
$\sum_n \frac{1}{i\omega_n -m}$, I can sum it up by calculating the sum of residues of the function $\frac{1}{z-m}g(z)$ at the poles where $g(z)=\begin{cases}
\frac{\beta}{\exp... | One possible approach is writing the sum of logs as a log of product and using the formulas for infinite products in Gradshtein and Ryzhik.
| {
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Why are we allowed to make algebraic calculation on units Is there math proof that we can cancel out units in Physics? For example:
$\require{cancel}distance = \frac{meters}{\cancel{second}} * \cancel{second}$.
So we see that seconds cancel out and we left with meters which is correct but how is it possible if it is no... | Good question. I don't have any elegant, deep mathematical answer for you. But let's consider an object moving at 3 m/sec and consider a time interval of 5 sec. We can lay out the object's progress along a line consisting of 5 sections, in each of which the object has moved 3 m. So the total distance moved is 3m + 3m +... | {
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Why doesn't a mercury thermometer follow the rules of volume dilatation? let's consider a classic mercury thermometer.
I do not understand why it does not behave like a "normal" thermometer which exploits volume dilatation. In a normal thermometer, I'd say that the mercury length would be proportional to its temperatu... | I think you are speaking of a clinical thermometer which records the maximum temperature it reaches. The thermometer has a narrow kink in the bore near the bulb that causes the mercury thread to break at that point when the volume of mercury in the bulb shrinks (the image you've posted actually shows that). As a conseq... | {
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Simplification using Newton's second law I am not sure if my simplification works in this problem:
Problem:
I have a beam which is strap around with cargo straps. First picture presents section through second picture. So applying Newtons second law:
$$F=G=\frac{m_{beam} g}{2} $$
so the F is the force in the cargo strap... | The forces you have calculated are acceptable. However there are other things you will need to consider from an engineering point of view.
Not so important:
Because the straps are not directly connected to beams, rather the beam is resting on it. The beam will also deflect due to self weight. To be safe I would also ch... | {
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What does it mean to treat space and time on equal footing? I often read from textbooks that in relativity, space and time are treated on an equal
footing. What do authors mean when they say this?
Are there any examples that show space and time are treated on an equal footing? Conversely, what examples show that space ... | Putting space and time on the same footing means to treat time as another dimension in addition to the other three physical dimensions. In the context of relativity, time is treated as another dimension (but within this idea of Spacetime space and time are not the same).
In classical Newtonian physics, space is treated... | {
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Meson as hadron and boson In wikipedia page about hadrons the following image appears:
I can understand why the intersection between hadrons and fermions are baryons, as a way to say a baryon is a kind of hadron composed of several quark fermions.
However, what is the meaning of the intersection between hadron and bos... | (Anti)quarks are spin 1/2, so two of them is either spin-0 or spin 1: bosons.
But it's more than that. The pions are (one of) the force carrying boson in quantum hadrodynamics, which is an effective field theory of nuclear interactions. Moreover, reactions like:
$$ p \rightarrow n + \pi^+ $$
look a lot like:
$$ \nu_e \... | {
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How could I see the distance light traveled from an airplane? It was nighttime. I was flying on an airplane. As we were landing we passed over a highway. I saw cars below with their headlights on. I could see that the light from their headlights only lit up a certain distance in front of them. Any object that fell past... | I just want to add one thing to BowlOfRed's answer.
Any object that fell past that distance would have probably looked dark to the driver.
Let $x_0$ be the distance from the driver to an object. Typically a few meters. Let $x_1$ be the distance from the object to the plane. 1000's of meters.
For an object lit up by t... | {
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Why does particle measurement cause quantum wavefunctions to collapse When we attempt to measure a certain property of a particle, how and why does its wave function collapse? I've tried to find answers on my own, but they've been far too complicated for me to comprehend. Would appreciate any answer with limited comple... | It postulates III that says,
If the particle is in a state $|\psi\rangle$, measurement of the variable (corresponding to ) $\Omega$ will yield one of the eigenvalues $\omega$ with probability $P(\omega)\propto |\langle\omega|\psi\rangle|^2$. The state of the system will change from $|\psi\rangle$ to $|\omega\rangle$ a... | {
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Glass state of water There is a lot of works on hard-sphere glasses where the spheres or other particles are squeezed and fail to find the global energy minimum being jammed in amorphous state. Is it possible to form a water glass by (perhaps, quickly) compressing water to very high density?
| Yes, water can form a "glassy" solid states, called amorphous ice.
Depending on conditions and formation process it can have quite different properties. In particular it is not necessary for it to be compressed to very high density: it is actually possible to obtain amorphous ice that is less dense than liquid water, b... | {
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Do 2d CFTs define healthy 4d QFTs? When doing 2d CFTs we typically complexify coordinates and formally consider $\mathbb C^2$, with the understanding that, in the end, we are to restrict to the real slice $\bar z=z^*$. If we do not impose this, but regard $z,\bar z$ as truly independent, does the resulting object defin... | Correlation functions in 2d CFT are single-valued on $\mathbb{C}$ but not in $\mathbb{C}^2$.
For example, in minimal models, four-point functions are of the type
$$ Z(z) = \sum_{i=1}^n c_i F_i(z)F_i(\bar z) $$
where $F_i$ is a hypergeometric function or generalization thereof, and $z$ is the cross-ratio of the four pos... | {
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Quantum mechanics and rigorous math I was reviewing a little of quantum mechanics in a rigorous way, so i realized there is a lot of concepts similar in words but different in its meanings, i would appreciate any help to understand it:
Kets -> It is the "physics entity" you are measuring: Momentum, energy, etc...
Opera... | Very short and brief summary of quantum mechanics, please comment if there are mistakes
Ket vs. State
Each equivalence class of kets (vectors) which differ from each other by a (multiplicative) complex number is called a ray in Hilbert space (which is a complete inner product space). Each ray represents a state uniquel... | {
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Net Work Done When Lifting an Object at a constant speed I am confused about the amount of work done when lifting an object at a constant speed. If you find the work done by you on the object and the work done by gravity on the object and add them the net work would be 0. How is there an increase in Potential Energy if... | If you lift a heavy box off of the floor and place it on a high shelf you have done work to increase the box's gravitational potential energy. The net work you have done against gravity is not zero. If the box later falls off of the shelf this potential energy is converted to kinetic energy as gravity accelerates it do... | {
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Can coldness be converted to heat energy? We know that the heat can be converted into heat energy with the help of thermoelectric generators, but why can't we generate energy from coldness?
Like the temperature of the universe in 1 K, can this be used in the near future to be used as an energy resource for probes or sa... | Heat is not “converted to heat energy”. Heat is the transfer of energy due solely to a temperature difference. Without a temperature difference there can be no heat. The consequences of that transfer can, but doesn’t necessarily, result in work.
In the case of the thermoelectric effect, heat can generate a voltage whic... | {
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Shouldn't the projection on the y-axis, of a radial vector in a circle making an angle theta with the x axis, also be the radius?
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 (si... | If think that shadow is not going to be the proper term here, since if you want to talk about shadows you have to say from where the light rays are coming. What we're using here is the idea of orthogonal projection in this, if you want still to think about shadows, the light rays come orthogonal to one of the axis.
For... | {
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Why does ponytail-style hair oscillate horizontally, but not vertically when jogging? 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 think the longitudinal oscillations of a ponytail are quickly damped (more precisely overdamped), since they involve layers of hair sliding along each other, as well as inelastic collisions of the back of the neck. On the other hand, the transversal oscillations require merely twisting the ponytail near the elastic b... | {
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Can spacetime be curved even in absence of any source? Einstein's equation in absense of any source (i.e., $T_{ab}=0$) $$R_{ab}-\frac{1}{2}g_{ab}R=0$$ has the solution $$R_{ab}=0.$$
But I think $R_{ab}=0$ does not imply that all components of the Riemann-Christoffel curvature tensor $R^c_{dab}$ be zero (or does it?). F... | You are right. $R_{ab}=0$ does not imply $R^{a}_{bcd}=0$. For one thing, $R_{ab}$ has 10 components (in $n=4$ dimensions), whereas $R^{a}_{bcd}$ has $20$ components. The simplest example I can think of is Schwarzschild solution, which has $R_{ab}=0$ everywhere but $R^{a}_{bcd}\neq0$. If you allow the inclusion of a cos... | {
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Can liquids exert/be affected by normal force? I am doing a problem in which I am drawing free-body diagrams for different objects in a system, and two of the objects which are included in my scenario are Earth and a body of water which is resting directly on earth (the tank/container is being ignored).
What is the for... |
I am looking for a force similar to the normal force, but as far as I can tell, the normal force can only exist between two SOLID objects, not a solid and a liquid.
Not quite; liquids can also apply/receive a normal force. The catch is that additional normal forces must act in the other two directions as well. (For e... | {
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Transformations in classical field theory and configuration space When transforming a field in classical field theory the transformation of the four-gradient of this field follows automatically. At least this is what i have learned in my lectures.
This circumstance kind of contradicts my understanding of the Lagrange f... | That seems to be a misunderstanding. The field-theoretic case behaves in essentially the same way as the point mechanical situation.
*
*On one hand, the arguments of the Lagrangian density $${\cal L}(\phi,\partial_t\phi,\partial_x\phi,\partial_y\phi,\partial_z\phi,t,x,y,z)$$ are independent variables in the same way ... | {
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Anti-symmetrized total tensor of two anti-symmetric tensors Suppose we would like to anti-symmetrize a tensor
$$T^{\mu_1, \mu_2,\ldots, \mu_n} = G^{[\mu_1, \mu_2,\ldots, \mu_r]} H^{[\mu_{r+1},\ldots, \mu_n]},$$
where $G$ and $H$ are anti-symmetric. One could do this iteratively by applying the anti-symmetrizer
$$\Lambd... | One can think of this problem as all different swaps with the components of the two tensors. With this in mind, we start by defining the index ordered tensors
$$G^{\{\mu_1,\ldots, \mu_r\}} = G^{[\mu_{j_1},\ldots, \mu_{j_r}]},$$
where $(j_1,\ldots, j_r)$ is a permutation of $(1,\ldots,r)$ such that $$\mu_{j_1}< \mu_{j_2... | {
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The thin target approximation in particle physics In the first paragraph of chapter 2 in this paper, the authors say that an effective volume is reduced to an effective area, when the thin target approximation is valid.
What is the thin target approximation, and why this approximation is valid when the interaction leng... | When a beam of $N$ particles hits a target of density $n/A$ (e.g. per square cm) with a reaction cross section of $\sigma$, the number of scattered particles is:
$$N_S = N\frac n A \sigma $$
It is standard to use an areal density for the target because that is what the beam sees: stuff in its way. The depth isn't relev... | {
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How does radiation (heat) take away momentum? In another post, I was taught that when we are moving (running, for example), radiation (in the form of heat, both from our muscles and friction with the ground) takes away from our momentum. That makes perfect sense and I understand.
I was also taught that heat/radiation i... | Radiation will not "know" that it is being emitted by a uniformly moving body, so from the prespective of the body it will be emitted uniformly in all directions. Momentum will be lost to the body to a very small degree, though, because the mass of the body will be reduced by a very small degree due to energy/mass equ... | {
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How to transform velocity 4-vectors to Zero Momentum Frame I have a particle $p$ with speed $u$ in lab frame approaching a stationary particle $q$.
The $p^{\mu}$ and $q^{\mu}$ velocity 4-vectors are:
$$p_{LAB}^{\mu}=\gamma_u(c, u, 0, 0)$$
$$q_{LAB}^{\mu}=(c, 0, 0, 0)$$
To get to ZMF, I need a standard lorentz boost wit... | Here are alternative approaches to @Philip's answer (where the masses of your particles are assumed equal).
*
*Although Galilean-velocities add linearly, [real-world Minkowskian-]velocities don't...as you found. In fact, Euclidean-slopes also don't add linearly. (Linearity of Galilean-velocities is more the exception... | {
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Isn't $\epsilon_{ij}$ an isotropic, rank-2 tensor? Definition of isotropic tensor: components are unchanged after rotation: $T_{ij}\rightarrow T_{ij}' \equiv R_{ia}R_{jb}T_{ij} = T_{ij}$
MathWorld says there is only one rank-2 isotropic tensor, $\delta_{ij}$.
But with
$$\epsilon_{ij}=\left(\begin{matrix}0&1\\-1&0\end{m... | I think @mikestone's comment is correct. The MathWorld site is talking about tensors in 3 dimensions, not 2D. In 3 dimensions (actually, in all dimensions $\geq3$), it can be shown that any isotropic rank-2 tensor is proportional to the identity ($\delta_{ij}$), see Richard Fitzpatrick's notes here, for example.
In two... | {
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How is most of the forces occurring around us related to electromagnetism? Here is an extract from my textbook-
Most of the phenomena occurring around us can be described under electromagnetism. Virtually every force that we can think of like friction, chemical force between atoms holding matter together, and even the... | In physics, There are four fundamental forces of nature which give a rise to other phenomenological force, for example, friction. Such forces are commonly encountered in everyday physics and are approximately described by empirical equations because the concept of force is meaningful only if one knows how to solve prob... | {
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Unruh effect: should Minkowski vacuum transform according to different observers? It's known that the Minkowski vacuum is observed as a thermal bath for Rindler observers, in paticular:
$\langle0_{M}|N_{M}|0_{M}\rangle=0 \space\space\space\space\space\space\space $ (1)
$\langle0_{M}|N_{R}|0_{M}\rangle \neq 0\space... | The fact that in your two equations there's $|0_M \rangle$ comes from what you want to measure. The first one is trivial to interpret: It is the number of particles in the Minkowski vacuum for the Minkowski observer. But the second one is a bit tricky: It is the number of particles in the Minkowski vacuum from the poin... | {
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If $Q = mC_p\Delta T$, shouldn't $C_p$ be updated every increment? Considering that the specific heat capacity of a material is a function of temperature, is it wrong to assume that $C_p$ is constant for notable differences in temperature ($>50\mathrm{K}$)?
It is something that I just noticed but can not find a conclus... | To reflect the dependence of $c_p$ on temperature, the equation should be $Q = m\int_{T_0}^{T_f}c_p(T)\enspace dT$. You perform the integration to obtain Q. Yes, $c_p(T)$ is a function of temperature, in general, but for solids over a small temperature range it is relatively constant.
| {
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How come the formula $W=Fd$ doesn't apply for energy stored in springs? I always thought that work is like the energy transferred and it is given by $W=Fd$, but this concept gets problematic for springs.
If the force $F$ is applied to a spring which compresses it by a length $d$, then apparently the energy stored in th... | I think that this question shows a misunderstanding of calculus rather than that of the
physics.
For constant forces, the work is defined as:
$$ W = F \cdot s$$
For applying this to calculate work of variable forces
Consider an interval of extension $(x_o, x_o+h)$, if we were to shrink the size of $h$ to become very sm... | {
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Relativistic energy of harmonic oscillator What is the relativistic energy of an harmonic oscillator:
$$\frac{m_0 c^2}{\sqrt{(1-\frac{v^2}{c^2})}}+\frac{1}{2}kx^2$$
Or
$$\frac{{m_0 c^2}+\frac{1}{2}kx^2 }{\sqrt{(1-\frac{v^2}{c^2})}}$$
I think the first one is true but I need an exact logic or derivation.
| What you need here is the special relativity version of the work-energy theorem.
The proof is given in many places, including that Wikipedia page, but you start out from the idea that the relativistic force is given by :
$$\vec{F}=\frac{d}{dt}(\gamma m_0 \vec{v})$$
and you will (after some math) get :
$$m_0c^2(\gamma_2... | {
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Mathematical Definition of Power I am a high school student who was playing around with some equations, and I derived a formula for which cannot physically imagine.
\begin{align}
W & = \vec F \cdot \vec r
\\
\frac{dW}{dt} & = \frac{d}{dt}[\vec F \cdot \vec r] = \frac{d\vec F}{dt} \cdot \vec r + \vec F \cdot \frac{d\vec... | The work done by a force is not defined by $W=\mathbf F\cdot\mathbf r$. Work is instead defined in terms of a line integral over a path (your equation just assigns a work for a force and position, which does not match what we mean by the work done by a force). We have
$$W\equiv\int\mathbf F\cdot\text d\mathbf r\to\text... | {
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Independent variables of the inner energy in thermodynamics the free energy is a function of the volume V and the temperature T. These two variables are called independent. On the other hand on can find the volume and the temperature as a part of the ideal gas equation, which means that they are related to each other.
... | The ideal gas equation links the temperature volume and pressure, so it allows you to determine one of these parameters in terms of the other two. So we can consider the ideal gas equation as determining the pressure in terms of volume and temperature, leaving $T$ and $V$ independent.
| {
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Why do low-energy waves produce heat, but high-energy waves do not? Radio waves, microwaves and infrared are known to produce heat and even cause burns, while visible light and ultraviolet are not. This seems counterintuitive to me, as the latter contain the highest amount of energy.
Why is this? Does it have to do wit... | I'd like to add to the other answers by mentioning that absorbance is a function of photon frequency (thus also the photon energy, through $E = h \nu$). For instance, here's a Wikipedia article on the absorbance of water.
| {
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Meaning/origin of the boltzmann curve I have physical data and I wanted to use a logistic function to fit them. In this context, I came across the so-called Boltzmann-fit which fits nicely to the data but since I wonder where does it come from:
I struggle to separate (if even possible) that Boltzmann-fit from the Max... | Most physicists would call this fitting by a Fermi function, since Fermi function
$$
f(E)=\frac{1}{1+e^{\beta(E-\mu)}}\approx_{\beta\rightarrow 0} e^{\beta(\mu-E)},
$$
which gives you Boltzmann distribution only in a high temperature limit (second equality). While it is not clear where the term Boltzmann-fit comes from... | {
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Why every system tends to be more stable? An entire topic of inorganic chemistry, i.e. chemical bonding, which is also one of the most important topics, is based on the idea of stability. But whenever I ask why every system tends to get stable, I never get a satisfactory answer. People say that's how nature "wants" to ... | A system state is called stable if the system returns to that state when is disturbed by a small amount. As well as that, if the system gets similar enough (which might not actually be very similar) to a stable state the system will transform to the stable state.
In this sense a system tends to become stable because st... | {
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Why is it impossible to measure position and momentum at the same time with arbitrary precision? I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is sharply peeked its fourie... | The OP wrote:
I understand that for a given wavefunction that if $\Delta x$ is small, $\Delta p$ will be big and how this arises from fourier transformations. But I fail to see how this prevents anyone from doing a simultaneous measurement of both $x$ and $p$ with infinite precision.
This seems to boil down to the is... | {
"language": "en",
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"source": "stackexchange",
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Why is it easier to handle a cup upside down on the finger tip? If I try to handle a tumbler or cup on my fingertip (as shown in fig), it is quite hard to do so (and the cup falls most often).
And when I did the same experiment but this time the cup is upside down (as shown in fig), it was quite stable and I could han... | Think about the position of the center of mass of the cup.
Assuming it's not one with an oddly heavy bottom or flimsy walls, the wallwill place that center of mass around the middle of the hollow interior of the cup.
Your finger acts now as a fulcrum point. Thus, the center of mass and your finger tip, in effect, form ... | {
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Why don't we have just one type of charge? Why do we need two? Why do we need to admit two types of charges (positive and negative)? Can't there be a third type?
| If you take a collection of materials (glass, amber, polythene, perspex, pvc, polystyrene....) and rub them with a soft insulating material, they acquire charges. You discover that all these rubbed materials can be put into just two categories. All those in one category repel each other and attract any of those in the ... | {
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Please explain the meaning of below statement Newtons second law is a local law.
(In the book,it says that it means that it applies to a particle at a particular instant without taking into consideration any history of the particle or its motion.)
Um, I couldn't understand what do they mean by " taking into considerati... | When the word local is used here in Newtonian physics to describe an object or interaction, it means “happening at a particular point in space at a particular time”. This means that you must ignore it’s previous history/trajectory.
For example, if we consider a local force $F(x)$ acting on a particle, this means that ... | {
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Completeness relation of spherical harmonics In spherical coordinates, the resolution of the identity can be written as $$ 1=\int_0^{2\pi}d\phi\int_0^{\pi}\sin\theta\, d\theta\, |\theta,\phi\rangle\langle\theta,\phi| \equiv \int d\Omega |\Omega\rangle\langle \Omega|,$$ where $|\Omega\rangle = |\theta,\phi\rangle$. For ... | For $\delta^{(2)}(\Omega-\Omega')$ to behave like a delta function, we should get $1$ when we integrate it over the surface of the unit sphere. In other words, we should have that
\begin{equation}
1=\int {\rm} d^2 \Omega \delta^{(2)}(\Omega-\Omega') = \int {\rm d}\theta {\rm} d \phi \sin \theta\delta^{(2)}(\Omega-\Omeg... | {
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Engine rotating a generator at its rated speed, but engine power exceeds power required? What would occur if a gasoline engine would be driving a generator (specifically, a permanent-magnet synchronous AC 3-phase sinusoidal generator) as its only load at the output shaft and if that engine is rated at i.e. 35kW @ 8000 ... | For a real application, the engine would have some type of feedback control that attempted to hold the engine at a constant rpm. If the load increased, the rpm would decrease, and more fuel would be sent to the engine to get back to the rpm setpoint. The opposite would happen if the load decreased. For the "extreme"... | {
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Work done when you bring an bringing an object down from a height I am going to explain this question through an example.
Suppose I lift an object I apply a force $mg $ then I apply additional force, that would be $ma $ so total force would be $m(g+a)$. My doubt is that the work done by a person in lifting a box by app... | Normally in lifting, you apply a momentary extra force to get the object moving, and then proceed at a constant speed. As Dale points out, the extra work goes into kinetic energy.
| {
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Some questions regarding graviational potential energy and the concept of potential energy in general Starting off, I first want to know the relation between work and potential energy.
$\Delta\mathbf U = - W $
How was this expression formulated?
Moving on,
My second doubt was in the derivation of the expression:
$\math... | Let's start by the definition of work. For simplicity I use,
$W = F \cdot \Delta x$
$W = m a_x \Delta x$
recall, $v^2 -v_o^2 = 2 a_x \Delta x $, so
$W = \frac{1}{2} m (v^2 -v_o^2 )$
$W = \frac{1}{2} m v^2 - \frac{1}{2} m v_o^2$
$W = K_f - K_i$
where $K$ is the kinetic energy.
Now, let's look at the conservation of ener... | {
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Why can ropes pull but not push? If I have object that is heavy, I can pull it with rope but cannot push it. Why? What breaks the symmetry of the system? I can push or pull anything if I choose, so why is the push possibility not possible?
| I think this is the most complex answer possible to OP's question; I don't know if I should be proud or ashamed of myself.
I can pull it with rope but cannot push it. Why? What breaks the symmetry of the system?
The system has symmetries, but not the one you are thinking about, you are confusing yourself. The true sy... | {
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Why don't opaque objects reflect light? My sister was doing a quiz and I tried to point her in the right direction by giving her scenarios to imagine. One of the questions in the quiz was:
Which of the following objects do not reflect light:
*
*Polished metal
*Mirror
*Undisturbed water
*Book
She suggested that ... | This is a case where there's a word that technically refers to a general category, but is often used to refer to a particular subset of that category. The term "reflection" can refer to any redirection of light, but is often understood to refer to specular reflection. If the teacher had asked "Which of the following ob... | {
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Derivation operators as arguments or the Hamiltonian In a book I am reading about QFT (Quantum field theory by Mark Srednicki ,page 48), I see the following equation:
$$
\int \mathcal D p\mathcal D q \exp\left[i\int_{\mathbb R} dt (p\dot q - H_0(p,q)-H_1(p,q) +fq+hp)\right] $$
$$=\exp\left[i\int_{\mathbb R} dt (H_1(i\d... | Let's look at an ordinary integral
\begin{equation}
\mathcal Z(h) = \int dx e^{-f(x) + xh},
\end{equation}
with $f(x)$ such that the integral is convergent. It should be obvious that
\begin{equation}
\int dx \, x \, e^{-f(x)+xh} = \frac{\partial}{\partial h} \int dx \, e^{-f(x)+xh}
\end{equation}
or
\begin{equation}
\i... | {
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Analytic solution to Kepler's Problem, exegesis From 'Solving Kepler's Problem' by Colwell, the first analytic solution to Kepler's Problem used a theorem of Lagrange, and later Burmann, to invert Kepler's equation. When you look on the internet for a proof you find these lines that begin the section on Burmann's theo... | first solve this equation for x:
$$-2\,{\frac {\varphi _{{b}}}{\varphi _{{{\it ss}}}}}+2\,{\frac {
\varphi _{{s}}}{\varphi _{{{\it ss}}}}}\,x+{x}^{2}
=0$$
where:
*
*$\varphi_b=\phi(z)-b$
*$\varphi_s=\phi'(a)$
*$\varphi_{ss}=\phi''(a)$
*$x=z-a$
you obtain :
$$x={\frac {-\varphi _{{s}}\pm\sqrt {{\varphi _{{s}}}^{2}+... | {
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Why can't dark matter lose energy by gravitational waves and collapse into itself? Because of lack of electromagnetic induction, dark matter can't lose its gravitational potential energy. That is preventing it from collapsing like an ordinary matter cloud in space.
But why can't dark matter lose energy by gravitational... | It is really hard to create gravitational waves and we only see a significant amount of energy going into gravitational waves under extreme circumstances. Any obvious example of this is the black hole mergers detected by LIGO, or the first indirect detection was from the loss of energy from a pair of neutron stars orbi... | {
"language": "en",
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Why does air pressure decrease with altitude? I am looking to find the reason: why air pressure decreases with altitude? Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses? Does earth’s spin cause a centrifugal force? Are the molecules at higher... | The air pressure at a given point is the weight of the column of air directly above that point, as explained here. As altitude increases, this column becomes smaller, so it has less weight. Thus, points at higher altitude have lower pressure.
While gravitational force does decrease with altitude, for everyday purposes ... | {
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Why doesn't decoherence spoil the double slit experiment? Imagine firing one electron at a time at a double slit. Clearly the wave function interacts with the atoms of the material, and presumably many electrons do not pass through. Why does decoherence from these interactions not spoil the experiment?
The question has... | One should distinguish the idealized model discussed in textbooks and real interferometers. Decoherence is indeed an issue in many experiments, which is why realizing such interferometers in practice has been challenging.
What is more surprizing, is that some degree of decoherence is present even in the simplest discus... | {
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Why is the net force acting on a massless body zero? I know that massless bodies can accelerate (in theory) even with the net force equaling to zero. But, why cannot there be a net force on a massless object? Why does it always have to be zero as a resultant in the end?
I'm talking about object whose mass is assumed to... | Massless objects cannot be accelerated. You cannot apply force on them. Massless object ALWAYS move on the shortest path between two points. The only two things that you can do to a massless particle are 1) in presence of gravity the shortest path between two points is not a straight line (i.e. Euclidian straight line)... | {
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How does a capacitor get charged instantly in AC whereas it takes infinite time in DC? I have seen when a capacitor is connected to a dc source it takes infinte time to charge, but when connected to ac it takes the potential of the source instantly,
probably the approach in the books is not adequate, please clarify,
He... | The site that you mention says
When a capacitor is connected across a DC supply voltage it charges up to the value of the applied voltage at a rate determined by its time constant.
However the time constant is $\tau = RC$ so it is not a property of the capacitor by itself, but rather the circuit.
Their example circui... | {
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If i wrote something in the sky what would the radius of visibility on the ground? If i wrote something in the sky 8500-10,000 ft high 40 ft tall letters what would be the visibility radius on the ground? Or what formula would i use to come up with the answer?
| Let's assume that you want to write your letters in a square large enough for a little phrase and spacing. Call $\theta$ the angle of the effective field of view (FOV) of the eye (most of our visible area is a little blurred, we have almost a 180° view but we can see clearly only a small angle). here's a little picture... | {
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Flavor changing weak neutral current and $Z^0$ boson In Peskin QFT p.725, it says:
The $K^0$ meson could decay by $Z^0$ exchange if this boson coupled to a flavor changing weak neutral current.
However, $Z^0$ boson does not couple to a flavor changing weak neutral current. Just look at the $Z^0$ current at Peskin Q... | We know by now that the Standard Model (SM) is a pretty good description of nature, so the effects of Beyond the Standard Model (BSM) physics are going to be small, at least in the regimes that we are able to probe experimentally. For that reason, it is very difficult to see the effects of BSM physics on a process wher... | {
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How many different vacuums are there in the string theory landscape? Different sources give different estimates, from $10 ^{100}$, $10 ^{500}$, $10 ^ {20,000}$, while others write that there are infinitely many of them.
|
How many different vacuums are there in the string theory landscape ?
I never studied string theory, however this question should be bend in slightly different direction.
Wiki on String-Landscape gives estimates in range $[10^{272,000}; \infty]$. But does it really matters ?
Question should sound like:
How many diff... | {
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Number of variables in the Hamilton-Jacobi equation In Goldstein's Classical Mechanics, while introducing the Hamilton-Jacobi equation, he argues that the equation $$H(q_1, ... , q_n; \frac{\partial S}{\partial q_1}, ..., \frac{\partial S}{\partial q_n}; t) + \frac{\partial S}{\partial t} = 0$$ is a partial differentia... | *
*The HJ equation is a non-linear 1st-order PDE in $n+1$ variables $(q^1,\ldots,q^n,t)$, namely the generalized positions and time, which in principle enter on equal footing.
*A complete$^1$ solution, known as Hamilton's principal function $S(q,\alpha,t)$, should not be conflated with the off-shell action functiona... | {
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Will this spaceship collide with the star? (time dilation) I thought of the above thought experiment and arrive on 2 conflicting conclusions. I can't seem to identify the flaw in my reasoning.
Suppose there is a star 4 light years from earth that has will explode and turn into a white dwarf in 3 years (as measured in t... | $t'=0$, $x'=0$
B: $t'=6-4\sqrt3\approx -.928$, $x'=8-3\sqrt3\approx 2.804$
C: $t'=4/\sqrt3\approx 2.309$, $x'=0$
As you can see, the order of events in the earth frame is first $A$, then $B$, then $C$ (the ship leaves earth, then the star explodes, then the ship reaches the star). The order of events in the ship frame... | {
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Does Work become state function in an Isothermal Process and what are other processes in which it happens? In a reversible isothermal process and for an ideal gas we know from the definition of Helmholtz free Energy
$dF= -SdT -PdV$.
And as temperature doesn't change for an isothermal process, $dT$ must be zero. So dF c... | The fact that work can equal the change in a state function, as in the case of an adiabatic process where work equals the change in internal energy, does not mean that work is a state function.
A state function is a system property. Work (and heat) is never a state function because work is not a property of a system. W... | {
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Why is there a specific negative sign in front of the $m_{12}$ term of the 2HDM Higgs potential? Why is there a specific negative sign in front of the $m_{12}$ term of the 2HDM Higgs potential?
(but not for the $m_{11}$ and $m_{22}$)
See for example: https://arxiv.org/abs/1106.0034
Eq. (2) Page 6:
$$
V = m_{11}^2\Phi_1... | Usually, arbitrary signs and phases are chosen to minimize the number of explicit signs and phases that appear later, for convenience. In the paper you linked, the sign chosen for $m_{12}^2$ ensures that it appears with a positive sign in the mass terms for the charged scalars in equation (5), and with a positive sign ... | {
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How to compute gauge potential $A$ from the field strength $F$? Let $F=dA+A \wedge A$ be the field strength that solves vaccum Yang-Mills equation.
The question is: how to recover the gauge potential $A$? Is there any standard way? or any theorem stating the solvability? Suppose the metric is $g=g_{\mu \nu}dx^{\mu}dx^{... | To supplement the answers that were posted earlier, here's an explicit example from ref 1. This example proves that $A$ is not always uniquely determined by $F$, not even up to gauge transformations, not even locally.
Work in four-dimensional spacetime with coordinates $(w,x,y,z)$, and take the structure group to be $S... | {
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Interpretation of Hooke's Law I often see people interpreting Hooke's Law $σ=Eε$ as,
"The deformation $ε$ that occurs when you subject a material to a stress $σ$."
This makes it sound like stress is an external stimulus that causes the material to deform. But from what I know, stress is an internal phenomenon, not an... | Unfortunately, both descriptions are misleading because both describe the relationship as a one-way cause-and-effect relationship. The correct way to describe it is
the stress is proportional to the strain
It doesn’t matter if the stress is given and the strain is obtained by Hooke’s law or if the strain is given and... | {
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How can $1/V$ be equal to $0$ in Boyle's Law? In relation to ideal gases, Boyle's Law states that pressure is inversely proportional to volume under constant temperature. In other words,
$$P \propto 1/V$$
Below is a graph that plots pressure, $P$, against inverse volume, $1/V$.
How can $1/V$ ever equal zero? How is th... |
How can $1/V$ ever equal zero?
Physically, it can't. This is just a point on a line - it does not have to correspond to an actual physical situation. It is like saying the average family has $2.3$ children - this does not mean any actual family can have $2.3$ children - it just means if you take a large number of fam... | {
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Why do neutrons have magnetic moments with spin? Neutrons are neutrally charged, but apparently they have magnetic moments with spin.
What is the intuition behind this?
| A neutron is a composite particle consisting of three pointlike quarks. These carry fractional electric charge which adds up to zero, so the neutron has no net charge. But since the quarks do carry nonzero charges, if they are spinning around inside the neutron then it is possible for the neutron to possess a magnetic ... | {
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How can there be current without charge? This might be a stupid question, but I actually think that it is not so obvious:
When solving Maxwell equations, depending on the problem usually a charge and current density are assumed.
However, how can there be any current without charge density?
I understand that in most pro... | In the absence of a changing magnetic flux, a current flow requires a separation of charges. If you connect a long looping uniform conductor to the terminals of a battery, a variable charge density is require to maintain a uniform field and current density in the conductor. There will be a positive charge density nea... | {
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"answer_id": 2
} |
Where does the law of conservation of momentum apply? Take the scenario of a snowball hitting a tree and stopping. Initially, the snowball had momentum but now neither the snowball nor tree have momentum, so momentum is lost (thus the law of conservation of momentum is violated?). Or since the tree has such a large mas... | Momentum is conserved only if there is no net external force on the system.
Consider the snowball and the tree as the system. In your case, the earth provides an external force on the tree, so the momentum of the snowball/tree system is not conserved. If the tree is "suspended" (not attached to the ground) momentum wo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/605982",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 7,
"answer_id": 3
} |
Can thermodynamics be considered logical? One of the laws says that heat won't flow from cool to warm and at the same time this same theory claims that there is a finite (albeit tiny) chance that it will, because there is always such a microstate.
We can also have a situation where all air molecules in the room can be ... | There are two different views on thermodynamics, two approaches.
We can build thermodynamics as a phenomenological theory based on some postulates. According to this theory, heat will not flow from a cold body to a hot one. Never ever. And in this theory there is no concept of a microstate at all. But this theory is ph... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/606095",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Do atoms always move in phase within the unit cell for acoustic mode phonons? In my condensed matter book it says 'For the acoustic mode, all atoms in the unit cell move in-phase with each otehr (at $k=0$) whereas for optical modes they move out of pahse with each other (at $k=0$)'.
I saw that in the example given this... | At $k=0$, acoustic phonons correspond to macroscopic translation of the entire crystal, which naturally are completely in phase and cost zero energy. This behavior is essentially by definition and is always true as acoustic phonons are the Goldstone modes of translation. In other words, the energy of the crystal should... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/606201",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What experiment confirms $\mathbf{J}^2 = \hbar^2 j(j+1)$? I learned that if we measure the spin angular momentum of an electron in
one direction $J_z$, we get $\pm \frac{1}{2} \hbar$. But if we measure
the magnitude of the angular momentum $\mathbf{J}^2$, we should get
$\frac{3}{4} \hbar^2$. What experiment gives the... | I suppose we measure spin component $S_z$ by measuring the shift in energy spectrum when we add a magnetic field, which gives an extra term $B_z S_z$ in the hamiltonian.
Similarly, to measure $S^2$ we probably need a term that relates it to some energy.
The one I thought of is Fine Structure correction of the hydrogen ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/606292",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 2
} |
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