Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Basics of centripetal force Suppose an object is moving in a circular path. We know that the net force that is working on that object is the centripetal force towards the center. But the object should have gone closer towards the center in that case due to the radially inward force working on it, but it doesn't. Why do... | When going in a circle at constant speed, velocity changes. Velocity is speed and direction. Direction changing, is velocity changing. Changing velocity is acceleration. So, it takes acceleration to move in a circle. By $F=ma$, that takes force. That’s called centripetal force, the force to keep something revolving. In... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How much energy was used to charge the inductor? Electrical systems question I am a math major, and I am taking a mandatory class that looks more like physics and the professor gave us an assignment with a question that I don't have any idea on how to solve it. The question is originally in portuguese, so, I will try m... | The battery delivers a constant voltage $V$. The voltage of an inductor follows the differential equation: $$V = L\frac{dI}{dt}$$ where $L$ is the inductance and $I$ is the current. And the energy is the integral of the power $E = \int{VI dt}$
| {
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Free space motion I was going through Kleppner and got this interesting doubt. At page 138 there is an article named rocket in free space.So if there is no external force. The fuel can expand rapidly or slowly without affecting final velocity of rocket. Or we can say the velocity of rocket change by same amount whether... | The difference is that in one case, the mass being accelerated is varying, but in the other case the force being applied is varying.
So in the case of the rocket, the amount of energy input will be the same total, regardless of how we do it through time. Same energy in. Also, same mass being accelerated by that energy.... | {
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What's the best answer to "how many bounces until the ball stops"? A problem question that has been coming has the form:
*
*How many complete trips between two plates moving towards each other can you make? (Given that you are moving between them at a constant velocity, until they both collide, and thus the space bet... | This is the simulation of bouncing ball with the co-efficient of the restitution $~\epsilon=0.9$
you start from the height $~h_0~$ with zero velocity .
Section 0
$$y(t)=h_0-\frac{g\,t^2}{2}\\
v=-g\,t\\
y(t)=0~\Rightarrow~,t_0^2=\frac{2\,h_0}{g}\\ v_{01}^2=-2\,g\,h_0$$
when the ball hit the floor it reach the velocity ... | {
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Is it possible to create a magnetic environment where it pushes and pulls at the same time, making the target “levitate”? To better understand why I ask this, the backstory is I’m getting more and more annoyed by rolling office chairs rotating, hitting my ankles, hard to switch directions when wheels having ~90 degrees... | You can create a spatial array of magnets which generates a specific spatial force profile against a corresponding magnet array.
Check out polymagnets:
https://vimeo.com/107166551
Spring Polymagnets attract until they pass through a defined transition point, passed which they will repel. These Polymagnets will come to... | {
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Does relativity mean that the crew of a relativistic rocket would experience less acceleration than in our frame of reference? I have been told regarding a 1 g rocket that "the amount you accelerate would be less due to relativity".
Does that mean that from the crew's time dilated perspective, they would experience les... |
Does that mean that from the crew's time dilated perspective, they would experience less acceleration than we observe in our frame of reference?
No, the crew’s proper acceleration (the acceleration they feel) is greater than the coordinate acceleration (the derivative of their velocity in our frame) that we observe. ... | {
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Why have we not found an interior Kerr solution? The Schwarzschild interior solution was found not so long after the exterior solution was found. I understand that Kerr solution is significantly more complicated and there are more conditions at the boundaries but is there anything deep or profound about the interior th... | Birkhoff's theorem guarantees that any spherically symmetric interior solution you write down will have the Schwarzschild geometry as its exterior field, so all you have to do is ensure that the interior stress-energy looks reasonable for matter.
In the rotating case, a no-hair theorem guarantees that uncharged black h... | {
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Non-Perturbative Effects Of Soliton in Quantum Field Theory I am reading Quantum Field Theory in a Nutshell by A.Zee. In Chapter 5 Section 6, Under the subtitle A nonperturbative phenomenon, He commented
"That the mass of the kink comes out inversely proportional to the coupling is a clear sign that field theorists co... | More generally, if one is doing perturbation theory in some coupling constant $g$, the result is a power series in $g$, i.e. non-negative powers of $g$. To get negative/inverse powers of $g$, one must include non-perturbative effects.
| {
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Simplest exactly solved model displaying a phase transition? The classical example of an exactly solved model which displays a phase transition is the 2D Ising model. However, all the proofs I've seen of this have been very long and complicated.
So, I wanted to know whether there were any other exactly solved models wi... | The simplest model demonstrating a phase transition is probably the Ising model with an interaction constant that is the same for all spin pairs:
$H=-J\sum_{i,j}S_i S_j$.
I will try to find a reference later.
EDIT (9/6/2021): https://homepages.spa.umn.edu/~vinals/tspot_files/phys5201/2015/hwk8.pdf
| {
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Damped harmonic motion initial conditions I was reading Halliday's section on Damped Simple Harmonic Motion, which stated that this equation:
$$-b\dot{x} - kx = m \ddot{x}$$
Is the differential equation that dictates the displacement of the object, and $b$ is the damping constant of the system.
The author claims that t... | Answers that came before me perfectly OK. I will just add one significant intuitive picture of what's going on.
Picture in your mind the oscillator starting at $x_m$ but with initial velocity running away from equilibrium position.
Why would you identify $x\left(0\right)$ with the amplitude?
Interesting exercise: Fix i... | {
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... | The second Newton's law is valid for inertial frames of reference.
If we are for example in a airplane that is braking after landing, any loose object will accelerate forwards, without any force that can be identified. On the other hand, if we hold the object, we do a force on it and it is at rest in the plane's frame.... | {
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Is it okay to sleep with the wifi router next to me? Where I sleep I have my wifi router right above me. I don't know if this is safe for my health since it emits radiation.
Some people say that it should be safe since the radiation emitted is non-ionising.
But other sources claim that even non-ionising radiation can h... | The wifi router, as well as cell phones and microwave ovens all produce non ionizing radiation. To date, the major concern for non ionizing radiation is its heating (thermal) effect on tissue. It is my understanding that the magnitude of the non ionizing radiation of wifi and cell phones is limited by regulations to be... | {
"language": "en",
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What does it mean that uncertainty can be calculated by the "smallest division on a scale"? I have been reading everywhere a little bit to understand the concept of uncertainty but I cannot understand exactly how to find the uncertainty value. On this explanation it says that the uncertainty can be calculated by the "s... | It might be easier to appreciate if you imagine using digital devices, such as weighing scales. Imagine you had one in your kitchen that displayed weight to the nearest gram, and another industrial scale, for measuring the weight of lorries say, that displayed weight to the nearest kilogram. Clearly the absolute uncert... | {
"language": "en",
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How to understand Black-Body Curves and get useful information from them?
Here I have got a black-body curve. It shows the amount of radiation released as the wavelength varies for different temperatures. But I don't seem to understand it much.
*
*How do we properly study a black-body curve (like this one) and draw ... | *
*The main thing to notice is that the peak moves to the left as the temperature increases, the peak of the $3000K$ curve is above 0.9 micrometers, but the peak of the $5000K$ curve is above about 0.6 micrometers, so by looking at the position of the peak the temperature of the body can be deduced.
*You should look... | {
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Why won't all voltage be used up on first resistor in series? tldr: I am having trouble conceptually understanding voltage between resistors in series, even though I know how to calculate it using Ohm's law. How do the electrons "know" there are more resistors after going through the first one? Why doesn't it use up al... |
From the perspective of the electrons, they don't know that there is another resistor down the line.
The current is a moving ensemble of electrons, with a group drift velocity, no single electron goes from the positive to the negative pole of a battery. Electrons interact with the lattice and the molecules of the ... | {
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Fire caused by friction with water Friction causes heat and heat causes fire, but could something catch in fire because of friction with a high speed water stream?
If so, what material would it be and how fast would the water speed need to be flowing?
| Ordinary water is a neutron moderator, so we can run water through a nuclear reactor with enriched uranium and get as much heat as we want. One could object that it would not be "friction" with water that causes heat, but at least it is "interaction" with water.
| {
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How come black body have more emissivity and more absorbtivity(a) at same time? We have two definitions to look at
Absorbtivity(a): the ratio of absorbed energy and incident energy on a body
$a_{BlackBody} = 1$
so if i have a tourch light that gives red light, in a dark room I point this tourch light at this black bod... | The red light, with power $P$, will be absorbed. The blackbody will be heated to equilibrium when it's temperature $T$ satisfies:
$$ \sigma T^4 A = P $$
Thus, it all depends on $P$. If $P$ is a 1 TW red laser and $A$ is a pellet, it could get to really hot...mega kelvins. If it's a 10 W light, and $A$ is larger, the ra... | {
"language": "en",
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Conservation of angular momentum in an inelastic collision
I have a question about the second method used to solve the problem above.
The moment of inertia with respect to the stick's midpoint after the collision is $ml^2/12 + ml^2/4$ or $ml^2/3$ so the angular momentum with respect to the stick's center after the co... | You can calculate moments of inertia about any axis you want. But if the system isn't actually rotating around that axis, then you can't use it to (directly) calculate the rotation speed.
Instead of all the parts moving with speed proportional to $r$ as the distance from your axis, the parts are moving with various sp... | {
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What can I assume about Mandelstam variables in four-photon scattering? In the case of four-photon scattering, the Mandelstam variables must satisfy
$s+t+u=0$
Where:
$
s=-(p_1+p_2)^2, t=-(p_1+p_3)^2, u=-(p_1+p_4)^2
$
And we know that $s>0$ is true because it is the total energy squared. What can I assume for $t$ and $u... | If I remember correctly Peskin & Schroeder derive some more general properties:
*
*$\qquad s > 0 \qquad, \qquad t \le 0 \qquad \text{and} \qquad u\le 0 $
*$\qquad t=0$ for $\theta =0$ and $u=0$ for $\theta = \pi\;$ ($\theta$ being the scattering angle)
*$\qquad s\ge |t|$
| {
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Does the frequency of light have any effect on gravitational lensing? General relativity considers gravity as the curvature of space-time instead of a force. Therefore, what is bent around an astronomical object is the space-time itself. The light just follows the path as regular.
In classical physics however, I think ... | Do you know that any mass with the the velocity of earth would take the same orbit?
so since "mass" for light in the more classical approach ist E/c^2 different light has different mass but since all have speed c the same path.
| {
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What happens when a helium white dwarf accretes enough matter? What happens when a helium white dwarf accretes enough matter?
Say you have a white dwarf made of helium, what happens when it's core becomes dense enough to fuse helium and how massive would it have to be for this to happen?
| If the white dwarf (WD) is accreting matter, whether or not it is composed of helium, it will undergo a type 1a supernova or form a cataclysmic variable.
The Chandrashekar limit (maximum mass for a stable white dwarf) is independent of the composition of the WD, what matters is the degeneracy pressure and the mass of t... | {
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Provided a unit vector and Force, how can I calculate it's components? Say I have a $F=kQ_{1}Q_{2}/r^{2}$ and a direction vector $(x, y, z).$ How can I find the component forces $F_{x}$, $F_{y}$, and $F_{z}$?
| To find the components of any vector $\bf F$ using unit vectors,
you can use the dot product between the vector and each unit vector.
So the x-component of $\bf F$ is $\bf F\cdot \hat i$ the y-component is $\bf F\cdot \hat j$ and the z-component is $\bf F\cdot \hat k$
If you have a "direction vector" $\bf u=(x,y,z)$ th... | {
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Rotation in 3D space Suppose a body that rotates around an axis. But the axis also rotates. Now, the axis of the rotation of the axis also rotates, and so on. How far we can go with it? Can it be extended to infinity like a power series?
|
Can it be extended to infinity like a power series?
Yes it can. This is possible not just in 3D space, but in 2D space as well. These motions are collectively called epicycles, and will be familiar to anyone who has produced patterns with a spirograph. Before Johannes Kepler realised that planetary orbits were ellips... | {
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Does a single atom vibrate? Thermal vibration looks impossible, but does a single atom in vacuum vibrate due to the electrons' or subatomic particles' actions? If yes, how much is that vibration and is there a way to stop it?
|
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.
Vibration is a classical mechanics ... | {
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How to understand the time reversal symmetry of position operator? How to understand the fact that position operator is symmetric under time reversal? I can visualize the momentum and magnetic field being odd under time reversal.
Got the same doubt for Electric field as well.
| You can easily find out which quantities are even and which
are odd upon time-reversal by considering a video showing
physical processes and then comparing it to the time-reversed
video showing the same processes backwards.
See also "T-symmetry - Effect of time reversal on some variable of
classical physics" for lists ... | {
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Do electromagnetic waves contain electrons? I understand that EM waves are oscillating electric and magnetic fields. But doesn't this mean that the wave itself contains charged particles that generate the fields?
| No. Electromagnetic Waves do not actually 'contain' anything.
Classically, you can describe them as perturbances of the Electric and Magnetic Fields in space that are in a certain relation ( such as: they satisfy Maxwell's equations and D'Alembert equation, aka the wave equation).
An electromagnetic wave can be describ... | {
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Understanding Space-time intervals and its types I am taking Introduction to Modern Physics class. There, we were studying spacetime intervals as a subsection of Lorentz's transformation. My professor said that $\Delta x^2-c^2\Delta t^2$ is invariant, and then he said us that it is a lightlike event if $\Delta x^2-c^2\... | An interval between two events is space like if it is not possible for light leaving one of the events to arrive at the location of the other before it happens.
Let's take an example. The Moon is about 1.3 light seconds away. Suppose I synchronise my watch with two friends, Como and Zaquette, on the moon. If I sneeze a... | {
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How to simplify this complex circuit? I am new to circuit solving and I tried to simplify this circuit, but I am unable to do so. I can't figure out which resistances are in series and which resistances are in parallel.
Do I have to use star-delta conversion here or the circuit can be solved without conversion?
I just ... | When you have such seemingly complex circuits, the best way to approach the problem is to name each node and see which elements are in series and parallel. Keep on finding the equivalent resistances of groups of elements like the two resistors in parallel on the extreme right of the circuit. When you hit a hurdle, use ... | {
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Would a pressurized container move by itself if opposite edges have different size surface area? If inside a closed container there is gas with higher pressure than outside the container, and one edge of the container has a larger surface area than the opposite side, would the container move by itself? Wouldn't there b... | The world would be a lot more interesting if that were true!
No. If you sum the normal forces over all sides of the shape, you'll see that the components in all directions still cancel to zero.
| {
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How is Newton's third law working here? I understand that if I were, for example, to throw a bowling ball in outer space then the ball would move away from me by the force I generated. But the ball would also exert a force on me in the opposite direction and move me away in the opposite direction of the bowling ball.
I... | The walls of the chamber that houses the compressed gas is pushed upon by the molecules inside the chamber. The actual gas molecules escaping through the nozzle do not push on the walls of the extinguisher though, but since there is pressure throughout the chamber, the escaping molecules near the nozzle push on the mol... | {
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Is the coordinate speed of light in vacuum in a point direction dependent? Suppose we could control gravitation inside a wire frame cube with a side length of $l$ at will (I assume some yet unknown technology). First we simulate empty space inside and when measuring how long a light beam takes to go through it is $t_0=... | The coordinate speed of light is indeed directionally dependent in general. However, that has nothing to do with gravity or stress energy tensors. It is all about the coordinates chosen.
For example, in flat Minkowski spacetime you can use Anderson’s coordinate system described on p 105 here https://www.sciencedirect.c... | {
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How do electrons absorb energy? I'm trying to understand how lamps work.
I have read that the way this happens is when voltage is applied. The free electrons move due to the electromotive force (EMF), and when they collide with the lattice filament inside the lamp, they push the electrons in the lattice's atoms to a hi... | The EMF, $\varepsilon$, corresponds to an electric field $\mathbf{E}$ within the lamp circuit. Neglecting induction,
$$ \varepsilon = \int_A^B \mathbf{E} \cdot d \mathbf{l} .$$
This field does work on electrons as they travel from terminal B through the lamp to terminal A. Within the filament the kinetic energy of the ... | {
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Why did Rutherford's atomic model predict a continuous emission spectrum for hydrogen? When researching the flaws of Rutherford's atomic model, I get that one of them is that it predicts the electrons would spiral and collapse into the nucleus.
However, I don't understand the second flaw which says it can't explain the... | You have sort of answered your own question.
That the electrons would spiral in toward the nucleus was shown by Maxwell, in that accelerating charged particles would emit radiation loosing their energy. That is the first problem, as you have pointed out.
But this is also related to the second problem, in that this woul... | {
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Graph for Coulomb Force vs $1/r$ My teacher told me that the graph for the coulomb force $F$ vs $1/r$ where $r$ is the distance between the 2 charges should be parabolic but I can't seem to understand why. I am aware that equations of the form $y^2=4ax$ are parabolic but why should $F$ vs $1/r$ graph be parabolic?
| The Coulomb force magnitude is given by
$$F=\frac{kQq}{r^2}$$
Pulling out the $(1/r)^2$ gives us
$$F=kQq\cdot\left(\frac1r\right)^2$$
So then F has a quadratic dependence on $1/r$, which is a parabola if you were to graph $F$ vs $1/r$.
If you still cannot see it, then call $1/r$ something else, like $x=1/r$. Then $F(x)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670380",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
Can particles smaller than Planck Length be detected? It is my understanding, that anything smaller than a Planck Length cannot interact with photons, because photons with such small wavelength are massive enough to collapse into a black hole (source). Particle of such size would not interact with electromagnetic force... | I will make the comment into an answer:
Note that the standard model of elementary particle interactions is a quantum field theory where the particles in the table
are axiomatically assumed to be point particles (photon included) .
In the abstract of a book :
Quantum Field Theory of Point Particles and Strings (Front... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What is wrong with the high-school definition of a vector? Why is the high-school definition of a vector as "a quantity with a magnitude and a direction" incomplete? For example, Griffiths Introduction to Electrodynamics book says:
The definition of a vector as "a quantity with a magnitude and direction" is not altoget... | In addition to this answer , here is another simple argument why definition of vector is not satisfactory. Electric current in simple circuits has both magnitude (Amps in SI units) and direction (positive to negative terminal or from high to low potential).
But electric current does not satisfy either the triangle law ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670634",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
"answer_count": 10,
"answer_id": 8
} |
Why can basis vectors change direction? I thought that basis vectors were of magnitude one and located at the origin and were each linearly independent, so how in things like polar coordinates can the basis vectors be moving?
| The short answer is: Because there is a separate vector space with a separate basis at every point of space and you can choose a basis for each of theses vector spaces independently.
To understand this properly you need the theory of manifolds (as explained in Dale's answer).
It is just an "accident" of Euclidean space... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 7,
"answer_id": 4
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Can Vera Rubin's findings be explained by a distribution of charge? Vera Rubin found that the rotational velocity of galaxies is much greater than expected at greater distances from the center. Gravity from an invisible mass is assumed to account for this measurement. Can we not account for such a force by a distributi... | Unfortunately (or fortunately), some back-of-the-envelope calculations show it is unlikely that flat rotation curves are caused by charge separation. The acceleration of the Sun when moving around the center of the galaxy is around $1.6\cdot 10^{-10}\mathrm{m/s^2}$, so, lets say, the acceleration caused by forces from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/670901",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
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Basic question about orbital speed I was reading a Sci-Fi book recently and had a weird thought:
I know that objects closer to a gravitational well need to move faster to stay in orbit and objects further away move slower. But if you want to increase your orbit/escape the gravitational well you have to speed up while i... | I will try to explain it mathematically. Our orbital velocity is given by formula:
$$v_{\text{orbital}}=\sqrt{\frac{GM_{\text{star}}}{R_{\text{orbit}}}}$$
It’s obvious that numerator terms are not going to change. So, if the orbital velocity changes, the radius of the orbit changes. Since they are inversely proportiona... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671179",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
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Current density operator derivation in Fourier space Free particle Hamiltonian is $H_0 = \int d\mathbf{r} \frac{\hbar^2}{2m}(\nabla\Psi^\dagger)(\nabla\Psi)$. The Fourier transform representation of $\Psi^\dagger(\mathbf{r})$ is
$$
\Psi^\dagger(\mathbf{r}) = \sum_ke^{-i\mathbf{k}\cdot \mathbf{r}} c_\mathbf{k}^\dagger
... | After a help from @Jakob, I solved it:
$$
\sum_\mathbf{q} (i\mathbf{q}) \mathbf{J_q} e^{i\mathbf{q}\cdot \mathbf{r}} = -\frac{i\hbar}{2m}\bigg\{\sum_{k,q}k^2 c_\mathbf{k}^\dagger c_\mathbf{k+q}-\sum_{q,q_1}(q_1+q)^2 c^\dagger_\mathbf{q_1}c_\mathbf{q_1+q} \bigg\}e^{i\mathbf{q}\cdot\mathbf{r}}
$$
Change dummy variable ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671287",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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The effect black holes have on light We all know that light loses its energy when it is moving through expanding space and time. And sense a black hole can be summed up to a super compressed space time, shouldn't that mean that a photon gains energy when it enters a black hole because it is experiencing the opposite ef... | Basically yes it does lose energy and it can not get it back. For your second qwestion well, we don’t know what happens in a black hole but we have general ideas of what happens in there and basically it’s just contrubiting energy into the black hole BUT a black hole could just be a incredibly different thing like a wo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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If our solar system and galaxy are moving why do we not see differences in speed of light depending on direction? May be a silly and simple question, but I've been wondering if:
The speed of light is constant, and
*
*When we're moving in the same direction (where both the emitter and the receiver move with the light ... | The speed of a wave is constant regardless of the source velocity. Only the frequency of the wave is affected by the source velocity. See this answer for sound waves: Does sound waves pick up the speed of its source?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 5,
"answer_id": 3
} |
Hydrogen line spectrum lately I have come across the hydrogen line spectrum, I quite understand it as I could easily solve all numerical questions. However, conceptually I feel stuck at two points.
*
*If an electron absorbs the em radiation of a particular wavelength to jump to a higher shell say $n=1$ to $n=3$, then... | 1.) An electron falling down from level n=3 can decay into the ground state in two ways, either directly into the ground state n=1, or first into n=2 and then into n=1. These decay paths have certain statistical probabilities, so from many atoms you will see three lines in this case with a relative intensity given by t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Particle in a one-sided infinite step function plus a delta-function attractive well Given the following potential:
$$
\begin{cases}
\infty & x\leq -d \\
-V_0 \delta(x) & x > -d
\end{cases}
$$
with d > 0
I would like to compute the condition that has to be verified in order to have at least one bound ... | My guess would be to say that you are right which would mean that there are no bound states for this potential.
I think this is the case since for a simple delta-function attractive well there is only one bound state, so if we add another condition (in this case the infinit step) it could remove that unique allowed sta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672083",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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"answer_id": 2
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Can a material generally score or cut itself by hand? I'm wondering if a given solid material can, in general, score or cut the same material, when applied by (at most) human muscular strength.
I've tried searching for this online, but it seems like a difficult-to-express search target. For example, the site Answers.co... | The material quality you're looking for is hardness. The Mohs Hardness Scale is an empirical table of minerals sorted by hardness. Two materials are said to be the same harness if each can scratch the other. A homogeneous or mostly homogeneous solid, like diamond, has an identifiable hardness. A nonhomogeneous solid, l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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Matrix element and Dirac notation If
$$
T=
\left[
\begin{array}{cccc}
e^{\beta J} & e^{-\beta J} \\
e^{-\beta J} & e^{\beta J} \\
\end{array} \right]
$$
and
$$Z = \sum_{S_i=\pm 1} ... \sum_{S_N=\pm 1} \exp{\beta J(\vec{S_1}\vec{S_2}+\vec{S_2}\vec{S_3}+...+\vec{S_{N-1}}\vec{S_N}+\vec{S_N}\vec{S_1})}
$$
Then why c... | $\newcommand{\e}{\boldsymbol=}$
$\newcommand{\p}{\boldsymbol+}$
$\newcommand{\m}{\boldsymbol-}$
$\newcommand{\gr}{\boldsymbol>}$
$\newcommand{\les}{\boldsymbol<}$
$\newcommand{\greq}{\boldsymbol\ge}$
$\newcommand{\leseq}{\boldsymbol\le}$
$\newcommand{\plr}[1]{\left(#1\right)}$
$\newcommand{\blr}[1]{\left[#1\right]}$
$\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672697",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
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Can the degree of entanglement be an order parameter in a phase transition? In most continuous phase transitions, there is a well-defined order parameter $\langle \psi \rangle$ of some observable that is zero above the transition temperature, and continously grows below the transition. In the cases that I am familiar w... | Entanglement over an ensemble can be used to tell measurement induced phase transitions. The idea arises in a quantum circuit where measurements and unitary gates take place randomly over time. The ratio between measurements and gates determines whether the system is driven to a "more entangled" or "more disentangled" ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672911",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
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Adding angular velocity vectors We know we can add two angular velocity vectors to get a total angular velocity. Whereas I more of less understand the basic principle and the mathematical formulation, I have problems in visualizing this addition. Example picture (from my old Resnick and Haliday book) is attached. Howev... |
I see it like this:
you obtain the angular velocity components from the
rotation matrix
the disk is rotating with the angle $~\varphi_z~$ about the z-axes the rotation matrix is:
$$\mathbf R_d= \left[ \begin {array}{ccc} \cos \left( \varphi _{{z}} \right) &-\sin
\left( \varphi _{{z}} \right) &0\\ \sin \left(
\var... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/673166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
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Proof that you can't disentangle two parties if you only operate on one Let $A$ and $B$ be two entangled systems. Can someone prove or sketch a proof of why you cant unentangle $A$ and $B$ by only acting on $A$ or $B$ alone? i.e. by only applying $\mathbb{I}_A\otimes U_B$, with $U_B$ unitary.
| For a "positive" proof (as in, a proof not by contradiction), write the Schmidt decomposition of a generic bipartite pure state $|\Psi\rangle\in\mathcal H_A\otimes\mathcal H_B$ as
$$|\Psi\rangle=\sum_k \sqrt{p_k}(|u_k\rangle\otimes|v_k\rangle),$$
for some positive reals $p_k\ge0$ summing to the identity, and orthonorma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/673397",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
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Age of a black hole Is there a way to measure the age of a black hole by find Hawking radiation or calculating the stable orbits around the black hole?
| No. The No-hair theorem tells us that an isolated black hole is completely described by its mass, angular momentum, and net electric charge. In fact, the charge is expected to be basically zero, so it's basically just the mass and angular momentum. Hawking radiation and orbits only depend on those parameters as well... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/673563",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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In the Aharanov-Bohm experiment, how are we sure that the electrons do not ever enter regions with $\vec B\neq 0$? In the Aharanov-Bohm experiment, we say that the electron passes through a region where the magnetic field $\vec B=0$ but the vector potential $\vec A\neq 0$. The electron never passes through the region w... | We can hypothesize an infinite potential barrier around the solenoid. The Aharonov Bohm effect can be shown theoretically all the same.
We can also hypothesize the solenoid to be infinitely thin. The area of the solenoid does not affect the Aharonov Bohm effect.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/673835",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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How do stars produce energy if fusion reactions are not viable for us? From what I've learned, fusion reactions are not currently economically viable as of right now because the energy required to start the reaction is more than the energy actually released. However, in stars they have immense pressures and temperature... | It is the fact that fusion reactions are very exothermic that makes them so hard to control.
Coal releases its chemical energy so slowly that a coal fire does not need any confinement - it does not blow itself apart. Refined hydrocarbons, such as petrol, release energy more violently, but the walls of a metal cylinder ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/674089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 10,
"answer_id": 5
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Concept of Gravitational potential energy Change in Potential energy corresponding to a conservative force is defined as $$\Delta U = U_f - U_i=-W_f$$ and gravitational potential energy is $$\Delta U = U_f-U_i = -W_g $$ Suppose a mass $m_1$ is kept at a fixed point $A$ and a second mass $m_2$ is displaced from point $B... |
I think is wrong as a reference point at r1 the potential energy at infinity should be infinite.
The potential energy at infinity is only infinite if it takes an infinite amount of work to get to infinity. However, because the gravitational force decreases rapidly with distance, a projectile rapidly reaches a space w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/674392",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
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Why can a very large body of water not store summer heat? On this page, it states "The key disadvantage of using a very large body of water to achieve heat exchange with a relatively constant temperature is that you are not able to store summer heat in that body of water – to have the benefit of retrieving those higher... | I find the statement wrong. Living in Greece and, when younger, swimming in the sea from end of May to beginning of November, I know that the large body of water , Corinth gulf , is much warmer in November than the small body of water of a connected sea lake. So large bodies of water store heat energy of the summer mu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/674852",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is an expression of a quadrupole as an expansion of dipoles possible? Would it be possible to express a quadrupole as an expansion of dipoles? Because a possible definition of a quadrupole seems to be: an electric field equivalent to that produced by two electric dipoles.
| You seem to mix up two things here: Which charge distributions generate what multipole fields and how multipole-expansion works.
Yes, you can reach a pure quadrupole field by a limiting procedure involving two dipoles (just take two anti-parallel dipole sources and let their distance go to zero from above).
But that do... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/675224",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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What is faster? Pure rolling or rolling with slipping? So we know that a ball will slide down an incline when there is no frictional force. Once you say there is static friction it causes a angular momentum which in turn causes a torque and makes the ball roll. Lets say the ball number one does pure rolling, where the ... |
you have those two equations:
$$m\,\ddot s=m\,g\sin(\alpha)-F_r\\
I_\theta\,\ddot\theta=F_r\,r$$
in case of pure rolling is $~\ddot s=r\,\ddot\theta~$ and in case of partial rolling $~F_r=\mu\,m\,g\cos(\alpha)~$
pure rolling
$$\ddot s=\frac{m\,g\,r^2\,\sin(\alpha)}{m\,r^2+I_\theta}
\quad \Rightarrow\\
s_1(t)=\frac{m\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/675684",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
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Second Kepler's law explanation What is the explanation for the second Kepler's law? Why is the law valid?
Is it that the total energy of a planet equals to the kinetic energy plus the potential energy?
| Kepler's second law
according to Newton's second law
$$m\,\mathbf{\ddot{r}}=F(r)\,\frac{\mathbf r}{r}$$
where $~F(r)~$ is central force
from here
$$\mathbf r\times m\,\mathbf{\ddot{r}}=\frac{F(r)}{r}\left(\mathbf r\times \mathbf r\right)=\mathbf 0$$
with
$$\frac{d}{dt}\left(\mathbf r\times m\,\mathbf{\dot{r}}\right)=
\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/675822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 1
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Understanding conservation of energy in a pulley problem I am trying to check if my understanding of conservation of energy is correct. Imagine a pulley problem like so with $m_2$ heavier than $m_1$ and the pulley is ideal (in the original problem I borrowed this from $v$, $m_1$, and $m_2$ are given:
and our goal is t... | The Energy is:
$$E=\underbrace{\frac 12 m_1\,v^2+\frac 12 m_2\,v^2}_{K_E}-\underbrace{\left(m_1\,g\,h_1-m_2\,g\,h_2\right)}_{P_E}=0$$
at $~t=0~$ you obtain the initial energy
$$E_i=E(v=0~,h_1=0)=m_2\,g\,h_2$$
with the conservation of the energy $~E=\text{const.}~$ you can obtain the final velocity when $~m_2~$ collides... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/675957",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
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Doppler Effect and Relativity paradox Let, Alice is moving towards Bob at very high speed. Therefore, events in Bob's frame will appear to happen slowly in Alice's frame due to time dilation. Since velocity is relative, the same is also true for Bob.
Now, since Alice is moving towards Bob, Bob's light will be blueshift... | "That means, time between two light pulses, therefore two events on Bob's actually decreases as seen by Alice."
No.
c=λf=λ/Τ
c in vaccum space must be fixed at all times. The frequency will increase (blueshif) but the wavelength will proportionally decrease to keep c fixed. Meaning the distance between B and A will con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676214",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Intuition for the trace-free energy-momentum tensor condition in CFTs It is a textbook exercise to show that
\begin{equation}T^{\mu}_{\,\,\,\mu}=0
\end{equation}
is a sufficient condition for there to be a conserved current associated with a dilation symmetry. This condition is very important in CFTs so my question is,... | I will elaborate the answer I gave in a comment.
As mentioned the trace of the stress tensor in a QFT is related to the $\beta$ function by $$T_\mu^\mu \sim \beta(g).$$ The $\beta$ function indicates how couplings change with a change of scale but in a CFT there is no scale so the $\beta$ function vanishes; CFTs are fi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676654",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Time averages of complex quantities If an electric field $E$ oscillates as $E_0\sin(ωt)$ then the average value of $E^2$ over one period of oscillation will be
$$E_0^2\left< \sin^2(ωt)\right>=E_0^2/2$$ since the average value of $\sin^2(ωt)$ is well known to be $1/2$.
However if we write $E$ using complex numbers as $E... | So the complex numbers that we use in Classical Electromagnetism are more of a mathematical trick. The electromagnetic waves are in fact "real" quantities, i.e. they are represented by sines and cosines. However, it is often easier to work with complex exponentials, and so we cheat a little: since any linear combinatio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/676827",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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Why are there both antinodes at both ends of the tube? I learned stationary/standing waves the other day. For stationary waves in open tubes, the textbook says both ends must have an antinode. Can anyone tell me why? (shown as figure)
And also, when playing with the instruments like guitar, what's the number of harmon... | It's a pressure node as the pressure at the open ends of tube is atmospheric pressure. It's then automatically a displacement antinode because the equation of motion
$$
\rho_o \partial_t v = - \partial_x P
$$
means that a standing wave
$$
P(x,t)= A\sin(kx) \sin (\omega t)
$$
with a pressure node at $x=0$ makes the v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677148",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Passive transformation, pseudo vectors and cross product Let's consider the passive transformation i.e. inversion only of the basis vectors (coordinate axes) and all other vectors remaining the same and check if the cross product is a pseudo vector.
After the inversion using a passive transformation a vector $a$ remai... | with
$$\vec a=a_1\hat g_1+a_2\hat g_2+a_3\,\hat g_3\\
\vec b=b_1\hat g_1+b_2\hat g_2+b_3\hat g_3$$
where $~a_i~,b_i~$ are the vectors components and $~\hat g_i~$ are the basis vectors
with $~\hat g_i\cdot\hat g_j=1~,i=j~$ and $~\hat g_i\cdot\hat g_j=0~,i\ne j$
the cross product
$$\vec c=\vec a\times \vec b$$
now $~\hat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677386",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
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High school physics problem - having trouble understanding This is a fairly straightforward problem which doesn't require the usage of more than one or two formula but I find it hard to grasp the concept behind this.
Let's say we have two trains, one which moves at the speed of $45 \frac{km}{h}$ and the other at the sp... | You want to visualize something that takes time to travel a distance. Its hard to imagine actual trains moving at actual speeds, so you would likely be better off with a substitute.
How about a Monopoly game board?
Two trains, two pieces.
Train 1 is 45km/h. Train 2 is 60km/h. The difference is 15km/h. Luckily, all thre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 9,
"answer_id": 6
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Averaging over spin phase-space for a cross section In Peskin and Schroeder the Dirac equation is solved in the rest frame for solutions with positive frequency:
$$\psi(x) = u(p) e^{-ip\cdot x}$$
$$u(p_0) = \sqrt{m} \begin{pmatrix} \xi \\ \xi \end{pmatrix},$$
for any numerical two-component spinor $\xi.$ Boosting to an... | The best analogy I can give is that the incoming and outgoing spins are in a mixed state. In a mixed state that is 50% $+z$ and 50% $-z$ for example, expectation values are equal to
\begin{equation}
\left < A \right > = \mathrm{Tr} [\rho A] = \frac{1}{2} \left < + \right | A \left | + \right > + \frac{1}{2} \left < - \... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677709",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Is there time reversal symmetry for delta potentials? I was looking at problem $4.6$ of Gasiorowicz's Quantum Physics, where he asks to prove that the scattering matrix of a potential of the form
$$V(x)=\frac{\hbar^2}{2m}\frac{\lambda}{a}\delta(x-b)$$
is a certain unitary ($S^\dagger S=I$) but not symmetric matrix. I t... | Tragically, the author of the book you reference uses a different convention for the $S$-matrix:
$$\tag{1}
\left(\matrix{C \\B}\right)=S_G\left(\matrix{A \\D}\right)
$$
Instead of
$$\tag{2}
\left(\matrix{B \\C}\right)=S_{RW}\left(\matrix{A \\D}\right)
$$
Where the subscript indicates "rest of world". The letters $A,B\d... | {
"language": "en",
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"source": "stackexchange",
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How to solve the Biot-Savart Law? I've currently trying to learn electromagnetism in depth and I tried to solve the Biot-Savart law, for a magnetic field generated by a current.
$$
\vec{B} = \frac{\mu_0}{4 \pi} \int{\frac{I \; \hat{r} \times \mathrm{d} \vec{\ell}}{r^2}}
$$
When I looked up for information on how to sol... | What about:
$$d \vec{B} = \frac{\mu_0 I d \vec{\ell} \times \vec{r}}{4 \pi r^3}$$
or
$$d \vec{B} = \frac{\mu_0 I d \vec{\ell} \times \hat{r}}{4 \pi r^2}$$
$B$ = magnetic flux density; $I$ = current in wire; $\ell$ = length of wire; $r$ = distance of a point in the field to a segment of the wire; $\mu_0$ = magnetic perm... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677949",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Conservation of mass from material derivative Let the mass be $m=\rho \text{Vol}$, where $\text{Vol}$ is the volume of the domain and the velocity is $u$.
Applying the material derivative, then
$$\frac{Dm}{Dt}=\frac{\partial (\rho \text{Vol})}{\partial t}+ u \cdot \nabla (\rho \text{Vol})=0$$
Since the volume is consta... | Both forms are perfectly consistent in the particular case that the divergence of the 3-D vector field is zero. Recall, that the mass continuity equation can also be written as:
$$\frac{D\rho}{Dt}=-\rho\cdot\operatorname{div}V.$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do we need insulation material between two walls? Consider a slab made of two walls separated by air. Why do we need insulation material between the two walls. Air thermal conductivity is lower than most thermal conductivities of insulating material and convection cannot be an issue in the enclosed volume: hot air ... | Complementing the excellent answers on convection; some heat can also transfer through radiation, if the internal surfaces of the two walls are not treated to counter this. Both the warm and the cold wall will radiate, but at different rates, and this results in an equalizing heat flow.
A quick calculation using [1] gi... | {
"language": "en",
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Protons and QED I have been researching quantum electrodynamics recently and I have found out that when electrons repel each other, they constantly exchange photons with each other. When two protons repel, do they also exchange photons? If not, what do they exchange (if at all anything)?
| This is the lowest Feynman diagram showing the exchange of virtual photons in electron electron scattering
|
Depending on the problem one would be studying with proton-proton elastic scattering, a similar diagram with "p" instead of "e" would be used for the electromagnetic interaction.
Considering that the protons are... | {
"language": "en",
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Can I apply Kirchhoff's current law to two separate nodes which are connected only by an ideal wire?
Suppose there are 2 nodes A and B in the above circuit. If A has 2 incoming currents $I_1$, $I_2$, and B has 1 incoming currents $I_3$, $I_4$, is it correct to write the equation of whole nodes and circuit as $I_1+I_2-... | In your drawing A and B are not separate nodes, they are different points on the same node. All points connected by a single contiguous conductor are a single node.
If you tried to treat them as separate nodes then you would have to consider the conductor between them to be a 0 ohm resistor. This would do nothing but a... | {
"language": "en",
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Stefan–Boltzmann law applied to the human body The average person consumes 2000 kcal a day, which is equal to ~100 W. Furthermore, if one uses the Stefan–Boltzmann law to calculate how much someone loses heat due to radiation, it can be seen that it equals
$$Q=\sigma T^4 \varepsilon A$$
$$Q\approx1000\ W$$
Considering ... | Building on the answers from Thomas Fritsch and fraxinus: Alternatively, we could find the ambient temperature at which the human body would not need any heat-control measures such as clothing, unusual exertion, or perspiration. Working the equation in reverse, we can solve for $T_\text{environment} $, given $Q_\text{a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How small would a neutron star be to see the entirety of it? How small in Schwarzschild radii would a neutron star need to be for its gravity to be strong enough to deflect light emitted from one side toward an observer on the opposite side? I know the figure is above $1.5R_s$.
| For a Schwarzschild spacetime outside the neutron star (i.e. spherically symmetric and non-rotating), the neutron star surface would need to be at a radial coordinate $\leq 1.76 r_s$ (e.g. Pechenik et al. 1983). This corresponds to an apparent radius at infinity of $\leq 2.68r_s$.
The derivation (and it is a numerical ... | {
"language": "en",
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Peskin and Schroeder equation 3.136 (book edition 1995) I'm studying Peskin and Schroeder's QFT and I'm confused by equation 3.136 on page 68:
$\textbf{Previously, on page 48, equation 3.62 says:}$
$\textbf{My question is: how do we deduce 3.136 from 3.62?}$ $\textbf{It doesn't seem to me that} \boldsymbol{\xi^s}\tex... | You must have an old edition. In my edition (3.136)has the $\sigma$ as well. Also, $\xi$ and $\eta$ are arbitrary spinors.
| {
"language": "en",
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Can current flow in a simple circuit if I enclose the battery in a faraday cage? So suppose I have a regular circuit with a battery connected to a resistor and a lightbulb.
Suppose now somehow the battery is inside a metal box (faraday cage) but the rest of the circuit is outside of it so the wire is maybe poked throug... | Good question, related to a controversial Veritasium video. My answer is yes, current will still flow and the bulb will still light. While the region outside the box is shielded from the field inside, there is no reason the portion of the wire outside the box can't generate its own E & B fields.
BTW, while I believe th... | {
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Vector Addition of velocity
In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with what speed?
I tried to solve this problem with the following way-
Let the upward speed of the mass M be x.
Then,
$$x=\... | You are working this problem backwards. Starting from the velocity $u$ and resolving it on $M$ in the vertical direction and adding the two sides up. This is incorrect since velocities do not add up like forces.
While a body might have multiple forces acting on it, there is always only one motion state (velocity + rota... | {
"language": "en",
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"source": "stackexchange",
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Scalar in compactification in several dimension In sec-$8.4$ $($String theory vol $1$$)$ Polchinski states that
With more than one compact dimension, the anti-symmetric tensor also has scalar components $B_{mn}$
I am not understanding why the scalar is identified to the element $B_{mn}$. The scalar should come from d... | First of all, when I hear "the trace part" of a metric in $D$ dimensions, I think of $g_{\mu\nu} g^{\mu\nu}$ which is just a constant.
Polchinski is talking about tensors which have a scalar as one of their restricted representations. In other words, exactly what you were doing by choosing indices that point in a compa... | {
"language": "en",
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Landau levels degeneracy in symmetric gauge I'm reading David Tong's lecture notes on the Quantum Hall Effect.
When symmetric gauge taken, a basis of the lowest landau level wave functions is
$$\psi_{LLL,m}\sim\left(\frac{z}{l_B}\right)^m e^{-|z|^2/4l_B^2},$$
where $z=x-iy$,
and we have
$$J_z\psi_{LLL,m}=\hbar m \psi_{... | *
*$r_\text{max}$ is the location where $|\psi|^2$ is maximized. Even after multiplying the wavefunction by $z^m$, $|\psi|^2$ is still symmetric under rotation around the origin (only a function of $|z|$), so in this sense the wavefunctions still represents concentric rings.
*Remember the integer $m$ actually labels... | {
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Does capacitance between two point charges lead to a paradox? Is it possible to have a capacitance in a system of two point charges? Since there is a potential energy between them and they both have charges then we can divide the charge by the potential and get capacitance.
However, capacitance is supposed to depend on... | Last page in this link:
Capacitance of an Isolated Sphere
We obtain the capacitance of a single conducting sphere
by taking our result for a spherical capacitor and moving
the outer spherical conductor infinitely far away
Result:
$C=4 π ε_0 R$
where R is the radius of the sphere.
As you are talking of point partic... | {
"language": "en",
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"source": "stackexchange",
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Seeing gauge-covariance of the wavefunction for a uniform magnetic field Consider the Hamiltonian
$$H=\frac1{2m}(\mathbf p-q\mathbf A)^2+q\phi$$
and let $\psi$ be a solution to the Schrödinger equation
$$i\hbar\frac{\partial\psi}{\partial t}=H\psi$$
Then if we gauge transform
$$\phi\rightarrow\phi'=\phi-\frac{\partial\... | Take the gauge $\mathbf{A}=Bx\mathbf{y}$ first. In this case, eigenstates are labeled not just by $n$, but also by $k_x$. In other words, one should really write $\psi_{n, k_x}(\mathbf{x})$. For each $n$, there is actually an infinite number (if the system is infinitely large) of degenerate eigenstates, all with energy... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why light radiates out of the bend in dielectric waveguides?
Why EM wave radiates out of the waveguide. Is this similar to centrifugal force?
| The confinement of wlectric field intensity within a dielectric waveguide depends upon refractive index, wavelength, and geometry of waveguide.
The total internal reflection is mostly used in ray model to diescribe the acceptance angles and propogation of light in optical fiber. The bending of optical fiber changes the... | {
"language": "en",
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If you were invisible, would you also be cold? If you were invisible, would you also be cold? (Since light passes through you, so should thermal radiation.)
Additionally, I'd like to know if you were wearing invisible clothes, would they keep you warm? In my understanding, the heat radiation from the body would pass th... | Warm dark matter is not what you may think, but rather a hypothetical component of dark matter, which may consist of, e.g., sterile neutrinos.
The point here is that temperature is essentially the average kinetic energy (at least for a gas), and it does not fundamentally matter whether the particles interacat with the ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "24",
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Landau and Lifshitz - collisions between particles In the book mechanics from Landau & Lifshitz, section 17 collisions between particles there are those two equations in page 46:
$$\tan \theta_1 = \frac{m_2 \sin \chi}{m_1+m_2\cos\chi}, \quad \quad \theta_2 = \frac{1}{2}(\pi-\chi).$$
How did they derive these equati... | You got so close to an answer.
The authors are considering a situation when $|\vec p_1|= m_1v$ and $|\vec p_2|= 0$
This means that $|\vec{AO}| = \dfrac{m_1^2\,v}{m_1+m_2}$ and $|\vec{OB}| = \dfrac{m_2\,m_1\,v}{m_1+m_2} =|\vec OC|$
Taking the common factor, $\dfrac{m_1\,v}{m_1+m_2}$ out of each of the lengths results in... | {
"language": "en",
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When a block slides down an incline, why does the incline move back, if the work is done by an external force (gravity)? If I put a point mass on the top of the incline, and if all surfaces are frictionless, I heard, that the incline is going to move back a little (depending on the mass difference), because momentum is... | As @Triatticus rightly mentioned, there is no external force in the horizontal direction. Hence the COM's x coordinate (assuming an x-y plane with x axis along the horizontal direction) should stay constant. Now as the point mass is moving away from, the incline plane has to compensate for that and hence it moves in th... | {
"language": "en",
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Spacetime effects on human scale objects? For a human standing upright on the earth, gravity would have a different value at the feet than at the head, and gravity influences the flow of time. Does the difference in the flow of time cause any effects?
I was toying with the idea that gravitational acceleration is just n... | The time dilation depends on the factor $\sqrt{1-\frac{2GM}{rc^2}}$ see for example gravitational time dilation
From this formula the ratio of the flow of time for two points with a height difference of $h$ is about
$$1+\frac{GMh}{r^2c^2}$$
and using data for the earth and $h=2$, the time difference that would pass ov... | {
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What does GR get right that QFT gets wrong, and vice versa? I wondering what precisely it was, in terms of predictions of observations, that General Relativity gets right, that QFT cannot explain. And what QFT gets right, that GR cannot explain.
I'm assuming GR cannot predict quantum effects, like wave-particle duality... | GR is not intended as a model of particle physics, and makes no predictions in that field, and QFT is not intended as a model of spacetime curvature and makes no predictions in that field either. They were formulated to solve completely different classes of problems and it is not particularly surprising that there are ... | {
"language": "en",
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If $\mathbf{F}_{net} = m\mathbf{a}$ then how is $m\mathbf{a}$ not a force? The question is in the title: If Newton's second law says that the sum of the forces acting on a body in a given direction is the same as the mass of the object times its acceleration in that direction, then how is $m\mathbf{a}$ not a force? Eve... | "I'm so hungry, I'd be willing to pay \$100 for a hamburger right now. In other words, my willingness to pay is equal to \$100."
"But a dollar is not the same thing as a willingness! Dollars are green pieces of paper, or balances in checking accounts, but a willingness is a psychological state!"
"Maybe so. But you s... | {
"language": "en",
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Where is quantum probability in macroscopic world? How can macroscopic objects in real world have always-true cause-effect relationships when underlying quantum world is probabilistic? How does it not ever produce results different than what is predicted by Newtonian physics, except for borderline cases?
| Expectation values (of position, for example) in QM track the classical analogues. For large objects, position is localized and so is momentum (given the relative smallness of planck’s constant) - which keeps the position localized. In turn, this means that the expectation values of position closely match what we actua... | {
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Can a rotating neutron star collapse to a black hole through a reduction in rotation? It is well known that non-rotating neutron stars cannot grow without bound, since an increase in mass causes a proportional increase in density, and accretion beyond a critical limit would cause it to collapse to a black hole.
However... | Rotation periods of the order of a millisecond can sustain a maximum mass that is only a few per cent larger than the maximum mass predicted by the TOV equations. Differential rotation can increase the effect, see this paper for some (very) extreme (and probably unphysical) examples. More details are given in the refer... | {
"language": "en",
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Does light have mass or not? We know light is made of photons and so it should not have mass, but light is a form of energy (light has energy) and has velocity ($c$), so according to $E=mc^2$, light should have mass... So what is correct?
| The value $E/c^2$ has sometimes been called relativistic mass, but we make an effort nowadays to discourage that term because it refers to a frame-dependent quantity, and it's more helpful to focus on the invariant mass. A free particle has energy-momentum relation $E^2=m_0^2c^4+p^2c^2$ (see here for a generalization t... | {
"language": "en",
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Do Einstein's two postulates allow for handling acceleration in special relativity or is something else needed? When I was taught special relativity, we started with Einstein's two postulates and worked from there. However we were also taught that a proper resolution of the twin paradox required general relativity - b... | I would guess you are referring to the clock hypothesis. Annoyingly I cannot find a web page that neatly describes this, but it is discussed in detail in the question What is the history of adding the Clock Hypothesis to Special Relativity? on the History of Science and Mathematics Stack Exchange.
As far as I know Eins... | {
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Why does mass bend the temporal dimension more than the spatial dimensions of spacetime? From my (limited) understanding of general relativity, most of what we experience as gravity is a result of the distortion of the temporal dimension, and not the spatial dimensions. Therefore, most of the spacetime curvature caused... | It is the result of our choice of time and spatial coordinates. For practical reasons, we use seconds and meters, so the accelerations of gravity in the earth and solar system are far from negligible.
Suppose that our perception of time were such that we used microseconds instead of seconds, while keeping meters for sp... | {
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Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it? My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true ... | I think you are referring to the diverge of the electrostatic energy of a point-like particle. In classical electrodynamics that is the energy of the electric field which is associated to the charge of the electron. As you are saying, the $1/r^2$ energy of the field diverges at the r=0 position and even its integral fr... | {
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Why bi-telecentric lens works with a finite focal length while it should be afocal system？ I bought a bi-telecentric lens for experiment. From all I've learned before, it accepts only axis-parelle incoming beams and exits the same parelle light, so it should be an afocal system with relatively constant imaging performa... | A telecentric lens is not necessarily afocal.
An a focal system is a system which accepts light from infinity (collimated light) and 'sends' it to infinity at the output (image is at infinity). The most typical example is a laser beam expander.
a telecentric lens is a lens where the aperture coincides with the back\fro... | {
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A coupled nonlinear dynamical system in four dimensional phase space I have come across a coupled nonlinear dynamical system given below
$$ r\, \ddot{x} + \dot{x} = \sin y~,$$
$$ r\, \ddot{y} + \dot{y} = \sin x~,$$
where $r$ is some real number and $\dot{x}$ denotes $\frac{d\, x(t)}{d\,t}$. Despite the fact that the sy... | Chaos is very common — regular behavior is actually the special case.
Your system is nonlinear and has more than 3 dimensions, that is in principle enough for chaos to be possible or even likely — see, e.g., 1, 2 or the books suggested here, but, in a nutshell, 3 dimensions give you enough "room" for the continuous tra... | {
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Does Newtonian mechanics work in polar coordinates? Our teacher suggested that Newtonian Mechanics only applies in cartesian coordinates. Is this true?
He gave this example.
Suppose there a train moving with constant velocity $\vec{v}=v_0\hat{x}$, with initial position vector $\vec{r}=(0, y_0)$, where $v_0,y_0$ are con... | The advantage of cartesian coordinates is that we can take vectors as simply indexed functions. But there is an additional feature that can not be forgotten when changing variables: coordinate basis.
The velocity vector of the OP example can be expressed in its complete form as:
$v_1(X^1, X^2) = V^1B_{11} + V^2B_{21}$
... | {
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"question_score": "27",
"answer_count": 10,
"answer_id": 5
} |
NMR/EPR with an RF electric field Is it possible to perform NMR/EPR spin alignment with an oscillating electric field instead of a magnetic field (so with a sample inside the RF electric field of capacitive plates rather than a RF magnetic field of a coil)? In other words, can an electric field align nuclei or does it... | No this will not work. The electron does not have an electrical dipole or higher moment. Note that an oscillating electric field implies an oscillating magnetic field not far away.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/685598",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
In the Double Slit Experiment, what is the longest time $T$ recorded between shots of particles, electrons, photons, etc.? How can we be certain that electrons fired do not leave some kind of residual interference for the next shot?
What is the longest time recorded between shots?
| You assume that spacetime is plastic, like skiers carving paths through the snow. I was told that this is not the case, in terms of current theory.
On the other hand, assume that the insides of the double-slit device are evacuated. Shoot a photon, let it collide with the sensor array. Then, flush the device with gas (l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/685676",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Has anyone charged an object with 1 coulomb? Why was such a ridiculously large charge chosen as the unit of charge? The fact that two balls charged with 1 coulomb each would repel/attract each other from a distance of 1 metre with a force sufficient to lift the Seawise Giant would suggest me otherwise, but has anyone e... | Actually the ampere (SI unit for electric current) was defined first
(in 1881, see Wikipedia: Ampere - History).
They chose this size for $1$ ampere, probably because at this time
such a current could be produced with a decent electrochemical battery,
and was easily measurable with a galvanometer by its magnetic effect... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/685916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "51",
"answer_count": 6,
"answer_id": 5
} |
Why in the first Friedmann equation quantity $ρ$ is directly proportional to Hubble's constant despite the fact that gravity counteracts expansion? Here is the first Friedmann equation:
$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}$$
We know that matter and en... | Your intuition that $\rho$ ought to slow the expansion is correct, but that intuition concerns $\ddot{a}$ not $\dot{a}$ (and indeed in the other Friedman equation you do see a minus sign).
The $(\dot{a})^2$ term comes from the expression for the curvature when the metric is of FLRW form. The Einstein field equation say... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/686048",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
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