Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Magnet spinning between two other magnets Suppose, we have two magnets, MA, MB, and we have a third magnet MC in between the two magnets.
Each magnets' north pole faces the other magnets south pole, and the magnets are placed horizontally side by side. We spin the magnet MC at a speed between super fast and slow. What ... | The middle magnet is spinning, so it attracts and repulses the other two magnets once per rotation.
It is spinning "super fast" - that is so fast that the attraction and repulsion phases are super short. The other magnets are just too heavy to even start moving visibly in one or the other direction, before the directi... | {
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Statistical mechanics: What is a "microscopic realization" of a system? What is a "microscopic realization" of a system?
The context is statistical mechanics. The microscopic system consists of many atoms (too many to track individually) with an assigned probability density function f(x,y,z,Vx,Vy,Vz,t).
The macroscopi... | Statistical mechanics relies on a probabilistic understanding of the world and as such one needs to define a probability space. In classical statistical mechanics the probability space consists of a domain which is the set of all possible microstates (that is the position and velocity vectors of all the particles in th... | {
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Problem with derivation of phonons in crystal
In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental frequencies is that the solution will be periodic in time,
and solution shoul... | There is nothing wrong with looking for plane-wave like solutions of the form $A \exp (i (\omega t - k x) )$. Given the linearity of the equations, and as @ignacio pointed out the fact that the $\exp (i k x_n)$ form a basis of solutions, you can write a more general solution as a combination of these plane waves. This ... | {
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"timestamp": "2023-03-29T00:00:00",
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Gravity and electromagnetism If light bends due to the curved spacetime,would not the act of bending light warp space? How does one describe curved light?
| Light does curve spacetime. This is discussed in the question Does a photon exert a gravitational pull?.
In many cases we are describing the interaction of very massive bodies with much lighter ones, for example a satellite orbiting a planet. In these cases it's a good approximation to ignore the curvature of spacetime... | {
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If everything is relative to each other in this universe, why do we keep the Sun to be the reference point? and study the solar system and universe relative to it and why not relative to the Earth?
| It's all about the context in which you want to analyze particular issue.
If you are studying the solar system, the most suitable, would be to consider the sun as the center of the system.
If you are studying the Milky Way, the sun is not a good reference point, you should take the center of the galaxy.
Similarly, to l... | {
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What is a flat rotation curve? Was reading about dark matter and the distribution of it throughout the galaxy. it said "For example, if rotation curves are flat this means-" what exactly does this mean?
| When you look at an image of a galaxy like our own, you can see that most of the visible mass is concentrated in the core and that the density of stars in this core region is approximately constant:
So let's compute the expected rotation curve.
The orbital velocity of a star at a distance $r$ from the centre of the ga... | {
"language": "en",
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How is electric field strength related to potential difference? I was looking at the derivation of drift velocity of free electrons in a conductor in terms of relaxation time of electrons.
Here a metallic conductor XY of length $\ell$ is considered and having cross sectional area A. A potential difference $V$ is applie... | The assumption is that the electric flux lines are going to go through the conductor parallel to the conductor. Under those conditions, the electric field within the conductor is going to have a constant magnitude, and point parallel to the conductor. I assume you're familiar with
$$E=-\nabla \phi\ \ ,$$
where $\phi$... | {
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Difference between heat capacity and entropy? Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is the amount of energy dispersed reversibly at a specific temperature. But they ... | All comments miss a point, or maybe I didn't get it right. I see it this way,
lets start with other forms of energy (kinetic and potential, for example) of an harmonic oscillator. We know for a non damped HO the relation between position "$s$" and velocity "$v$" is given by total energy $E_o = \frac{1}{2}kx^2 + \frac{1... | {
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Demostrating possible equivalence of two tensors Is there anyway to see by inspection that a form like
$$a(x^2 )^{-3} (g _{μσ} x_{\rho} x_{ ν} + g_{μρ} x_{σ} x_{ ν} +g_{νσ} x_{ρ} x_{ μ} + g_{ νρ} x_{ σ} x_{ μ} ) $$
may be equivalent to (i.e reduced down to or reexpressed) $$
b(g _{μν} x_{ ρ} x_{ σ} + g_{ ρσ} x_{ μ} x... | Indeed, if no values of $a$ and $b$ work for across different sets of indices, then the forms are not equivalent.
In fact, these two forms are not equivalent even under the restriction of the metric being diagonal (and thus are not equivalent under a general metric). The diagonal case is easy to analyze, and you gave a... | {
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Is there any evidence that matter and antimatter continuously appear and disappear on the edge of a black hole? I heard Stephen Hawking got a Nobel prize for this, someone said there was no evidence for it which I find quite strange since he got an award for it.
| There is plenty of evidence for the underlying quantum field theoretical description of the vacuum.
*
*The (complete) quark content of the nucleons has been measured, and includes both flavors not in the valence content (strange, charm (?)) and lots of anti-quarks. Everything that isn't valence content ($uud$ for a ... | {
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Projectiles Launched at an Angle with unspecified Initial Velocity I'm attempting to do my Physics homework, and I did the first one right, but that problem gave me initial velocity. This problem gives me only the angle relative to horizontal and the distance it covers. Can anyone help me figure out where to start? I'v... | First, you have to find the maximum height of the ball. In order to do so, we use the condition that $v_{y}=0$.
$$0=v_{0}\sin(\alpha)-gt_{H}$$
From this, the time to reach the maximum height $t_{H}$ is
$$t_{H}=\frac{v_{0}\sin(\alpha)}{g}$$
From the vertical displacement, we obtain the maximum height using $t_{H}$
$$H... | {
"language": "en",
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What is going on in front of and behind a fan? Why is it that when you drop paper behind a fan, it drops, and is not blown/sucked into the fan, whereas if you drop paper in front of a fan, it is blown away?
| Think about the air around the fan at any given time:
The amount of air flowing into the fan must equate to the air flowing out of the fan.
The amount of air that passes through an area in a given time is related to the velocity of the air i.e. the faster the air is moving, the more air that can flow through a fixed a... | {
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What happens to a photon after it is absorbed by an antenna? I recently have read about interception of wireless information, however this mentions that people can intercept the information, and then somehow the recipient also gets the information. Regardless of this context, what happens to the actual photon if it is... | The radio waves or microwaves that are used for communication don't contain just one photon. They contain a bunch. (Maybe someone will do the math for how many photons a standard radio broadcast antenna is producing each second; it'll blow your knee-high off even if you're wearing sandals over them.)
Consider for examp... | {
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How to determine your position underground? Crossed my mind after random rant on wikipedia that lead me to articles about chronometers and measuring position.
Let's assume I were trapped in the underground laboratory with lots of equipment but without any access to the surface. Would I be able to properly determine my... | John's answer gives some ideas for latitude and longitude. You could measure your altitude (read depth) by measuring the weight of a known mass. In a perfectly uniform, spherical Earth, the weight is proportional to your distance from the center.
| {
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Can you choose the variables of a state function? I'm confused. I was first introduced to entropy as a state function of internal energy and volume
$$S(U,V) \Rightarrow dS = C_v\frac{\mathrm{d}T}{T} - p\frac{\mathrm{d}V}{T} $$
wich is the thermodynamic identity, but now I see that it can also be written as
$$S(T,p) \... | Note that I am working in unit-mass bases (with lower-case symbols).
*
*Since,
*
*We have,
*
*So that,
Notes:
*
*The internal energy is a function of the constant volume specific heat, and the latter is a function of temperature.
*The enthalpy is a function of the constant pressure specific hea... | {
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A James Clerk Maxwell Disproof One of my favorite physicists to learn about was James Clerk Maxwell, for the fact that he unified the study of E&M in physics and he would often disprove theories that did not work as a Mathematician.
I remember my physics professor mentioning a disproof Maxwell had done with what was t... | Are you talking about the famous derivation of the displacement current, where Ampère's law is both true and false depending on what surface you choose to integrate through, despite the same boundary, as below:
(Image from WikiMedia commons http://commons.wikimedia.org/wiki/File:Displacement_current_in_capacitor.svg)
... | {
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Eigenfunctions for $1s$ hydrogen Schrodinger equation I am a computer scientist and started my Phd in material science. The second course os my Phd is material simulation by computer. One the task is show the verification of the eigenfunction $1s$ from time-independent Schrodinger equation.
I dont want any answer, I ju... | The time-independent Schrödinger equation for the hydrogen atom is
$$-\frac{\hbar^2}{2m}\vec \nabla^2\psi-\frac{e^2}{4\pi \epsilon_0r}\psi=E\psi $$
If your aim is just to verify that the $1s$-wave function
$$\psi_{100}=\frac{1}{\sqrt{\pi a^3}}e^{-r/a}\hspace{2cm} a\equiv \frac{4\pi\epsilon_0\hbar^2}{me^2} $$
is indeed... | {
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Blowing your own sail?
How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?
| The question is whether this is a form of "pulling yourself up by your own bootstraps". Clearly the driving force here is the leafblower the skater is wearing, which takes ambient air with zero average momentum and sends it out a vent with large average momentum. One would expect, absent some deviousness having to do w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/135548",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What makes a material adhesive (or sticky)? I currently have a bandage on my arm that isn't sticking to me but definitely sticks to itself. It brought up the question:
What makes a material sticky? What's happening on the molecular level? Why do some materials stick to some things better than to others?
| There are several different types of adhesion. As pointed out by Ryan S. :
Electrical, like when a balloon sticks to your head after a good rubbing. Chemical, like plastic cement will "melt" the plastic pieces to be bonded together. And the most common, physical, which is extremely hard to make an example of without a ... | {
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Forces while squeezing a toothpaste tube When I squeeze a tube of toothpaste, I am working with 2 squeeze forces toward tube. What causes the toothpaste to go out of the tube? (instead of remaining stationary)
| From a fluid dynamics perspective, your applied force induces motion via the Navier-Stokes equations:
$$
\rho\left(\frac{\partial}{\partial t}+\mathbf v\cdot\nabla\right)\mathbf v\propto\mathbf f_{body}
$$
where $\rho$ is the density of the toothpaste, $\mathbf v$ the velocity of the toothpaste, and $\mathbf f_{body}$ ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What technology can result from such expensive experiment as undertaken in CERN? I wonder what technology can be obtained from such very expensive experiments/institutes as e.g. undertaken in CERN?
I understand that e.g. the discovery of the Higgs Boson confirms our understanding matter. However, what can result form t... | Just to mention the latest developments brought up from neutrino science, it seems that the useless, wimpy, weakly interacting neutrinos (and their anti-neutrino sisters) can be harnessed to detect and monitor nuclear reactors anywhere in the world that violate non-proliferation agreements
I remember a discussion abou... | {
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Differentiating the Hamiltonian Operator, $\hat{H}$ Firstly let $\hat{H}$ denote the full energy of the electromagnetic wave. I'm trying to differentiate the Hamiltonian operator with respect to the components of momentum, i.e. $$\frac{d}{dp_x} \frac{d}{dp_y} \frac{d}{dp_z} \hat{H}$$
To do so, I need to write the Hami... | The momentum operators $\hat{p}_x,\hat{p}_y,\hat{p}_z$ are operators. They can be represented as infinite dimensional matrices acting on an infinite dimensional Hilbert space. The Hamiltonian $\hat{H}$ can also be represented as a infinite dimensional matrix.
One can generalize the notion of a differentiation to diffe... | {
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Did Newton argue that particles speed up when entering a more dense medium? Statement:
Newton argued that particles speed up as they travel from air into a dense, transparent object, such as glass.
From this source, I gather that he did argue that the light particles sped up when entering a more dense medium. However... | "From this source, I gather that he did argue that the light particles sped up when entering a more dense medium. However, it just doesn't make sense."
It does make sense. They enter the medium at a higher speed, then slow down. If Newton had said they continue to move at a higher speed within the medium, he would have... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/136036",
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Can a bullet really fly through space forever? Some people says that if it would be possible to shoot a bullet so high that it would get over the Earth gravitational pull, the bullet could fly through space forever, because of no deceleration of friction (and if there wouldn't be any more particles in the space, of co... | I think your confusion is about whether a bullet could truly escape the earth's gravity if gravity extends forever. You are worried that the bullet will always feel a non-zero gravitational force, and therefore it will stop at some point.
You are correct that the bullet will feel a non-zero gravitational force. This c... | {
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Standard Usage of the word "per" Math guy here. What is the usual meaning of "x per y per z?" Is this (ignoring details) (x/y)/z or x/(y/z)?
Sorry to be mundane.
| Two examples that come to my mind are acceleration and intensity.
Acceleration is measured (in SI units) in "meters per second squared" = $\text{m}/\text{s}^2$, but it is also commonly said as "meters per second per second," which matches your first option.
Likewise, intensity is measured (in SI units) in "joules per ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/136195",
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Difference between high-level and low-levels of electromagnetic radiation can someone please explain me what we mean by 'high-level' or 'low-level' in electromagnetic radiation? for example, it is believed that high-level microwave radiation is harmful to human but not the low-level one.
what is this level here we are... | An important factor in determining how much energy electromagnetic radiation carries is its intensity, which is just the power per area. In fact, it can be found in the wikipedia article that intensity is sometimes taken to be synonymous with 'level' (even though it is not really correct), so surely this is the right v... | {
"language": "en",
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Why does Energy-Momentum have a special case? I was reading Energy-momentum, and I came across this simplified equation:
$$E^2 = (mc^2)^2 + (pc)^2$$
where $m$ is the mass and $p$ is momentum of the object. That said, the equation is pretty fundamental and nothing is wrong when looked upon, I similarly also believed thi... | The above answers are all good, but I want to add something else. You can derive the energy-momentum relation from at least principle, the action is $A=-m\int \sqrt{1-v^2}{\rm d}t$ . Lagrangian is $\cal L$$=-m\sqrt{1-v^2}$, then you can get momentum $p$ from derivative with respect to $v$ (this is the real momentum, no... | {
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"timestamp": "2023-03-29T00:00:00",
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Derivation of the average Velocity formula with constant acceleration (using calculus) I have been looking at
$$
v_{avg} = \frac{v_{i} + v_{f}}{2},
$$
when the acceleration is constant, where $v_i$ is equal to the initial velocity and $v_f$ is equal to the final velocity.
How can you derive this using calculus?
$$
v_... | There is one error in the derivation, if you want to have $v(t_i)=v_0$, you must have
$$v(t) = v_0 + a(t-t_i)$$
You also have to use the fact that $v_f = v(t_f)$. Once you use all this, you should be able to divide out $t_f-t_i$ in the corrected version of your last line and get the result you seek.
| {
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Handedness of Reference Frames? I am developing a new derivation of the Lorentz transformation which I think and hope is more attractive to students than those I have seen in currently available texts. I am carefully defining and discussing the important concepts of homogeneity and isotropy of space.
My question is thi... |
[...] my question concerns two relatively moving observers. Can one of them distinguish that the other has adopted the oppositely handed coordinate frame?
What information does observer A have about observer B? If all A knows about B is B's state of motion, and if he assumes that B is going to choose coordinates in w... | {
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Why is the shape of lightning or an electric spark a zig-zag line? Why is the shape of the lightning (or an electric spark) always of a zig-zag nature? Why is it never just a straight line?
Image source.
| The lightning is just electricity, a huge burst of electrons that try to find the path of least resistance through the molecules of the atmosphere to the ground.
The electrons come from many different places in the clouds
and the atmosphere is not homogeneous: there are differences in humidity, temperature, density, p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/136694",
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Spiral galaxies and gravity lenses Spiral Galaxies must have a great deal more mass than elliptical galaxies of the same size in order to account for the flat velocity curve. I've seen references of eight to ten times the visible mass. So then Spiral Galaxies should act as much better gravity lenses than an elliptica... | The problem is that galaxies come in all sorts of sizes and therefore with different lensing strengths. The experiment would be to measure the lensing of elliptical galaxies then compare this with their mass and see if the lensing looks bigger than the observed mass would suggest.
The trouble is that while lensing meas... | {
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Is the ground state closest to the uncertainty relation? For simplicity, suppose we are only talking about discrete energy levels, i.e., bound state case. The energy levels are $E_1, E_2\cdots$, and the corresponding wave functions are $\psi_1, \psi_2 \cdots$.
My question is, is it true that $\sigma_x \sigma_p$ is mini... | Take it as you want, but this is the way I interpret the necessary existence of a ground state (at finite energy) for any bound system in quantum mechanics. The idea, in my view, consists in finding the minimum energy value of a Hamiltonian of the form $H = \frac{\vec{p}^2}{2m} + V(\vec{x})$ under the statistical const... | {
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Trouble understanding the concept of true and apparent weight I need help understanding the concept of true weight vs apparent weight. I understand this much: if someone is standing in an elevator on a scale, the further up they go the less the reading on the scale becomes. But why is this? Is it that distance affects ... | While it is true that the gravitational force dissipates with respect to distance squared, that is not the reason a scale would output a "different weight". A scale does not actually measure weight, only it's response to it. That is, the scale reads the normal force. If the elevator was motionless, the normal force wou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/137047",
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The Earth is spinning, so why don't we jump and land on a different location? I know there are similar questions on StackExchange but I think it is different and detailed.
The earth is spinning 465 meters/second so why don't we jump and land on a different location?
I googled about this question and I got some answers:... | When planes fly in the west direction they are basically doing what you suggest: the position of the Sun stays almost fixed and the Earth rotates below them. Still to do that they burn a lot of fuel: first they need to come at a stop with respect to the Sun, which means getting some speed with respect to the Earth, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/137191",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Will 5 pizzas in the same Hot Bag stay warmer than 5 pizzas in 5 separate Hot Bags? For example, say I am delivering 5 pepperoni pizzas to 5 different addresses. In one scenario, I Keep all 5 in the same insulated Hot Bag, I carry that bag to the door, and I quickly remove one of the pizzas from the bag to give to the ... | With the two options, the temperature difference and bag insulation R-factor are the same.
The five-bag option has five times the surface area (if truly "separate" and not stacked). So the one big bag should be the better choice.
A less snicker-inducing version of the "two people - two sleeping bags - how to keep war... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do we estimate $10^{23}$ stars in the observable universe? Now, I read somewhere, that there are $10^{23}$ stars in the observable universe. How did scientists estimate this?
| An alternative method to John's answer is to look at the total number of atoms in the observable universe. Thanks to measurements of the cosmic microwave background, we have a fairly precise estimate of this number. Indeed, we know that ordinary matter makes up about 4.9% of the energy content of the universe. In this ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/137341",
"timestamp": "2023-03-29T00:00:00",
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Ball Bearing Inside a Hollow, Spinning Rod: where is the logical flaw? As described in the title, suppose we have a frictionless, hollow rod that is rotating in the $xy$-plane with some fixed angular velocity $\omega$. The rod is pivoting around its midpoint. Suppose we place a ball bearing inside of this rod such that... | You seem to realize that the rotational analog for Newton's law is important here. This law states that the net torque $\tau$ on an object and its angular momentum $L$ are related by $\tau = \dot{L}$.
If I read you question correctly you seem to think that because $\ddot{\phi}=0$, that the angular momentum $L$ must be... | {
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Time energy uncertainty principle $ \sigma _{H}\sigma _{Q}\geqslant \frac{h}{4\pi }\frac{d\left \langle Q \right \rangle}{dt}$
$\Delta E = \sigma _{H}$
$\Delta t = \frac{\sigma _{Q}}{d\left \langle Q \right \rangle / dt}$
$\Delta E \Delta t \geq \frac{h}{4\pi }$
Q is any observable
I know that $\Delta E$ represents the... | As an example, http://en.wikipedia.org/wiki/Particle_decay, you can regard $\Delta t$ as the lifetime of the particle decayed.
| {
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Penning Trap Simulation I'm currently working on a particle tracker and I would like to implement a Penning trap. I think I might have a problem with the field of the electrical quadrupole. My idea was to place 2 dipoles and overlay their electrical fields, so that the tracked particle would be in the middle of the res... | The underlying problem of your trap design is that two dipoles can't make a quadrupole!
You are probably aware of the multipole expansion of electric (or magnetic) fields. This is where the terms "dipole" and "quadrupole" come from. As a physics student, one often encounters the exterior multipole expansion. This is wh... | {
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Estimating the force needed to increase height of a mountain? How would you estimate the force required by a tectonic plate to make the height of a mountain increase when it pushes against another?
I've used a method to try and do it for Mt Everest and have ended up with 8x10^(-7)N required to increase its height which... | In really simple terms the equation f=mg can be utilised. It calculates the gravitational potential energy of the mountain and therefore the energy needed to lift a mountain.
| {
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What is the difference between diffraction and interference of light? I know these two phenomena but I want to know a little deep explanation. What type of fringes are obtained in these phenomena?
| Both interference and diffraction result from superposition of the EM waves. Inteference result from the superposition of two different coherent sources whereas in diffraction superposition result from different parts of the same source. So we speak about diffraction resulting from a wide slit or circular aperture and ... | {
"language": "en",
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Can time be interacted with? Astronauts come back to Earth younger than they would have been had they stayed on Earth for that same period of time. They are traveling so fast relative to the Earth that time slows down for them. Does that mean that the astronaut interacted with time? Does time interact with speed? And i... | As for "why", that is either simple or complex! The simple answer is that it is a consequence of the speed of light being constant for all observers. That means when travelling relative to each other they both measure time differently. This site provides a simple math explanation
OTOH, time is measured differently in d... | {
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Derivation of Maxwell stress tensor from EM Lagrangian From Noether's theorem applied to fields we can get the general expression for the stress-energy-momentum tensor for some fields:
$$T^{\mu}_{\;\nu} = \sum_{i} \left(\frac{\partial \mathcal{L}}{\partial \partial_{\mu}\phi_{i}}\partial_{\nu}\phi_{i}\right)-\delta^{\m... | Hint: The canonical stress-energy tensor from Noether's theorem is not necessarily symmetric, and often needs to be improved with appropriate improvements terms. This is e.g. the case for EM. See also e.g. this Phys.SE post and links therein.
References:
*
*Landau and Lifshitz, Vol.2, The Classical Theory of Fields,... | {
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What would happen if an accelerated particle collided with a person? What would happen if an accelerated particle (like they create in the LHC) hit a person standing in its path?
Would the person die? Would the particle rip a hole? Would the particle leave such a tiny wound that it would heal right away? Something else... | A charged particle will create charge separation (ionization) along its path. This will cause harmful chemical reactions to occur in the body, including DNA damage. The effects of these chemical reactions depend on their amount. The body can heal from a low amount on its own, while a high amount will cause radiation si... | {
"language": "en",
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What is an order parameter? I've seen order parameter used in two different ways. One is to distinguish between an ordered and an unordered phase, like whether the net magnetization is stable or not. The second way is to distinguish what the magnetization is, up or down.
More broadly, does it just mean a macroscopic o... | An order parameter distinguishes two different phases (or orders). In one phase the order parameter is zero and in another phase it is non-zero. It does not have to be macroscopic.
For example, in the BCS theory of superconductivity the order parameter is called the gap $\Delta$. It can be interpreted as the binding e... | {
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Two soft questions about spin and the particle nature of electrons How can we define spin as the spin of an electron around it's own axis if an electron is described by a probability cloud of finding an electron in a point in space? How does that probability cloud spin around it's own "axis"(I find this ill-defined too... | Spin is not defined as the spin of electron around its own axis. Spin is the intrinsic angular momentum of the electron - intrinsic meaning it does not arise from the electron's motion, but is a property of electron itself.
The electron in the atom "can" be described as a particle if you are using the Bohr model of the... | {
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Finding 3-Sphere Christoffel connection coefficients using variational calculus, Sean Carrol problem I have A 3-Sphere with coordinates $x^{\mu} = (\psi,\theta,\phi)$ and the following metric:
\begin{equation}
ds^2 = d\psi^2 + \text{sin}^2\psi(d\theta^2 + \text{sin}^2\theta d\phi^2)
\end{equation}
I know how to get the... | The strategy is to recall the geodesic equation,
$$
\frac{d^2x^\lambda}{dt^2}+\Gamma^\lambda_{\,\mu\nu}\frac{dx^\mu}{dt}\frac{dx^\nu}{dt}=0\tag{1}
$$
From your Lagrangian, you'll end up with equations of the form
\begin{align}
\ddot{\psi}&=f(\psi,\,\theta,\,\phi,\,\dot{\psi},\,\dot{\theta}\,\dot{\phi})\\
\ddot{\theta}&... | {
"language": "en",
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Heisenberg's Unified Field Theory While searching in the Internet, I came to know about Werner Heisenberg's attempt to obtain an Unified Field Theory (see the book Introduction to Unified Field Theory of Elementary Particles). But also it has been mentioned that since this theory is non-renormalizable, it wasn't a succ... | Good references were provided by Conifold here.
To sum up, there were several problems with this initial approach: spinors where observable physical objects due to their dimension of $-\frac{3}{2}$, the introduction of a dimensioned coupling constant lead to non-renormalizability, etc.
You may want to check out this vi... | {
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Nature of tension in a massless rope I'm faced with a conceptual problem, where I am supposed to describe the motions of the following system (two masses on each end of a totally inelastic rope hanged on a pulley):
I understand that there is the gravitational force acting, and also a second, opposing force in the rope... | The nature of the rope force is such that the accelerations of the two masses are connected. If the two heights are $y_1$ and $y_2$, then the their sum is constant, and their derivatives are equal to zero
$$ y_1 + y_2 = \ell \\
\dot{y}_1 + \dot{y}_2 = 0 \\
\ddot{y}_1 + \ddot{y}_2 = 0 $$
So the nature of the force is su... | {
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Lorentz Transformation at t=0 Suppose I have two reference frames $S$ and $S'$, where $S'$ is moving with velocity $v$ with respect to $S$.
The Lorentz transformation equation for time in reference frame $S$ is given by:
$$t'=\gamma\left(t-x\frac{v}{c^2}\right)$$
where $\gamma$ is the Lorentz factor.
Now for an event h... | The interpretation is that two events being simultaneous as measured in frame $S$ doesn't imply that the events are simultaneous in frame $S'$. Which events count as being "simultaneous" depends on the frame of reference. This is known as the relativity of simultaneity.
Added clarification due to comment:
The coincid... | {
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Why is the Moon not redder at moonrise/moonset? Okay we all know about Raleigh Scattering, which makes the sky blue. And by the same token, sunsets appear red because sunlight traveling through more atmosphere will "lose more blueness" as it's scattered away.
But what about the Moon? The Moon is just reflected sunlight... | Is this not a question about human physiology rather than physics?
We are discussing the variations in observed response of the human eye to light with different qualities: overall intensity, and distributions over the visible spectrum.
This question seems to ascribe all of the observed differences (or lack thereof) t... | {
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The pole and the barn paradox (stretching the pole) The basic variant of this paradox makes sense to me but I have problems in proving mathematically variation of this non-paradox.
So lets imagine that we have barn and pole which is stationary to the barn and they both have rest length $L_0$. Moreover, we are given tea... | There's going to be a distortion of the pole during the acceleration period that goes away. The pole bearers should observe that they are holding a pole with length $L_{0}$, assuming that it's rigid. Note that it will start out length contracted from their potential, though, so during your $\Delta t$, they will stret... | {
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Weight versus gravitational force What is the difference between weight and gravitational force? I am a beginner who want to study physics properly.
| Newton law of gravitation is given by:
$$F = G \frac{m_1 m_2}{r^2}=\left(G \frac{m_1}{r^2}\right) m_2$$
The gravitational constant, $G$, the weight of Earth, $m_1$, and the radius are constants, so:
$$G \frac {m_1}{r^2}=(6.6742 \times 10^{-11}) \frac{5.9736 \times 10^{24}}{(6.37101 \times 10^6)^2}=9.822$$
Hence, the eq... | {
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A hypothetical question on mechanics Being located in a tropical region, I am quite acquainted with the Ceiling fan. I have a question about it.
If the top, that is, the axle (I'm not sure of the terminology: I mean the part which is thin, rodlike, attached to ceiling)...is rigidly fixed, then when the fan is turned on... |
If, neglecting friction, I keep both top and bottom of the fan free to move (like maybe in outer space), and I turn on the fan, what will happen?
Some satellites use something very much like this to keep the satellite pointing in the right direction, and do so without using rockets. It's called a reaction wheel. The ... | {
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Storing a Planet-sized Chunk of Metal Inside a Star Would it be physically possible to "store" a planet-size or larger sum of metal, say gold or platinum, inside a star by letting it fall to the core?
Would it be possible to detect which stars had these treasures inside them?
(This is for a Sci-Fi project, but I'd like... | "Storing" something implies the purpose is to put is somewhere safe so that it can eventually be retrieved. Heavy metals should eventually sink to the center of a star, but how are you going to retrieve it? Even in a science fiction context, it's hard to imagine a plausible means or retreiving a large pile of heavy m... | {
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Moment of inertia of rods Ok so I'm extremely comfortable with calculating moment of inertia of continuous bodies but how do we do it for a system not continuous.
For example if 3 rods of mass $m$ and length $l$ are joined together to form an equilateral triangle what will be the moment of inertia about an axis passing... | @DrChuck's answer is correct. Generally speaking the total moment of inertia is the sum of the moments inertia calculated individually. You have to be careful about the the axis of rotation thought: if you wanted to calculate the moment of inertia (with respect to any axis) of a T shape created from 2 identical rods, y... | {
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What does the $c$ in $eV/c^2$ stand for? I have been wondering(also searching) for what does the $c$ in eV/$c^2$ stand for?
(For example, mass of the electron is $0.511 \, \text{MeV}/c^2$.)
I have read that this unit has been derived from Einstein's equation, $E=mc^2$, but how it is possible, We use the symbol $c$ for ... | For physicists it can be very annoying that our historically evolved units of measurement cause the speed of light $c$ to differ from unity. So physicists often apply a trick to avoid distracting conversion factors corresponding to the numerical value of (powers of) the speed of light popping up in their equations. Tha... | {
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Is there a difference between the speed of light and that of a photon? As in the title I am curious whether there is a difference between the speed of photon and the speed of light, and if there is what is the cause of such a difference?
| I haven't done this in a long time, but my understanding from Feynman's QED is that the speed of a photon is unknown (Heisenberg) - photons traveling in a vacuum are around the speed of light +-, but at any instant the speed differs due to uncertainty. The photons going faster and slower than light speed cancel in the ... | {
"language": "en",
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What happen to a spoon which is detached from the satellite? Suppose a spoon is a part of satellite but after detachment from the satellite Does it fall to the ground straight or does is take a parabolic path or any other path before coming to the surface of Earth
| The spoon will keep moving until orbital decay takes control and it reaches the earth over several orbital periods.
To explain why, imagine a spoon hung to a satellite traveling at a constant velocity (ignoring any accelerations, for ease of understand) of $x$ and therefore all its components must be travelling at the... | {
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Is this an entangled state? Is the following state entangled?
$\left| \psi \right> = \alpha_0 \beta_0 \left| 00 \right> + \alpha_0 \beta_1 \left| 01 \right> + 0 \left| 10 \right>+ \alpha_1 \beta_1 \left| 11 \right>$
I 'know' it is an NOT an entangled state, but I here's where I am a bit confused. It says $ \alpha_1 \be... | It is an entangled state, as you concluded yourself it cannot be written as a direct tensor product. To recap again:
$$
\left(
\begin{array}{c}
\alpha_0\\
\alpha_1\\
\end{array}
\right)
\otimes
\left(
\begin{array}{c}
\beta_0\\
\beta_1\\
\end{array}
\right) =
\left(
\begin{array}{c}
\alpha_0 \beta_0\\
\alpha_0 \beta_1... | {
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Final velocity of a spring I need to calculate the velocity of an object when it is thrown by a spring; we have to calculate the velocity from $U=\frac 12 kx^2$.
Now I know that $U=L=F\cdot S$ and $S=\frac{v_f^2-v_0^2}{2a}$. Here's what I did:
$$U=L=F\cdot S=ma\cdot S\rightarrow L=ma\cdot \frac{v_f^2}{2a}=\frac{m\cdot ... | Yes, alternatively you can use that the potential energy of the spring is transformed into kinetic energy of the object. This is simpler than considering the work $L$ done by the spring. The result is however the same:
$$
U=E_{kin}\\
\Rightarrow \frac{1}{2} k x^2=\frac{1}{2}m v^2\\
\Rightarrow v=x\sqrt\frac{k}{m}
$$
| {
"language": "en",
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What does the "size of the universe" mean if the Universe is infinite? There are questions that may seem to be similar to this one, but I've yet to find an answer.
I have come to understand that a flat universe, that is to say a curverature of $k=0$ which means that $S_k(r) = r$. The FLRW metric polar coordinates:
$$ds... | All statements like "when the universe was the size of a grapefruit" refer to the currently observable universe. As the universe has a finite age and light travels at a finite speed (and there is nothing infinite going on with expansion), the observable universe is a finite patch.
I discussed some of the different noti... | {
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Planets and Pluto? Neptune? If one of the rules to be a planet is that it needs to clear ALL objects from their orbit, does this also make Neptune a non-planet? Since it has thus far failed to clear Pluto from it's orbit. Or does this rule not really apply to planets and we should welcome Pluto and a few other dwarf pl... | Neptune actually is the dominant gravitational force in the region of the Kuiper belt in which Pluto resides. In fact, if you look at the image below, the belt is being cleared out by Neptune:
In fact, there is a class of objects, suitably named the plutinos, that have been captured by Neptune. Solar system models hav... | {
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How stable are Benard Cells when the thermal gradient begins decreasing? I've found lots of information on the formation of Benard Cells and convection currents but very little information about what happens to the self-organized structures when the energy gradient being applied begins to get smaller.
Do the complex st... | The dimensionless Rayleigh number characterizes buoyancy driven convection. When the Rayleigh number is below a critical value, heat transfer is primarily by conduction (e.g. no Benard convection cells). When the Rayleigh number is above the critical value, heat transfer is primarily by convection (e.g. Benard convec... | {
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Forces Create Angular Acceleration And "Straight" Acceleration - But How Much Of Each? Let me set up the following problem for a rectangle floating in space:
*
*We know its dimensions.
*We know its mass.
*There's a force pushing it for a known amount of time - we know the angle & magnitude of the force.
*We know ... | If you look at the planar motion, with the force $\vec{F}=(F_x,F_y)$ going through a point $\vec{r}=(x,y)$ applied to a rigid body, then the equations of motion are:
$$ \begin{align} F_x & = m \ddot{x}_C \\ F_y & = m \ddot{y}_C \\ (x-x_C) F_y - (y-y_C) F_x & = I_C \ddot{\theta} \end{align} $$
where $(x_C,y_C)$ is the l... | {
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Defining creation and annihilation operators Creation and annihilation operators can be defined in several different ways, some more general than others. We usually choose to denote by $a$ the annihilation operator and by $a^\dagger$ the creation operator.
It can be seen that the two operators must be Hermitian adjoin... | It boils down to a matter of convention. Nothing stops you from choosing the annihilation operator to be $a^\dagger$.
Still, in quantum field theory, you decompose e.g. a scalar quantity in plane waves
$$ \Phi(x) = \int \frac{d^4 k}{4 \pi} \left( a(k) e^{ik\cdot x} + a^*(k) e^{-ik\cdot x} \right)$$
where obviousely the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Kinetic energy vs. momentum? As simple as this question might seem, I failed to intuitively answer it.
Let's assume there is a $10,000$ $kg$ truck moving at $1$ $m/s$, so its momentum and KE are: $p=10,000$ $kg.m/s$ and $KE=5,000$ $J$.
Now if we want to stop this truck, we can simply send another truck with the same ma... | The truck keeps going. Assuming the rope does not break, then the kinetic energy ends up in elastic potential energy in the rope. The rope will stretch. If you ask what happens if you assume a rope that cannot stretch, bzzt. No such thing. The rope will either stretch or break.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the Weak force? In this Particle Physics books I'm reading it explains Weak force with Beta Decay, a Neutron turns into a Proton after emitting an electron, so after it emits an electron one of the neutrons down-quarks turn in to an up-quark, and for this there needs to be a force, which is the Weak force. This... | The weak force acts on particle that have weak hypercharge, just as electromagnetism acts on objects with electrical charge and gravity acts on objects with mass.
All the quarks and leptons have weak hypercharge, so the weak force act on them.
The description you have been given of beta decay is incomplete because it d... | {
"language": "en",
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Explanation for negative specific heat capacities in stars? I've just found out that a negative specific heat capacity is possible. But I have been trying to find an explanation for this with no success.
Negative heat capacity would mean that when a system loses energy, its temperature increases. How is that possible i... | Consider a satellite in orbit about the Earth and moving at some velocity $v$. The orbital velocity is related to the distance from the centre of the Earth, $r$, by:
$$ v = \sqrt{\frac{GM}{r}} $$
If we take energy away from the satellite then it descends into a lower orbit, so $r$ decreases and therefore it's orbital v... | {
"language": "en",
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For a massless pulley moving upwards with acceleration, is the upward force equal to the downward force? Imagine a massless and frictionless pulley with two weights hanging either side of the pulley by a massless string.
Like this except not attached to a ceiling
Rather than being fixed to a ceiling, the pulley is bein... | In the equation $F_{net}=ma$, normally we would assume that $F_{net}=0$ implies $a=0$ on the right-hand side. However, for a massless object, we can satisfy the equation by having $F_{net}=0$, $m=0$, and $a\ne0$. In reality, of course, the pulley is not massless, so $m$ is small, $a$ is some nonzero number, and $F_{net... | {
"language": "en",
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Why is $\pi$ used when calculating the value of $g$ in pendulum motion? I am trying to intuitively understand why $\pi$ is used when calculating the value of $g$ using the harmonic motion of a pendulum:
$$g ~=~\frac{4\pi^2L}{T^2}.$$
Does it have something to do with the curvature? I am thinking something along the line... | First notice that simply by considering the dimension of the parameters involved, one can deduce that the time period of oscillations should go like
$$T\propto\sqrt{\frac{\ell}{g}}. $$
This is because $g$ is acceleration hence has the dimensions of Length over Time squared and so the only way the quotient can have the... | {
"language": "en",
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Is a suit that hides a soldier's heat signature fundamentally possible? I recently played "Crysis", a game where the protagonist wears a suit that allows the player to hide both himself and his heat signature. Then I watched Iron Man 3, where a kid suggests that Tony Stark should have implemented retro reflection panel... | Such technology is in its infancy, but it definitely exists. The images below are produced by several companies promoting their thermal/IR camouflage clothes. Obviously the applications are well-suited for the military, so who knows what more the military has developed.
This last image is made by a company called Bl... | {
"language": "en",
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"source": "stackexchange",
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How can I estimate the density of fog? I'm working on investigating the effect fog has on drag. I have assumed an air density of $1.225 \frac{\text{kg}}{\text{m}^3}$ for dry air, but I don't know what value for density I could assume that would be typical of fog.
I can't even reason out whether or not fog is more dense... | Anyone who has ever seen fog pour over a mountain range can tell you that it is significantly more dense than either moist or dry air. It does, after all, settle to the bottom of valleys....
See https://www.dailymail.co.uk/video/news/video-1031660/Incredible-wave-fog-rolls-Canadian-mountain-range.html for a nice exam... | {
"language": "en",
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Unification of the electroweak theory Can the electroweak theory be described by the spontaneous symmetry breaking of $SU(3)$ to $SU(2)\times U(1)$?
| In fact it is possible, see the paper Spontaneous Breaking of Symmetries by Li Fong Li. In general for the Adjoint Representation of $SU(n)$(the octet for $SU(3)$) you can have the following breaking (when $\lambda_2>0$, a parameter in the general potential):
$SU(n) \rightarrow SU(l)\times SU(n-l)\times U(1), \;\; l= ... | {
"language": "en",
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What is the four-dimensional representation of the $SU(2)$ generators? Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress.
I am trying to extend the Dirac field equation with a coupling to a $SU(2)$ gauge field:
$$(i... | Comment to the question (v4): OP seems to effectively conflate spacetime symmetries and internal gauge symmetries. They act in different representations, or more precisely as a tensor product of representations.
For instance the fermion $\psi$ carries two types of indices, say $\psi^{\alpha i}$, $\alpha=1,2,3,4,$ and ... | {
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Is it a postulate or a well proven fact that speed of light remains constant w.r.t any observer? We usually heard that speed of light in vacuum $c$ remains same no matter how observer is moving?
I am wondering whether is it taken as a postulate or a proven phenomenon that $c$ is constant irrespective of observer's spee... |
I am wondering whether is it taken as a postulate or a proven phenomenon that c is constant irrespective of observer's speed?
Either one. Both.
Einstein took it as a postulate in his 1905 paper on special relativity. From it, he proved various things about space and time.
The frame-independence of $c$ is also experim... | {
"language": "en",
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Is $E^2=(mc^2)^2+(pc)^2$ or is $E=mc^2$ the correct one? I have been having trouble distinguishing these two equations and figuring out which one is correct. I have watched a video that says that $E^2=(mc^2)^2+(pc)^2$ is correct, but I do not know why. It says that $E=mc^2$ is the equation for objects that are not mo... | The equation $$E^2=(mc^2)^2+(pc)^2$$ represents the correct energy-momentum relationship. It gives the total energy $E$ for an object of invariant mass (rest mass) $m$ that is observed to move with momentum $p$. This equation is applicable regardless whether the object is observed to be in motion ($p \ne 0$), or is obs... | {
"language": "en",
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Is this expression for the kinetic energy of a spinning disk revolving about a second axis correct? My question is motivated from a question from another user. You can see the configuration of the rotating system here: https://physics.stackexchange.com/q/143377/.
I am not interested in all the complicated arguments of... | This is simple, take the linear and angular velocity of the center of mass (point B) and combined them with the inertial properties
*
*Linear Velocity of B : $\vec{v}_B = (0,d \omega_1,0)$
*Angular Velocity of B : $\omega_B = (0,0,\omega_2-\omega_1)$
*Mass of disk $m$
*Mass Moment of Inertia of Disk $I_{zz} = \fr... | {
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Can there be force without motion? I am confused. Can you have a force or tension without motion?
Take for instance two robots with jet packs connected via a cord, each is flying in opposite directions.
The tension of the cord is measured through a sensor of some kind. At some point, the net forces of the robots become... | A net force acting on a body should do some work. For the simplest conservative case, the applied work will appear as the change in potential energy of the system. The object is not moving. But the potential energy creates a tension on the system. An example is a spring with its one end fixed. You apply a force that ca... | {
"language": "en",
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Why is quasineutrality required for a gas to turn into a plasma? Why is quasineutrality a required condition for a plasma to exist?
Quasineutrality means that no density of electrons and ions should almost be equal but not exactly equal. Can anybody explain this this condition is required?
| Plasma potential.
Often electrons move faster than ions and leave the plasma at a higher rate. The plasma becomes positive until the positive 'plasmas potential' slows down the rate of electron loss from the plasma until it is the same as the rate of positive ion loss. The electrons are partially held in the plasma by ... | {
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Using the force law to obtain total energy of an electron as a function of its radius I am working on a problem which starts saying determine the total energy of a hydrogen atom with an electron moving with momentum $p$ at a radius $r$.
For that part I got:
$E = \frac{p^2}{2m_e} - \frac{e^2}{r}$
Which is just the kine... | If the orbit is circular, then $p=\rm{const}$ and $r=\rm{const}$. $E$ is constant and negative (for a bound state) even though the orbit is not circular. So, one can determine $r$ from this equation: $$r=\rm{e}/\left(p^2/2m_e-E\right).$$
The minimum is zero (no kinetic energy, only the negative potential one), which i... | {
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How do you pronounce $\vec{A} \cdot \vec{B}$ and $\vec{A} \times \vec{B}$? I'm French.
I would like to know:
*
*How do you pronounce $\vec{A} \cdot \vec{B}$ : "A scalar B" or "A dot B" ?
*How do you pronounce $\vec{A} \times \vec{B}$ : "A vectorial B", "A vector B", "A cross B" or "A times B" ?
In French we say "A ... | The first bullet would be read "$A$ dot $B$" or "The dot product of $A$ and $B$"
The second bullet would be read "$A$ cross $B$" or "The cross product of $A$ and $B$"
| {
"language": "en",
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Adding a tracer to the surface of a water droplet I have a 2 mm water droplet generated by a syringe and falling down. I am using two perpendicular cameras to capture simultaneous frames from it. I need to track the droplet during the time and reconstruct it (through consecutive frames). However, only the border of the... | I would consider using water with a dye like a deep blue to be nearly opaque. Illuminate with an array of LEDs. Each bright spot reflected from the droplet is an LED. You can add a few strategic red LEDs among all white as reference.
Working out the most convenient geometry will tell if you need the LEDs on some curved... | {
"language": "en",
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How would behave theoretical matter with negative mass? I wonder if there is any possibility to evaluate theoretical characteristics of matter with negative mass? This is not thing of anti-mass but classical matter just with negated weight. I thing that if you would put it on surface of the Earth it would fly to heaven... | Well, one of the basic facts from General Relativity (the commonly accepted theory of gravity) is the so-called Equivalence principle, which basically states that all kinematic behaviour of a particle in the gravitational field does not depend on the particle's internal properties (like mass). So it would not fly to he... | {
"language": "en",
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Confusion with rotation operator definition in Shankar In Shankar quantum mechanics on page 306-307 it has the following:
12.2. Rotations in Two Dimensions
Classically, the effect of a rotation $\phi_0\mathbf{k}$, i.e., by an angle $\phi_0$ about the $z$ axis (counterclockwise in the $x\ y$ plane) has the following ef... | $R(\phi_0,k)$ is the operator that rotates your co-ordinate system. But it is not suitable to apply a 2x2 matrix, as in this case, to a vector in Hilbert space. Mind that Hilbert space is unlike an ordinary orthogonal position space.
Thus, using $U$, you map the operator into an equivalent operator which can operate on... | {
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What is a rocket engine thrusting against in space? I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut wouldn't be able to push in the empty space with his hands or legs to mov... | If I'm not wrong, it's basically the same principle in which an astronaut would throw something in empty space and, with so, move in the opposite direction.
It's not thrusting against something but throwing energy and power by burning fuel according to the law of inertia... I could be wrong so I'd like someone more kno... | {
"language": "en",
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Difficulties in understanding basic energy equation in quantum mechanics While reading a text book about basics of Quantum Mechanics, I came across a situation in which it is said that
$E=\hbar\omega$ and also
$E = \frac12mv^2=p^2/2m$
where
$h$ Planck's constant
$\hbar=\frac{h}{2\pi}$ Planck's reduced constant
$\omeg... | The relationship
$$
v=\lambda\nu=\frac{\omega}{k}
$$
describes the phase velocity ($v_p\neq v$) and not the group velocity ($v_g=v$), so it should be
$$
v_p=\frac{\omega}{k}=\frac{\hbar\omega}{\hbar k}=\frac{E}{p}=\frac{p}{2m}=\frac{v}{2}\tag{1}
$$
which does follow from the de Broglie relation ($p=h/\lambda=\hbar k$)... | {
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Radio wave propagation in ionosphere Radio communication is based on the concept that a radio signal incident on the ionosphere is reflected if the frequency of the wave matches the plasma frequency.
But what exactly happens? Is it based on the electrons in the ionosphere absorbing and re-radiating the energy if the fr... | Exactly the same happens as when light reflects off a metal surface. In both cases you have an electron gas that interacts with the light. In the case of a metal it's a dense (almost) free electron gas, and in the ionosphere you have a very dilute electron gas formed by ionisation of air molecules.
The incoming electro... | {
"language": "en",
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Comparison between entropy and internal energy Why is entropy change a better way of determining a spontaneous process compared to the change in internal energy?
| The change in internal energy is not a relevant quantity for spontaneous evolution of a system. Consider an isolated system made of two blocks of the same material at two different temperatures such that $T_1>T_2$. Heat will flow from $1$ to $2$ but the total change in internal energy is $\Delta U_{1+2}=0$. This inform... | {
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Why do we add the spin angular velocity and orbital anglar velocity when asked to calculate total angular velocity of Gyroscope? Normally when we talk of angular velocity we mean how the angle of a vector changes with time with respect to an origin.Thus the oribital angular velocity of gyroscope makes sense to me.Howev... | It's as simple as adding the two vectors, the vector that determines the orbital rate relative to your reference frame and defined origin, and the vector that defines the spin angular velocity relative to the spin axis of your gyroscope. The two vectors are tip to tail connected and their sum is just the vector connect... | {
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What exactly is color? What is color?
“The property possessed by an object of producing different sensations on the eye as a result of the way the object reflects or emits light”…. You might say.
So take a white object and paint it “red”. What property of the paint now makes the object appear red?
“Pigmentation!” … you... | OK the answer is not microscopic level but beyond that. It is in atomic level.
*
*Metal complexes are often colored. These colors come from the d-orbitals because they are not involved in bonding. This is because they do not overlap with the s and p orbitals of the ligands. Most transitions related to colored metal ... | {
"language": "en",
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Does drag produce heat? When a solid object moves through a fluid drag is produced. Does this drag produce heat?
I believe drag should produce heat as it is the friction between fluid and surface of object. Is this true or not?
| Actually drag is NOT completely the friction between the object and fluid. Sometimes there can be almost no friction, but still highly significant drag. In a non viscous fluid, there is no friction between the object and the fluid, but there IS still drag. The phenomenon of ram pressure transfers momentum losslessly be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145105",
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How fast does an electron travel in a circuit? How is it possible to calculate the speed of an electron in a circuit? What factors does it depend on?
| Individual electrons may have a range of speeds in a circuit (thermal motion, scattering, absorption, photon etc..)
However the current (or drift velocity) gives the average speed of the whole electron cloud (not a single electron).
Note again single electrons may have a range of speeds (from slow to very fast, near ... | {
"language": "en",
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What is the link between observation wavelength and spatial resolution of an instrument? It seems that when capturing and emitting EM waves matter proceeds differently depending on the wavelenght. According to an answer from another question, EM energy is captured following three modes: electronic transition (e.g. for ... | The answer would have to depend on a specific scale. i dont think there is an answer to this question without determining a scale.
A scale will fix the dimensions and the relative wavelengths that are relevant to the spatial resolution of objects.
Lets say one wants to observe a cubical object which radiates (very high... | {
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Correlation between equations of elliptical orbits and pendulums The equation for the period of a pendulum is:
$$T=2π\sqrt{\frac{L}{g}}$$
Where 'g' is the acceleration due to the gravitational field and 'L' is the length.
The equation for the period in of a body travelling along an elliptical orbit is:
$$T = 2π\sqrt{\... | The equation for the period of a pendulum $(T=2π\sqrt{\frac{L}{g}})$ is only an approximation. That equation assumes, among other things, that gravity doesn't change with height, and that $\sin(\theta) = \theta$.
Even if there were a connection between that approximation and elliptical orbits, that would not imply any... | {
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Tractor wheels -- large vs small This question has stumped me for over a month now:
Why is it that a tractor has large wheels at the back and small wheels in the front?
Current ideas:
*
*small wheel in front --> lower center of mass--> less likely to tip over, moment.
*large wheels in back provides more torque,... | One of the reasons is that if the wheel axle is above the attachment point it drives the wheels downwards when pulling increasing traction.
Think of the opposite, where the attachment point is really high it will force the front wheels off the ground limiting the pull force so the tractor does not flip.
So what happen... | {
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"source": "stackexchange",
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What is the phase shift incurred by a sound wave as a result of reflection? While studying waves I read the fact that a sound wave gets shifted by $\pi$ as a result of reflection against a surface. But I am unable to prove that fact.
Assuming the interface to be a node I can prove that there is a phase shift of $\pi$ b... | A wave e.g
$$\sin (kx + \omega t + \phi)$$
when reflected runs in the opposite direction. In other words gets a rotation by $\pi$ or what amounts to the same thing gets a phase shift by $\pi$.
$$\sin (kx + \omega t + \phi + \pi)$$
Tentative proof:
Let's say a wave $\psi \sim e^{i(kx-\omega t)}$
on reflection the wave... | {
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"answer_id": 0
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How can the linear momentum can be understood physically? Currently reading Classical Mechanics by Herbert Goldstein, and I'm trying to understand every concept physically. Speed can be understood physically, as the distance traveled within a certain amount of time, it makes sense to me. By contrast, I can't attribute ... | The idea of momentum is the idea of "quantity of motion". You want to be able to formulate in some sense the idea of "how much motion there's in this particle?" and you can think about the simplest model for that like that: the faster the particle moves intuitively more motion there is, so the quantity of motion should... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145796",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
How many more galaxies are out there in the Universe (beyond the observable radius)? Let's say that the number of large galaxies in the observable universe is $n$ (approximated to 350 billion).
If the universe is homogenous and isotropic, what are the estimations for the total number of large galaxies in it?
$5n$, $10n... | You assume homogeneous and isotropic structure. That limits the possibilities as follows: It is just as likely that there are observers at the 'edge' of our Observable Universe as there are here. Assume two exist opposite each other. They both see the same Universe we do. Repeat the argument with them. Now consider the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/145893",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 2
} |
What is $Q_p/Q_e$ experimentally? What is the experimental value of the ratio between the proton and the electron charge? Or more generally, is there a table that lists the ratio of the different nuclei charges to that of the electron?
|
[PDG] quoted something like $(q_p+q_e)/e$ without defining these quantities,
That is exactly what you asked for. Recall that the charge on the electron $q_e$ is negative and that on the proton $q_p$ is positive, so the sum there is exactly the difference in their magnitudes. Taking it as a fraction of the defined bas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/146000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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