Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Can a virtual image created by a mirror have position in front of the mirror? I dont think so, because then the rays will intersect and the image will be real.
Please let me know if you know a case in which a virtual image is formed in front of the mirror.
| The first sentence in your question is the answer. With a virtual image, the rays appear to come from an object behind the mirror. The important words there are "appear to." There is no actual object behind the mirror from which the rays are emanating. If there is a real image in front of the mirror and you view it fro... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Zero stress boundary conditions for the acoustic wave function When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
| Strictly speaking: never. Outside the idealized models there are always at least a bit of radiation impedance so the pressure on the boundary is not truly zero.
But let's focus on idealized models. Usually the zero pressure boundary condition is used for open ends of the waveguides or for the free surfaces of solid bod... | {
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Excitation energy of carotene using the particle in a box model I'm practicing for an exam and I came across the following question:
The linear, conjugated π-electron system of a carotene molecule comprises 11 atoms and the distance between two atoms is 1.4 Å. Calculate the excitation energy and the wavelength of the ... | The energy is:
$$ E = \frac{n^2h^2}{8mL^2} $$
Your mistake is that you have $L$ not $L^2$ in the denominator so your answer is a factor of $L$ too small.
| {
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Shadow of a ripple? Suppose a stone is thrown into a pool of crystal clear water and its a bright sunshiny morning. You can observe a shadow of the wave in the bottom of the pool. Why does this happen? Is it due to superposition of light or some other thing?
| You can actually think of the ripple as a travelling lens.
If you take a radial cross section through the ripple, it'll have a curved profile. Now just like a magnifying glass causes a bright spot in the middle of where you focus incoming light, it also causes a darker region around it.
This is what you're seeing on t... | {
"language": "en",
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Why does the human body feel loud music? I was sitting close to a speaker and I could feel the sound coming from it all over my body, especially in my heart, and it pounded with the loud beats of the music.
Was my heart pounding because of the excitement at listening to the music or was I really feeling the sound in my... | Along with your pounding heart, you're also experiencing the effects of resonance. In simple terms, there are certain frequencies of sound waves which correspond to the "natural" vibration frequency of your bones. At these frequencies, your bones vibrate with a greater amplitude than other frequencies, and you can thin... | {
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When a pn junction is formed, why is a positive region of charge formed on the n side of the junction? I understand that when electrons diffuse from n-side to p-side, negative charge is developed on the p-side. But the mere absence of electrons on the n-side doesn't make that positively charged. The n-side must be neu... | When n and p crystals are brought closer the excess electrons in n and excess holes in p begins to diffuse to p and n region respectively which is a phenomena relating to the concentration gradient. The electrons which diffuse in the p region from n region actually come from the donor ions (like P, As ). So as these el... | {
"language": "en",
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How is the conservation of momentum satisfied in long-range attraction such as electromagnetism and gravity? I'm not a physicist, but my understanding is that electromagnetism (including attraction between opposite charges) is mediated by the photon, and gravity is probably (hypothetized to be?) mediated by the gravito... | If you consider things classically (for the moment forgetting about virtual particles as mediators of the force) things get more clear.
For instantaneous forces (which do not exist in nature), momentum conservation comes from the fact, that the forces in nature fulfil Newtons axiom actio = reactio, meaning, that for tw... | {
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Can I use the grand canonical ensemble for a photon gas? I have been reading about photon gases at https://www2.chem.utah.edu/steele/doc/chem7040/chandlerch4.pdf. They do the analysis using a canonical ensemble.
Since photon numbers are not conserved, I would have thought it would be more appropriate to use the grand c... | The grand canonical ensemble allows the number of particles of your system to fluctuate but makes the assumption that it is constant amongst the reservoir and system combined i.e.
$$
n_{res} + n_{sys} = const
$$
For the case of photons this is not true.
| {
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Does a Static $E$-field Increase the Gauge Invariant Vector Potential Without Bound? The gauge invariant formulation of Maxwell's Laws (7.13):
Indicates that the transverse electric field is the time derivative of the transverse vector potential.
This gauge invariant vector potential increases without bound as long as... |
This gauge invariant vector potential increases without bound as long as there exists a static electric field. Indeed, even when the electric field is removed, there appears to be no mechanism by which the gauge invariant vector potential disappears.
Static electric field has zero transversal component; entire field ... | {
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Usage of singular or plural SI base units when written in both symbol as well as name I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name.
I have framed this question under two parts, namely, Part (a) and Part (b). Each part has three sentences whi... | One never pluralizes unit abbreviations.
Your link goes to the BIPM, the body responsible for maintaining the definitions of the international system of units, and is authoritative. The folks at NIST agree and address most of your questions.
I would say
*The pipe is 0.75 m long.
or
*The pipe is 75 centimeters... | {
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What's my $\mathrm dM$? Gravitational Potential inside a circle of mass
I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring.
So we start with:
$$\Phi=\int G\frac{\mathrm dM}{r}$$
Let's assume that the... | It depends, is the ring infinitely thin? In other words, do they give you $\lambda$ (density per length) or $\rho$ (density per volume). If they give $\lambda$, then $dM=\lambda rd\phi$. This is because $rd\phi$ is a differential length, and multiplying it by $\lambda$ gives you the differential mass at that point. The... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172141",
"timestamp": "2023-03-29T00:00:00",
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About Lorentz Group In definition of orthogonal matrices we say that the a matrix $A$ is orthogonal if $A^TA = I$, while for Lorentz Group it is written as $\Lambda^Tg\Lambda = g $. And we say that Lorentz transformation forms an orthogonal group
My Question is why do we insert the $g$ in the above definition?
| $g$ denotes the metric. For Euclidean space the metric is just the unit matrix $I$. For Minkowksi space, which is of interest when talking about the Lorentz group it's the Minkowski metric $\eta_{\mu \nu}$. The lower right matrix inside the Minkowski metric is the 3-dimensional unit matrix and therefore for the space-... | {
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Perception at relatavistic speeds If one were to be traveling at near the speed of light, their mass would be $m_{rel}= m_0 / \sqrt{1 - \frac{v^2}{c^2}}$. For the mass to double the speed would have to be $86.6\%c$
[edit]
To better phrase the question, perhaps I should use relativistic momentum: $p_{rel}=m_0v/\sqrt{1 ... | From the reference frame of the space ship, your body is stationary. When you swing your arm back and forth, it has a non-zero speed in this frame, and thus its mass, or rather momentum, increases. The space ship's velocity of $v_\mathrm{ship} = 0.866c$ doesn't add to this. That means that the increase in momentum is e... | {
"language": "en",
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Could I break the sound barrier using circular motion? (And potentially create a sonic boom?) Ok, Lets say I get out my household vaccum cleaner, the typical RPM for a dyson vaccum cleaner reachers 104K RPM, Or 1.733K RPS. In theory, this disc would be travelling with a time period of 0.00057692307 seconds, If we take ... | The answer is "yes", for speed of sound, and "maybe" for the sonic boom.
It is not the speed a problem, but the apparition of different pressures along a surface or on sides of a surface and the shock waves. The extremities of the turbine inside of a vacuum cleaner can function at speeds above speed of sound if the vib... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172451",
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Translational versus dilatational zero modes? Why are the zero modes of the SU(2) Yang Mills instanton referred to as translational or dilatational zero modes?
Is this standard terminology?
| Instantons are characterized by the winding number and a set of collective parameters (e.g. location of the centers of the instantons, their sizes and the inequivalent orientations in the global group space / space-time).
Quantum fluctuations of a unit winding number instanton can either leave the collective parameter... | {
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Why temperature of liquid drops after spraying through a nozzle? We have tested in our lab as mentioned in the picture.
We connected hot water at $130^\circ F$ at $40 Psig$ to a nozzle (bottle sprayer). We measured the temperature differences inside tank and after spraying and found that there is a temperature drop of... | Given the cooling attendant to evaporation of even small amounts of water, it's likely that it is the source of the cooling effect.
A question was asked above,
"Have you also tested at different relative humidities of the surrounding air?",
but it was not answered.
You should carefully measure the volume in the hot w... | {
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Cooper instability assuming triplet pairing I am stuck on a question in Chapter 11 of Advanced Solid State Physics by Philip Phillips, which asks to do the Cooper instability calculation for triplet pairing.
I attempt to solve the Schroedinger equation
$ [-\frac{\hbar^2}{2 m} (\nabla^2_1 + \nabla^2_2)+V(r_1 - r_2)] \ps... | After Fourier transform you get an equation
$\displaystyle (E-\frac{k^2}{m})\alpha_{\vec{k}}=\sum_{\vec{k}'}V_{\vec{k}\vec{k}'}\alpha_{\vec{k}'}$
Here $V_{\vec{k}\vec{k}'}\sim \int \mathrm{d} \vec{r} e^{i(\vec{k}-\vec{k}')r}V(\vec{r})$.
Now we need to make some simplifying assumption about $V$. For $s$-wave, usually w... | {
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Why is $F=ma$? Is there a straightforward reason? Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplicat... | If a particle is left alone in an inertial system, it will travel on a straight line, that is
$$ \frac{d\vec{v}}{dt} = 0 \tag1 $$
it will not change the magnitude and direction of its velocity. This is an empirical fact. So if a particle does change its velocity the right hand side of (1) is not zero. Lets call it $\ve... | {
"language": "en",
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If the Earth is a good conductor of electricity, why don't people get electrocuted every time they touch the Earth? Since the Earth is a good conductor of electricity, is it safe to assume that any charge that flows down to the Earth must be redistributed into the Earth in and along all directions?
Does this also mean ... | Electricity isn't a gas that expands out to shock anything in contact with it. Electricity is a flow from high voltage to low voltage. Touching a charged object is only dangerous if you become a current path--if it uses you to get somewhere. Even if the earth had a net charge, you aren't providing it anywhere to go, s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "39",
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Force between two finite parallel current carrying wires Remark: This is not a homework question...It is pure out of theoretical interest. I asked this the mathematics-community a couple days ago and got no answer, so I figured I'd try here.
Most standard physics textbooks compute the force two infinite wires exert on ... | Let's call the circuit in the origin circuit one and it's line element $\mathrm{d}l_1=(0,\mathrm{d}y_1,0)$ and the one to it's right $r_2=(d,y_2,0)$ then the force between them is $\mathrm{d}F_{12}=i \mathrm{d}l_2 \times B_1$ where
$$B_1=\frac{\mu_0i}{4\pi}\int_{l_1} \frac{\mathrm{d}l_1\times \Delta r}{(\Delta r)^3}$$
... | {
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Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$ I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT.
Cosmology: The cosmological constant enters the Einstein equations. In the special case of the Friedman universe it enters the Fr... | Trying to answer my old question myself: The cited piece is talking about an infrared cutoff, which basically amounts to giving the propagating particle a mass which appears squared in a propagator. So I think, what is meant is considering
$$\lim_{\Lambda\to 0}\int \frac{d^4p}{p^2+\Lambda}$$
and this $\Lambda$ of cours... | {
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Does the microgravity environment in highly elliptical orbits differ from circular orbits? I think everyone understands the microgravity environment broadcast from the ISS. But the ISS stays in a fairly circular orbit, the acceleration of gravity should be fairly uniform, the altitude and velocity changing very little.... | To first order, no. The definition of an orbit is that it's a free-fall trajectory — since everything around you is always experiencing the same acceleration as you are, you cannot actually perceive this acceleration without some external reference (like measuring your velocity compared to the Earth, and how fast it c... | {
"language": "en",
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Quantum anharmonic ocscillator $E_0(\lambda)$ curve or table I am looking for the exact data on $E_0(\lambda)$ for the anharmonicity $\lambda x^4$. The perturbative expansion is the following: $E_0(\lambda)\approx 0.5(1+1.5\lambda -5.25\lambda ^2+41.625\lambda^3-...)$, but I need a curve or a table for the exact values... | The problem is not exactly solvable. But the recent paper
http://journals.jps.jp/doi/abs/10.7566/JPSJ.83.034003 gives exact Pade-approximants of various orders, which are probably quite accurate.
| {
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Prove that $(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$
Prove $$(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$$ where $A$ is an operator.
Can anyone explain how to go about this question? Writing it as a power series gets confusing.
So basically I get:
$(e^{i\lambda A})^\dagger=\sum_{n=0}^\infty ({(i\lambda)... |
Prove $$(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$$ where $A$ is an operator.
Can anyone explain how to go about this question? Writing it as a
power series gets confusing.
So basically I get: $(e^{i\lambda A})^\dagger=\sum_{n=0}^\infty({(i\lambda)}^n\frac{A ^n}{n!})^\dagger=\sum_{n=0}^\infty({(-i\lambda)}^... | {
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What exactly is the mass of a body? What determines it? The term "mass" is very common. But what does it depend on? How is it known?
| What is physics? Physics is the modeling with mathematics of observations in the world around us. It is a way of creating a logical sequence that can be predictive and not only explanatory. It reduces the innumerable constants one would need to describe, for example , the trajectory of a ball with just space coordinat... | {
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Do magnetic fields cause ionisation of gases? I am doing my final year engineering project on Magnetic Field Assisted Combustion and was curious to see what people thought about it.
Companies sell rare earth magnetic arrangements to be attached to fuel lines of gas burners and they are said to improve combustion effic... | i would say yes. magnetic field does ionize the gas. "Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons". and this as a topic already. Can I produce radio waves by waving my hand? therefore the gas MOVING through a magnetic field would acc... | {
"language": "en",
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At what point does force stop translating an object and start purely rotating it? At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to translate?
This question assumes that the b... | If there is no fulcrum, if there is no fixed pivot, a body will always translate.
Such point does not exist. If the body is free, it can only translate but can never only rotate: if the impulse is at the Center of Mass linear velocity will be 100% , the minimum percentage of translational velocity is 25%, and it is rea... | {
"language": "en",
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Scalar and vector defined by transformation properties In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix $ \lambda $ .
Why is this important? I get that it leads to other... | Just as a quick example: say that the dot product were not invariant under transformations. Then let's say that we have two reference frames, A and B, where reference frame B is rotated and displaced with respect to A and which moves at a constant speed w.r.t. A (where $v\ll c$).
Then the researcher in A wants to cal... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can the gravitational constant be directly measured? The value of the gravitational constant $G$ is $6.67384\times 10^-11 {\rm m}^3{\rm kg}^{-1}{\rm s}^{-2}$. This value is used in the formula to calculate the attractive force between two objects with mass, my question is:
since it is a constant why does it have units?... | The gravitational constant is an empirical physical constant found through experimentation, a famous one being the Cavendish experiment.
You can read more about it here.
| {
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Is it possible to formulate a Hamiltonian for a damped system? I recently found out that it is possible to formulate a Hamiltonian for a system with time-dependent coordinates such that the Hamiltonian is not the same as the energy When is the Hamiltonian of a system not equal to its total energy? and that has me wonde... | The following might help:
$H = \frac{1}{2}(mv^2 + kx^2) + \gamma mkvx$
decays exponentially with time along the solution of the damped system. Check by differentiating $H$ with respect to $t$ and using the equations of the system. So the "energy" $H$ decays exponentially instead of remaining constant.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174376",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Probability of photon emission If a photon of a given wavelength is absorbed by an electron (for simplicity, let's assume the electron has only one excited state), does the probability that the electron jumps to its excited state and emits a photon as it falls back depend on the incoming photon's wavelength (is the ele... | There is an equation that helps a lot understanding this issue: Fermi's golden rule
$$
W_{i\rightarrow f}=\frac{2\pi}{\hbar} \left|\left<f\right|H'\left| i\right> \right|^2 \rho
$$
It describes the transition rates from one state to another.
$\rho$ is the so called Density of States (DOS) of final states. This system h... | {
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Will the electrostatic force between two charges change if we place a metal plate between them? If a thin metal plate is placed between two charges $+q$ and $+q$, will this cause a change in the electrostatic force acting on one charge due to another? What is the concept behind this? What will happen if the metal plate... | As the electrostatic charge is two body attraction or repulsion,The force between them will not be affected but The permittivity increases on inserting metal plate Which causes decrease in the Electrisratic force between two charges.
| {
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"url": "https://physics.stackexchange.com/questions/174514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 4
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Can gyroscope work in zero gravity? Most ships have two or more gyroscopes to balance on water, man made satellites uses gyroscope for orientation as they fall around earth. All these applications seems to be associated with gravity, therefore how can a gyroscope works in zero gravity?
| Gyroscopes depend on the conservation of angular momentum. Orientation and navigation gyroscopes are finely balanced/symmetrized so that gravitational fields will not exert external torque and modify the angular momentum.
As the container which holds the gyroscope moves, a gimbal mount allows the gyroscope to maintain... | {
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Beginners Textbooks in physics Hello I am fifteen and I already know everything that my school has been teaching me so I have been going ahead. I have already been studying mathematics far past where I am at school, but I am very interested in physics. I want to learn everything up to advanced topics such as super-st... | I don't know how much you are adept at mathematics but before you begin physics, you ought to study calculus from Thomas' Calculus & Differential & Integral Calculus by Richard Courant.
Now, first of all, you'll come across Newtonian Mechanics. For this, I would recommend A.P.French's Newtonian Mechanics. Unlike Lectur... | {
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Why do snorkelers not need to wear corrective glasses when snorkeling with goggles on? I am myopic ~ -2.75 sph +1cyl. When I went snorkeling they tell you not to wear glasses behind the goggles. Surprisingly, underwater, things remain in focus with goggles on even without prescription lenses, while things outside the w... | Wearing the mask underwater doesn't do anything to enhance your vision, but it does make objects in the water appear larger/nearer. This is due to the refraction of light at the air/mask interface (more info in my answer to this question). The objects are magnified by a factor approximately equal to the ratio of the ... | {
"language": "en",
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Are there any scales other than temperature that have different zero points? For most physical measurements, zero is the same regardless of the units used for the measure:
$0 \mathrm{mi} = 0 \mathrm{km}$
$0 \mathrm{s} = 0 \mathrm{hr}$
but for absolute temperatures, different systems have different zeros:
$0 ^\circ\math... | Time, in which case each system's zero point is often called its epoch:
http://en.wikipedia.org/wiki/Epoch_%28reference_date%29
| {
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How can static friction do work?
By definition, the work done by a force is $W = F\cdot d$, so how can static friction do work?
Can this force move the body a distance of $75~\text{m}$?
| Static friction does not produce or consume work in most of the times. For example for a solid body that rolls without sliding the velocity of the base point $A$ is $\vec v_a = \vec v_{cm} + \vec v_{tangential} \Rightarrow v_a = v_{cm} - \omega R = \omega R - \omega R =0$ which implies that $x_a = 0$. The static fricti... | {
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Sun and planets orbit each other Do not the planets and the Sun revolve in orbits around each other and the shape of the orbit depends on where the center of gravity of the system is? The greater the mass of the Sun, the closer the orbit approximates a perfect circle.
| To say that the orbit becomes more circular the greater the Sun's mass is not true. Instead, the eccentricity (i.e. how much the shape of an orbit varies from being circular) is governed by a couple of factors.
If you have a planet orbiting about the Sun with a mass much less than that of the Sun, and you know the foll... | {
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Why does the pion not undergo netural particle oscillation? $K$, $B$ and now $D$ mesons exhibit neutral particle oscillation, where we see the spontaneous interchange between a particle and its antiparticle, i.e. $K^0 \Leftrightarrow \overline{K}^0$, $B^0 \Leftrightarrow \overline{B}^0$ and $D^0 \Leftrightarrow \overli... | Answer transposed from a comment: the $K$, $D$, $B$ have nonzero "flavor quantum number" (strangeness, charm, and beauty, to be specific). The analogy you should pursue is the $J/\psi$ or "charmonium," made of a charm quark and charm anti-quark.
| {
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What does it mean that a magnetic field's flux vanishes through any closed surface? I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote:
A fundamental property of a magnetic field is that its flux through
any closed surface vanishes.
Can someone explain this in simpl... | If the flux in and out of a surface cancles, there is no need for magnetic charge in which field lines can end or start (e.g. like the electric charge). One expresses this like
$$ \nabla \cdot \vec{B} = 0 $$
wich means
$$ 0 = \int_V \nabla \cdot \vec{B} ~ dV = \int_S \vec{B} \cdot d\vec{S} $$
where $S$ is the surface o... | {
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Phase space Lagrangian? Reading out of this lecture series we define a phase space Lagrangian $\mathcal L$ to be a function of $4n+1$ variables namely $q,\dot q,p,\dot p,t$. My question is, what space is this function defined on? (I know that the $\dot p$ is there for names sake only).
My stab at an answer is it is a ... | Let $X$ be the phase space. Then $L_\text{ph}(q,p,\dot{q},\dot{p},t)$ is a function on $TX\times \mathbb{R}$1, since the coordinates of $TX\times\mathbb{R}$ are precisely the coordinates of $X$, i.e. $(q,p)$ and their derivatives $(\dot{q},\dot{p})$ (and time $t$).
If Hamilton's equations are fulfilled, there are relat... | {
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How do waves have momentum? A question on a practice test I'm taking is as follows:
By shaking one end of a stretched string, a single pulse is generated.
The traveling pulse carries: A. mass B. energy C.
momentum
D. energy and momentum E. mass, energy and momentum
How would one describe the momentum of a wave?
| According to quantum mechanics, $p=\frac{h}{2\pi}k$,where $k$ is wave vector and $h$ is Planck's constant. As we know $k={2\pi\over \lambda}$, where $\lambda$ is the wavelength of the wave. So momentum and wavelength are associated to each other. Moreover we can view as the motion of the every particles as well as wave... | {
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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip? I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance.
Am I correct?
Veritasium/Minutephysics video on... | The question is so ambiguous that it allows a resounding yes. This is because "balance" is not defined, neither are the dimensions and the material used for the pencil, nor the location of where the "balancing" is to happen.
The material and the shape of the surface to balance the pencil on, are not specified, nor the... | {
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Why do we use capacitors when batteries can very well store charges? Can batteries be used instead of capacitors? I am trying to figure out a basic, superficial and any obvious difference between the two.
| I've to make an electronic circuit 'RC' and the relation between current and tension between two nodes must be fulfilled by a capacitor 'C' (it integrates the current; see the relation in the WP). I can use a battery with a constant tension to power the circuit ($V_{in}$in the second image) but not to model that relat... | {
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Meaning of Time Reversal Symmetry I was wondering if someone could give a simple explanation of what is meant by time reversal invariance. Is it analogous to spatial translational symmetry? If so, how? By spatial translational symmetry I mean the following. Suppose, for example, one has a solid consisting of an array o... | Time reversal essentially means a system looks the same if you reverse the flow of time. The only difference beeing that things like velocity go in the opposite direction. In condensed matter systems it is represented as a unitary matrix times complex conjugation $\mathcal{T} = U\mathcal{K}$. A simple system that follo... | {
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General Relativity visualization software As I am approaching the study GR, I was wondering if there are softwares that allow a quick visualization of custom metrics, curvature, and particle motion even in the limited context of 2D space.
Playing with equations is fun, but it would be more fun if I could play with var... | I've been looking at this Java archive
General Relativity (GR) Package written by Wolfgang Christian, Mario
Belloni, and Anne Cox
It includes a lot of simple programs about Newtonian mechanics, special relativity and general relativity, including the aforementioned GROrbits.
It doesn't permit custom metrics - you a... | {
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Is there any physical meaning for the inverse metric? I've been wondering if we can attribute any physical meaning to the inverse metric. I mean when we talk about the metric itself, there are lots of insights we can have towards its role in spacetime, yet I cannot see any physical meaning for the inverse metric. For n... | Another way of looking at user40330's answer is to think of the inverse metric as the map from the space of one-forms (or differentials, if you prefer) and mapping them to the space of vectors (or directional derivatives, if you prefer that language), and then thinking of the metric as the inverse of this map.
Namely... | {
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How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory? It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula
$$L=I-V+1$$
where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. I would like to know the proof of this statement.
| Page 140 of Srednicki's QFT textbook provides a much simpler proof:
This can be seen by counting the number of internal momenta and the constraints among them. Specifically, assign an unfixed momentum to each internal line; there are [$I$] of these momenta. Then the $V$ vertices provide $V$ constraints. One linear com... | {
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Calculating wind force and drag force on a falling object I'm trying to numerically integrate the motion of an object (say, a falling vertical cylinder). Here, there's a drag force: the wind "acting" on the body (presumably adding horizontal velocity) and the air itself slowing down the vertical motion.
Is it correct t... | "The vertical drag is greater" Could this be "lift"?
The vertical and horizontal velocity components do indeed produce a higher net velocity vector, but the vertical and horizontal kinetic energy components also have a Velocity squared function.
Interestingly, if you dropped an unpowered object from a tower in a 2 mp... | {
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How to calculate the normal force exerted by a fulcrum off-center? So I know that $F_N$ exerted by a fulcrum right under the centre of mass for, say, a long horizontal rod, is equal to $mg$. But what if the fulcrum is off the centre of mass either to the right or the left -- how would you calculate the force exerted by... | Be careful - you are applying the reasoning about a static situation to a situation that is not static. This rod will be rotationally and linearly accelerating, so you can no longer assume the net force or net torque is zero - $\Sigma F_y = m a_y$, and $a_y \ne 0$.
If the rod is instantaneously horizontal and at rest,... | {
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Speed of gravity within a mass We all consider that gravity travels at the speed of light. Light travels at the speed of light except when it is in a medium ,say glass, where it travels slower.
What happens when gravity passes through a distributed mass. Will it still travel at the speed of light or will each atom abso... | The acceleration of gravity is that itself. The bigger the mass the more gravity pulls on the object. Especially with a force. This could be simplified into an equation we learned in Intro-Physics, F=ma or f=mg
| {
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Entropy - Gas Inside A Closed System Reaches Maximum Entropy Filling a box with a certain amount of gas with a specific total energy and allowing the gas to reach a maximum entropy state, what happens next?
Would the gas remain in a maximum entropy state indefinitely?
What would prevent the gas atoms/molecules to end u... | The gas could fall into a state of low entropy randomly. It is important to remember that the laws of thermodynamics are probabilistic, and they say not what will happen but what usually will.
| {
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What is meant by the term "single particle state" In a lot of quantum mechanics lecture notes I've read the author introduces the notion of a so-called single-particle state when discussing non-interacting (or weakly interacting) particles, but none that I have read so far give an explicit explanation as to what is exa... | It means a single particle Schrödinger equation determines the behavior of the particle. The only time a particle is in a single-particle state in an N particle system is when there are no interactions between particles - i.e., in an ideal gas. In the real world single particle states are always an approximation. E.g.,... | {
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Are there other less famous yet accepted formalisms of Classical Mechanics? I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are other accepted formalism of the same which are n... | Kane's Method is another accepted formalism (Thomas R. Kane) which is a method for formulating equations of motion.
| {
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Deriving the equation for the speed of a block down an incline using work - keep getting the wrong constant So the question is:
There is a block of mass $m$ travelling along an incline that makes an angle $\theta$ with the horizontal. If the block is pushed up the incline with an initial velocity $v_o$, what is its sp... | In your first approach I believe you got a wrong sign. It should be $$v_f = \sqrt{v_0^2 - 2g d \sin(\theta)},$$ otherwise your speed will increase with distance.
In your second approach seems like you are equating the work of the gravitational force to the difference of the mechanical energy. However, the work of a fo... | {
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What compounds or elements only have one phase or two phases? Wood appears to be one. I think gases like helium and hydrogen cannot exist in the solid state under normal pressures, correct? And why do those "phase cheaters"-- those elements/compounds which sublimate directly, skipping a phase, or "procrastinators"-- el... | Wood can only be solid because it's a very specific arrangement of atoms. If you liquified or vaporized all the elements in it, they wouldn't be wood. You also can't have liquid crystals, unless you count liquid crystals. Or a liquid computer.
| {
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Can Ampere's law be applied to 3D loop Usually in textbooks Ampere's law is just illustrated using 2D loops which forms a plane. Can the law be applied to 3D loops which cannot form a plane surface within the loop?
In a 3D loop which surface should we count when we count the current? In 2D case it is easy because there... | In the case of a planar loop, the surface that it bounds does not have to be a plane. It could bubble out. Ampere's Law is still valid (assuming the other conditions for validity are met).
Ampere's Law applies to any loop, and any surface bounded by the loop. I guess I'd better add that I don't know what happens in ... | {
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Superstring vacuum amplitude on the torus My question is how to obtain the superstring (Type II A and B) vacuum amplitudes on a torus. They are given in Polchinski's String Theory Vol. 2 equation (10.7.9):
$$Z_\psi^{\pm}=\frac{1}{2}[Z^0_0(\tau)^4-Z^0_1(\tau)^4-Z^1_0(\tau)^4\mp Z^0_0(\tau)^4].$$
I understand how each in... | One way to think about this is the following. In general, the partition function (which is the integrand of the vacuum amplitude and not the vacuum amplitude itself) will be of the form
$Z_\psi^{\pm}\propto\sum_{a,b}C[^a_b]Z^a_b(\tau)$
where $a$ and $b$ sum over the different sectors as given in the text and the $C$s a... | {
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Units of eigenvectors Consider for example a mass matrix $M$, $\lambda$ one eigenvalue and $X$ a corresponding eigenvector. Then $[M]=\text{mass}$ (the brackets indicate the "unit operator"), and $MX=\lambda X$ so $[M][X]=[\lambda][X]$, so $[\lambda]=\text{mass}$. That's why for example in oscillators, the pulsations ... | The units of the eigenvector can be anything you choose. Normally you want them to be dimensionless, but other choices can be sensible on occasion.
The reason that any dimension is valid is because if $X$ is an eigenvector, then $\mu X$ is also an eigenvector for any scalar $\mu$, which can in principle have any dimens... | {
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What is the meaning of " $\Psi$ is not a measurable quantity in itself"? I want to know that why the wavefunction $\Psi$ as a complex quantity (i.e $A+iB$ form) in quantum mechanics and somewhere I have studied that $\Psi$ is not a measurable quantity in itself that's why we multiply it by a it's complex conjugate $\P... | Ψ is supposedly a probability density amplitude. ΨΨ* is the probability density which in theory can be measured. For example in electron diffraction through a crystal a statistical measure of the electrons in, divided into the electrons out in a small region divided by the volume would allow ΨΨ* to be approximately mea... | {
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What mechanism creates bubbles in water that stays awhile If I fill glass jar with tap water and let it stay, small bubbles will appear on the side of jar after a while.
I am wondering what processes create those bubbles and what conditions require to meet?
My thoughts:
*
*Water impurities, i.e. dissolved salts, m... | You pretty much summed it up.. but an important factor is the history of the water. For example water that has been subjected to temperatures exceeding $35^oC$, would have lost most of its dissolved oxygen (the main gas dissolved in water). On the other hand water that has been vigorously shaken would have replenished ... | {
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Can electricity flow through vacuum? People say yes, and give a wonderful example of vacuum tubes, CRTs. But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?
| Conduction of Electricity in Solutions, Gases and Vacuum
https://youtu.be/7q8f-QJlpsA
What should be the definition of "Electricity"?
http://www.ivorcatt.org/99mcattq.jpg
http://www.ivorcatt.co.uk/97rdeat4.htm
http://www.ivorcatt.co.uk/x18j100.pdf
Ivor Catt states here that electric charges do not "exist".
http://www.i... | {
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Submarine Speed Detection A submarine can use sonar (sound traveling through water) to determine its distance from other objects. The time between the emission of a sound pulse (a “ping”) and the detection of its echo can be used to determine such distances.
Alternatively, by measuring the time between successive echo ... | The round trip time of the ping is unknown; but we do know that the difference in round trip time between sub stationary and sub moving is 0.02 seconds.
Let us write $D$ for the distance to the cliff when you send the ping; if you are traveling at a speed $v$, and the speed of sound in water is $c$, then we can write d... | {
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How are the theoretical properties of a gravity train linked to orbital properties? Whilst perusing a question on WorldBuilding, a link was given to an article about Gravity Trains.
Some of the answers on the question, and the Wikipedia article, state a travel time of 42 minutes between any two points on Earth. The Wi... | It takes about 45 minutes for a low Earth circular orbit to go from one side of the Earth to the other say From New York, USA to Perth Australia. If a hole could be tunneled through a uniform density Earth and you were to jump in the hole gravity would act like a spring and it would take you about 45 minutes, (if no a... | {
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What could explain the presence of Promethium in stars? [This is pretty much a copy and paste job from Technetium question but I wanted to add this one in case there was some other explanation] So, I understand that PM doesn't exist in nature [though, I don't know why every reference I see regarding PM says that and th... | I found this paper discussing the production of promethium in stars. The paper suggests several possibilities:
*
*Fission of heavy or superheavy nuclei
*Spallation of heavy nuclei by high energy protons
*Reactions of Nd and Sm with low energy nucleons: the s-process
The longest half life of any promethium isotope ... | {
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Do the same equations of motion imply the same Lagrangians? If two Lagrangian (densities) $\mathcal{L}$ give the same equations of motion, are they equivalent?
| As it happens, it is not necessary that two Lagrangians that have the same equation of motion have the same functional form. Consider the Lagrangians $L_1 = T-V$ and
$$L_2 = \frac{1}{3}T^2 + 2TV - V^2$$
where $T = \frac{1}{2}m\dot{x}^2$ and $V(x)$ is the potential energy. They both lead to the same equation of motion:
... | {
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What are the units of the creation and annihilation operators? The creation and annihilation operators - also known as ladder operators are;
$ \hat{a}^\dagger$ and $\hat{a}$ respectively.
Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + \frac{1}{2}\right)$
and knowing that the units of $\hat{H}$ are... | The units of $\hbar$ are in fact J.s/rad. (thanks AV23) this is because $\hbar = \frac{h}{2\pi}$ the units of h are J.s and the units of $\pi$ are rad. Thus we have J.s/rad. (thanks Noiralef)
Thus the ladder operators are in fact unitless.
On reflection this is the only logical possibility as they move between differ... | {
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Why is the gauge potential $A_{\mu}$ in the Lie algebra of the gauge group $G$? If we have a general gauge group whose action is $$ \Phi(x) \rightarrow g(x)\Phi(x), $$
with $g\in G$.
Then introducing the gauge covariant derivative $$ D_{\mu}\Phi(x) = (\partial_{\mu}+A_{\mu})\Phi(x).$$
My notes state the gauge potenti... | The gauge potential is an object that, when introduced in the covariant derivative, is intended to cancel the terms that spoil the linear transformation of the field under the gauge group. Every gauge transformation $g:\Sigma\to G$ (on a spacetime $\Sigma$) connected to the identity may be written as $\mathrm{e}^{\math... | {
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Counting higher-order corrections in "ABC theory" I am trying to understand how to enumerate higher-order Feynman diagrams.
In his book on Elementary Particle Physics, Griffiths considers a simple "ABC toy theory" which has:
*
*three (scalar, massive) particles A, B, and C (which are their own antiparticles), and
*... | The 8 is correct. The diagrams where you connect one outgoing and one incoming line are equivalent to the ones, where you connect one outgoing line and the internal line, as both lead to the vertex-correction diagram.
| {
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Conceptual explanation of the Single particle partition function The Single particle partition function is defined mathematically as
$$\text{Z=$\sum $}g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$
But what is the physical interpretation of the partition function and it's significance to Thermodynamics? I'm seeking a simple y... | Partition functions are a measure of the allowed volume in (microscopic-)configuration space for the system, and as such they are the normalizing function for probabilities expressed as volumes in configuration space (and assuming the applicability of the ergodic hypothesis).
I know that this is very abstract, but it ... | {
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Is this symmetry factor in Peskin wrong? I am trying to compute the symmetry factor of a Feynman diagram in $\phi^4$ but i do not get the result Peskin Claims. This is the diagram I am considering
$$\left(\frac{1}{4!}\right)^3\phi(x)\phi(y)\int{}d^4z\,\phi\phi\phi\phi\int{}d^4w\,\phi\phi\phi\phi\int{}d^4v\,\phi\phi\ph... | Contrary to your previous question Problem understanding the symmetry factor in a feynman diagram
the roles of the three vertices are not different so you have from the expansion of the exponential a $1/3!$ but it does not get compensated by the choice of role assignement.
Here this choice amounts to deciding who conne... | {
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What's the differences between time in Physics and time in everyday use? OK. This question might sound as not a good question, but the word 'time' is so confusing to me. I mean thermodynamics says time is the product of entropy. Relativity says time is relative. Quantum Mechanics says time doesn't exist, and that we ca... | The oldest perspective is the philosophical one established by Aristote; modified by Mach and then Barbour
*
*Time is an aspect of change (ie motion)
There is the mathematical perspective
*Time when mathematically conceived is just a parameter in the equation.
This in fact has nothing to do with time - it's ... | {
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The Higgs field vs the Higgs boson As I see it the Higgs boson is the mediating particle of the Higgs field and get its own mass from the Higgs field. Isn´t this circular? I mean, for instance, an electron creates a radial electric field but in no way it can interact with the field it created.
So my question is: how ca... | Mass comes from things other than the Higgs field--the latter is just the main contributor. What gives the Higgs boson its mass is still up for debate--for a more detailed discussion, see the following post:
How does the Higgs Boson gain mass itself?
| {
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Correct vector space of eigenkets of angular momentum When we say an particle is in the state:
\begin{equation}
|l,m\rangle,
\end{equation}
what is the underlying state space, as a vector space? Is it a tensor product vector space, of dimension:
\begin{equation}
l\times(2l+1)\ ?
\end{equation}
How can I find the matri... | For orbital angular momentum, indeed, $L = x\times p$ even as a quantum operator, see this question.
When writing a ket $\lvert l,m \rangle$, this is meant to live in the $2l+1$-dimensional space $\mathcal{H}_l = \mathbb{C}^{2l+1}$ on which the representation of the angular momentum algebra labelled by $l$ exists ($m$ ... | {
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How to measure temperature of a laser cooled sample at picoKelvin temperatures? I'm reading about laser cooling.. my question is: how can the temperature of the sample be measured? (using laser cooling we can reach $10^{-12}K...)$
| The temperature is not measured in the sense of using a thermometer. Instead it is calculated from the velocities of the particles in the trap.
Temperature is related to the velocity distribution by the Maxwell-Boltzmann equation. Under normal circumstances we are usually starting from a known temperature and calculati... | {
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How to use Ampere's Law for a semi-infinite wire with current? Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. The magnetic field obviously has cylindrical symmetry whe... | Ampere's law (for a steady current) states that
$$ \oint \vec{B} \cdot d\vec{l} = \mu_0 I$$
If we consider an infinite wire, then symmetry tells us that the B-field at the point $A$ and all other points on a circle of radius $(R+y)$ is constant in magnitude and is in the azimuthal direction. Hence the magnitude of the ... | {
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What does "interact via strong force" mean?
*
*I was just wondering if the words "strong force" and "strong interaction" are interchangeable?
*Also, these are referring to "strong nuclear force", correct?
*Then what does it mean for particles to "interact via the strong force"?
*Also, where does the weak force co... | In the context of nuclear or particle physics the phrase "the strong interaction" means the same thing as "the strong force". In fact we rarely write a formula for the strong force in the sense that we write Coulombs law for the electrostatic force. Both terms are refering to the strong nuclear force.
In the context of... | {
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Does friction act on a wheel rolling at a constant speed One of the things I've seemed to have taken for granted is that its the friction the floor exerts on a rolling wheel that prevents slip from occurring.
However, I ran into something that challenges that assumption: the contact point of the wheel on the floor has ... | Maybe this thought experiment? Suppose you have a frictionless wheel and surface, in a vacuum, etc., and you spin up the wheel and push it forward so that its linear speed just matches the rotational speed and it moves along the surface with no slippage, i.e. zero net velocity at the point of contact. In this scena... | {
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Why can't a magnet change a charged particle's speed? I know that magnetic force acts perpendicular to the direction of the original velocity, so the velocity in that original direction is unchanged, but once the magnet starts acting, the particle's velocity in the direction of the force goes from zero to nonzero -- wo... |
I know that magnetic force acts perpendicular to the direction of the original velocity
No, the magnetic force acts perpendicular to the current velocity.
Once the direction of the velocity changes, the direction of the force changes as well.
Cast in math:
$$ m\dot{\vec v} = \vec F_L = \frac q c \vec v \times \vec B ... | {
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Calculating Christoffel symbols from Lagrangian I was given the following metric for a sphere
$$g_{\mu\nu} = diag(1, r^2, r^2\sin^2\theta)$$
and tasked to calculate the Christoffel symbols. There are 2 ways that I know of to calculate them. One is from the equation
$$2\Gamma^{\alpha}_{\beta\gamma} = g^{\alpha\rho}(g_{\... | The geodesic equation is
$$ \frac{d^2x^\mu}{dt^2} + \Gamma^\mu_{\nu \rho} \frac{dx^\nu}{dt}\frac{dx^\rho}{dt} = 0$$
The coefficient of $\dot{\phi}^2$ you're seeing corresponds to $\Gamma^r_{\phi\phi}$.
| {
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Weight distributions If a man is standing on two weighing machines (scales), with one foot on each, Will both machines show equal weight or his weight will be distributed in two machines?
| Remember Newton's first law $\sum F=0$. Vertically you have this:
$$\sum F_y=N_{scale1}+N_{scale2} - W=0$$
The scales will feel and display the $N_{scale}$ force. Solving for either scale force you will see that they share the total weight $W$. Together they must lift the whole weight $W$, not individually.
| {
"language": "en",
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Does lithium-6 "decay" when hit by a neutron? I am talking about the nuclear reaction
$$
^6\text{Li} + n \rightarrow\ ^4\text{He} +\ ^3\text{H} + 4.78\text{MeV}
$$
A neutron hits a lithium-6 nucleus and together they form an alpha and triton particle. Is it valid to say that the lithium nucleus "decays" when hit by a n... | What happens depends on the energy of the neutron. At lower energy, it can simply merge with the $^6$L to form $^7$L. At a higher energy it can cause the $^6$L to fission, and at even higher energy it can break the $^6$L into pieces (spallation). This last mechanism is being studied for neutron induced fission, where t... | {
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Is true black possible? Black is the absence of light because it absorbs light, but when we create black paint or black objects, light is always reflected, either in all directions in matte or smoothly in shiny black objects, making it never a true black. Would it be possible to use polarization to create an object tha... | A true black surface would need a temperature of 0 Kelvins as anything with heat will have excited electrons and will emit photons. However, dark matter is an example of purely black matter it only means that dark matter does not consist electrons.
Theoritically, a purely black object would be one that does not radiate... | {
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What do we mean by this statement : "some positive charge is put on a metal piece"? What do we mean by this statement : "some positive charge is put on a metal piece" ?
(I know it will be distributed on the surface of the metal piece, if metal is isolated.)
Electrons are negatively charged particles.
Protons are posit... | Its not like putting any charge but simply making that metal piece charge to be positive.
It can be done simply charging metal piece by :
*
*Friction
*Induction
*Conduction
*or by the Removal of a Charge (Grounding)
While seeing question I come to know that you already asked one question and there also you aske... | {
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If atoms are mostly empty space, why doesn't light pass through everything? Atoms are mostly empty space, and although I now understand why matter doesn't pass through other matter, why don't photons pass through the empty space of the atoms? Is it the same sort of idea as matter passing through other matter?
| They taught me that in high school too (i.e., that matter is "mostly empty space.") Only thing is, it's not true.
Solid matter is mostly filled with electrons. Yeah, the mass is all concentrated in the relatively tiny nucleii, but the mass is not what photons interact with, and the mass is not what defines the physic... | {
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Why don't we build helicopter based space shuttles? As seen in this video: the principle of the helicopter does work in space. So we could make a helicopter based space shuttle! It would be easier to navigate with it than with propulsors.
| the video show that the principle of helicopter works in a zero-g (no gravity) environnement, not that the principle works in space.
The helicopter is able to lift on earth (and int the space shuttle) because of the viscosity of the air. Whitout any friction, there is no move.
In space, there is really few particles. S... | {
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Notation of vectors It's very common to see $\text{F} = 30 \text{ N}$ when the problem is unidimensional. Yet, force is a vector. Shouldn't I write $|\overrightarrow{F}| = 30 \text{ N}$? Because if I write $\overrightarrow{F} = 30 \text{ N}$ I'm saying that the vector is equal to an scalar. On the other hand, I rarely ... | No, you should not write "$\left|\vec{F}\right| = 30\textrm{N}$", because it's no better than "$F=30\textrm{N}$"
Since force is a vector, you could write out the list of components, either as a parenthetical list or a column vector:
$$\vec{F} = \left(30\textrm{N}\right) = \left[ 30\textrm{N}\right]$$
You could also wri... | {
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D'Alembert Equation and standing wave As we know the d'Alembert Equation is
$$
\frac{\partial^2\psi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2}
$$
for an undimentional string.
Now if we seek standing wave solution, we put $\psi(x,t)=f(x)g(t)$ can you tell me a physical argument which shows if $\p... | A very simple way is to look at the nodes of the standing wave. As the name suggests, the nodes are not supposed to move as time goes on.
Suppose $x_0$ is one of the nodes at a particular time instant $t_0$, then we have $\psi(x_0,t_0)=0$. If position and time can be separated, then we have $f(x_0)g(t_0)=0$, which giv... | {
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quantum fluctuations and the virtual particles In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in Feynman diagram computations as virtual quanta with arbitrarily high moment... | I think you should not take the Peskin and Schröder quote too seriously.
They are likely just using the Fourier relationship "short distance <-> high momenta" and the idea that there are propagators $\langle \phi^2 \rangle$ (which are the "fluctuation"/variance of $\phi$, see this post) associated to the Feynman lines ... | {
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Propagating higher order Hermite Gaussian modes. What are complex amplitude coefficients? I've been tasked with writing a code (in MatLab, but I'm currently using Mathematica because I don't know MatLab %\ ...) to simulate the propagation of a Gaussian beam.
I don't really know anything about optics, so I'm learning on... | Turns out that due to orthogonality relations of Hermite-Gauss poly's, Hermite-Gauss modes are orthonormal, so
$$
\int \int u_{n,m} \left(u_{n',m'}\right){}^*dxdy=\delta _{m,m'} \delta _{n,n'}
$$
Then a's can be found by multiplying both sides by conjugate of u and integrating ...
| {
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Is molecular vibration just phonon modes for a single molecule? I'm reading about Raman Scattering, of which a big part is measuring the energy lost to/gained from Molecular Vibrations. I wasn't totally clear on exactly what is "vibrating" in vibrational modes (is it the electron around the nucleus? Or the whole atom, ... | *
*In this context, vibration usually refers to the relative motion of the nuclei.
*In a periodic solid (crystal), vibrational modes are called phonons. We can say, for example, that a normal vibrational mode of a branch $s$ with wavevector $\mathbf{k}$ is in its $n$th excited state, or equivalently, that there are $... | {
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How electrons move so fast in a electric circuit? Whenever we switch on a bulb......it takes almost no time to glow up.....But we know that the atoms of a solid are tightly packed and there is a very little space between them.
So how the electrons travel through them irrespective of so much blockages in the conductor??... | You might be asking how metal is such an efficient conductor.
Some of the electrons move freely as a fluid. They are not locked in place around the atoms, and don't need "room" in the classical sense.
Here is a wikipedia page going over the real details.
On a scale much larger than the inter atomic distance a solid c... | {
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How much UV is reflected by glass? On a sunny day, how much of the Sun's UV is reflected by windows?
I suppose this boils down to what are the refractive indices of common window glasses, so that one might solve the Fresnel equations.
Also, at the risk of being off-topic, how safe is viewing this reflected light?
| I'd say about 4% of the intensity for perpendicularly incident light, increasing to nearly 100% when the angle of incidence is almost zero.
These are the numbers you get from the Fresnel equations (for $n = 1.5$ which is a typical value for glass) as you suggested.
While glass absorbs UV the absorption should not be so... | {
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Momentum conservation in FRW spacetime The spatially flat FRW metric in Cartesian co-ordinates is given by:
$$\mathrm ds^2 = -\mathrm dt^2 + a^2(t)(\mathrm dx^2 + \mathrm dy^2 + \mathrm dz^2)$$
As I understand it, since the metric does not depend on the spatial co-moving co-ordinates $x,y,z$ then there are Killing vect... | Canonical momentum is conserved, but proper momentum density is proportional to $\frac{1}{a}$ where $a$ is the scale factor.
| {
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Odd order of colour fringes around cloud The other day I took this photograph of a thundercloud that moved between myself and the sun. Around the edge of the cloud there were some coloured fringes that I first took to be a variant on a normal rainbow (yes, I know that a rainbow is visible when looking away from the su... | It could be due to the moisture in the air around the cloud. The moisture would make the light refract much more because it is denser, making the rainbow thinner and leaving yellow and blue out.
| {
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"url": "https://physics.stackexchange.com/questions/184608",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is it possible to write the fermionic quantum harmonic oscillator using $P$ and $X$? The Hamiltonian of the quantum harmonic oscillator is
$$\mathcal{H}=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2$$
and we can define creation and annihilation operators
$$b=\sqrt{\frac{m\omega}{2\hbar}}(X+\frac{i}{\omega}P)\qquad{}b^{\dagger... | Assuming that $X=X^\dagger$, $P=P^\dagger$ and $[X,P] = i\hbar$, let me try
$$f = \sqrt{\frac{m\omega}{2\hbar}}\left( \alpha X + \frac{\beta}{m\ \omega } P \right) $$
where $\alpha$ and $\beta$ are complex numbers of modulus one. From this follows that
$$ \hbar \omega \left( f^\dagger f - \frac{1}{2} \right) = \frac{P^... | {
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Difference between fusion plasma and fluorescent lamp plasmas How is the plasma in a compact fluorescent lamp (CFL) different from a plasma in say ITER or the sun? Why does ITER need 100MK and a CFL can work at practically room temperature (apart from the filament)?
Or could ITER also create a plasma by charging the ga... | A compact fluorescent lamp belongs to the glow discharge plasmas. Usually you have electron densities on the order of $n_e \approx 10^{16}\,\mathrm{m}^{-3}$, electron temperatures on the order of $T_e\approx 1\,\mathrm{eV}$ and ion temperatures being at least an order of magnitude lower. The degree of ionization is $1\... | {
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Does Time change over temperature? I am not a physicist, I am just an engineer.
But I dared to ask whether the temperature changes the perception of time.
Let's consider a particle that "stops" at absolute zero. I was thinking as a hypothesis, that our perception of time changes and the particle actually does not stop... | No. In fact the official definition of the second is:
The duration of 9,192,631,770 periods of the radiation corresponding
to the transition between the two hyperfine levels of the ground state
of the caesium-133 atom at absolute zero.
So time is still alive and kicking at absolute zero.
| {
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"answer_id": 1
} |
Maximum angle for highway lane change I am preparing to fight a traffic ticket from a speed camera. There is a lot more to that story, but the info I need right now involves the angle at which a car can change lanes, in terms of vehicle angle relative to the direction of traffic flow. I have a 2009 VW Golf Kombi (this ... | The fastest possible way to do a lane change is to fully steer one way on the traction limit and then steer on the opposite way again on the traction limit.
The traction limit is $\mu g = \frac{v^2}{r}$ where $g=9.81\;{\rm m/s^2}$ is gravity, $\mu=0.8\ldots0.9$ is the coefficient of friction (half it in the rain), $v$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/185238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
What would be the rate of acceleration from gravity in a hollow sphere? Lets say the Earth is hollow and you are in the center of it (Same mass except all of it is on the outside like a beach ball) If you move slightly to one side now your distance is closer to that side therefore a stronger gravitational force however... | The answer is that inside a spherically symmetric shell of matter (your hollow earth or massive beach ball) there is no gravitational force anywhere - you will not "fall" in any direction, whether you are at the centre or not, regardless of the radius of the sphere.
This is a classic result of both Newtonian Gravity, a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/185298",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 2,
"answer_id": 1
} |
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