Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Generalized method for dealing with circuit involving symmetry? I'm a physics tutor for high school students. I'm finding it difficult to teach students how to exploit symmetry while finding equivalent resistance of a given network of resistors. I was Googling but couldn't find any generalized method that is applicable... | The common approach is to first deduce several equalities using the symmetry of the configuration of the circuit (namely the geometry) which is fairly easy and can be figured out following your instinct. Then, they will ask you to reverse the potential difference applied and figure out several other equalities. These u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/356645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Where does the magnetic field energy of a charged particle moving with a uniform velocity come from? Consider a charged particle initially at rest with respect to an inertial frame.
Let a force act on it so that it gains a velocity 'v'.
It now produces a magnetic field that has some energy associated with it.
My que... | I quote from the 1938 edition of the Admiralty's handbook of wireless and telegraphy, anonymously written but clearly from the highest level of specialist knowledge. "Magnetic field energy is clearly inertial in character, just as electrical field energy is clearly kinetic in nature, due no doubt to the the motion of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/356800",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Derive the Lagrangian that yields the free Schrödinger's equation from Galileian Invariance The Lagrangian Density $$L(\Psi, \Psi^*)=i \hbar \dot{\Psi} \Psi^* + \frac{\hbar^2}{2m} \Psi \Delta \Psi^*$$ will yield the schroedinger equations for $\Psi$ and $\Psi^*$. Can we derive this Lagrangian Density, if we impose on... | Galilean invariance only impose the combination $i\partial_t-\frac{\triangle}{2m}$ to any power. This means that the action
$$
\int_{t,x} \sum_n \psi^*\left(i\partial_t-\frac{\triangle}{2m}\right)^n\psi,
$$
is invariant. You need additional constraints (like "simplicity", whatever that means, or comparison to experimen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/357091",
"timestamp": "2023-03-29T00:00:00",
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Derivation of Newtons second law of motion from the principle of conservation of energy Is newton's second law a consequence of the principle of conservation of energy? How can we arrive at
net force = rate of change of momentum
using only the law of conservation of energy?
| It is true that Newton's 2nd law with conservative force $$m_i{\bf a}_i ~=~-\frac{\partial V}{\partial {\bf r}_i}, \qquad i~\in~\{1, \ldots, N\},\tag{1}$$
implies conservation of the mechanical energy
$$E=\sum_{i=1}^N \frac{m_i}{2}{\bf v}_i^2 + V({\bf r}_1, \ldots,{\bf r}_N).\tag{2}$$
But the opposite $(2)\Rightarrow... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/357186",
"timestamp": "2023-03-29T00:00:00",
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Does the Conventional Current flow consist out of anything? (virtual photons) I've red that virtual photons are a way of interpreting the electromagnetic force between charged particles. Is convention current a electromagnetic field or force? Or is it a movement of positive charge carriers?
I just red some thin... |
I wonder if conventional current flow is an electric field.
Conventional current flow is not physical. It literally is nothing but a math trick. It's how electronics engineers understand and analyze circuits. It is based on an old, invalid understanding of what electricity is, but it still works in the context in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/357432",
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Ball falling through viscous fluid experiment - strange results I did an experiment in which I dropped three different sized spherical beads (4mm, 6mm, and 11mm diameter) with the same densities through a viscous liquid (a water-detergent solution). They all fell the same distance, but the biggest one fell a full ten s... | You have pointed out the difference between rain drops (large radius) and mist drops (small radius) which fall much slower.
When terminal velocity $v$ is reached the viscous drag on a sphere of density $\rho$ and radius $r$, $6\pi r v \eta$, is equal to the apparent weight of the sphere $\frac 43\pi r^3 (\rho -\sigma... | {
"language": "en",
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Rotation matrix in $ict$-$x$ plane I am reading about SR. The book starts by going over the ordinary rotation matrix, e.g.
$\left( {\begin{array}{cc}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta \\
\end{array} } \right)$
which takes $x\rightarrow x'$, $y\rightarrow y'$.
Then it goes on to say that if the... | Note first that working with imaginary time to teach special relativity has fallen way out of favor, it's not considered good pedagogy! And I don't think "hey plug in an imaginary axis" is a very good physical or mathematical argument. But with that out of the way...
The only thing I'm going to do is motivate why when ... | {
"language": "en",
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As the sun expands, will its Roche limit also expand? So my friend and I had a debate. He stated that we don't have to worry about the sun consuming the Earth ─ we'll already be broken apart by then. He states that as the sun expands, its Roche limit will also expand. The Earth will have been broken apart long before t... | You are correct, and your friend is not.
So long as the Sun remains spherically symmetric, its gravitational field can be replaced with the field of a point mass at its centre of mass, which is what determines the Roche limit (so, in particular, it fixes both the gravitational field and the gravitational field gradient... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Spin-1 Particle System Measuring Angular Momentum Suppose a spin-1 system ($l = 1$) has a particle set in the state of the eigenstate in the $L_{x}$ basis, given as such: $$ |1, m_{x} = +1 \rangle = 1/2 \begin{pmatrix} 1 \\ \sqrt{2} \\ 1 \end{pmatrix}$$. The $L_{z}$ component of its angular momentum is measured and the... | The initial outcome $L_z=-1$ will project you initial state to the appropriate eigenstate of $L_z$. After normalization, the state after this measurement will be $\vert 1,-1\rangle=(0,0,1)^T$. To get the various probabilities of $L_x$ will require you to construct all three $\vert 1,m_x\rangle$ eigenstates and then w... | {
"language": "en",
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What causes light to refract? The common answer to this question is that light refracts because its speed changes in different materials. But this means that the photons has internal attraction between each other. Is that the case? Otherwise is something else like density of different materials the reason why light ref... | There an many ways to look at this problem. I am going to add, light refracts because its path satisfies Fermat's Principle : "light travels between two points along the path that requires the least time, as compared to other nearby paths.”
Given the 2 different speeds of propagation in media 1 and 2:
$ v_2 \sin{\theta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/358268",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Does the brightness of day follow simple harmonic 'motion'? Is it really true that the brightness during the day on earth follows simple harmonic motion? My teacher mentioned this as an example but it doesn't feel obvious to me by any stretch of the imagination (at least for a tilted earth). So how can we work out whet... | The brightness may be periodic, but it is not “simple harmonic”. Simple harmonic requires that each full cycle follows a sinusoidal function. (Clearly not true at night.)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/358406",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to change Pressure and Temperature "The triple point of a substance is the pressure and temperature at which all three phases coexist in equilibrium."
Take water for example.
Let's say I put some water in a rigid container and add some heat.
Then both the temperature and pressure rise because the volume is consta... |
Does that mean the triple point can only exist in that size of a container??
No. The ideal gas law you show applies only to gases. So the $n$ in that equation is not the total amount of substance, but only the amount in gas form.
Let's imagine you have two different containers (of different size), but you put the s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/358897",
"timestamp": "2023-03-29T00:00:00",
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Will warm pizza get colder in deep space? If my Hot Pizza is in deep space and there is no gas molecules around it, how would it dissipate it's energy?
There are neither conduction nor conviction, and since the Pizza is solid it can't radiate its heat
will it stay hot?
| Heat may be considered to be movement of particles. The particles of your hot pizza oscillate. An accelerating electric charge creates an electromagnetic field. The oscillating particles of the pizza emit photons in the wavelength of the field the particles create, generally infrared radiation. As the particles on ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A confusion in the representation of states in $k$-space In the book "Introduction to Quantum Mechanics" by Griffiths, chapter 5 section 3 (Solids), the author states the following:
...Each intersection point in $k$-space represents a distinct stationary state. Each block in this grid, and hence also each state, occ... | Each block contains 1/8 of 8 vertices, because each vertex also belongs to 8 blocks.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Basic concepts of ionization dectectors I am reading "Techniques for Nuclear and Particle Physics Experiments" by William R. Leo. I have some questions about the ionization detectors chapter (chapter 6). In chapter 6, there is a figure like this:
I understand the basic concept of how the signal is registered (radiatio... | The electronics there implement a simple high-pass filter that prevent flow of the DC high-voltage supply to the DAQ (or ground) but allows the (rapidly changing) signal pulse to pass almost unaffected.
The very simple form used here is acceptable because there is suck a stark difference between the signal you want to ... | {
"language": "en",
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Do fields describing different particles always commute? Is it true that field operators describing different particles (for example a scalar field operator $\phi (x) $ and a spinor field operator $\psi (x) $) always commute (i.e. $ [\phi (x), \psi (y) ]=0, \forall x,y $) in interacting theory?
Or is it true only at eq... | lurscher asks for a physical interpretation of CR Drost's correct answer. I'm answering separately because my response was too long to fit into a comment.
In the trivial case where the two fields are completely uncoupled - either directly or indirectly by way of both being coupled to some third field - the Heisenberg a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359610",
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"source": "stackexchange",
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Refraction when angle of incidence is equal to 0 degree Ok i know that mathematically or by snell 's law it can be proved but i want to know that what is its physical significance? I mean why it does not refract at 0 degree?
| Looked at using the Huygens-Fresnel principle: each point in the wavefront will arrive on the surface at the same time. Each point is a new source emitting with the new wavelength, but as they all arrived at once, their waves are all in step so the wavefront stays the same.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the oscillation frequency of a buoyant cylinder? Suppose a cylinder sits upright in "dry water" (zero viscosity). The cylinder has half the density of the water, and we'll ignore the dynamics of the atmosphere.
If I push the cylinder down some past its equilibrium, the buoyant force pushes back up. If I slowly ... | Let $\rho_{fl}$ and $\rho$ denote densities of the fluid and cylinder; $g$ the gravity field; $H$ the height of the cylinder and $A$ the area of the cylinder.
The cylinder is at a height $h$ above it's equilibrium position. There is a net downward force, equal to the downturn buoyancy force in magnitude.
$$|F|=\rho_{f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359929",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are work and energy considered different in physics when the units are the same? There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed.
What I am asking is this: Why in physics when ... |
Why in physics when the units are the same that does not necessarily mean you have the same thing.
Consider these two different things:
*
*The amount of floor space in your house
*The fuel economy of your car
Both are measured in square-meters.
References
Why can fuel economy be measured in square meters?
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Location of lens having effective focal length We know a/c to Gullstrand's equation that the effective focal length of two lenses separated by a distance $d$ is given as $$\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2},$$ but the equation doesn't clarify on the position of the lens having this effective ... | If you were to switch the two lenses by a single thin lens, then the answer is tricky, because you can't just literally remove the two lenses from your optical table and put somewhere a lens of effective focal length expecting everything else would be the same.
What you can do is make an equivalent lens system: a box c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/360199",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Simple question about Schrodinger equation (time independent) For a quantum mechanical description of a system (like a small molecule) we can write:
$$\langle\psi|\hat {H}|\psi\rangle = \overline E$$
Question:
Is that energy the same as zero Kelvin energy obtained by statistical mechanics (using $E_n$ energies and par... | Statistical mechanics does not really apply to the kind of system your equation refers to: your equation is good for a pure quantum state $\psi$. In statistical mechanical terms, the system's microstate is exactly and fully specified by $\psi$, and you can't really therefore talk about a system's temperature when it is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/360315",
"timestamp": "2023-03-29T00:00:00",
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If I say time is the fourth dimension am I wrong? As far as I know the prevailing view is that time is the fourth dimension, but I've read there is also a spatial fourth dimension and even higher spatial dimensions after that so I hesitate to say that time is the fourth dimension. So, if I say time is the fourth dimens... | The "sort" of dimensions is really arbitrary.
What is true is that in classical mechanics time is another label to distinguish events, and special relativity enhances this point of view because there are some reference transformation that "mix" time with space (they are Lorentz transformations).
In general relativity t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/360621",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Understanding the equation for Potential Energy I am having a hard time understanding why Potential Energy can be calculated in the following way:
$$ \Delta U = U_f - U_i = -\int_{x_i}^{x_f} F_x dx $$
In particular, I don't understand why there is an integral in that equation. That is to say, why is it integrating the ... | Let us take for example the elastic potential energy:
$$U(x)=k\frac{x^2}{2}$$
The force is given by:
$$F(x)=-\frac{\partial}{\partial x}U(x)=-kx$$
As Señor O said in the comments, this is true only for conservative force fields.
If we want to get the potential from the force, we have to integrate the force:
$$U(x)=-\in... | {
"language": "en",
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Is energy $E$ in Schrödinger equation an observable/ Can $E$ be measured? Take this quantum approach to estimate mean energy of a molecule:
$$\langle\psi|H|\psi\rangle=\overline E$$
Question:
Is $E$ an observable? How we can compare it to an experimental value? i.e how to experimentally measure it and what are the stat... | What you wrote is an expectation value, which means an average on some state $|\psi\rangle$ over all possible eigenvalues of the operator under analysis, weighted with the probability of that eigenvalue occurring on that state $\psi$.
So, yes, $\hat H$ is an observable (we reserve this term for operators and the quanti... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Turbulence Model on Unsteady Navier Stokes I am asking you if the Unsteady (Time-Dependant) Navier-Stokes Equation is able to predict accurately the Flow Turbulence? I know that the RANS (with different Turbulence Models like Spalart–Allmaras, k–ε and k–ω models...) is the most used method for simulating the Turbulence... | There is no correct turbulent solution of the Navier-Stokes equation. There are various approximations. The nonlinear term is approximated linear with dynamic viscosity, which is chosen from the condition of coincidence with the field experiment. Or they introduce a mean of values, but this results in more unknowns tha... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is a compact symmetry transformation? I am taking a course on particle physics, I am not familiar with a lot of mathematical terminology. So I don't properly understand what topology actually means. So when I looked up on the web for the definition of compact or non-compact symmetry transformation, I face terms re... | Loosely speaking (to avoid topological terminology), compact transformations are expressed in terms of parameters which have finite range, v.g. the rotation angle $\theta$ so that the rotation
$$
R(\theta)=\left(\begin{array}{cc}
\cos(\theta) & \sin(\theta)\\
-\sin(\theta) & \cos(\theta)\end{array}\right)\, , \qquad 0\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361740",
"timestamp": "2023-03-29T00:00:00",
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What is the total energy of the Universe? The Law of Conservation of Energy states that:
Energy can't be created nor can be destroyed. It only changes from one form to another.
According to this the total energy in a closed system never changes. I was wondering what this constant energy is when the closed system is t... | Regarding the conservation of energy in the Universe, the questions linked by Qmechanic (Total energy of the Universe, Is the law of conservation of energy still valid?, Is the total energy of the universe constant?, Conservation of Energy in General Relativity) have answers that already address this is some detail. Re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361875",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does light heat transparent mediums? I was thinking that if a photon is travelling in the vacuum at $c$, then enters a transparent medium so it's speed becomes $0.8c$, the photon has lost energy. What is that energy transformed into? Is the surface being heated?
| No, Light doesn't imparts heat to the transparent medium. As far as the decrease in speed of light is concerned, energy of the 'visible light waves' depends upon the frequency of light not on speed. As the reduction in speed is nullified by the reduction in wavelength. (ref. Einstein's Photoelectric Equation)
Note: Li... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362057",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
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Conformal field theory using Mathematica Can someone suggest some online Mathematica codes/packages that deal with performing standard CFT computations like OPE expansions, computing different conformal blocks etc.
| Conformal Bootstrap
A page by an associate professor at Brandeis University has provided a notebook to implement the Virasoro algebra in Mathematica, and compute conformal blocks. It can also teach Mathematica other operator algebras.
This paper also provides ancillary files which include notebooks that can be used to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Does the temperature coefficient of a material depend on temperature? In my textbook, a relationship is plotted between the resistance of the material and the temperature, and the temperature coefficient is defined as the slope of that graph divided by an arbitrary resistance $R_1$ on the graph. Does that mean that the... | The temperature coefficient is often defined defined as $\alpha = \dfrac{R_{\rm T}-R_0}{R_0 \, T}$
where the temperatures are in degree Celsius and the reference resistance $R_0$ is measured at $0^\circ \rm C$.
Which gives the equation $R_{\rm T} = R_0(1 + \alpha\, T)$ ie a linear relationship between resistance and ... | {
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Work done by the piston versus work done by the surrounding Suppose a massless, frictionless piston assembly initially has a higher pressure than the external (atmospheric) pressure, and it is pinned so that the piston does not move. Once the pin is removed, the piston would expand until the pressure inside the piston ... | The pressure on both sides of the unpinned weightless piston is always the same. In case of any difference, the piston would quickly move pressuring the external gas locally above the atmospheric pressure. Your setup is not static and only can be solved by aerodynamics. However, in the limited scope of your question, t... | {
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"url": "https://physics.stackexchange.com/questions/362568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Use of negative frequency for the sake of simplifying mathematics? How can we use the idea of negative frequency for the sake of simplifying mathematics if negative frequency does not exist (to my knowledge) in nature ? For example, when plotting the spectra of a Fourier series.
|
negative frequency does not exist
Depends on how you define frequency. If defining such a thing as negative frequency makes the math easier (it does), why not do it? It's probably less objectionable than defining an imaginary anything, and we do that all the time.
| {
"language": "en",
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"source": "stackexchange",
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How do we know that certain quantum effects are random? I was looking at a website that claims to generate random numbers from observation of quantum effects. This lead me to question how we know that the numbers are truly random.
When we observe a probability wave and it collapses in one place into a particle, how do ... | There are two main views. The first view relates to the Copenhagen interpretation of Quantum Mechanics. According to this interpretation, a particle does not have a specific path, but travels like a wave. Upon detection, the wave function collapses and the particle appears at a random point on the screen (according to ... | {
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EMF generated by a rotating rod I am confused by the following example in my textbook.
Question:-
A metallic rod of length $l$ is rotated with a angular velocity $\omega$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $l$, about an axis passing through t... | Sorry for my poor english !
The above explanations seem very clear to me. It is necessary to close the circuit to make a measurement.
We can, however, give a more formal formulation that takes up the idea of field lines cut by the circuit.
The emf is defined as the circulation of the force per unit of charge, here the ... | {
"language": "en",
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Is there any quantum mechanics process in a prism? Red light has longer wavelength than say blue light and so bends the least as it travels much faster in the same medium. My question is since energy is not stated in the above explanation, is QM required for prism to work?
| You are right! Classical electromagnetic theory is sufficient to describe how light refracts at an interface (Snell's law). Then, if you stipulate that refractive index is frequency-dependent, you get the light-dispersing behavior of a prism. Of course, if you want to know why there is dispersion in glass, you have to ... | {
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In physics sometimes we find energy that is negative. What does the negative sign indicate? Sometimes we see energy that is negative, for example, the energy of an electron in orbit. We know energy is something that can do something. In this view does negative energy mean something opposite someway?
| Absolute energies have no observable effect, it is only changes in energy that have physical meaning. How to interpret a negative energy depends on the context.
In the example you give of an electron bound to an atom, the energy is measured with respect to the electron being free from the atom and infinitely far away. ... | {
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Does providing more heat to a pan of boiling water actually make it hotter? Sometimes my wife has a pan of water 'boiling furiously'. Is the extra heat (wasted in my opinion) actually making any difference, apart from reducing the amount of water in the pan - which could be done by pouring some away?
| Since most of the water is being cooled by the environment, 100ºC water will only be in the bottom of the pan. Increasing the heat will actually make a difference, since bottom water will boil faster and it will transfer more heat to top cool water, before being cooled by ambient temperature.
| {
"language": "en",
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"source": "stackexchange",
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Why is a centered parallelogram not a 2D Bravais cell, but a centered rectangle is? We had a disagreement regarding 2D Bravais lattices during a lecture. The lecturer told us that a centered rectangle forms a Bravais lattice in 2D, but a centered parallelogram isn't:
We couldn't come up with a satisfying definition of... | I think this is mainly a matter of convention If you take the monoclinic 2D lattice then you certainly can draw a centred unit cell on it:
(image from Wikipedia)
but there is nothing to be gained by doing so because the primitive cell is just as useful.
As a general guide we tend to use a primitive cell as our first p... | {
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Does relativistic speed increase gravitational attraction? If something is moving past me at a relativistic speed, does its gravitational force on me increase as its speed increases? That is, not as if its speed is changing, but if multiple of the same (rest) mass go past me in the same path, is the gravitational attra... | Yes. Gravitational attraction in general relativity is based on an object's energy, and an object's energy is greater when its speed is greater.
| {
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What are the boundary conditions for the electron in a hydrogen atom? From what I understand, the wave equation for an electron can be constructed using the "particle in a box" model in three dimensions. However, what would be the boundary conditions in this case? In other words, what are the potential energy barriers?... | Obviously the potential varies smoothly so there are no "barriers" so to speak. (as far as I'm aware there are no discontinuous potentials in reality)
Examples of boundary conditions in the case of the hydrogen atom would be that the radial wavefunction should go to zero at the origin and at infinity, and that the angu... | {
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Rotations of eigenstates of $S_z$ I have a question regarding the rotation of spinors in a spin-1/2 system.
We have a Spin generator $\hat{S}$ for rotations of spinors.
A rotation around the axis $\vec{n}$ with the angle $\phi$
is generated by the operator:
$$
D_{\vec{n}}(\phi) = \exp(-i\phi \hat{S}\cdot \vec{n})
$$
... | When you rotate spin operators i.e.
$$D_{\vec{n}}(\phi) \cdot (\hat{S} \cdot \vec{m}) \cdot D^{\dagger}_{\vec{n}}(\phi),$$
it is the same as if you would rotate (right-hand) the vector $\vec{m}$ around the vector $\vec{n}$ at angle $\phi$. It is a consequence of algebraic properties of spin operators (they span $su(2)$... | {
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If fluid flows faster through a narrower pipe, why do hourglasses work? I'm essentially describing a fallacy due to a flaw in my understanding, and I'm trying to understand what the flaw is.
I know that if a pipe narrows, the fluid moving through it will move faster to preserve the same volumetric flow rate.
But, by th... | The flaw in your reasoning is that you're presuming that the fluid is being forced to flow faster.
Yes, if you have a situation where you want the same volume of fluid to flow through a thinner pipe, the fluid must be made to "flow faster". However, to say that the fluid "will move faster" somehow implies that the flui... | {
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The twin paradox and general relativity The twin paradox in special relativity has been discussed over and over again. Send a twin on a spaceship out to someplace or another accelerating at Earth gravity, then have it go through a series of decelerations and accelerations -- all at 1g -- so it returns to Earth, where... |
bob.sacamento asked: "But what about general relativity? "
In general relativity the twin that stayed on the planet can be younger than the twin travelling up and down again, thanks to the principle of maximized proper time.
bob.sacamento asked: "In a related question, what if we had triplets instead of twins and th... | {
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Why is it "bad taste" to have a dimensional quantity in the argument of a logarithm or exponential function? I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although I suppose i... | Orthodox view
A bit of a formal take at it: $\exp x$ can be expressed as a series:
$$\exp x=1 + x +\frac{x^2}{2!} + \frac{x^3}{3!} + \cdots + \frac{x^n}{n!} + \cdots$$
So if $x$ has unit $X$, then the terms of this series have respective units
$$\text{None}, X, X^2, X^3, \cdots X^n, \cdots$$
which is not dimensionally ... | {
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Calculating acceleration of a particle from Radiation Pressure I am trying to calculate the the acceleration of a particle from radiation pressure, assuming all radiation is absorbed. I got $$\Delta \vec{p} = \frac{\Delta U}{c_0}$$ and the intensity $I_S$=$1367 \ \frac{W}{m^2}$.
I think that $\Delta U = I_S A$. Since ... | The total energy $\delta U$ is also proportional to time. So, the energy deposited is $I\times Area\times time$ given that the radiation is falling normally on the body. Else you have to take a $cos\theta$ component.Now, it's trivial to see that the acceleration will be constant if the intensity is constant.
| {
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Why can a coupled wavefunction of 2 nucleons seemingly arbitrarily give two different expressions? When looking at the Isospin representation of a proton-neutron system (with the notation $|I,I_3\rangle$), you can go from an uncoupled to a coupled representation like this:
$$\textstyle|\frac{1}{2},+\frac{1}{2}\rangle|\... | It seems there is a bit of confusion here. A state like
$$
\textstyle\vert \frac{1}{2},\frac{1}{2}\rangle_1\vert \frac{1}{2},-\frac{1}{2}\rangle_2 \tag{1}
$$
does not transform into itself under permutation of the particle index so is neither symmetric nor antisymmetric. As written, (1) describes distinguishable nucl... | {
"language": "en",
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What does the Kretschmann scalar really tell us about the geometry of spacetime? The Kretschmann scalar is one of the measures of spacetime curvature. For flat (Minkowski) spacetime it is zero. The dimensions of the Kretschmann scalar are $[L]^{-4}$. What does that physically signify about the geometry of spacetime?
| If we restrict ourselves to vacuum solutions then the Kretschmann scalar has a nice simple interpretation as the strength of the local tidal forces.
This happens because for a vacuum solution the Ricci tensor is zero so the Kretschmann scalar depends only on the Weyl tensor, and this tells about the tidal forces acting... | {
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Tensorpart of NN potential The potential of the nucleon nucleon interaction includes a tensor part which is given by:
$S_{12}(\hat{\pmb{r}}) = \hat{\pmb{r}} \cdot \pmb{\sigma_1} \hat{\pmb{r}} \cdot \pmb{\sigma_2} - \frac{1}{3} \pmb{\sigma_1}\cdot\pmb{\sigma_2}$
Where $\hat{\pmb{r}}$ ist a unit coordinate space oper... | In view of your comments I have explained my answer. It is usual to define the non-central potential in such a way that its average over all directions is zero. However integrating over all angles only the first term would give,
$ \frac{1}{4\pi}\int({\pmb{r}} \cdot \pmb{\sigma_1} )({\pmb{r}} \cdot \pmb{\sigma_2})d\ome... | {
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Is torque in an electric motor generated from repelling magnetic dipoles and the Lorentz force on a solenoid? So in an electric motor the torque is generated from the Lorentz force on the current carrying wire by the interaction with the outer magnetic field. There is also another interaction between the magnetic dipol... |
There is also another interaction between the magnetic dipole created by the solenoid (or wire) and the external magnetic field which would drive the motor as the B-fields repel and attract each other periodically.
Your statement, that the rotor is a coil of a current carrying wire and a magnetic field is - beside th... | {
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Where does the energy for electron degeneracy pressure come from? I just watched a web video about white dwarf stars. It mentions that the star’s electrons flow among the degenerate matter. Since most of the electrons can’t be in the lowest state, due to Pauli’s exclusion principle, they get bumped to higher states and... | The energy comes from whatever force pulled the electrons into such a dense volume in the first place--in this case, gravity.
When the star is 'normal sized', like the Sun, electron degeneracy produces a small amount of pressure. As the star makes its way along the path to a white dwarf, the electron degeneracy pressu... | {
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Light bulb longevity I have a summer home in North Carolina where there are more people in the summer than in the winter. Light bulbs seem to last longer in the winter when there is less demand on the system. I suspect the line voltage drops with the higher use. Would this affect the life of the bulb?
| You may have noticed that filament light bulbs often fail when the bulb is switched on.
This happens because when a bulb is switched on for a short period of time the current through the bulb exceeds its normal operating current.
This behaviour is shown for two different wattage filament light bulbs in the graphs below... | {
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Density matrices, off-diagonal terms, coherences and correlations I'm trying to better understand the off-diagonal terms of the density matrix - an often brought up question on this site I realise. Specifically my confusion at the moment concerns the interpretation of the real and imaginary components of these off-diag... | So long story short, those terms are basis-relative and cannot be given a truly deep philosophical meaning: being Hermitian, the density matrix is diagonal in some orthogonal basis; you just aren't looking in the right one.
With that said we can certainly look a little more in-depth at a state of the form $$\rho = \beg... | {
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Why don't spectacles form these weird images? It's an established fact that:
*
*Convex lenses produce inverted images of objects beyond the focus, on the other side of the lens.
*Any object placed at a finite distance from a concave lens appears to be somewhere between the focus and the optical centre when viewed f... | The eye itself has its own lens that is intended to create an image at the retina. IF this lens is faulty for one reason or another, the image does not form at the retina - rather, it forms in front of or "behind" the retina. The additional lenses (glasses) shift the path of light rays by a small amount before they e... | {
"language": "en",
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Why do phones land face down? Layman here.
I'm not sure if this is the case or not, but my anecdotal evidence is that mobile phones, especially large screen phones, tend to fall face down when you drop them; much to the owner's dismay, this leads to cracked screens.
I'm sure there is a scientific explanation for this, ... | A physicist working at Motorola actually did this experiment as part of a promotional push for shatter-proof screens. This same physicist had previously written a paper on the same question, applied to the classic "buttered toast" problem (does toast really land butter side down?).
The short answer is: the way the phon... | {
"language": "en",
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Wave function of many particle I read that the wave function of a system of many particles is formed from the product of the wavefunctions of the individual particles. What is the logic behind it?
| This question is not answered in standard textbooks. To me, this signals that standard quantum mechanics doesn't ask 'What is the wave function for a many-particle quantum system?' I read on the internet various work-arounds for this, but to me they seem not to really tackle the principled question 'what is the quantum... | {
"language": "en",
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Poisson's equation in regions Suppose I have two regions in space. Region 1 and region 2.
In Region 1 I have a bunch of charges, and in region 2 I have no charges.
Is it true that Laplace's equation is satisfied in region 2?
| The Poisson equation is a differential equation. Any differential equation on $\Omega\subset \mathbb{R}^n$ can be written in terms of a differential operator $\mathfrak{D}$ mapping functions on $\Omega$ to functions on $\Omega$ as
$$\mathfrak{D}f=j$$
where $j$ is what sometimes is called a source term. When $j = 0$ the... | {
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Can redshift be used to create an accurate accelerometer in a phone? Currently, accelerometers use small springs which produce wild fluctuations and inaccuracies.
Because light's speed is limited and compresses when its source moves in the direction it's going, and decompresses when it does the opposite, it seems we co... | You can measure rotational velocity very accurately with a fiber optic gyroscope. When you are rotating, the path length along one direction "is shorter". Whether you consider that a red shift or a phase shift doesn't really matter - you are using the finite speed of light to determine the rotation.
Measuring absolute ... | {
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Why is the correlation function a power law at the critical point? I’m taking my first exam in statistical field theory and critical phenomena. I’ve reached a point in which we use the fact that the pair correlation function decays as a power law at the critical point:
$$\left<\psi(x)\psi(0)\right> \sim\frac{1}{x^{D-2+... | I am not expert but I am learning, the scaling law is related to the re-normalization group, see famous K.G.Wilson paper :
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.4.3174
The scaling laws result form the re-normalization group for above case.
| {
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Why is work done equal to $-pdV$ only applicable for a reversible process? In thermodynamics, when we're interested at gases, I know that the work done can be written to be $-pdV$ for a reversible process ($p$ is the pressure of the system, and $V$ is the volume of the system).
This is because $$dW=Fdx=-pAdx=-pd(Ax)=-p... | Suppose that gas of pressure $p$ is contained in a vessel behind a piston of area $A$. In order to get the piston to move you will have to supply an external force
$$
f = p A + \epsilon
$$
where $\epsilon$ is the force due to friction, or anything else that prevents the piston from moving freely. Hence the work done on... | {
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Mass eigenstates and weak eigenstates of neutrinos I am aware that similar questions have been answered earlier. But still I am not able to convince myself on following question:
*
*If mass(/energy) eigenstates are eigenstates of the Hamiltonian operator, which operator is connected to weak eigenstates and what is i... |
which operator is connected to weak eigenstates
AFAIK interactions are not connected to operators in a one to one relation. There are four interactions, the electromagnetic, the weak, the strong and the gravitational, characterized by the corresponding ( em, weak, strong) interaction coupling constant
These interac... | {
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Turning a bike, why does it lean? I realize this seems like a pretty simple issue of drawing a free body diagram, but I just can't seem to figure it out.
If a bike leans, then it must have had a torque that made it lean. I considered the centripetal force, in this case friction, as a possible source for this torque, b... | The bike would lean in the other direction, due to centripetal force, without a cyclist. A cyclist leans the bike on purpose into the turn, to counteract said centripetal force.
The torque involved is the cyclist's weight as they lean into the turn.
| {
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Using integrals to expand a vector in continuous basis I am new to quantum mechanics. I have been trying to understand why when we want to represent a function $$\psi(x)$$ as a ket in continuous basis |x> we us the integral:
$$\vert \psi(x)\rangle =\int\psi(x)\vert x\rangle dx$$
where in non-continuous basis it is :
$... | You want to think of
$$
\psi(x)=\langle x\vert\psi\rangle
$$
as a (complex) number interpreted as the “component” of $\vert\psi\rangle$ on the basis vector $\vert x\rangle$,
with $\langle x\vert\bar x\rangle=\delta(x-\bar x)$. This way
\begin{align}
\vert \psi\rangle &= \int\,dx\, \psi(x) \vert x\rangle \, ,\\
\psi... | {
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Mass and Newton's Second Law While trying to understand the second law of Newton from "An Introduction to Mechanics" by Kleppner and Kolenkow, I came across the following lines that I don't understand:
"It is natural to assume that for three-dimensional motion, force, like acceleration, behaves like a vector. Althoug... | If mass is a vector quantity then how does one find the total mass of two vector masses after they are combined?
Is there really any evidence that two objects of equal magnitude mass $m$ when joined together exhibit variations in the magnitude of their combined mass varying from $0$ to $2m$?
| {
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$dU=dQ$ and $dU=TdS$, but $dQ$ not always equal to $TdS$? Why? $$ dU = dQ+dW $$ $$ dU=TdS-pdV $$ The equations above are always true for a thermodynamic state of a certain system. Now let's say that we have a situation where $dW=0$, this tells us that $$ dU=dQ $$ $$ dU=TdS $$But still I can't write $ dQ=TdS $, since th... | For an arbitrary process between equilibrium states of a closed system, we have
$$
\Delta U = Q + W
$$
which is just conservation of energy.
If the process happens quasi-statically, state variables are well-defined at each point in time and we can go to an infinitesimal description
$$
dU = \delta Q + \delta W
$$
where
... | {
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Newton's first law and Inertial systems
Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that inertial systems exist is a statement about the physical world.
According to me, th... | Well, since everything is relative to another, there isn't any standard inertial reference frame. So, you first consider a particular frame to be inertial( generally everything is calculated w.r.t earth even though it's in circular motion, which means it's accelerating), and calculate everything else w.r.t it.
For your... | {
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Twin paradox Doppler shift explanation I was reading the wikipedia article on the twin paradox and came upon the section describing it in terms of the relativistic Doppler shift (link).
The image below illustrates the received signals from Earth to ship (left) and ship to Earth (right).
The explanation states that on... |
But doesn't this conflict with the concept that time seems to run slower for objects moving relative to an observer? This explanation would lead one to believe that the rate at which an observer sees a moving object travel through time depends on whether the object is moving towards or away from the observer.
Time in... | {
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Force on plate of parallel plate capacitor with dielectric If we have a parallel plate capacitor whose charge is +Q and the polarization charge as Qp as shown in the figure..
then while finding the force acting on the left plate of the capacitor for instance, shouldn't the force due to the polarized charge -Qp and +Qp... | Agreeing with @Aniansh that the two induced surface charges on both faces of dielectric are separated by a finite distance and therefore must cast a net electric field at a point beyond the dielectric boundaries because one surface will always be closer to the point than the other. However when we are talking of capaci... | {
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Physics interpretation of the expectation value of an electrons spin components Suppose I have an electron that is in the spin state
$$\chi =A\begin{bmatrix}3i \\4\end{bmatrix} $$
If I calculate the expectation values of its spin components $S_x$ $S_y$ $S_z$, I get
$$\langle S_x \rangle= 0$$
$$\langle S_y \rangle = -\h... | Expectation values are just average values; namely if you do a measurement of the spin at the direction in question "many times" with "identical" setups, the average values of your spin measurements at that direction should be equal to the expectation value given by quantum mechanics.
That said I think your statement a... | {
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Is there an antimatter sweet spot? More Details:
Is there a spot with antimatter where the repulsive force of its nucleus and the attractive force of the positrons cancel out? As in if I took a heavy antimatter atom, ionized it, would there be a scenario in which electrons get attracted to the positrons around the anti... | If you start with neutral antimatter atom, then you would have to add positrons in order to make it positively charged so that it would attract electrons. While it would be possible to then add electrons to an orbital, that electron would quickly find a positron and annihilate, leaving behind the original atom.
Matter-... | {
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Is wave made of particles? I always feel confused about the concept of wave. I don't know why we have to develop a term called "wave"? To me, wave made of particles oscillating up and down periodically.
Is wave just a collection of particles or is wave an identity independent of particles?
For example:
A Wave on a str... | Light is both a wave and particle according to wave-particle duality. In-fact, this is true for every object in the universe.
For e.g. : Light behave as a particle in the photoelectric effect whereas as wave in the double-slit experiment.
And, light wave does oscillate perpendicular to the direction of propagation; tha... | {
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Do higher frequency/energy levels in the EM spectrum mean higher temperatures? I am trying to find concrete evidence that for example, light in the optical spectrum would be hotter than infrared light because it has a higher frequency, and that is directly proportional to energy. Is energy directly proportional to temp... | It's complicated. If we are talking about temperature of an object then yes. The hotter the object is the higher the electromagnetic wavelength frequency it generates. From infrared to UV going from 200 degrees to 4000 celcius. In terms of radiation absorption. On a black object then the hottest frequency is about yell... | {
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Why am I able to see objects within 25 cm? My book defines:
The closest distance for which the lens can focus light on the retina is called the least distance of distinct vision or the near point. The standard value (for normal vision) taken here is $25\, \text{cm}$ (the near point is given the symbol $D$.)
However, ... | The least distance of distinct vision is the minimum distance your eye lens can focus on an object without any strain. This means the eye is in a relaxed state. But eye is a self adjusting lens. When you try to see an object closer than 25 cm(for a normal eye), your eye automatically adjusts the focal length thus decre... | {
"language": "en",
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Mercury's precession I read in an article about Mercury's precession that Newton's law of gravitation predicts such precession of planets ;but fails to caluclate the precession of Mercury.But most of popular science books or other articles on the internet suggest that Newton predicts identical ellipses whereas the rea... | If two bodies orbit each other and the mass of one of them is much larger than the mass of the other body, the equations of motion can be solved exactly. In polar coordinates the solution is given by:
$$r(\theta)=\frac{l}{1+e\cos{\theta}}$$
This is the equation of an ellipse. As the OP correctly mentions, the actual or... | {
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If an astronaut orbits earth, can both Time Dilation and Gravitational Time Dilation affect it? I am very new at all of this stuff and this one thing bugs me very much...
If an astronaut is orbiting earth, it should be experiencing Time a bit faster than those on earth, correct?
Well then because of the speed he is tra... | Yes on both counts. There is time dilation due to the orbital velocity (special relativity), and there is also time dilation due to the Earth's gravity field (general relativity). The signs of each of these are opposite, but the magnitudes can be different, leaving a net effect. The example I am most familiar with i... | {
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Why does a room not warm up faster when I put the heater's thermostat on a higher value? I would say it should warm up faster because the difference in temperature between the room and heater is higher.
Edit: I am talking about a convection heater.
| The thermostat in a heater is usually an on-off device. It senses the room temperature and runs the heater at full power as long as the room is colder than the target temperature. If the room is hotter than the target temperature, the thermostat turns the heater off.
(In a narrow temperature interval around the target... | {
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Quantum State Representation with Commuting Operators Let $[A,B]=0$. Then, we can find a set of eigenvectors $\{|a_n,b_n\rangle\}$ common to both $A$ and $B$. According to this, and my own understanding, it makes sense to write an arbitrary quantum state as
$$\tag{1}|\Psi\rangle=\sum_n \sum_i c_n^i |a_n,b_n,i\rangle,$$... | If you think of $a_n$ and $b_j$ as eigenvalues, it is quite possible for the eigenvalue $a_n$ to occur more than once, but there is no reason for all eigenstates of $\hat A$ with eigenvalue $a_n$ to have the same eigenvalue of $\hat B$.
An easy example would be eigenstates of the hydrogen atom. The eigenstates $\vert ... | {
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Will current flow if there's no return path? Here is the problem I was trying to solve:
Find the potential difference between the points A and D
I used Kirchhoff's voltage law for the left loop and right loop and found out the current through the left loop to be $\frac{10}{2+3}$ A (2A) and for the right loop $\fr... |
If there exists a potential difference between B and C of 4V, charges
should flow, right?
No, if there were a current through the 1 ohm resistor, the voltage $V_{CB}$ could not be $4\,\mathrm{V}$. This result is an elementary application of KVL and Ohm's law:
$$V_{CB} = I_{CB}\cdot 1\Omega + 4\,\mathrm{V}$$
See th... | {
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Bremsstrahlung radiations Why are Bremsstralung radiations ignored in case of heavy ions(such as $\alpha$ particles) and not for $\beta$ particles when calculating the rate of energy loss of the heavy ions moving in some medium. (Bethe formula)
| The power radiated from charged particles is proportional to the square of their acceleration. If equally charged particles are subject to the same accelerating electromagnetic forces then particles with greater mass (i.e. the ions) will experience a much smaller acceleration and therefore emit much, much less power.
| {
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Renormalization of a Feynman diagram with zero bare mass Consider the Feynman diagram below:
in the case of $\phi^4$ theory where there is no bare mass:
$$\mathcal{L}=\frac{1}{2} \partial_\mu \phi\partial^\mu\phi-\frac{\lambda}{4!} \phi^4$$
the contribution of this diagram is given by:
$$I=\frac{-i\lambda}{2} \int \fr... | In dimensional regularization, loop integrals which do not depend on physical external momenta are automatically regularized to be zero. This is so because, in absence of a mass scale, the integral is both UV and IR divergent and the divergences are regulated to zero.
Then, in dimensional regularization, you can regula... | {
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Reading the y value of the Branching fraction diagram for Higgs boson decay modes I am simply confused about the way y-axis is scaled in the figure below. So for example, if I were to read off the branching fraction value for Higgs decaying to ZZ, how would I precisely read the value?
Photo Courtesy: University of Ed... | The "branching fraction" is the fraction of decays that occur in a particular channel; all of the branching fractions for all of the decay channels must add up to $100\%=1$. This is a graph predicting how a Standard Model Higgs would decay as a function of its mass, which was much more interesting before we managed to ... | {
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How to maximize Peltier devices' cooling capacity? I am currently working on a project requiring the use of Peltier devices. I have attached the cool side of the device to a copper plate and the hot side to a heat sink with a fan.
*
*What would be the best way to isolate the copper plate from the hot side?
*Shoul... | inside the device, the cool side is already in physical contact with the hot side: they form a junction through which electricity is flowing, and it is that flow of electricity which makes one side of the junction get hot and the other side cold. the very best you can do to maximize the usefulness of a peltier thermoj... | {
"language": "en",
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Higgs Boson abundance in the universe What's the Higgs boson abundance in the universe, in $\%$? In total? Does it even make sense? I cannot find any estimate on the internet.
| The Higgs boson is one of the components along with the Goldstone bosons in two doublets of scalar fields. The three Goldstone bosons couple to the $Z,~W^\pm$ to introduce a longitudinal component to their dynamics, which corresponds to mass. The remaining particle couples to nothing. It has a mass of $125\,\mathrm{GeV... | {
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Finding a path of beam in a gradient-index media I'm trying to find a polynomial that describes a path of a beam in a gradient index media.
It is a path of least time (Fermat's principle) meaning that it takes path that takes the least time to get from A to B, not the shortest one.
The velocity of a beam is non-linear.... | Almost exactly this problem is explained in detail in these notes. I refer you to those notes for the derivation. They conclude that it's better if $y$ is the independent variable, in which case you have to minimize the integral
$$\int n\cdot d\ell = \int f(y)\sqrt{1+x'^2} dy\\
\rightarrow\\
\frac{d}{dy}\frac{\partial}... | {
"language": "en",
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How does an electromagnetic wave move? Somewhere I found the explanation that the EM fields create and destroy each other during the oscillation (I suppose by Faraday's law) and this makes the wave "move".
I can't imagine this because unitary vectors in E,B and k directions are a right hand ordered set of vectors and ... | Short answer
You've got half of the answer right when mentioning Faraday's Law of Induction, which tells us how electric fields can be generated from time-varying magnetic fields. The other half of the answer involves Ampère's Law with Maxwell's correction, which tells us how magnetic fields can be generated either fro... | {
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Why are some materials dull rather than shiny (cloth, coal, matte paint etc.)? The converse of this question is perhaps "why are metals shiny". From what I understand, metals are covered by a sea of free electrons that oscillate in response to incident light/EM wave, and the oscillation is in turn associated with anoth... | The most important aspect for the difference between matt & shiny surfaces is the roughness of the surface; if it is rough it scatters light in many directions looking rough, whereas if it is smooth light is reflected in the same manner and so appearing shiny.
| {
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Nuclear Fusion: Why is spherical magnetic confinement not used instead of tokamaks in nuclear fusion? In nuclear fusion, the goal is to create and sustain (usually with magnetic fields) a high-temperature and high-pressure environment enough to output more energy than put in.
Tokamaks (donut shape) have been the topolo... | Because that's just one of the many alternative approaches to fusion, and resources are limited.
Nuclear fusion seems very promising, but for all approaches tried so far the challenges have proved to be more numerous and difficult to overcome than initially expected $-$ and the magnetized target fusion that General Fus... | {
"language": "en",
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Why is then the mobility of holes lesser than the mobility of electrons?
In a semiconductor, mobility of holes is less than the mobility of the
electrons.
However, we know that, when an electron leaves its place, a hole is created. In other words, electron mobility constitutes hole current. Since moving electrons c... | The conduction electrons reside in the conduction band and the missing electrons (holes) reside in the valence band of the semiconductor. The conduction band electron effective mass is usually smaller than the valence band hole effective mass.This is one of the reasons that in a semiconductor the electron mobility is u... | {
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How many spectral lines are emitted by atomic hydrogen excited to the n-th energy level? This is a question from Irodov's Problems in General Physics.
The Rydberg formula for calculating the wave number of a spectral line is:
$$
n = R(1/n_f^2-i/n_i^2)\,.
$$
where $n_f$ and $n_i$ represent the final and initial states o... | First the formula is wrong. It should be:
$$\tilde \nu = \dfrac{1}{\lambda} = R \left(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2}\right)$$
where $\tilde \nu$ is the wavenumber of the line, R is the Rydberg constant. Both $n_f$ and $n_i$ are positive integers such that $n_f < n_i$.
The OP asked: However, what if two spectral line... | {
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Why do fundamental particles have a specific size? If Quantum Field Theory is accurate, all particles are actually just excitations of the field in which the particle interacts.
Therefore, wouldn't it be possible to have particles of any conceivable size, provided the energy, couldn't you have a photon the size of a bu... | The standard model is a collection / list of the properties of quantum entities, it does not describe the quantum entities themselves that possess those particular properties.
So the words electron, quark etc, are really just shorthand for a bunch of properties that have been measured. That's all physics, as an empi... | {
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In semiconductors when electrons jump from VB to CB, do they leave behind their parent atom's nuclei? In semiconductors/conductors when electrons jump from VB to CB, do they leave behind their parent atom's nuclei?
If yes, when this happens in Si (electron jump from VB to CB) why don't they ionize Si to Si +?
If no, w... | First, the electrons in the valence or conduction band are not localized to a single nucleus. They move about in the crystal lattice much like atoms in a gas, so we call them an "electron gas".
Second, the conduction and valence bands are bands of states of electrons, not of whole molecules. Finding an electron in one... | {
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Inverse Square relationship using paint problem confusion I want to ask a question about the inverse square relationship using an aerosol paint spray mentioned in my book.
I am reading the book Advanced Physics by Steve Adams, and it mentions this in the book.
Imagine you are holding an aerosol paint spray at $50$cm ... | The spray comes out as a cone with opening angle $\alpha$ such that $$\tan\alpha=\frac{10cm}{50cm}=\frac{1}{5}$$
If you double your distance to the wall, then the opening angle $\alpha$ stays the same and therefore the radius of the paint patch $r$ is such that
$$\frac{1}{5} = \tan\alpha = \frac{r}{100cm}$$
If you solv... | {
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Why does gravity need a graviton? Einstein theorized that gravity is a phenomena manifested by the curvature of spacetime, in effect it IS the curvature of spacetime. If this is so, why do we need a graviton to convey the force of gravity? If I have mis-understood Einstein then I would appreciate a little help in gras... | The short answer is that we need $G_{\mu\nu}$ to be quantised because $T_{\mu\nu}$ is. You can try getting around that by e.g. replacing the stress tensor with its own expectation in the Einstein field equations, but that causes all sorts of headaches people have investigated, such as nonlinear quantum mechanics.
| {
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Solving the Lie algebra of generators: path from algebra to matrix representation Given the Lie algebra, what is the systematic way to construct the matrix representation of the generators of the desired dimension? I ask this question here because it is the physicists for whom representation of groups is more important... | If you have the structure constants, i.e. the coefficients $f_{ab}^c$ in the commutation relations $[T_a,T_b]=\sum_c f_{ab}^cT_c$ with $a,b,c\in \{1,\ldots p\}$ then you can construct $p$ matrices $M_a$ (labelled by $a$) of size $p\times p$ with entries $(M_a)_{cb}$. These matrices will be a $p\times p$ representation... | {
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Intuitive logic behind this beautiful result of successive time of collisions of two bodies INPhO 2017 Problem 3
Two identical blocks A and B each of mass $M$ are placed on a long inclined plane (angle of inclination = $\theta$) with A higher up than B. The coefficients of friction between the plane and the blocks A a... | The equation giving the position of each individual block is
$$x=x_0 + v_0 t + a t^2 $$
with $a$, the acceleration, dependent on the friction. The distance between the blocks is given by $\Delta x=x_A - x_B$. If you write down an expression for $\Delta x$, you will find it has the same form as the equation for $x$, but... | {
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Path integral kernel dimensions and normalizing factor I am currently reading Quantum Mechanics and Path Integrals by Feynman and Hibbs. Working on problem 3.1 made me wonder why the 1D free particle kernel: $$ K_0(b,a) = \sqrt\frac{m}{2\pi i \hbar(t_a - t_b)} \exp \left(\frac{im(x_b - x_a)^2}{2\hbar (t_b - t_a)} \righ... | The main point is (as Ref. 1 mentions in Problem 3.1) that the probability distribution (coming from the path integral) is only relative, i.e. its normalization is unphysical over an unbounded position space $\mathbb{R}^d$. See also this and this related Phys.SE posts and links therein.
References:
*
*R.P. Feynman a... | {
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Do the distances and velocities observed from galaxies other than Milky way really show that every point in the universe is the center? Hubble's observation from redshift shows a pattern that the speed of the galaxies is proportional to their distance, by using those informations we can map the position of the galaxies... | Basically, yes. However, when calculating what would be seen from the vantage point of other galaxies, relativity has to be taken into account. So if the distance from Galaxy A to Galaxy B is, as calculated from the earth's frame of reference, x times the distance from Galaxy A to Galaxy C as calculated from earth, it ... | {
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Temperature of gas leaking into chambers An initially evacuated and thermally isolated chamber has a small hole opened in its side through which an ideal gas effuses from the outside. The gas outside is at standard temperature and pressure.
A second, smaller hole directly opposite the first hole on the opposite side of... | The temperature of the ideal gas will be the same at all times in all chambers whose walls are maintained at the standard temperature or are thermally isolated. The expansion of an ideal gas into vacuum doesn't perform any work therefore there is no temperature change.
| {
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Unitary Transformation of Eigenstates Suppose I have two operators, $A$ and $B$, with eigenstates $A \lvert a \rangle = a \lvert a \rangle$ and $B \lvert b \rangle = b \lvert b \rangle$, where $a$ and $b$ are all unique. Furthermore, suppose that $A$ and $B$ are related by a unitary transformation $$A = U B U^{-1}.$$ T... | Well, a similarity transformation for an invertible (not necessary unitary) operator$^1$ $U$ does generically change the eigenspaces but does not change the eigenvalue spectrum $\{a_1, a_2,\ldots, \}=\{b_1,b_2,\ldots\}$. Hence it would be inconsistent to claim that all the eigenvalues $\{a_1,a_2, \ldots, b_1,b_2,\ldots... | {
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Experiment on friction coefficient Here you can see the results of the experiment about a friction coefficient:
The mean of the friction coefficient becomes 0.262 but when I do a linear regression in the form of y=mx the slope is 0.31. Shouldn't it be the same? I used $F_N$ as x values and $F_D$ (friction force) as y ... |
The mean of the friction coefficient becomes 0.262 but when I do a linear regression in the form of y=mx the slope is 0,31. Shouldn't it be the same?
No.
Linear regression and arithmetic mean are not the same thing.
Linear regression is trying to fit a linear plot to the points you gave it with the best $R^2$ value.... | {
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"url": "https://physics.stackexchange.com/questions/378240",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Does Fluctuation Theorem prove the 2nd Law of Thermodynamics? Does Fluctuation Theorem or Crooks Fluctuation Theorem prove the 2nd Law of Thermodynamics from statistical point of view?
https://en.wikipedia.org/wiki/Fluctuation_theorem
https://en.wikipedia.org/wiki/Crooks_fluctuation_theorem
| Yes, the fluctuation theorem gives (among other things) the probability that a system will evolve from a state of greater statistical entropy toward one of smaller entropy. The second law of thermodynamics is only probabilistically correct for large but finite systems, and the fluctuation theorem gives the correction ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378398",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
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