Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is it the term "telescope" the same as a "detector"? For example, in this reference, MITO: muon telescope they use the term telescope but clearly the "telescope" is a muon detection system. And they also talk about angular resolution, angular aperture, etc. So my question is focused in, is the term telescope the same a... | A particle detector is not necessarily a telescope, although in a specific context the terms could be interchangeable. It is like word engine used by firemen or word pot used by parents of a small child - the word is rather general, but no one is confused about its specific meaning. The technical term in speech theory ... | {
"language": "en",
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How necessary are the laws of physics given the impossibility of violating the law of conservation? The Damascene theologian Ibn Taymiyya believed that God originates things ex materia, not ex nihilo or without prior material conditions, arguing that this latter type of creation entails a logical contradiction. Althoug... | You can certainly break some of the current laws of physics without violating energy conservation. Energy conservation comes from the idea that the laws of physics do not change with time (i.e. what holds today holds yesterday as well). This in turn is a consequence of Noether's theorem.
Noether's theorem permits other... | {
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Age of a black hole Is there a way to measure the age of a black hole by find Hawking radiation or calculating the stable orbits around the black hole?
| No. The Hawking radiation could tell us the black hole's remaining lifetime, or equivalently how much mass it has. But that doesn't tell us anything of the following (which are all equivalent): how much mass it's shed; how much it once had; how long it's existed for. The argument for orbital details is analogous.
| {
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Why should a dipole have zero net charge? Why can a dipole not have two unequal charges separated by a distance? Is there any significance for the dipole being defined as electrically neutral?
| The concept of a dipole moment, and other moments such as a monopole, quadrupole, etc, comes from the process of writing a field as a sum of components called multipoles. This is known as a multipole expansion of the field. The reason we do this is that it can make calculations quicker and easier because it allows us t... | {
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Why bother buying efficient lights if you are already heating your house? Assume I live in a location where at any time of day and any time of year, I need to heat my house. Assume further that I have a room with no windows. In this case, does it make sense for me to buy efficient light bulbs, considering that any inef... | Heating house with electricity is one of most expensive ways (if not THE most expensive).
Normally houses are heated with coal/oil/firewood/natural gas/heat pumps/RTGs, and only rarely with electric heaters. The electric heating is just more expensive than other sources.
The heat is not "lost", but there are cheaper op... | {
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Euclidean space to Minkowski spacetime Can you continuously deform (i.e., shrink, twist, stretch, etc. in any way without tearing) four-dimensional Euclidean space to make it four-dimensional Minkowski spacetime?
| Both 4D-Euclidean space and (3+1)D-Minkowski spacetime are 4D-vector spaces.
Indeed, $\vec R=\vec A+\vec B$ is the same operation in both spaces.
What differs is the assignments of square-magnitudes to the vectors and the assignments of "angles" between the vectors, which are both provided by a metric structure added t... | {
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How do stars produce energy if fusion reactions are not viable for us? From what I've learned, fusion reactions are not currently economically viable as of right now because the energy required to start the reaction is more than the energy actually released. However, in stars they have immense pressures and temperature... | As I see the core of your question is based on the “exothermic/endothermic” problem.
Fusion reaction is exothermic both on earth and on stars. When one binds two light elements, one ends up releasing energy always. The negative energy balance of fusion apparatus on earth is not due to the fusion reaction mechanism itse... | {
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Concept of Gravitational potential energy Change in Potential energy corresponding to a conservative force is defined as $$\Delta U = U_f - U_i=-W_f$$ and gravitational potential energy is $$\Delta U = U_f-U_i = -W_g $$ Suppose a mass $m_1$ is kept at a fixed point $A$ and a second mass $m_2$ is displaced from point $B... | Other answers are making this way too complicated.
The potential energy equation you quoted is only valid outside of a uniform sphere of mass. Inside a uniform sphere, the potential energy is actually constant. Therfore that constant should be set to the minimum of potential energy.
$U(r < R) = C$
$U(r=0) = U(r = R) = ... | {
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What does a Umlaut (double dot) above an angle mean? I'm reading a paper on double pendulums and there is an equation of motion that contains a double dot (Umlaut) above an angle. What does this mean / is this a standard notation in equations of motion?
| It means the second time derivative.
In other words, $$\ddot\theta=\frac{d^2\theta}{dt^2}$$ which represents the angular acceleration of an object (which is a pendulum bob in your example).
These, and indeed first time derivatives (or even more than first, second etc.) are very common in physics (and in engineering an... | {
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Why can a very large body of water not store summer heat? On this page, it states "The key disadvantage of using a very large body of water to achieve heat exchange with a relatively constant temperature is that you are not able to store summer heat in that body of water – to have the benefit of retrieving those higher... | The article is wrong. Consider the following: a popular form of heat pump HVAC uses coils of pipe buried in the ground and in communication with the subsurface water table. The ground water reservoir stays at an almost constant temperature year round (52 degrees F where I live) and furnishes heat in the winter and cool... | {
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Theoretical minimum temperature required to melt any material Reading about this (New material has a higher melting point than any known substance) got me curious.
Given a pressure level (like 1 atm) and a sufficiently hot temperature, I have the intuition that no material stays solid, and turns to plasma if hot enough... | Using the Debye model leads to the Lindemann melting formula for the melting Temperature: see reference), for p = 1 bar there is an upper limit for a given material structure.
$T_m = \frac{4\pi^2 A\, r_0^2 k_B \eta^2 }{9N_Ah^2}\Theta_D^2\,$ in K with A atomic mass, $r_0$ interatomic distance, $\eta$ Lindemann factor = ... | {
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How do we measure time? I'm having a little trouble trying to put to words my problem and I apologize in advance for any causation of trouble in trying to interpret it.
We define periodic events as those events that occur over equal intervals of time. But, don't we use periodic events themselves to measure time (like a... | A professor of mine once defined time as follows:
Time is what a clock measures.
which I assume is an of-quoted anglicization of Einstein's:
Zeit ist das, was man an der Uhr abliest
In other words, you build a clock (we all know what that is) and time is the thing who's change it measures.
Of course you may ask "Ok... | {
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How often is a non-coordinate and non-orthonormal basis used in GR? I wrote a program that takes as input the basis vectors if electing to use an orthonormal basis, or metric components if using the coordinate basis, and outputs non-zero Christoffel symbols and components of Riemann, Ricci, and Einstein tensors, as wel... | Coordinate bases are rarely orthonormal in GR. They're often orthogonal (in which case the metric is diagonal), but in general the basis vectors associated with each coordinate do not have a norm of $\pm1$. If you could truly establish an orthonormal set of coordinate basis vectors, then I'm pretty sure that your space... | {
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Contraction in SR vs GR I've always had a bit of fuzziness concerning relativistic contraction which I will try to put into words.
Iiuc in SR, moving objects contract in the direction of their travel, as measured by rulers at rest w.r.t. said objects. A traveling ruler when compared to the static one will appear shorte... | Laser light is already relativistically contracted with respect to LIGO. Therefore, its contraction is not phase-locked to the apparatus reference frame sensing gravity waves of much longer wavelength.
| {
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Transformation of field strength tensor in non-abelian gauge theory The field strength tensor is defined as
$$F_{\mu\nu}^a=\partial_\mu A^a_\nu-\partial_\nu A^a_\mu +g f^{abc} A_\mu^b A_\nu^c$$
where $f^{abc}$ are the antisymmetric structure constants and $A_\mu^a$ the gauge fields which transform as follows:
$$A_\mu^a... | Just turning my comment into an answer.
I haven't checked the algebra, but often in these kinds of calculations you need to use the Jacobi identity,
\begin{equation}
^{}^{}+^{}^{}+^{}^{}=0.
\end{equation}
It would conceptually make sense if you end up needing to use it here, since the Jacobi identity is needed for $^{}... | {
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Error Propagation for division Let's say I have a measurement $x$ with an uncertainty $\Delta x$. I also have a constant $C$ which has no uncertainty.
I want to find the uncertainty of $y$, which is defined as $C/x$. How do I find the uncertainty $\Delta y$? I know that IF I instead defined $y = C*x$ then $\Delta y = C... | For small $\Delta x$
$$y+\Delta y=\frac{C}{x+\Delta x} = \frac{C}{x(1+\Delta x/x)} = y(1+\Delta x/x)^{-1}=y(1-\Delta x/x) $$
So $\Delta y = -y\frac{\Delta x}{x}$
If $\Delta x$ is larger, for a specific $y$, a straightforward way is to work out $y$ in two cases, using $x + \Delta x$ and $x - \Delta x$ and see what $\De... | {
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If space is a vacuum, how do stars form? According to what I have read, stars are formed due to the accumulation of gas and dust, which collapses due to gravity and starts to form stars. But then, if space is a vacuum, what is that gas that gets accumulated?
| Space is not a full vacuum. It's mostly a vacuum, and it's a better vacuum than the best vacuums that can be achieved in a laboratory, but there's still matter in it. See interstellar medium.
In all phases, the interstellar medium is extremely tenuous by terrestrial standards. In cool, dense regions of the ISM, matter... | {
"language": "en",
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Propagator of harmonic oscillator at specific times It is well known that the propagator (kernel) of a simple harmonic oscillator is given by
$$
U\left(x_{b},T;x_{a},0\right)=\sqrt{\frac{m\omega}{2\pi i\hbar\sin\omega T}}\exp\left\{ \frac{im\omega}{2\hbar\sin\omega T}\left[\left(x_{a}^{2}+x_{b}^{2}\right)\cos\omega T-2... | OP's troubles are (partly?) caused by the fact that OP's eq. (1) only holds for $0<T<\frac{\pi}{\omega}$. OP's eq. (1) lacks the caustics/metaplectic correction/Maslov index. The corrected formula
$$\begin{align} K(x_b,T;x_a,0)~=~&\exp\left[-i\left(\frac{\pi}{4}+\frac{\pi}{2}\left[\frac{\omega T}{\pi}\right]\right)\rig... | {
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Squared Summation of Terms using Einstein's summation convention In working with QFT and Maxwell's equations, terms such as:$$\left(\partial_\mu\,A^\mu\right)^{2}$$ often appear. Since I am new to this, I am not sure of the expansion. That is, is it 4 terms squared or is it 4 squard terms:
$$\left(\partial_0 A^0\righ... | Here, standard rules of algebra should apply, i.e. the summation should be performed first and then squared (it is obvious once you write out the summation symbol instead of using Einstein's notation):
$$(\partial_\mu A^\mu)^2 = \left( \sum_{\mu=0}^3 \partial_\mu A^\mu \right)^2 = (\partial_0 A^0 + \dots)^2$$
Note that... | {
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Does the temperature of the gas inside a balloon changes with it expands in a vacuum chamber or does it remain constant? I've been trying to figure out if a balloon expanding in a vacuum chamber undergoes a isothermal, adiabatic or a mixture of both processes and I saw that my problem actually comes to knowing whether ... | If the expansion is rapid, it will be adiabatic. If the balloon is rubber which must be stretched, the pressure will be higher inside than outside.
| {
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Is the double slit pattern a standing wave? This question is about terminology. The double slit pattern has nodal lines and antinodal lines, and therefore resembles a standing wave. However, the antinodal lines within the double slit pattern resemble travelling waves. Do the terms standing wave and travelling wave have... | Yes, the interference pattern produced by two slits (or, equivalently, two oscillators with the same frequency that are in phase with each other) is a type of two dimensional standing wave.
The nodes, where the amplitude of the combined wave is zero, lie along lines where the difference in the distance from the two sli... | {
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Does vacuum spacetime have an inherent curvature? I am a complete novice in physics beyond the high school level, so please excuse anything wrong in my question.
So I have recently read that according to General Relativity, the presence of mass in spacetime causes spacetime to become curved and that is how gravity aris... | A spacetime without matter or energy is called a vacuum spacetime. There are flat vacuum spacetimes as well as vacuum spacetimes with curvature.
The reason for this is that, like most differential equations, different solutions can be obtained for different boundary conditions, even given the same sources.
So just like... | {
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What is the Hydrogen and Helium composition of the Sun in terms of their different states? What is the Hydrogen and Helium composition of the Sun in terms of:
Hydrogen: (1) molecular, (2) metallic and (3) ionized compositions?
and
Helium: (1) atomic, (2) metallic and (3) ionized compositions?
This seems difficult to fi... | Roughly speaking the hydrogen and helium in the Sun become fully ionised at depths of about $\sim 10^7$ m below the photosphere once the temperature rises above about $(2-3)\times 10^4$ K (the larger number is appropriate for helium).
Thus atomic hydrogen and helium only exists in the outer $10^7$ m of the Sun and even... | {
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Why only the wavelength and speed of refracted light traveling inside a transparent material changes and not its frequency? When monochromatic light waves travel from one medium to another the frequency never changes.
A transition to a denser medium will result of a slow down of the propagation speed v of the light wav... | The constant value of $f$ is easiest to understand by thinking about the wave model of light rather than the particle model.
If the frequency of the light wave inside and outside of a material had different values then there would be a discontinuity in the electric and magnetic fields at the boundary of the material. T... | {
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High school physics problem - having trouble understanding This is a fairly straightforward problem which doesn't require the usage of more than one or two formula but I find it hard to grasp the concept behind this.
Let's say we have two trains, one which moves at the speed of $45 \frac{km}{h}$ and the other at the sp... | Let $t$ be the time elapsed by the second train since it started to move.
The positions of the first train and the second train relative to the same starting point are $x_1(t)$ and $x_2()$ as follows.
\begin{cases}
x_1(t)= S_\text{ref} + v_1 t\\
x_2(t)= v_2 t
\end{cases}
where $S_\text{ref}$ is the initial relative pos... | {
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Averaging over spin phase-space for a cross section In Peskin and Schroeder the Dirac equation is solved in the rest frame for solutions with positive frequency:
$$\psi(x) = u(p) e^{-ip\cdot x}$$
$$u(p_0) = \sqrt{m} \begin{pmatrix} \xi \\ \xi \end{pmatrix},$$
for any numerical two-component spinor $\xi.$ Boosting to an... | Because The spine can only have two possible (discrete) values, (+1/2 and -1/2), the integration is appropriate for continuous spectrum.
| {
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Can lenses and mirrors be described in terms of beamwidth and directivity? As a first background, I am an Electrical Engineer with experience in antennae design for microwave bands.
Lately, I have been interested by optical devices, and I notice one strange phenomenon: when reading about a lens or a parabolic reflector... | Yes, they do, most of the time! There area a few caveats, though. Optical "antennas" are also made for thermal noise like sun light but RF engineers have not much use for such non-coherent signals. The higher the sidelobes the less practical use these formulas obviously would have, and note that the operation of optica... | {
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The change of mechanical into electromagnetic waves and vice versa I know that sound is a type of mechanical wave, so the human eardrum changes mechanical energy into electronic energy (impulses) so the information may be processed by the brain.
Question: As satellites transfer info by electromagnetic waves that are al... | Amending the previous answer, which refers more to air pressure, there is also the piezoelectric effect of some materials that can be used to transform mechanical waves and pressure from various other media apart from air, like solids, liquids etc., directly to electrical signals that can be then further processed.
App... | {
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Why do we need insulation material between two walls? Consider a slab made of two walls separated by air. Why do we need insulation material between the two walls. Air thermal conductivity is lower than most thermal conductivities of insulating material and convection cannot be an issue in the enclosed volume: hot air ... | If the air gap between the walls is wider than approximately 0.5 inches, the warm wall will heat the air, causing it to rise. The cold wall will cool the air, causing it to fall. This will set up a circulating air flow between the walls which transfers heat across the gap to a greater degree than expected. Insulatio... | {
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Would a high energy Hydrogen atom start emanating electromagnetic radiation? We know that the total energy of the hydrogen atom is proportional to the inverse of the square of the principal quantum number $n$:
$$E_n \propto -\frac{1}{n^2}$$
So at high quantum numbers the energy spectrum tends towards a continuum.
Shown... | High energy orbitals can in some respects be represented by classical Bohr orbits but have strictly speaking still to be described my quantum mechanical wave functions, especially when it comes to calculating the transition probabilities to other states. High energy orbitals of all neutral atoms become increasingly hyd... | {
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Can we measure $10^{-12}\ \mathrm{N}$ force? I would be interested to measure a very small force, say in the order of $10^{-12}\ \mathrm{N}$? Is this possible? What equipment is needed?
My setup
Assume that I have a relatively heavy machine say between 5-10 kg that I want to measure if it produces this thrust, which ac... | The question is, a $10^{-12}\rm\,N$ force applied to what. A force of $10^{-12}\rm\,N$ applied to a hydrogen atom, with mass $10^{-27}\rm\,kg$, would produce an acceleration $F/m = 10^{+15}\rm\,m/s^2$.
A torsion pendulum is absolutely a way to allow very feeble forces to cause observable, macroscopic motion.
My favorit... | {
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Why doesn't a parallel circuit violate conservation of energy? Let's imagine a hypothetical circuit where there are a large number of wires placed in parallel to each other, hooked up to a simple power source.
We know that voltage at each wire would be equal $V_{total}=V_1=V_2=...=V_n$ where $n$ approaches a large numb... | It sounds like you'd have a circuit like this:
+----[ voltage source ]-----+
| |
+----[ resistor/wire ]------+
| |
+----[ resistor/wire ]------+
| ... |
From the electrical engineering 101 standpoint, adding more wires just decreases the ... | {
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Does the height a person jumps from onto a rod, affect the rotational height of a rod? I was explained in a lecture that if lets say, I jumped from height h and grabbed onto a vine, I would reach y height at the tip of the swing. But if I were to jump from 2h, I would still reach the same height (y) when swinging. This... | It might depend on the total length of the vine. Let's say the vine only has length $y$ and you swing all the way to the top when you jump from height $h$. Then, when you start with more energy because you jump from height $2h$, there's no higher you can go when you're still holding on to the vine, so you'll also make ... | {
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Can gravitational lenses change over human time scales? Gravitational lensing is caused by the chance alignment of the observer, the lens, and the source. Obviously these are not permanent events as the earth will move in and out of a focal point as the three objects move relative to each other.
My question is: over wh... | In general no. Typical gravitational lenses are clusters of galaxies. Distant clusters move at high speeds because of the expansion of the universe. But their peculiar velocities (deviation from a pure Hubble flow) are typically hundred of km/sec, perhaps $10^{-3}$ c. In $100$ years, they might move $0.1$ light year.
U... | {
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Can current flow in a simple circuit if I enclose the battery in a faraday cage? So suppose I have a regular circuit with a battery connected to a resistor and a lightbulb.
Suppose now somehow the battery is inside a metal box (faraday cage) but the rest of the circuit is outside of it so the wire is maybe poked throug... | Yes. From the Maxwell equation: $$\nabla \times \mathbf B = \mu_0 \mathbf I$$ we can know the directions of the $\mathbf B$ vector field using the right hand rule. Inside the battery, the E-field is from + to - ($\mathbf E = - \nabla V $). In the external resistance it has the same direction of the current.
Using the r... | {
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Does anyone know of an adjustable focusing mirror? Does anyone know of an adjustable focus mirror? Allowing short sight and long sighted people to see clearly in a mirror with no specs on. Is it even possible?
| The only adjustable optical component I know of is the lens in your eye. It changes focal length by being flexible. Muscles around the edge of the lens stretch it and change its shape.
As far as I know, all other lenses and mirrors are rigid. Their focal length is fixed.
Camera achieve a variable focal length in one of... | {
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Perspective on the renormalization group From reading the renormalization group description from high energy theory texts like peskin & schroeder, one may be tempted to think it has to do with regulating infinities.
However, my impression of the renormalization group once you rotate to euclidean time is that it is a ma... | The high-energy physics point of view of the RG ("putting infinities under the rug") is now quite dated, but unfortunately is usually still the first version of RG that one enconters.
A more modern implementation a la Wilson (only 50 years old now...) can indeed be interpreted as a transformation of probability weights... | {
"language": "en",
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Why does a body accelerate when there is a force applied to it? Why does a body accelerate or changes velocity when a force is applied on it?
How force acts upon things to make them accelerate?
| As others have pointed out, $F=ma$ is a definition of force (and mass for that matter). The reason we invented the concept of force, as defined by this equation, is because it makes things very simple and elegant. We want to understand how things move. We note that objects usually move we constant velocity. The special... | {
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Is there any *global* timelike Killing vector in Schwarzschild geometry? I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as:
$$
ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}^{2}$$
one can find a Killing vector $\xi=\par... | The are only four Killing vectors of Schwarzschild. They are $\partial_t$ and the three rotational Killing vectors. No linear combination of these is globally timelike within the horizon, so there is no global timelike Killing vector.
I suppose whether or not Schwarzschild is static depends on one's definiton of "stati... | {
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Does capacitance between two point charges lead to a paradox? Is it possible to have a capacitance in a system of two point charges? Since there is a potential energy between them and they both have charges then we can divide the charge by the potential and get capacitance.
However, capacitance is supposed to depend on... |
How does one resolve this paradox?
As a general prelude to this answer, I would like to mention that it is well known that classical point charges lead to some unresolvable paradoxes in classical EM. Personally, I do not consider this an indication of an inconsistency in classical EM, but an indication that classical... | {
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Is electrostatic charge on floor connected with slippage? I have some foam puzzle mats for sports in my flat. I noticed that every time I remove them after some days, the floor underneath where the mats were is very slippery. How is that? This is valid for the wooden and also the stone part of my floor.
My guess is tha... | Electrostatic charge buildup is unlikely to be the cause of the slipperiness. Even if the floor did have a static charge, I think it would actually increase friction by a tiny amount, since it should (very slightly) attract your feet to the floor. This the same as if you charge a balloon by rubbing, it will stick to a ... | {
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Work done in sliding a block across a table, as seen in different inertial frames Suppose, I'm pushing a block across a smooth table.
The length of the table is $d$, and the force that I applied is $F$.
According to an observer at rest, standing next to the table, the work done is $W=F.d$. Since there is no other force... | Trula is right and here are the details.
Relative to the observer moving at $u$, the work done by the force is
$$W=F(d+ut)=F(d+u\times\frac{2d}{v}) = Fd(1+\frac{2u}{v})\tag1$$
since the time for the mass to cover the distance $d$ is $\frac{d}{v/2} = \frac{2d}{v}$ from the average speed of the mass.
The apparent gain in... | {
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If you were invisible, would you also be cold? If you were invisible, would you also be cold? (Since light passes through you, so should thermal radiation.)
Additionally, I'd like to know if you were wearing invisible clothes, would they keep you warm? In my understanding, the heat radiation from the body would pass th... |
if you were wearing invisible clothes, would they keep you warm? In my understanding, the heat radiation from the body would pass through the cloth.
Clothes don't just block the radiated heat, they also stop conduction and convection with the ambient air. I haven't done the calculations but I suspect invisible clothe... | {
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Physical reasons for why systems are chaotic? Are there any reasons why a system would exhibit chaotic behavior? Or is this something only found through numerical modelling or experimental testing?
For example, the simple forced, damped pendulum or the duffing oscillator. Were these experimented on and it was found tha... | You model the system with differential equations and evaluate the differential equations (without necessarily needing to use computer simulation or experimentation, although both, especially simulation, are powerful tools). By so doing you predict under what conditions the system will exhibit chaotic behavior and what ... | {
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Can I conclude that acceleration happens a bit later after force is felt? We define forces like electric force, magnetic force and gravitational force etc, to be caused by field lines such as electric field, magnetic field and gravitation field respectively. Since these fields take time to reach the object on which the... | mathematically acceleration exists at time = zero, before there is any displacement or velocity since both involve a time integral.
However, because material objects are not infinitely stiff, forces between objects being pressed into contact build according to Hooke's law for elastic solids which means that accelerati... | {
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Spacetime effects on human scale objects? For a human standing upright on the earth, gravity would have a different value at the feet than at the head, and gravity influences the flow of time. Does the difference in the flow of time cause any effects?
I was toying with the idea that gravitational acceleration is just n... | That can be thought the other way around. Suppose a spaceship in the outer space with an acceleration $g$. The crew would feel 'gravity' normally as in the Earth.
But according to relativity, for the ship keeps the same distance between parts, (as it should be to keep its integrity), the 'bottom' portions must have a b... | {
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What does GR get right that QFT gets wrong, and vice versa? I wondering what precisely it was, in terms of predictions of observations, that General Relativity gets right, that QFT cannot explain. And what QFT gets right, that GR cannot explain.
I'm assuming GR cannot predict quantum effects, like wave-particle duality... | GR is the theory meant to explain the forces meant on a macroscopic scale far larger than even newtonian mechanics. Thus it only explain macroscopic objects, taken from a past answer it is not a particle physics model and cannot explain microscopic particles in the same way QM or QFT would do.
| {
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Clarification on the displacement in the definition of Work I'd like to ask a question about work. The definition of work gives us a way to calculate the work done by a force along a path but in practice it's not always clear what path to take in consideration. Moreover, this fact that work is defined along a path is n... | The effect of the rolling friction is to decrease the net force: $F_{net} = mgsin(\theta) - F_{fric}$. $$F_{net} = ma \implies mgsin(\theta) - F_{fric} = m\frac{dv}{dt} $$
When there is no slip, the friction force can be expressed in terms of the momentum of inertia and angular acceleration $$F_{fric} R = I\frac{d\omeg... | {
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Where is quantum probability in macroscopic world? How can macroscopic objects in real world have always-true cause-effect relationships when underlying quantum world is probabilistic? How does it not ever produce results different than what is predicted by Newtonian physics, except for borderline cases?
| Statistical mechanics is a field that gives some good perspective to this. It's quite common that the math works out where you have an equation to describe your system, and there is a variable $N$ in your equation for the number of particles. If $N$ is a small value, the equation and your system still look very quantum... | {
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Is there a notion of a "Majorana boson"? In a similar manner to how we can define Majorana fermionic operators $\gamma_j$ via
$$
c_j \propto \gamma_{2j+1} + i \gamma_{2j}^\dagger,
$$
where the $c$'s are fermionic creation/annahilation operators. These operators are super useful when dealing with fermionic systems. Im w... | The correspondingly defined objects for bosons are the position operator $x=(a+a^\dagger)/2$ and the momentum operator $p=(a-a^\dagger)/2i$, respectively.
| {
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Does light have mass or not? We know light is made of photons and so it should not have mass, but light is a form of energy (light has energy) and has velocity ($c$), so according to $E=mc^2$, light should have mass... So what is correct?
| When the value of mass is given as mc^2=hf, or m=hf/c^2, this is the equivalent newtonian mass, which appears in momentum for example.
Under Special relativity, it has no mass.
| {
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Why does mass bend the temporal dimension more than the spatial dimensions of spacetime? From my (limited) understanding of general relativity, most of what we experience as gravity is a result of the distortion of the temporal dimension, and not the spatial dimensions. Therefore, most of the spacetime curvature caused... |
Why aren't all four dimensions distorted equally
Although spacetime is often used term one should clearly understand that space and time aren't interchangeable one into another; similarly when they talk about curvature of space-time it's by definition curvature of space relatively to time.
Why aren't all four dimens... | {
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At what speed would a wind affect a bullet? Firing a gun loaded with the fastest bullet (.220 Swift 1,422m/s or any bullet that is super fast and excellent aero dynamics) in a close range (2cm) from the tip of an air blower. What would be the speed of the air coming out of the air blower to be able to deflect the bull... | For the bullet traveling directly at the air blower, to stop the bullet within $2cm$ needs, from the equations of motion a deceleration of $5\times10^{7}m/s^{2}$
Air resistance is $$F=\frac{1}{2}\rho ACv^2$$ see for example this website
For air $\rho = 1.2$, $C=0.2$ (estimate) and $A=\pi r^2$ with $r=2.8\times 10^{-3}m... | {
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Temperature of 1kg of matter when squeezed to its event horizon Let’s say I have 1kg of matter at room temperature (300K), held in a spherical configuration. I symmetrically squeeze this until it forms a black hole. What formula (formulae) would I use to (or how can I) calculate the new temperature of the 1kg of matter... | When the air in a room is at $300 \mathrm{K}$, objects placed in that room only acquire a temperature of $300 \mathrm{K}$ as well if they can come to equilibrium with it. This will not be the case for a black hole. The purely classical prediction is that all of the air molecules will eventually fall into the black hole... | {
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Is there a name for the type of boundary condition where the initial boundary values are known but are not held constant over time? I'm exploring the heat equation to model a particular 1D scenario, and I understood the Dirichlet and Neumann boundary conditions, but neither are sufficient for my scenario. Assuming a ro... | If there are boundary conditions
$$
\phi_0(t) \equiv U(0,t),\\
\phi_1(t) \equiv U(L,t),
$$
and the initial condition
$$
f(x) \equiv U(x,0),
$$
then you have what is called time-dependent boundary conditions, see e.g. these lecture notes. The problem statement in your question represents a special case, where only the v... | {
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How does intensity depend on slit-width regarding Fraunhofer diffraction? For a single slit, considered to be infinitely long, with size $b$ the intensity at any angle is given by:
\begin{equation}
I(\theta)=I(0) \bigg( \frac{\sin \beta}{\beta} \bigg)^2
\end{equation}
where,
\begin{align}
\beta=(\frac{\pi b}{\lamb... | If we double the slit size it is assumed I(0) would double, the intent of the formula is to show the variation with angle that describes the observed pattern.
The formula dose not care if one person uses a 1 watt laser and the next a 2 watt laser or if the person exposes the image for 1 second while the next exposes fo... | {
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How come the number of wandering electrons is same as the number of the positive ions? My book mentions the following:
Cause of resistance : When an ion of a metal is formed , its atoms lose electrons from its outer orbit . A metal ( or conductor ) has a large number of wandering electrons and an equal number of fixed... | Strictly speaking, it should be charge of ions, rather than number of ions. However, the ionization energy of an atom increases the greater the charge of the atom. For instance, the first ionization energy of Al is $577.5 \text{kJ mol}^{-1}$, while the second ionization energy is $1816.7$, more than three times as much... | {
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Variations in Refractive Index of Materials It's quite a common fact that different types of glass have different refractive indices. Most sites I've found attribute these differences to variations in the 'density' of the glass, which is not very satisfying of an answer.
My questions:
*
*What is the underlying physic... | Heavy glasses are mainly heavy because the use elements such as lead with many nuclei. As a result, these materials also have more electrons per atom, especially in the higher (more loosely bound) orbitals.
The looser bound the electrons, the more they will react to the electric field wave. How exactly this increases t... | {
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Is the sensation of apparent acceleration within the frame or visible force source enough to know if that frame is non-inertial? In Renato Brito's book Fundamentals of Mechanics, a property of the non-inertial frame is defined as follows:
Non-inertial referential is any one that presents acceleration in relation to an... | Indeed you are correct, it is not necessary to refer to a second frame in order to determine if the first is inertial. You can simply use accelerometers. If the acceleration relative to the reference frame is not equal to the acceleration measured by the accelerometer (for all accelerometers) then the frame is non-iner... | {
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Rotation of a freely falling body Suppose a straight rod with one end denser than the other is dropped from a height at an angle. Will the rod hit the ground at the same angle or will air resistance cause it to straighten and hit the ground with the denser end? What will happen if the same thing is repeated in vacuum?
| The denser end has less bouyancy and will start tilting downwards eventually in a precessing motion. when damped it will point straight down.
In a vacuum, the entire rod will have no bouyancy, so it will drop straight down without experiencing any torque.
| {
"language": "en",
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How can supercapacitors not implode? How can supercapacitors store $5\,\mathrm{coloumbs}$ and not implode due to the enormous force between the plates ($10^{15}\,\mathrm{N}$ if the plates are $1\,\mathrm{cm}$ apart)?
| This is a good question. It comes down to two factors: The 'plates' have dielectric material separating them, and the effective size of the plates is large, relatively speaking.
The dielectric material has positive and negative charges that align themselves with the electric field of the electrodes. Fig 2 in this link ... | {
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Why in the first Friedmann equation quantity $ρ$ is directly proportional to Hubble's constant despite the fact that gravity counteracts expansion? Here is the first Friedmann equation:
$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}$$
We know that matter and en... | You ignored the $k$ term, but it's crucial here. $k$ is the curvature not of spacetime but of constant-$t$ spatial slices, so it depends not only on spacetime curvature (represented by $ρ$ and $Λ$) but also on the extrinsic curvature of the spatial slice in the spacetime (represented by $\dot a/a$). You can think of th... | {
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How mass of different components in a solution get affected in centrifugation process? Centrifugation technique is used in laboratory or even at home to separate colloidal solution with variable densities constituents.Example butter from milk
So How does Centrifugation help in separating different densities components ... | It’s the density, not the mass, that matters.
In the rotating frame of reference, the “apparent gravity” that appears due to the (fictitious) centrifugal force will be many times higher than g.
Suspended particles are subject to gravity, buoyancy, and the individual impacts of other molecules in the liquid. For small p... | {
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Will a planet rotate if it is the only being in the universe? As a senior student , I have been wondering whatever the word inertia mean . Is inertia lying in the interaction between all the objects , or is it the nature of a space even without anything put into it ? In our life it seems like the latter , since whereve... | @ummg's comment that you might want to read about Mach's Principle, https://en.wikipedia.org/wiki/Mach%27s_principle, is the right answer to your question.
Along the same lines, you might think about linear motion. Consider a universe with just two rigid bodies, say $m_1$ and $m_2$, and a compressed spring (of negligib... | {
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Is energy really Conserved in rolling motion? Energy is conserved in pure rolling motion. Then why does the ball stops its motion after some time. I think it's not the case of air drag only. Does all work gets Transferred to surrounding in the form of heat?
| In an ideal case, once rolling starts, friction stops acting as there is no relative motion at the point of contact and the ball keeps on rolling.
In a real life scenario, there is some deformation at the point of contact, and the normal shifts slightly and no longer passes through the centre. On performing torque anal... | {
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What mechanism will force mechanical watch to tick slower when go fast, due to relativistic effects? To make mechanical watch tick slower, watch tick rate must be changed, oscialtion of balance wheel must be SOMEHOW changed, how would speed change oscialtion of balance wheel, due to relativistic effects?
I dont unders... | The tricky thing is: it is not the watch that ticks differently, it is time itself.
Let us consider the situation you proposed on the comments: you are on a fast rocket and there is a clock on Earth. What do you see? You see your watch ticking just as usual, while the clock on Earth (which you are looking at e.g. with ... | {
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"The resultant of two forces of equal size, that form an angle, is lowered by 20% when one of the forces is turned in the opposite direction."
"The resultant of two forces of equal size, that form an angle, is lowered by 20% when one of the forces is turned in the opposite direction."
Does anyone know how one would g... | In first case the two forces are defined as:
$$\vec{F}_1 = F \hat{\imath} \quad \text{and} \quad \vec{F}_2 = F \cos\alpha \hat{\imath} + F \sin\alpha \hat{\jmath}$$
and their resultant force is:
$$\vec{F}_R = F (\cos\alpha + 1) \hat{\imath} + F \sin\alpha \hat{\jmath}$$
When you take force $F_1$ to point in the opposit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/687447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How did Ernest Sternglass’ phenomenologically incorrect model of the neutral pion predict its mass and lifetime so accurately? In 1961, Ernest Sternglass published a paper where, using what seems to be to be a combination of relativistic kinematics and Bohr’s old quantisation procedure, he looked at the energy levels o... | It is a coincidence. The claim in the article can be summarized as
$$
\frac{\alpha}{2}\frac{m_\pi}{m_e}=0.96
$$
which is close to $1$. This relation doesn't have a deep origin, it is just a coincidence of numerical factors. Particle physics has dozens of numerical parameters, and thousands of possible ways to combine t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/687820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Why do we need the concept of Gravitational and Electric Potential? I understand that we need potential energy for the concept of energy conservation. However, why would we come up with a definition like 'energy required per unit mass/charge to bring the mass/charge from point A to B. The part says 'per unit mass/charg... |
However, why would we come up with a definition like 'energy required
per unit mass/charge to bring the mass/charge from point A to B.
First of all, the concept of gravitational or electrical potential is that it is an absolute quantity requiring the assignment of some point a value of zero potential. It is has no re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/687983",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How to draw the phase plane of this equation? Using various computational tools, it's possible to draw a phase plane from two first-order ODEs or a single second-order ODE. However, when there is a parameter in the equation and we don't know the value of the parameter, is there any way to draw the phase plane and see t... | Comment masquerading as an answer, to avoid macaronic sequences.
Looks like T is dross, to be eliminated as =−(+), for
some constant c.
You may then divide your two ODEs with each other, and get /
as a function of x and y, much less pretty than Lotka-Volterra, but straightforward to plot numerically for selected values... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Dirac-delta-distribution charge densitity Are the charge distributions $$\rho(\vec{r})=\frac{Q}{2\pi R^2}\delta(r-R)\delta(\vartheta-\pi/2)$$ and $$\rho(\vec{r})=\frac{Q}{2\pi r^2\sin(\vartheta)}\delta(r-R)\delta(\vartheta-\pi/2)$$ of a charged circle the same? I would say yes because integrating over them gives the sa... | Yes, since $\delta(r-R)\delta(\vartheta-\pi/2)$ is zero everywhere except $\left(r,\vartheta\right)=\left(R,\theta/2\right)$, we can replace
$$
\frac{Q}{2\pi r^2\sin(\vartheta)}
$$
with its value at $\left(r,\vartheta\right)=\left(R,\theta/2\right)$:
$$
\frac{Q}{2\pi R^2}
$$
If you have a copy of Griffiths E&M he discu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/688479",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Would light bend the other way, if I use antimatter instead? Imagine the following setup: an antimatter straw, an antimatter glass filled with antimatter water and we have antimatter atmosphere just in case. My question is: does Snell's law still apply here as though they are regular matter, if I were to observe the st... | We think antimatter refracts light like “ordinary” matter, but we don't know for certain. As the Wikipedia article on antimatter says:
There are compelling theoretical reasons to believe that, aside from the fact that antiparticles have different signs on all charges (such as electric and baryon charges), matter and a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/688618",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric field of an electron in motion in a wire How do I correctly model the electric field of an electron in motion in a wire? I could treat the electron as a point charge moving through the wire. If I use the Liénard Wichert equations, they will predict radiation if the wire turns, since the electron is being accel... | The electrons in a conductor occupy quantum momentum and energy states in a band structure. I think that it is not possible to model them as classical moving charges as for Liénard Wichert equations.
For example, even without any external E-field applied, each electron has a momentum, so they are all moving. As the con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/688744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How would Newton explain mirages? Suppose we think of light as photon packets with tiny momentum, then with this picture in mind, go and see the refraction of light in mirages:
We see that the packets of light photons must be continuously under a nature of force since it must change natural path direction. How would N... | This is not how photons are viewed. They are not moving particles in the Newtonian sense, and this has to do with the wave-particle duality of quantum theory. Light is absorbed by matter like a particle but propagates like a wave. Photons are the quanta of energy passed to matter. So refraction is an example of the wav... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Particle density vs. Probability Density in Quantum Mechanics I am currently reading trough "Bose-Einstein Condensation and Superfluidity" by Pitaevksii and Stringari and noticed some inconsistencies in my reasoning.
In Chapter 5 (Non-uniform Bose gases at zero temperature) the authors introduce the condensate wave fun... |
How can something that describes a probability density be a quantity
that represents a particle density?
That is open for extensive qm interpretations, and your question is related to "what is the physical property of a qm object before its measured".
I know that in quantum chemistry, that a working assumption is tha... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity? Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and... | The principle itself is the connection and not the other way around.
The principle of relativity is the idea that the state of constant speed of a reference frame must be impossible to detect from within, i.e, if you don’t witness acceleration by yourself, then you’re doomed to be ignorant about who was accelerated amo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/689192",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
"answer_count": 9,
"answer_id": 8
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Uncertainty notation: I am unsure of how the parentheses notation works If I have a value of $5.868709...×10^{−7}$, and an uncertainty of $7.88431...×10^{−12}$, is it correct to write this as $5.86871(8)×10^{−7}$ or $5.8687(8)×10^{−7}$?
A problem I have with the first is the values used to calculate the $5.868709...×10... | Your uncertainty of $7.88431 \times 10^{-12}$ can be written as $0.0000788431 \times 10^{-7}$. But the value itself, $5.868709 \times 10^{-7}$ is known only to 6 decimal places, so the uncertainty cannot sensibly be given to more than 6 decimal places when expressed with the same $10^{-7}$ multiplier. So we could give ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/689790",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
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How does potential energy increase with no work? If you're dragging an object up a hill at a constant velocity, work is technically 0 (as acceleration is 0), but potential energy constantly increases. How would you represent this situation mathematically, and how does the potential energy increase despite a lack of wor... | If the speed stays constant, the net work is zero, but the work done by the individual forces may not be. In your case,
\begin{align}
W_{\text{net}} = W_g + W_{\text{drag}} = 0
\end{align}
So both you and gravity are doing work, it's just that whatever work you do by dragging, gravity does minus that: $W_g = - W_{\text... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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General Method for Calculating Excluded Volume In section 5.3 of Kardar's Statistical Physics of Particles, the van der Waals equation is given as:
$[P+\frac{u_0 \Omega}{2}(\frac{N}{V})^2][V-\frac{N\Omega}{2}]=Nk_BT$
The van der Waals parameters are identified as $a = \frac{u_0 \Omega}{2}$ and $b=\frac{\Omega}{2}$. Her... | *
*He means the spatial dimension.
In $d=1$ if you consider a 3-particle hard-ball cluster (3 hard-ball particles each overlapping with the remaining 2) it can only happen by taking two overlapping particles and slapping the third one in the middle. The 3-particle overlap will be the same as the overlap between two in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/690217",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Aurora Borealis As we know that during a solar flare, a large number of electrons and protons are ejected from the sun.
Some of them get trapped in the earth’s magnetic field and move in helical paths along the
field lines. The field lines come closer to each other near the magnetic poles.
Hence the density of charges ... |
So is it possible to (or a device already exists of which I am unaware) concentrate the magnetic fields of the earth say near your house for enjoying the view?
In general, no. In principle, yes. The magnetic moment of the Earth's magnetic field is huge. While we can generate large magnetic fields for short periods... | {
"language": "en",
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Measurement on mixed states I have a conflict between my lecture notes on quantum mechanics, where it is stated that the probability of measuring an eigenvalue $a_i$ on a mixed state with desnsity matrix $\rho$ is
$$
\operatorname{Tr}(P_i \rho P_i)\ ,
$$
where $P_i$ is the projector for the subspace corresponding to $a... | The latter is correct.
By the cyclic property of the trace.
$$Tr(\rho P_i) = Tr(P_i \Sigma_i | \psi_i \rangle \langle \psi_i|) $$
$$= Tr(\Sigma_i \langle \psi_i | P_i | \psi_i \rangle) $$
This equals the expectation value of operator $\langle P_i \rangle$ (the probability of measurement).
The Wikipedia article has a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/690484",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Electric flux due to a point charge through an infinite plane using Gauss divergence theorem I'm learning the basics of vector calculus when I came across this problem:
A point charge +q is located at the origin of the coordinate system. Calculate the flux of the electric field due to this charge through the plane $z ... | The error in your original derivation is that
$$
\frac{\partial (\sin \theta)}{\partial r} = 0,
$$
and so $\vec{\nabla} \cdot \vec{E} = 0$ as well. (Except when $r = 0$, but that's another story.) A partial derivative implies that the other two coordinates ($\theta$ and $\phi$) are held constant. By looking at the d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/690654",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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By how much protons dipole moment inside a nucleus attenuate the culomb force between them? By how much protons dipole moment inside a nucleus attenuate the culomb force between them? As up quarks repel more than down quarks the protons should be oriented with the positive side looking away from the centre of the nucl... | The electric polarizabilities for the proton and neutron, catalogued for example by the Particle Data Group, are about a thousand times smaller than you would expect from doing dimensional analysis. In a hand-waving way, this is because strong interaction makes the "medium" inside of a proton "stiffer" than the "medium... | {
"language": "en",
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Relationship between angular and translational velocity on inclined surface I have been researching about rolling motion and I was calculating a way to predict the translational velocity of the object at the bottom of the incline. I know that the kinetic energy of a cylinder undergoing rolling motion is given as
$$E_k ... | Linear tangential speed $v_t$ of a particle at radius $r$ from the axis of rotation is
$$v_\text{tan} = r \omega$$
The fact that the cylinder is only partially filled does not affect the above equation, it affects only moment of inertia of the body. Please note that many equations for rotational motion assume that body... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What causes time warping in the space-time? I was reading through some blogs/articles and watching youtube videos that explained to non-physicists such as myself - how time warping or a gradient in time flow around any object can create gravity. I am able to understand the mechanics (minus the math, I'm not a physicist... | Marco's answer is an excellent explanation of time dilation as different path lengths, and I do hope you've read it. But just to supplement it: the reason that paths through time can be "curved" is because matter (and energy, and everything else that exists) bends both space and time.
The common pop-sci picture of a bo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 7,
"answer_id": 3
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Why "in" and "out" states $\Psi^\mp_\alpha$ are eigenstates of total Hamiltonian $H$? "in" and "out" states, $\Psi^\pm$, with reference to Weinberg Vol. 1 pages 109 and 110 could be defined by
$$\Psi_\alpha^\pm = \Omega(\mp \infty)\Phi_\alpha\tag{3.1.13}$$
where
$$\Omega(\tau) = \exp(+iH\tau)\exp(-iH_0\tau).\tag{3.1.14... | This is an assumption of the Hamiltonian. Weinberg states
...suppose we can divide the time-translation generator $H$ into two terms, a free-particle Hamiltonian $H_0$ and an interaction $V$,
$$H=H_0+V$$
in such a way that $H_0$ has eigenstates $\Phi_{\alpha}$ that have the same appearance as the eigenstates $\Psi^+_{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Lorentz transformation of annihilation operator In Srednicki's Quantum Field Theory, chapter 4, the author claims that the Lorentz transformation for given a scalar field $\varphi(x)$,
\begin{align}
U(\Lambda)^{-1} \varphi(x) U(\Lambda) = \varphi(\Lambda^{-1}x),
\end{align}
"implies that the particle creation and annih... | What Srednicki is trying to say with the first equation you have written (well, maybe the with the second too) is that both the field $\varphi(x)$ and the creation/annihilation operators do not have a vector or a tensor nature. Rather, they are scalar quantities and as scalar quantities they should transform under Lore... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Analysing a system of pulleys?
I'm quite unsure on how to solve these questions.
For part (b), my approach was that the tension in the lower cable would have to be greater than or equal to $2m$ for both the masses to be lifted.
Using Newton's second law on the lower pulley, and assuming the pulleys to be massless, the... | As long as mass B is partially supported by the surface, then the acceleration of mass A is twice that of M. If the surface is not a factor, then the acceleration of M puts A and B into an accelerated frame, in which has a relative acceleration of a'.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is my bluetooth signal able to exit my microwave? I was shopping for a bluetooth meat thermometer. Since this device would also be used in my combo (conventional and microwave) oven, which is shielded for microwaves, I expected the device to not work.
So, I decided to make the following test before ordering:
*
*p... | Just some rough numbers: say the oven produces ~1kW=60dBm RF power of which only 1mW=0dBm is allowed to leak out then the window's leakage is about -60dB. If your Bluetooth is radiating about 1mW =0dBm and your receiver has about -90dBm operating threshold meaning it will receive 0-60=-60dBm still having some 30dB (1,0... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691958",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Question about the Wave equation I have a question. I was looking for the Wave equation (first Eq. of this wikipedia page).
I saw for the first time a version of this equation during an Acoustic course, where we obtained it for the sound wave combining the Euler equation, the Continuity equation, the general gas equati... | The wave equation is a "general" differential equation that describes waves in several contexts.
It is given by
$$\partial_t ^2 u = v^2 \Delta u$$
and has has general solution (in 1D)
$$u(x, t) = f(x-vt)+g(x+vt)$$
i.e. the sum of a function "moving" to the left with velocity $v$ and one moving to the right. That is, w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What is causing this sign difference in the centrifugal term between Lagrangian and Hamiltonian formalism? Consider a central force problem of the form with the Lagrangian
$$
L(r, \theta, \dot{r}, \dot{\theta}) = \frac{1}{2} m \left( \dot{r}^2 + r^2 \dot{\theta}^2 \right) - V(r),
$$
where $r = |\vec{x}|$. Since $\theta... | You can't insert a the solution of the equation of motion back into the Lagragian. You must eliminate the conserved quantity bu using a Routhian. See the section on cyclic coordinates and on central forces in spherical coordinates.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692349",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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On an infinite plane, with gravity the same of that of Earth, how far could light at an arbitrary angle travel until bending to hit the plane? Now, I'm a complete idiot, so bear with me.
I've recently come across the idea that standing an infinite flat Earth would in theory appear the same as standing inside a hollow e... | For a proper calculation you will have to consider a spacetime metric that produces the same gravitational field as in your setup, and then find the null geodesics (paths of light) in this metric. I think this shouldn't be very difficult to calculate.
However we can probably also get an order-of-magnitude estimate just... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What Lorentz symmetries do electric and magnetic fields break? When we turn on an external (non-dynamical) electric or magnetic field in (3+1)-dimensional Minkowski space we break rotational invariance because they pick out a special direction in spacetime. Does this also break boost invariance?
What about in (2+1)-dim... | Under boosts,the fields transform into each other in a prescribed way. If we define the direction of the boost to be the $x$-direction, then we have
\begin{align*}
E'_x &= E_x & E'_y &= \gamma(E_y - \beta B_z) & E'_z = \gamma(E_z + \beta B_y) \\
B'_x &= B_x & B'_y &= \gamma(B_y + \beta E_z) & B'_z = \gamma(B_z + \beta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692681",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What does Griffith mean by adding a prime on integration variables? In the book "Introduction to Electrodynamics" by Griffith, the author mentions electric potential as a point function writes the equation for electric potential as
Then in a side note he write "To avoid any possible ambiguity, I should perhaps put a p... | When talking about integrals, the variable of integration is "dummy", in the following sense. Suppose $f:\Bbb{R}\to\Bbb{R}$ is a function, then for any $x\in\Bbb{R}$,
\begin{align}
\int_0^xf(t)\,dt=\int_0^xf(s)\,ds=\int_0^xf(\xi)\,d\xi=\int_0^xf(\ddot{\smile})\,d \ddot{\smile}=\int_0^xf(@)\,d@=\int_0^xf(\sharp)\,d\shar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692837",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Speed of heat through an object According to the Heat equation (the PDE), heat can travel infinitely fast, which doesn't seem right to me. So I was wondering, at what speed does heat actually propogate through an object?
For example, if I have a really long iron rod at a constant temperature (say 0 Celsius), and one en... | It seems to me that what you are looking for is the thermal diffusivity, as this is the coefficient that balances the rate and area of the temperature change:
$$\partial_tT=\alpha\nabla^2T\implies\alpha=\frac{\partial_tT}{\nabla^2T}
$$
and has units of area per time ($\partial_t$ has units of inverse time, $\nabla^2$ h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693112",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 4
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Can we derive Boyle's law out of nothing? My textbook states Boyle's law without a proof. I saw Feynman's proof of it but found it to be too handwavy and at the same time it uses Boltzmann's equipartition theorem from statistical mechanics which is too difficult for me now.
So to state roughly what Boyle's law is, it s... | The pressure exerted by a gas on the walls of its container is proportional to the frequency with which the molecules strike the walls. The larger the container, the more time on average a molecule spends between collisions with the container walls and thus the lower the pressure.
Consider a cylindrical container. If t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 5,
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Feynman diagrams for neutral pion decay into electron-positron pair The main Feynman diagram I've seen corresponding to this decay is the following:
What I don't understand is why is it not possible for the up-antiup quarks that form the pion to annihilate into a single virtual photon, and then have that virtual photo... | Charge conjugation, C, contrasts even and odd numbers of photons in states and amplitudes.
The $^0$ has C=+, but one photon has C=—, and hence two photons +.
By contrast, the $\rho^0$, with C=—, can and does couple to one photon, the heart of the Vector Dominance Model.
Note the Z has no well-defined C, as the weak int... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693363",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Electric field of a point very far from uniformly charged rectangle sheet I was wondering what is the Electric field at a point which is very far from a rectangular sheet and it is also above the center of the rectangle. So form a mathematical perspective you get Electric field due to a finite rectangular sheet of char... | $\arctan(\theta)\approx \theta-\frac{\theta^3}{3}$ near $\theta=0$ so
\begin{align}
\frac{\sigma}{\pi\epsilon}\arctan\left(\frac{ab}{4r^2}\right)
\approx \frac{\sigma}{\pi\epsilon}\frac{ab}{4r^2}\tag{1}
\end{align}
and since $a\times b$ is the area, $\sigma\times a\times b=Q$, the charge
on your plate. At this level o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693777",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Is there a physically meaningful example of a spacetime scalar potential? From Misner, Thorne and Wheeler, page 115.
0-Form or Scalar, $f$
An example in the context of 3-space and Newtonian physics is temperature $T\left(x,y,z\right),$ and in the context of spacetime, a scalar potential, $\phi\left(t,x,y,z\right).$
I... | If you have a vector or tensor field, then you can get a scalar field by contraction.
Examples:
$J^\mu$ = 4-flux of some quantity. Scalar field: $\rho = \sqrt{J^\mu J_\mu}/c$. Interpretation: proper density.
$k^\mu$ = 4-wave vector; $x^\mu$ = 4-position. Scalar field: $\phi = k^\mu x_\mu$. Interpretation: phase of a pl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693884",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Can two waves be considered in phase if the phase angle is a multiple of 2$\pi$? Question is essentially what the title states. Wavefront is defined as the locus of points that are in phase. So I wanted to know if the locus would be the points of only a single circle or multiple circles whose points all have the same d... | I believe that the term wavefront is used to refer to the pulse that was produced by the source at the same time. So when we define wavefront we define it as a locus of points with same phase, where a phase difference of $2\pi$ is not considered in the locus.
All the points on the green circles are in phase but a singl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
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