Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Different frequencies working together How do the different waves of EM spectrum present in the environment not interfere with each other? If they do, how does everything work properly?
The radio waves of mobile phones and wi-fi work together. Why don't they collide with each other, since they are physically present?
| They do interfere with each other, but the outcome is not a problem so long as the device that's receiving or using the signals is tuned to pick out the relevant frequency.
For instance, resonant circuits will only be driven properly in a narrow range of frequencies around the resonant frequency. A mixture of waves wit... | {
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Is there a commonly used unit of measure (other than temperature units) that is not absolute? I live in a country where we use Degree-Celsius(°C) to measure the temperature.
Sometimes from one day to the other, the temperature rises from 10°C to 20°C and I hear people say, "Wow! Today is twice as hot as yesterday!".
I ... | Gravitational potential energy is another physical quantity that is measured relative to an arbitrary starting point.
In many derivations, the zero point for the potential energy of a mass is taken to be a point an infinite distance away, and all the potential energy is negative.
A hydro electric engineer would take th... | {
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How can the thrust due to radiation pressure be amplified in photonic laser thruster? The thrust is amplified due to repeated bouncing of photons between two mirrors as shown in the diagram in this: Why does repeated bouncing of photons produce amplified thrust when the answer in 'Mirror problem of radiation pressure'... | There is a difference between "multiple photons" and "repeated photons". If one photon keeps bouncing back and forth, it can carry a little bit of impulse from one mirror to the other on each round trip. When you have multiple photons, each of them can do this. So your "amplification" comest from either
*
*Waiting a... | {
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Current in a fluorescent tube that is not in a circuit In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van de Graaff (VDG) generator. Due to the VDG's E-field, this causes a large potential difference between both ends of the tube. He then sa... | When the VDG sphere is 'charged' to say $300kV$ or greater, the moisture in the air around it is able to conduct a very small $<100\mu A$ electric current, which is enough to dimly light the fluorescent tube.
| {
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How were the ratios of distances between planets and the Sun first calculated? I was reading some literature and I found that long before the actual distances between other planets and Earth or distance between Sun and Earth were known, physicists had calculated the ratios between these distances. Can anybody tell me t... | The relative distances of the earth, sun and moon were determined by Aristarchus. See my summary here. By measuring the size of the earth (as e.g. Eratosthenes did) these can be turned into absolute distances.
Once heliocentrism was introduced the planetary distances could be determined as follows:
Distance from Venus ... | {
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The interference pattern of a wave along a line Why the answer is B, but not C?
Is it true that the pattern cannot go beyond $A_0$ and $-A_0$ at the same instant?
| The integral of both initial waves must be ~0 (it is cancelled out) and adding those two together yields a 0 integral too. So the resulting wave-function must be symmetric. Also, energy conservation implies that the amplitude must be $\sqrt 2 A_0$.
So answer C seems to be correct.
| {
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What is dimension and how many types of dimensions are there in the universe? What is dimension and how many types of dimensions are there in the universe? I mean how many total dimensions are there? I have only heard about 2d and 3d. Other than these two, are there any other dimensions. If yes than please explain each... | 'What is meant by "dimension"?'
As the question is asked above, I think we are talking about the nature of reality. In our physical world, 3 dimensions are required to differentiate any and all points that any physical object can occupy.
If our universe was static that would be sufficient but the universe and its conte... | {
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Pressure in the grand canonical ensemble when momentum integration limits depends upon volume When one does not want to consider the thermodynamic limit, it is possible in some systems to consider a dependance of the volume on the integration limits of the momentum. For example:
$$\mathcal{Z} = \sum\limits_{N} \int d^{... | You are right, $pV= k_B T \ln \mathcal Z$ is only guaranteed in some systems (namely extensive ones). If you suspect your system is not extensive, for example if it has physics that depend on surface area and not just volume, then you can't use this expression and you have to use the partial derivative you named.
But c... | {
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What is antimatter? Can you give a visual example of what is antimatter?
With the re-opening of Large Haldron Collider scheduled in Mar 2015, I'm reading that they smash two particles together to try to re-create particles that might have been there are the beginning of the Big Bang, and this includes antimatter?
Is an... | Paul Dirac in the 1930's described a vacuum as not empty space but as an infinite sea of negative energy particles.
His famous 'Dirac Equation' has a negative energy solution for the electron, he interpreted this solution by saying that since Pauli's Exclusion Principle states that 'no two electrons (fermions with hal... | {
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Who is doing the normalization of wave function in the time evolution of wave function? In the Schrödinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations simultaneously. Why not? I know it does... | I think it's a very good question.
As a specific case for example for the $\psi$ of a particle, we say that $\int||\psi_t(x)|| = 1$, and what does it mean? it means that we have a particle. it means it can be found in a time in some space. and how do we say that?
I think it's just a logical reasoning and it's accordin... | {
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Why do things here on Earth fall down? I want to have an answer with that question above for my physics lesson. I really don't have an idea about it, so, I ask help from you guys and hope that someone can help me with it.
| In Newtonian mechanics:
Things fall due to the gravitational force of Earth. This force between 2 masses $M$ and $M'$ is given by: $$F = G\frac{M \cdot M'}{r^2}$$.
This force is a central conservative force due to mutual attraction.
The rise of General Relativity:
Albert Einstein,in 1915, looked at the gravity through... | {
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How do electromagnetic waves travel in a vacuum? This is perhaps a total newbie question, and I will try to formulate it the best I can, so here it goes. How does an electromagnetic wave travel through for example, the vacuum of space?
I usually see that waves are explained using analogies with water, pieces of rope, ... | Since, electro magnetic waves have electric and magnetic vector. Due to this EM waves show electric and magnetic field. An electric and magnetic field have no need a medium to show thier effect. Hence in the presence of electric and magnetic field vector which vibrate perpendeculer to each other and get pertervation E... | {
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Electromagnetic waves in vacuum If there is no source then also there is electromagnetic waves described by Maxwell equation. how if there is no source then existence of EM waves. What gives energy to this EM waves. Is it vacuum fluctuation or something else?
| The fact that you can solve Maxwell's equations in vacuo means that the vacuum can propagate electromagnetic waves. It cannot generate them, since as you point out there are no sources (charges and currents). The waves were generated somewhere else, where there was a current or a charge moving around, and you are just ... | {
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Are we comoving observers of space expansion? In cosmology:
A comoving observer is the only observer that will perceive the
universe, including the cosmic microwave background radiation, to be
isotropic. (Wikipedia)
According to this definition, is Earth considered as a comoving reference frame, or are we supposed to... | We have a small peculiar velocity with respect to the comoving frame, this can be seen as a dipole in the CMB data. (CMB gets doppler shifted)
This dipole (and the monopole) is usually subtracted before doing further analysis of the CMB. I think (but I am not sure about this) that measuring the CMB-dipole is the best a... | {
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Sign of the totally anti-symmetric Levi-Civita tensor $\varepsilon^{\mu_1 \ldots}$ when raising indices I am confused with the sign we get when we want to raise or lower all indices of the totally anti-symmetric tensor of any rank. Take the metric to be mostly plus ($-+\ldots+$). Then is it
$$\varepsilon^{ijk}=\varepsi... | To not confusing by these things you must know exactly what are the Levi-Civita symbols $\varepsilon$ and what are the Levi-Civita tensor $\epsilon$. Then you also need to know that the Hodge dual has no any confusion when they had defined with Levi-Civita tensor.
$$
\star H^{\mu \nu} = \frac{1}{2}\epsilon^{\mu \nu}{}... | {
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Are there new physics scenarios that predict low lying hadrons? There is a significant ongoing experimental effort to search for new hadrons with masses in the GeV range. This is used to find the spectra of QCD bound states, with a particular emphasis on finding exotic resonances such as the tetraquark. To my knowledge... | Some popular supersymmetric extensions of the Standard Model predict masses of the squarks (superpartners of the quarks) that could be detected with the LHC.
If you mean any mainstream model that predicts a different mass spectrum of the quarks than observed at LHC? I don't know of such a model and if there would be a... | {
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Defining Reference Directions for Voltage and Power (sign convention)
My professor decided to use the above reference directions when calculating power in circuits. He says that when power > 0, power is consumed. When p < 0, power is generated.
This definition is counter intuitive to what I would have assigned--I wou... | Consider a resistor. Label one terminal "+" and the other one "-".
When current flows in to the + terminal (like in your left-hand diagram), Ohm's law tells us that the voltage at the + terminal is higher than at the - terminal and the value is given by $V=IR$.
And we know that in this situation, electrical power is c... | {
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Do particles always flow from high to low pressure? In a recent question, it was stated that
particles in high pressure air always flow to lower pressure.
In a pipe with a constriction, fluid flows from from low to high pressure after the constriction. (From here.)
How are these concepts related?
| The statement "fluid flows from region of high pressure to region of low pressure" in the original question may be corrected as "velocity of fluid increases from region of high pressure to region of pressure and decreases from region of low pressure to region of high pressure." Comments solicited.
| {
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Closed system, gas change in time I'm trying to find out how to determine how a pressure of gas changes in time, but I can't find a way.
I have a system with constant volume $V$ (closed system, exchanges heat with environment through walls), the system is heated to temperature $T_0$ and then left to cool down on its ow... | I am not sure how much it will help, but normally temperature drops in proportion to the difference in temperature - and as you point out pressure is directly proportional to temperature - so the temperature will drop by exponential decay and the pressure will also drop in this way as well.
| {
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If wave speed is dependent on medium only, then how to reconcile $v\propto f$? I have read and learnt in many places that velocity of a wave depends only on the medium through which it travels. It is clear from this that the velocity of a wave doesn't depend on the frequency of the wave because both the sound of a roar... | The equation is correct, but you incorrectly stated that wavelength "depends" on frequency.
The two (wavelength/frequency) are both part of the same property of a medium. As the wavelength increases in a given medium, the frequency decreases. If the frequency increases, the wavelength will decrease inversely.
Wavelengt... | {
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Magnetic field between two concentric inductors Suppose we have two inductors with $n_1$ and $n_2$ turns, of radii $R_1$ and $R_2$ $(R_1 > R_2)$ respectively and length $l$. They are aligned concentrically and the smaller inductor is wholly inside the bigger one (i.e. the smaller one doesn't stick out). The currents fl... | A Note About A Certain Simplifiation
When we say that the field between these inductors is homogeneous, it's actually a simplification. These inductors have an effectively zero magnetic field outside of them because the field produced from one segment of wire effectively cancels out the field produced from a segment on... | {
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Is differential geometry used in solid state? I'm an undergraduate in physics interested in a career in solid state. While I know that any additional math is helpful--I am on time constraints, and can only take a few supplemental classes.
That said, is differential geometry used much in solid state physics? I'm aware o... | On the very theoretical side of solid state physics is the holographic AdS/CFT correspondence which links strongly coupled condensed matter systems to gravitational theories. Recent work has been done on describing things like phase transitions in this theory. For example models of superconductivity in the gravity dual... | {
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How quickly is motion transferred in a solid object? Just for example: assume an iron bar one foot in length. If you push on one end, the entire bar will move. This seems instantaneous. but actually, from my understanding, the atoms all push against each other in a very fast "wave" - making the entire bar move.
Now, sa... | This is actually a really interesting question, but the answer is simpler than you might think. The pressure wave propagates along the bar at the speed of sound in whatever material the bar is made of. This is because sound is nothing more than pressure waves, and so the speed of sound is by definition exactly what y... | {
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Would a rotating magnet emit photons? If so, what causes the torque that gradually slows the rotation? If a magnet is rotating around an axis perpendicular to the axis north-south axis of the magnet (which I assume to be cylindrically symmetric), in space (so no-gravity/freefall or friction), should it still slow down ... | If you move a magnet, you create an electrical field around the magnet perpendicular to its direction of motion. As the magnet accelerates, the electrical field evolves, and generates a magnetic field. I don't know the specifics, but I'm guessing that if you spin the magnet, this magnetic field will act counter to the ... | {
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How to determine angular frequency of this system? I am self studying on harmonic motion and springs. One of the problems is:
Two identical objects of mass m are placed at either end of a spring of spring constant k and the whole system is placed on a horizontal frictionless surface. At what angular frequency w does th... | The trick here is to realize that both masses are moving, and the point on the spring that is stationary is midway (in general, at the center of mass). Once you know which part of the spring is not moving you can fix it, and look at just one mass. You now have a shorter spring - length $\ell/2$ - and thus a higher freq... | {
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Is the shell theorem only an approximation? I've read the shell theorem during gravitation lectures, i.e. I know it states that the net gravitational field inside a 3D spherical shell or a uniform 2D ring is zero.
Now, assume a thin spherical shell. If I put a particle inside the shell, so that it was infinitesimally c... | If you put a particle very close to the border, the force from matter very close to it will be very strong, as you say. But that is only a small portion of the shell; all the rest is pulling the other way, towards the center. The shell theorem guarantees that these forces cancel exactly.
| {
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If an object falls - regarding air resistance - does the Potential or Kinetic energy get converted into thermal energy as it is falling? I read a paragraph on the transfer of potential energy to kinetic energy and heat from this website:
Even if air resistance slows down the ball, the potential energy is
the same (M... | The friction with the air indeed slows down the falling ball. The friction is minimal if the ball stays in place (i.e. there may be only some friction due to air currents.) But if the ball moves the friction is bigger because as the ball moves, it pushes away the air molecules to make room. The friction opposes the bal... | {
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Is there a physical interpretation of a tensor as a vector with additional qualities? What is a tensor? has been asked before, with the most highly up-voted answer defining a tensor of rank $k$ as a vector of a tensor of rank $k-1$.
But if a scalar is defined as a physical quantity with a magnitude, a vector as a physi... | I think a safer way, at base level, of thinking of a tensor, is to think of it as a function that takes in $n$ vectors, and spits out a number, and in each of it's arguments, satisfies:
$$T(a{\vec v} + b {\vec w}) = aT({\vec v})+ bT({\vec w})$$
where $a,b$ are numbers, and ${\vec v}, {\vec w}$ are vectors, and the othe... | {
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What position of the center of gravity can make the front wheels of the car lift off the ground? I have a question regarding the position of center of gravity required to just lift off the front wheel of a vehicle
Consider a vehicle of mass $m$ having a center of gravity at height $h = 0.5m$ from the ground. The coeffi... | We often use the sum of torques about an axis to find the case of zero rotation by finding where the sum is zero. The reason this works is that the case of no rotation must also be a case of no rotational acceleration and therefore no change in angular momentum.
$$\tau_1 + \tau_2 + .... = I \frac{\Delta L}{t} = 0 $$
B... | {
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How much additional light does Earth receive from the Sun due to Earth's gravitational field? I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field.
Is it a significant amount of light (>1% of total light)? Is it... | Earth's gravitational field causes Earth to retain a gaseous atmosphere, which both absorbs light itself and refracts light towards the surface. Estimating the altitude of the optically thick part of the atmosphere as somewhere between 6 km and 60 km, this atmosphere effectively increases the cross-sectional area of t... | {
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General relativity: is curvature of spacetime really required or just a convenient representation? I'm not really far into the general theory of relativity but already have an important question: are there formulations that can do without spacetime curvature and describe the general theory of relativity/all associated ... | In traditional GR, the possibility that spacetime can be curved is a fundamental requirement and moreover gravity is a fundamental force. However, in entropic gravity, it's argued that gravity is not fundamental and is an entropic effect and hence curvature is also not fundamental but an emergent property.
| {
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Conservation of angular momentum in a free rod When a collision is elastic and no external torque acts on a system, angular momentum is conserved
I found this example and checked the results:
A ball (m = 1 Kg , v = p =+22 m/s, Lm = +11, Ke = 242 J) hits the tip of a rod (M = 10Kg , length = 1m, $I = 10*1^2/12$ = 5/6 ) ... | Yes, angular momentum is conserved if you do the problem correctly.
If you assume the ball bounces back along exactly the same path it followed before the collision, there are three degrees of freedom: the velocity of the ball, the velocity of the rod, and the rotational rate of the rod. There are three constraints: co... | {
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How to observe Floquet state? The Schrodinger equation is
$$i\hbar\partial_t\psi(t)=H(t)\psi(t).$$
Now, given that the situation that the Hamiltonian is periodically driven, i.e., $H(t+T)=H(t)$, then the equation can be solved by the Floquet ansatz,
$$\psi(t)=e^{-i\varepsilon_n t/\hbar}u_n(t),$$
where $\varepsilon_n$... | They have been observed in the following experiment:
Observation of Floquet-Bloch States on the Surface of a Topological Insulator.
YH Wang, H Steinberg, P Jarillo-Herrero and N. Gedik. Science 342, 453 (2013), arXiv:1310.7563.
In this paper, there is a periodic laser pulse hitting the sample which gives a time-per... | {
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Can a conservative field produce a torque? I am asking whether the following Lagrangian for a point moving in a conservative field, can be correct :
$L(r, v, \omega) = \frac {mv^2}{2} + \frac {I \omega^2}{2} - U(r)$.
$r$ is the distance between the equipotential surface on which the movement begins and the equipotenti... | The answer to the title of this question, "Can a conservative field produce a torque?" is yes. For example, a non-uniform gravity field (e.g., the Earth's gravity field) results in a gravity gradient torque on an object with a non-spherical mass distribution. This torque is sometimes problematic for artificial satellit... | {
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Advection operator How are exactly $u_j\partial_ju_i$ and $u_i\partial_j u_i$ related?
And what is their relation to ($\boldsymbol{u}\cdot\nabla)\boldsymbol{u}$ and $\boldsymbol{u}\cdot(\nabla\boldsymbol{u})$ ?
I ask this because:
$$[\mathbf{u}\cdot(\nabla\mathbf{u})]_{i}=u_{j}\partial_{i}u_{j}=u_{x}\partial_{i}u_{x}... | Your math is correct, $\left(\mathbf u\cdot\nabla\right)\mathbf u\equiv\mathbf u\cdot\left(\nabla\mathbf u\right)$. This should make sense because the commutative property holds for dot products.
Personally, I prefer to view $\mathbf u\cdot\nabla$ as an operator that acts on something (in this case, a vector, but it co... | {
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How does a supersonic flight speedometer work? I'm sure today they can use GPS and radar, but I was pondering the queation when I saw a film clip of a vintage analog dial labeled in mach number. I'm supposing that the usual way of measuring the pressure drop of the air flow would not work in this case. So what does?
| The pitot tube measures stagnation (i.e. dynamic) air pressure.
There is also a static port that measures the actual air pressure.
This is enough information.
First of all, the pilot cares about "knots indicated air speed" (KIAS).
That is not true speed over the ground.
(A "knot" is one nautical mile per hour.
A nautic... | {
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Need of small charge in definition of electric field? Why do we need infinitesimally small charge in definition of electric field? Since the test charge cannot exert force on itself, F on test charge will not change whatever the value of test charge q is. So, F/q will be same for any value of test charge. Then why do w... | Ideally, test charge should not affect the charge distribution of the source. An infinitesimal charge will ensure, for example, that the electric field it produces does not redistribute charges on any conductors in your system. A large test charge would polarize nearby objects, thus affecting the field you're trying to... | {
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Why is an airplane able to increase thrust without moving? I was just watching some documentaries and saw planes building up power in the turbines without moving. I thought about it and remembered, that this happens before every take off.
So, why is this possible? A planes thrust isn't related to the ground, but to the... | Brakes, m'boy, brakes.
Big planes, not surprisingly, have big brakes. And they are easily capable of locking the wheels up. The engine thrust would have to exceed the static friction breakaway force for that plane's weight before it started sliding down the runway.
Aircraft carriers work a bit differently - when your a... | {
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Is there a mathematical explanation for why there occur bound states if the effective potential falls below zero? Usually in physics textbooks, if the effective potential of the radial schroedinger equation
$$-\frac{d^2}{dr^2}u(r) + \frac{\ell(\ell+1)}{r^2}u(r) + V(r)u(r) = E u(r)$$
falls below zero in some subinterval... | There need not be any bound state if $V(r)$ is chosen appropriately. Even a potential $V(r)=-V_0$ for $r<R$, $V(r)=0$ for $r>R$ will have no bound states if the potential is sufficiently shallow: see wikipedia.
| {
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How does "pushing-start" a dead-battery manual car work? A few days ago the battery of my car went (almost) dead. As it is a manual car, my father once told me that the way to get it going without jumper cables was to push it or let it roll down a hill, sink the clutch, shift to 2nd gear and then let go the clutch.
Aft... | The purpose of the starter motor (using the battery) is to get the engine moving so that the combustion cycle can be initiated. The combustion cycle is self-sustaining, but it relies on the pistons moving to compress the air/fuel mixture, so you have to get them moving in the first place somehow. By putting the car in... | {
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Sending information faster than light If I could ever send my friend any information faster than light it would violate causality. If he just guesses the information and acts on it before he could ever receive it, everything is fine. What is different here?
I can understand that nothing can ever move faster than light ... | The equations of special relativity imply that a hypothetical superluminal signal would arrive at the receiver before it was transmitted from the source. Since the effect precedes the cause, the "law of causality" would be violated. Therefore superluminal signals are not considered possible -- if the special theory is ... | {
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Which modes are excited when a drum is struck? I've been searching quite extensively for an answer to this question but I cannot find anything definitive. The most I can see is that "one or several" modes become excited, but this is never parameterized by any relevant factors. I imagine it depends on the location of th... | The functions which describe the vibrating modes of a circular drum are the Bessel functions of the first kind $J_n$, they form a complete set so you can express any function as a series of Bessel functions (Fourier-Bessel Series), they also satisfy an orthogonality relation, then knowing the function $F$ which approxi... | {
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If the solar system is a non-inertial frame, why can Newton's Laws predict motion? Since there is no object in the universe that doesn't move, and the solar system likely accelerates through space, how did Newton's Laws work so well? Didn't he assume that the sun is the acceleration-less center of the universe? Shouldn... | There are two main reasons it is practical to ignore the pseudo forces due to the rotation of the earth/sun about the galaxy. First, the accelerations are pretty small, and second, they are pretty uniform.
The sun moves around galactic center at about 800,000 kilometers per hour, but it takes around 250 million years t... | {
"language": "en",
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Absolute (as opposed to relative) concept of inertial frame In mechanics there is a relative concept of "inertial frame": frame A is inertial with respect to frame B if A moves uniformly with respect B. That concept is easy to understand.
There also seems to be an absolute concept of "inertial frame". I keep reading th... | An inertial frame is one with respect to which Newtons second and first laws are valid.There is no ideal inertial frame in the universe although the heliocentric refrence frame fixed with the center of the sun can be regarded as an inertial frame with a high degree of accuracy. If we assume the heliocentric frame as an... | {
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What is a reasonably accurate but simple model of the Milky Way's gravitational field? I am putting together a toy program which shows how stars move around in the galaxy.
To run the simulation I need to know strength of the Milky Way's gravitational field at any location in it. I'm looking for a model (e.g. a collecti... | Deriving the galactic mass from rotation has the following chart (on the right) for the enclosed mass as a function of radius
| {
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Why do we call a white led with high color temperature "cool"? one can buy LED bulbs with defined color temperature.
why cool white = many kelvins (= high temperature?)
why warm white = few kelvins (= low temperature?)
| Any and every object naturally gives off light that is to a good approximation that of a blackbody. The amount of each wavelength given off is dependent on the object's temperature.
For cool enough objects, most of this emitted light is too far into the infrared to be seen by our eyes. Once something gets to be hot eno... | {
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Metric tensor in SRT I just read on this webpage that we have (click me) $g_{\alpha \beta} = g_{\alpha}^{\beta} = g^{\alpha \beta}.$
Now, although I understand that the first and the last one are equal, I don't think that the term in the middle is the same as the other two, cause we should have $(g_{\alpha} ^{\beta}) ... | That statement is nonsense.
While it is true, that, in flat space, the components of $g^{\mu\nu}$ and $g_{\mu\nu}$ are exactly the same, the equation $g^{\mu\nu} = g_{\mu\nu}$ is not a valid equation - the indices don't match.
As you correctly observe
$$ {g_\mu}^\nu = g_{\mu\rho}g^{\rho\nu} = {\delta_\mu}^\nu$$
since $... | {
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Is $∣1 \rangle$ an abuse of notation? In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow has transformed into a ket.
But when you look up material online, it seems that the ... | What they're saying is that $|3\rangle$ represents the third energy eigenstate of the oscillator. So, it replaces something like $\psi_3$.
Writing $|3\rangle$ requires context - you would have to explain that you were going to number the nth energy eigenstate of the harmonic oscillator as $|n\rangle$ before using that... | {
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Superpositions: forcing particles into a state According to a MinutePhysics video ("How to See Light") physicists won a Nobel Prize for showing that creating a certain superposition state for a particle and observing the particle state after it interacted with light, may allow us to prove the presence of a photon witho... | The latest study on this subject that I could find, "All-Optical Control of a Single Spin Employing Coherent Dark States," uses 2 lasers to keep the particle in a coherent "dark state," which I understand to be a superposition where spin direction has not been determined, and hence, not measured. My question is, could ... | {
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Do we know where newly formed quark-antiquark pairs come from in the process of hadronization? The only explanations I have found are very vague, such as "spontaneously created from the vacuum" and because "it is more energetically favorable".
| Here is a Feynman diagram of hadronization, i.e. parton showers
For this argument I am using the diagram as input of a quark antiquark pair from an incoming hadron interacting by a gluon and scattering as an off mass shell quark- antiquark.( in the figure the input is QED)
the curls are gluons, the light blue and ... | {
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Basic quantum entanglement question Please consider commenting on this basic quantum entanglement question or point me to articles that may enhance my knowledge.
Does quantum entanglement only occur in pairs, or can three or more particles become entangled?
| Entanglement with more than two particles is allowed. Mathematically, you could write, for example,
$$|\psi\rangle = a|111\rangle + b|000\rangle.$$
Here, if you measure particle 1 to be in the "0" state, then you know immediately what the entire wave function is after measurement.
One applications is quantum error corr... | {
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What is the speed of sound in space? Given that space is not a perfect vacuum, what is the speed of sound therein? Google was not very helpful in this regard, as the only answer I found was $300\,{\rm km}\,{\rm s}^{-1}$, from Astronomy Cafe, which is not a source I'd be willing to cite.
| Given the low density of gas, the speed of sound would be a direct function of the temperature of the gas ie the speed of the molecules/atoms. Since this varies from about 2.7K to millions of degrees near some stars, the speed of sound can change quite a bit.
| {
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Why would two protons repel? I understand that two protons would repel due to them both being positively charged, however, wouldn't the strong force act on the two protons pulling them together? Would this mean that in this case the electromagnetic repulsive force is greater than the strong force? If so why? If not why... | The electromagnetic repulsion between two protons is a long-range force, depending on $1/r^2$, where $r$ is the separation of the two protons.
The electromagnetic repulsion between two protons is not the reason that they do not stick together; if they are forced together (or can tunnel through the Coulomb barrier) then... | {
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What does the statement "the laws of physics are invariant" mean? In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is
the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference)
What does ... | "the laws of physics are invariant..."
means that they wouldn't vary or change.
Meaning that any experiment done in one inertial frame would give the same result as the same experiment done in another inertial frame.
It could be any experiment at all, for example, seeing how the momentum of a ball changed if a given fo... | {
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Tensor product of two different Pauli matrices $\sigma_2\otimes\eta_1 $ I'm solving problem 3.D in H. Georgi Lie Algebra etc for fun where one is to compute the matrix elements of the direct product $\sigma_2\otimes\eta_1$ where $[\sigma_2]_{ij}\text{ and }[\eta_1]_{xy}$ are two different Pauli matrices in two differen... | Each Pauli matrix has two non-zero elements. Therefore, direct product of Pauli matrices will have four non-zero elements. Your answer, unfortunately, has eight.
| {
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Is $ds^2$ just a number or is it actually a quantity squared? I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime Physics. But I have also heard $ds^2$ its just a notational dev... | As already mentioned by others, $\mathrm ds^2$ is used as suggestive notation for the metric tensor
$$
g = \sum_{\mu,\nu}\mathrm g_{\mu\nu} \, dx^\mu\otimes\mathrm dx^\nu
$$
In case of a positive definite metric and given a curve $\gamma:[0,T]\to M$, it has a precise meaning in terms of either the length function
$$
s_... | {
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Is the expression $S=K \log(\Psi)$ appearing in Schrödinger's first paper well defined? I am currently reading Schrödinger's papers and happen to have some questions that maybe some expert in the field could clarify for me. Like what happens with
$$S = K \log(\Psi)$$
when $\Psi<0$. If I understood correctly, in his pap... | If you consider the complex logarithm, then $\log z=\log|z|+i\arg z$. (plus integer multiples of $2\pi i$ for different branches.)
Now if $z\in \mathrm{R}$ and $z<0$, then $\log z = \log(-z) + i \pi$. So the action $S$ has just changed by an additive constant. However, adding something to your action does not change th... | {
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Is the method of images applicable to gravity? It is well known that the method of images is a useful tool for solving electrostatics problems. I was wondering why this technique is not applied when considering newtonian gravity?
Obviously there is no "negative mass" to correspond to a negative charge in electromagneti... | The method of images works on the electrostatic case because the axis of symmetry of the mirror charges induces an equipotential line that is equivalent to the infinite conductor surface. In gravitational physics, there are no known instances of a physical surface that is at the same potential in the gravitational fiel... | {
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What physical evidence is there that subatomic particles pop in and out of existence? What physical evidence shows that subatomic particles pop in and out of existence?
| $$\sin(x) = x-\frac{x^3}{3!} + \text{trigonometric fluctuations}$$
Above you can see why I don't like the language of "quantum fluctuations" -- what people mean by them is just "terms in perturbation series we can't make classical sense of". Similarly the phrase
... particles pop in and out of existence...
is a ye... | {
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Why do most formulas in physics have integer and rational exponents? I mean, why is $F=ma$? Why not $m^{0.123}$, $a^{1.43}$ or some random non-integers or irrational?
I hope you understand that my question isn't limited just to force, energy, velocity, etc.; it also extends to the area of a square, circle, etc. and all... | I think everyone has missed the obvious answer: because the equations of physics simply use math to model the way the universe works. Put some fractional exponent in your F = ma, and the answers come out wrong.
Now if you're asking why the universe happens to be that way... Well, I don't know, but I think it's more ... | {
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Why is Bose-Einstein condensation a phase transition? Bosons may succumb to a Bose-Einstein condensation at a certain critical temperature $T_c$, thus entering the BEC phase.
The only thing I know about the BEC is that since we are talking about bosons it is possible for all of them to occupy the same ground state. As ... | This is a very good question. It turns out that the phase transition occurs precisely when the chemical potential becomes equal to zero (assuming that the ground state energy is at zero). The order parameter in the BEC is the "macroscopic wave function" or rather the square root of the single-particle reduced density m... | {
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Could dark energy just be particles with negative mass? The title speaks for itself.
Dark matter: We see extra attractive force, and we posit that there are particles which create such a force, and use the measure of that force to guess their locations.
Dark Energy: We see extra repulsive force.
Only thing is, dark ene... | Matter and dark matter are also evenly distributed throughout the observable universe, at least on the largest scales. What makes dark energy different isn't that it is uniformly distributed, but that it has a constant density. The amount of dark energy per cubic meter of universe is the same regardless of the total vo... | {
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How can we define the energy stored in a (conservative) force field? I have come to know from my textbook that energy is stored in the E-field of a capacitor, in the B-field of an inductor and so on. Take the example of an inductor. The derivation bewilders me completely. From Kirchhoff's Loop Rule, we take the the vol... | The energy stored in a field is the energy required to create it. In your case of the inductor there is no field when no EMF is applied. When we apply an EMF a current flows and does work, and the work goes into creating the field.
When we talk about the energy of e.g. a charge in an electrostatic field, we normally as... | {
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What information do $|\psi(0)\rangle$ and $|\psi(t)\rangle$ represent? I am starting to feel comfortable with the role of the unitary operator in quantum mechanics. For instance, one of the equations I have seen is
\begin{equation}
|\psi(t)\rangle = U(t) |\psi(0)\rangle
\end{equation}
I understand what a unitary oper... | The Schrödinger equation is an ordinary differential equation of first order and its solution requires one initial condition which is your $\psi(0)$. Imagine you would like to do a quantum experiment. the first step is to prepare your system in a known state ( eg $|\uparrow\rangle$ for a qubit). This state corresponds ... | {
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Why is the bottom part of a candle flame blue? What’s the explanation behind the bottom part of a candle flame being blue? I googled hard in vain. I read this. I don’t understand how it’s explained by the emission of excited molecular radicals in the flame. I read that a radical is a molecule or atom which has one unpa... | The red, orange, yellow, and white parts of a candle flame results from glowing soot. The color in this part of the flame is indicative of the temperature. The spectrum in this part of the flame is fairly close to that of a black body.
The blue part of the candle flame at the bottom of the flame results from chemilumin... | {
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Spacelike to timelike four vectors First at all, let me just say that I'm not a Physicist, I study mathematics. So, I have this question. If you have a spacelike four vector, is there any transformation that could change it to be a timelike four vector? I mean, I know that every Lorentz Transformation (LT) preserves th... | Yes, there are transformations that take timelike vectors into spacelike vectors and viceversa. Consider $(t,x,y,z) \mapsto (x,t,y,z)$. You could event throw a Wick rotation, $(t,x,y,z) \mapsto (i\ t,x,y,z)$, as a transformation that takes timelike vectors and returns spacelike vectors.
Now, these transformation do not... | {
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Closure Relation For Operator With Degenerate Spectrum Suppose we have an observable represented by a Hermitian operator, $A$. Further, $A$ has at least one eigenvalue that is degenerate. For concreteness lets say $A |\alpha_i> = \alpha | \alpha_i>$ for $i = 1,2, \ldots, n$. When writing the closure relation must we in... | You must include all of the eigenkets.
To show this, I must create notation for all of the non-degenerate eigenkets. Let's call them $\left|\beta_i\right\rangle$, each of which has a unique eigenvalue $\beta_i$, and $i=1,2,3...,m$. Now, I'll prove by contradiction that leaving out even one of the degenerate eigenkets c... | {
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$\mathrm{\rho^0}$ meson decay via the weak interaction? Of course, the $\mathrm{\rho^0}$ meson can decay in $\mathrm{\pi^{+}\ \pi^{-}}$ through the strong interaction. Using Feynman diagrams, I cannot understand why the same decay couldn't happen through the weak interaction. I attach the diagram I've drawn.
Strong dec... | Note that rho meson has no strange quark i.e. its strangeness quantum number is zero. Similarly the decay products positive as well as negative pion has no strange quark ie. Strangeness quantum number is zero for decay products too. Thus, strangeness is conserved in this decay process of neutral rho meson. Now note tha... | {
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Cosmology: what is a quantity that is called "$h$" in regard to angular size of a galaxy? I am trying to solve a Cosmology problem, but a certain quantity $h$ appears in it, of which I do not know the definition (I have never seen it mentioned anywhere before). So I thought maybe someone here could tell me what this $h... | This is explained in the Wikipedia article on Hubble's Law: http://en.wikipedia.org/wiki/Hubble%27s_law
In particular,
"Dimensionless Hubble parameter
Instead of working with Hubble's constant, a common practice is to introduce the dimensionless Hubble parameter, usually denoted by h, and to write the Hubble's paramete... | {
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Why doesn't the speed of the wind have an effect on the apparent frequency? A boy is standing in front of stationary train. The train blows a horn of $400Hz$ frequency . If the wind is blowing from train to boy at speed at $30m/s$, the apparent frequency of sound heard by the boy will be?
The answer: The frequency rema... | The Doppler Shift formula $f'=f(\frac{v \pm v_{obs}}{v \mp v_{source}})$ only works if the wind (or the medium that the sound is moving in) is constant. Therefore, if the wind is moving at a constant speed, change the reference frame so that the wind is stationary.
In your case, change the reference frame so that it is... | {
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Bounded operator - definition? As mentioned also in Bounded and Unbounded Operator, an operator $A$ is said to be bounded, if
$$\|Af\|\leq k \|f\|,$$ where the constant $k$ does not depend on the choice of $f$ (let us consider a map to the same Banach space).
However, in a mathematical physics text I came across a def... | TL;DR: The property bounded, bounded from above, and bounded from below are different things, cf. Wikipedia.
In detail, consider a densely defined symmetric linear operator $A:D\subseteq H \to H$ in a complex Hilbert space $H$. Let $$\langle A \rangle_{\psi}~:=~ \frac{\langle \psi, A\psi\rangle}{||\psi||^2}$$ for $\p... | {
"language": "en",
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Diffusion current and resistance of a diode In a diode, there is a resistance in the p and n region, and electric field is required to move the charges in forward bias conditions. My question is: when there is diffusion current is the electric field helping the diffusion current because of the resistance? Thus can we ... | There seems to be some confusion about carrier motion on your part. Carrier diffusion occurs all the time - in a field-free region the net will eventually go to zero in steady state (but carriers are still moving and diffusing around). Drift current is the result of the (slight) bias in charge carrier motion caused by... | {
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Eigenstates into which a system can be projected after a measurement I'm currently reading Dirac's Principles of Quantum Mechanics, on page 36, he says:
Another assumption we make connected to the physical interpretation of the theory is that, if a certain real dynamical variable $\xi$ is measured with the system in ... | This phenomenon is called the collapse of the wave function. It is one of the tenets of the Copenhagen interpretation of quantum mechanics.
The eigenstates $|\xi_i\rangle$ of the $\Xi$ operator form a complete set. From linear algebra we have
$$I=\sum_i|\xi_i\rangle\langle \xi_i|$$
where $I$ is the identity operator. W... | {
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How could a cord withstand a force greater than its breaking strength? How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?
My attempt to answer this question is that we could use a counter weight. But I don't really understand the concept behind coun... | Use a ramp, an incline of 53° will work.
Otherwise You need to double up the cord.
The third option is to just carry the 10 kg object down the stairs.
| {
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What is the correct way to treat operators that has "time" in QM? I don't know if this question has already been resolved but considering that $i\hbar\partial_t$ is the energy operator, and $\partial^2_t$ is the waves operator (or helmholtz), I can't accept that $t$ itself isn't an operator
What is the argument here th... | To say that something is a (linear) operator you have to specify the space where it acts. You may say that, for example, wavefunctions of quantum mechanics are maps: $t\to \psi(t)$ that are continuous in $t$ with values in $L^2(\mathbb{R}^d)$. If we restrict to compact time intervals $[0,T]$, we may denote the space of... | {
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What is basically the difference between static pressure and dynamic pressure? What is basically the difference between static pressure and dynamic pressure?
While studying Bernoulli's theorem, I came before these terms. The law says:
When the fluid flows through a small area, its pressure energy decreases & kinetic e... | Dynamic pressure is not really pressure at all. It represents the amount that the pressure would increase if all the fluid's kinetic energy per unit volume could be converted to pressure by blocking the flow (say with a pitot tube). On the other hand, static pressure is another name for just "plain old pressure" exer... | {
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Non-zero potential measured on the surface of an insulator After driving a screw into an alumina firebrick and applying a 5kV potential, I measured a ~4.5kV potential using a high voltage probe at other locations on the brick surface.
Firebrick is generally considered an insulator at room temperature. Using a mega-ohm... | You present both a static and a quasi-static case here. Let's consider them one at a time:
1) Static case: You applied a large potential to the screw relative to ground, which charged the screw. The firebrick is a good insulator, but not perfect, so the charge on the screw should polarize the material slightly, creat... | {
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Calculate the approximate number of conduction electrons So i have the following problem: A cube of gold 0.1 meters on an edge, calculate the approximate number of conduction electrons whose energies lie in the range from 4.0 ev to 4.025 ev.
But I'm not clear on how to start. could someone offer any help?
| I wasn't going to answer since I don't know exactly what your professor had in mind, but since I've been prodded by Sofia here is my suggestion. However don't treat this as gospel as I may have completely the wrong idea of the question.
I would guess that you're supposed to treat the cube as an infinite 3D potential we... | {
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When does Pauli's exclusion principle kick in? Imagine that I prepare a fermion in the $\left|\uparrow \right\rangle$ state and a second one far away in the $\left|\downarrow \right\rangle$ state and set them in a path for collision.
According to Pauli's exclusion principle, the composite wave function must be anti-sym... | To say you have put them into states, you have implicitly considered them as part of a single system (independent of how "far away" they are from each other). The wavefunction is anti-symmetric by definition, so they will behave corresponding to the Pauli Exclusion Principle "from the start".
| {
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Understanding magnetic force on charged particle if we put any charged motionless or static particle in the constant magnetic field, then why does it don't feel a magnetic force?
Mechanism by which electric and magnetic fields interrelate
I have read the above article which suggested that the magnetic field is the re... | The Lorentz force law is
$$\mathbf{F}=q[\mathbf{E}+\mathbf{v}\times\mathbf{B}]$$
Only a moving particle experiences a magnetic force, but the electric force is always felt.
| {
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Are electrons miniature black holes? For something to be a blackhole, it must have gravity and the radius must be smaller than the schwarzschild radius for its mass.
-Electrons have gravity
-Electron are theoretically believed to be infinitely small points
Since it has gravity it is capable of being a black hole. Since... | Electrons are very close to the energy of self-capacitance of a quantum of charge.
The size of the electron is very close to $r_e$, the energy supposed if one tries to charge a sphere of that radius with a single electronic charge, ie $mc^2 = e^2/4\pi\epsilon r_e$.
| {
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What is the meaning of the negative sign in $W = -\Delta U$? What is the meaning of the negative sign in $W=-\Delta U$?
As far as I understand, $W=-\Delta U=-(U_\mathrm f-U_\mathrm i)=U_\mathrm i-U_\mathrm f$.
While $U_\mathrm i$ is the initial potential energy (before applying the work), and $U_\mathrm f$ is the final... | $U$ in your equation in potential energy, and $W$ is internal work. That is, the work done by forces within the system. The system in question here comprises the object and the earth, and the internal force is gravity. The work that you do to lift an object is external to the system, and does not appear in your form... | {
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Solution to Schrödinger equation I'm trying to solve the Schrödinger equation for a given potential. With some assumptions I end up with:
$$\frac{\hbar^2}{2M}\frac{d^2u(r)}{dr^2} = - \left(E - V(r)\right)u(r)$$
Since it's a square well potential I'm looking at, I have for the first region ($r \leq r_0$) that $V(r) = V_... | First, the $k$ in the first region is incorrect. Check your signs. You should have
$$k_{I} = \sqrt{2M(E-V_o)}/\hbar.$$
Second, your solution to the second region will have sine and cosine solutions with
$$ k_{II} = \sqrt{2ME}/\hbar.$$
Real exponential solutions will occur in each region if $E<V_o$ in region one and/or... | {
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How eddy current brakes function Take the following example:
where a rectangular sheet of metal is entering a constant magnetic field at $v \dfrac{m}{s}$. Due to Faraday's law of induction + Lenz's law, we can state that an eddy current will be generated to oppose the increase of magnetic flux through the sheet of met... | I had a fundamental misunderstanding of eddy currents. I believed that eddy currents were formed simply in the part of the metal that was already submerged in the magnetic field, but in reality it is actually something like
(source: boredofstudies.org)
this, where only half the eddy current is actually in the field. I... | {
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Flux linkage of 2 coils in series I have a question about magnetic circuits. I am an engineering student, therefore I will neglect some minor errors.
There is a simple magnetic circuit with 2 coils ($C_1$ & $C_2$), with $N_1$ & $N_2$ turns and $i_1$ & $i_2$ currents. Coils are in series and connected with 1 magnetic co... |
Why is there the term $2N_1N_2i_2$(...) in the last part?
Two coupled inductors are not two two-terminal circuit elements but, rather, one two-port network, e.g.
where
$$M = k\sqrt{L_1L_2} $$
thus, the reason for the $N_1N_2$ terms. Note that as the coupling $k$ goes to zero, we recover the two independent inductor... | {
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Can an object appropriately isolated from its surroundings become colder than its surroundings? Consider a sealed box, well-insulated on all sides, except for the lid which is transparent to infrared. An object is placed inside the box and the box is evacuated (purpose being to thermally isolate the contents of the box... | Yes, this works. It's called radiative cooling. This phenomena has been known for a long time, considering the ancient Egyptians used to make ice this way.
Ideally, something open only to a clear sky would "see" the temperature of space, which is the microwave background radiation. In practise there is enough stuff ... | {
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Proof that a traceless strain tensor is pure shear deformation How can i proove that the traceless part of linear strain tensor $e$ in the Euler description:
$$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} \right)$$
is alway a pure shear deformation i.e. it does cons... | this website may help you I fonund this on Google books
https://books.google.com/books?id=yNXVBAAAQBAJ&pg=PA234&lpg=PA234&dq=Proof+that+a+traceless+strain+tensor+is+pure+shear+deformation&source=bl&ots=RmwzNuwndU&sig=BeNMc5oRLSxrUWBOfD_bpSrIWG0&hl=en&sa=X&ved=0CCwQ6AEwAmoVChMImYGa0uHmyAIVliuICh35UAiy#v=onepage&q=Proof%... | {
"language": "en",
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If a black body is a perfect absorber, why does it emit anything? I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According to Wikipedia:
A black body (also, blackbody) is a... | In simple words
Black body radiation means a body - independent of its color - that absorbs all the wavelength falling on it in the form of energy and does not reflect any of that wavelength, but instead it radiates what it absorbed with different wavelength.
That is why a star is considered a black body, since it just... | {
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My physics teacher gave us this equation $v= -3 +3t$ She asked us if the body was accelerating or slowing down, and I immediately said that it was accelerating (because the $a=3>0$). Then she said that I was wrong because the direction of the acceleration vector was the opposite of the direction of initial speed($v_0=-... | The sense of acceleration has nothing to do with the sense of velocity. Bodies always have negative acceleration due to gravity regardless if they are going up or down. What is important is the convention as to which direction a positive displacement occurs.
In your case all you know that the acceleration vector is in ... | {
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Missing a factor of $\sqrt{\frac{\hbar}{m}}$ in a QFT Practice Problem. Can someone explain why? I am doing problem 2.3 on page 27 of Quantum Field Theory for the Gifted Amateur.
Use eqns 2.46 and 2.62 to show that
\begin{equation}
\hat{x}_j = \frac{1}{\sqrt{N}} \left(\frac{\hbar}{m}\right) \sum_k \frac{1}{\sqrt{2... | Dimensional analysis shows the book's answer is wrong. Let's work it out. I should obviously get length because this is a position operator. Since neither $e^{\text{i}jka}$ nor the creation annihilation operators have units, I can ignore those terms.
This reduces to
\begin{equation}
\sqrt{\frac{1}{m}s\frac{m \cdot L^2... | {
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Neutrino Reaction: Is the Following Reaction Allowed? Is the following reaction allowed and why?
$$
\nu_e \to e^- + \mu^+ + \nu_{\mu}
$$
I would say it is allowed since individual lepton number and charge are conserved.
| Also : Lepton number conservation law, respectively Barion number conservation law, are laws which explain if any reaction can occur or not. Every particle has its own leptonic (barionic) number, and for the reaction to occur, the sum of those numbers in the right side of the equation MUST be equal to the sum of lepton... | {
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Why aren't all black holes the same "size"? The center of a black hole is a singularity. By definition, a singularity has infinite density. So how can a black hole with a different mass or density be described?
| Although we don't have a quantum theory of gravity, we think we have some reliable knowledge about the properties of black holes from general relativity.
One thing we think we know is the so-called "No-hair conjecture", which says that black holes can be described by just three numbers: mass, charge, and angular momen... | {
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What kinds of behavioural anomalies can a zero-field-cooled (ZFC) / field-cooled (FC) split indicate? If a material shows a spiltting in the ZFC and FC curves, is it necessarily superparamagnetic, or could there be any other reason for the irreversibility?
I have heard spin glasses also show ZFC-FC split; but whatever ... | A zero-field-cooled/field-cooled split in the magnetic susceptibility vs. temperature doesn't have to be superparamagnetism. In the case of superconductors, if we apply a field to the material and cool past T$_c$, some flux can be trapped inside, but if we cool first and then apply field, that flux will be shielded awa... | {
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Time dilation as an effect of energy density Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation?
i.e. Higher energy density==>Slower rate of time?
| In both GR and SR, the passage of time is dependent upon the energy state - in the special theory, the passage of time logged by two clocks in relative motion depends upon the kinetic energy $(v^2/c^2)$ difference whereas in the general theory, the passage of time depends upon the gravitational potential $(2GM/rc^2)$. ... | {
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How to calculate the increased pressure drop due to a restriction? Assume I have a straight pipe with diameter D1 and a volumetric flow, Q flowing through it. The inlet pressure is P1 and the outlet pressure is P2.
Now, assume I've added a restriction in the middle of that pipe, which takes the form of another pipe wit... | In an ideal fluid, assuming the diameter of the pipe after the contraction is the same as the diameter of the pipe before the contraction, $P_2^\prime = P_2$. There is no effect of the contraction downstream from the contraction itself.
If we consider an inviscid, isentropic, incompressible flow, the total pressure in... | {
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Weinberg's spontaneous broken symmetries Steven Weinberg in his second volume of QFT's book (in section about spontaneously broken symmetries, in subsection about Goldstone bosons) writes following:
if we have linear transformation of fields
$$
\tag 1 \varphi^{m} \to \varphi^{m} + i\varepsilon \sum_n t^{mn}\varphi_{n}... | He considers this case, because for this case, the effective action $\Gamma[\phi] = -\mathcal{V}_3TV(\phi)$, such that the $<H>_{\Omega}/\mathcal{V}_3 = V(\phi)$. Basically so that he could use the results of section 16.3.
| {
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Length contraction alongside acceleration Let's have a ship, a target and a ship traveler which we use as point of view. Assuming no other object are observed and we are so far from any other object that gravity distortion are negligible, I'm confused of the effect of length contraction during acceleration (usual lengt... |
This exceeds the speed of light, which seems incorrect.
During acceleration, the speed of light may seemingly be exceedet from the viewpoint of the accelerated observer. This is why one talks about "uniform relative velocity" when talking about inertial frames, in which the speed of light may not be exceedet. When yo... | {
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Mass, energy, and entropy. I have a seemingly simple question about the relation between these three that for some reason doesn't make sense to me. If entropy is the disorder of a system, then a low entropy state is one of higher energy. As we know, mass is energy. From here we must say that the more mass something has... | Drop a glass on the floor -> Entropy increases.
Drop another glass on the floor -> Entropy increases again.
From above we conclude that a big pile of broken glass contains more entropy than a small pile of broken glass. We also happen to know that a big pile of broken glass has larger mass than a small pile of broken g... | {
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Why is a hexagon such a stable shape for materials? A hexagonal lattice is famously the shape of graphene, the source of the 2010 Nobel prize. The shape also shows up in beehives and in the basalt columns of Giant's Causeway in County Antrim.
"Causeway-code poet-4". Licensed under CC BY-SA 2.0 via Wikimedia Commons
Wh... | Hypothesis: Considering transverse stress and strain, the hexagonal unit completely tiles the space within the structure without gaps and combined with this property, comes closest to a emulating a circle which most symmetrically distributes stress and load.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168638",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
Conceptual question on Gauss's Law
*
*By my understanding, the electric field in the surface integral expression for Gauss's Law represents the total electric field and any point on a closed Gaussian surface. However, when we employ Gauss's Law to find the electric field within a uniform charge distribution, we ignor... | Gauss law is sometimes used to find the electric field, but this is usually confined to situations where there is a strong symmetry that allows you to conclude that the electric field you're looking for is precisely the one in Gauss law, and moreover it reduces to something easy to evaluate, like the product of the mag... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168714",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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