Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Two boys pull a rope in the two edges with the force 50 N each. Will the rope rip if it can handle only a pull of 80 N? I think we should make the sum the two forces 50+50=100 N and say it can't handle? Can you explain me using the 3rd Newton Law?
| This question comes up again and again, in different guises.
If you pull on a rope with a force of 50N, then the tension in the rope is 50N, not 100 N. It's no different whether the other end of the rope has a weight of 50N on it, or whether it's attached to an anchor point in the wall, or to another boy.
Newton 3 talk... | {
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Parallel Universe Moving Backwards in time We know that different parallel universes- if they truly exist - are governed by different sets of laws. But, Could there be a parallel universe that is moving back in time(?) - in different direction the flow of time in our universe?
| We know that different parallel universes- if they truly exist - are governed by different sets of laws.
No we don't. If parallel universes exist, we know nothing about them. They could have the same laws, different laws, or no laws.
in different direction the flow of time in our universe - ?
The only thing that really... | {
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Temperature of electroweak phase transition How does one estimate the temperature at which electroweak phase transition (EWPT) occurred? Somewhere I have read it is around 100GeV but the reason was not explained.
| Let's define $T_{EW}$ the temperature where the coefficient $m^2_H(T)$ of the operator $H^2$ in the SM lagrangian vanishes:
$$
m_H^2(T=T_{EW})=0\,.
$$
For $T>T_{EW}$ the Higgs vev is vanishing, the EW symmetry in unbroken, and the elementary particles are massless. For $T<T_{EW}$ the the vev is non-vanishing, $v_T\prop... | {
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What are galactic speeds measured against? The Earth moves through space at 67,000 MPH. The Milky Way travels through a local group at 2,237,000 MPH.
Wouldn't you need a fixed point to be able to measure velocity against? After all, compared to the total speed of our Milky Way, the Earth isn't moving through space. Wha... | There are a number of different frames of references.
For the velocities of celestial objects we use: (i) The geocentric frame: This is a velocity measured with respect to the Earth's centre. Obviously this is quite useful for artificial satellites, but also for things like meteors. (ii) The heliocentric frame: this is... | {
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Does spacetime have a "mass" value? or What is "Spacetime" made out of? When measuring the MASS within the Universe, does "space" or "spacetime" have a value?
I only ask, because when speaking of expansion, space is expanding. Could it be possible, to reverse the process, by "uncreating" space?
For if it can be created... | Given that all existing matter and space had a common origin, it seems reasonable to assume that there is a possibility that if you could calculate the net mass of all the matter in the universe this value might be matched by a negative mass of what remains (i.e. space). If this was true then space itself would have a... | {
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Does lunar module need the same amount of fuel for landing and take off? Let's assume there is no atmosphere and let's assume there is no change in weight due to fuel consumption, will reactive rocket need the same amount of fuel for landing on a planet as for take off?
In theory - I think - you need the same escape ve... | Alternative - just because it's fun to think about these things.
Moving away a bit from the traditional rocket science, in principle you could land with very little fuel and a good set of wheels/brakes: apply a small fuel burn to change your orbit just enough to make a glancing pass at the surface of the moon, then app... | {
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Light in a box with positron walls instead of electrons I understand that with a hollow cube with the inner walls covered in mirrors given a light source briefly, the light would eventually be absorbed. This is due to electron excitation I believe. So suppose the cube had walls of positrons instead of mirrors, since th... | I'm imagining a box made completely out of anti-matter so that your situation is realistic.
Positrons are the antiparticle of the electron (i.e., the anti-matter equivalent). Meaning, in this case, they're identical to electrons except for charge.
Photons, though, have no charge. So don't give a hoot whether a charged ... | {
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What do units like joule * seconds imply? I can easily understand what divisive units imply, but not what multiplicative units imply.
What I mean is, when I read "$12 \:\mathrm{eggs/carton}$", I mentally convert it to, "There are 12 eggs for each carton". I get that.
But, when I see units like joules * seconds, $\:\m... | Building on the answer that Johannes gave:
Imagine you have a broad band source of energy, transmitting on multiple frequencies. It might be the sun, or it might be a RF transmitter, or ...
Now we are going to measure the energy transmitted in each wave band for a certain time, and plot this as a function of the freque... | {
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How does airborne laser system deflect the laser beam? In the Airborne Laser system, the laser beam is directed from the nose of a Boeing airplane towards the target. In this system, the angle of laser beam with respect to airplane body can be changed at the nose of the plane.
What kind of material can deflect such hig... | The ABL beam director system is, or at least was, available in schematic form somewhere on the LockheedMartin website.
To answer your specific question: the mirrors in the system are highly developed to withstand high-energy laser beams without damage. The coatings are quite specialized and the substrates are design... | {
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What can we learn from a band structure diagram? Other than the band gap and its magnitude, what are the things that we can immediately learn about the properties of the material just by glancing at its band structure?
Can we say something about the bonding? Can we see if the material exhibits some exotic properties li... | Depending on what is shown in the band diagram, you can see if it's a topological insulator. Most band diagrams just show what's going on in the bulk material -- what you'd get with an infinitely large chunk of material with not surface. However, to be a topological insulator, you need surface states that conduct. Thes... | {
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Using infrared temperature sensor to measure water surface temperature Can I use infrared temperature sensor (such as TS118-3) to measure water surface temperature?
I'm afraid some effects such as reflection of infrared waves from water surface and blinking because of the water ripple will make it impossible.
| Yes, water is the ideal material to measure because water (specifically ice water at 0 °C) is the material used to calibrate IR sensors for temperature readings. You do not have to worry about "reflection" as IR sensors do not themselves emit any of the IR (see page 3) used in the measurement, they just receive the IR ... | {
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Close or open circuit? A electric source provides a non electrostatic influence on the charges inside the source which pushes the positive charges from the negative terminal to the positive one. Does this happen when the source is part of a close circuit or of an open one?
| I know it is the back electromotive force in a circuit carrying coil for which such case occurs. Most electrical components carry coil , that's why back emf occurs in open or close loop circuits because every coil discharging current must produce magnetic field and such fields comes with polarity and will likely attrac... | {
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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 ... | Fahrenheit is not "absolute" either, by your definition. 0 degrees Fahrenheit is equivalent to -17.8 degrees Celsius; absolute zero is -460 degrees Fahrenheit.
| {
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Is it possible to "focus" a radio wave to target an area much smaller than its wavelength? Recently I was reading about a technology that uses radio waves to stimulate neurons to fire. The radio waves have the advantage of being able to pass through the skull (hence being non-invasive) but they are very coarse. Would i... | something like the microwave generator in the microwave oven can shoot out energy waves of different spectrum. and its is relatively focused like the laser beam.
human brain wave of thoughts present in brain as small area patterns. mind control/manipulation and detection hence achieved.
| {
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What is the initial angular momentum of a rigid body given an offset impulsed force? What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$?
For a homogeneous sphere I said the imparted angu... | When you have an impulse $F\Delta t$ (I prefer that notation over $m\Delta v$ because it allows impulse to be imparted without worrying about the mass of the thing giving the impulse), then
*
*The momentum of the center of mass changes as though the impulse was applied there, so $$m\Delta v = F\Delta t$$
*The angul... | {
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Why are some elemental materials grey? How does grey occur in elemental materials such as metals? I believe that grey arises from the simultaneous reflection and absorption of all colors of the spectrum (in different atoms of course), as mixing opposite colors on the spectrum would do. How would this occur in a one-ele... | A clean un-oxidized metal surface is not usually grey but rather reflective like a mirror.
In fact, mirrors are constructed by coating a sheet of glass with a thin layer of metal atoms.
The grey color of a slightly oxidized surface, which includes almost metal surfaces you encounter in daily life, look grey because som... | {
"language": "en",
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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'... | The answer is misleading. If you consider one photon it is giving each mirror a kick every T seconds. There is no "continuous pressure". Now multiply that by N photons.
| {
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Does a positive or negative charge attract a neutral object?
Three objects are brought close to each other, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that:
(a) objects A and C possess charges of the same sign.... | This is the phenomenon of electrostatic induction.
Since "neutral" objects are made out of many positive and negative charges in equal measure, some of which can move, the presence of an electric field from a charged object will move these charges, and result in a region of opposite (to the object creating the field) c... | {
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Selection of system in Conservation of momentum I came across a question in which a cart is moving and having sand. Suddenly the sand valve malfunctioned and the sand starts falling from the cart. So momentum of which system will remain conserved.
| First, define clearly what is in The System; it can be anything you want. This definition is then fixed.
If any part of this system experiences a force from outside the system in a particular direction, then the total momentum of the system in that direction is not conserved.
If all the forces on any part of the sy... | {
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Total angular momentum in QFT
Can anyone show explicitly how the QFT total angular momentum operator $$\hat{\vec{J}} = - i \int \frac{d^3p}{(2 \pi)^3} \hat{a}^{\dagger}_{\vec{p}} ( \vec{p} \times \nabla_{\vec{p}}) \hat{a}_{\vec{p}}$$ gives $$\hat{\vec{J}} |\vec{0} \, \rangle = 0~?$$
Derivation of all the above is her... | If the state you're using is just the vacuum, then my comment to your question applies. If otherwise $|\mathbf 0\rangle = a_{\mathbf 0}^\dagger|0\rangle$, then just use that $[a_{\mathbf p},a_{\mathbf q}^\dagger] = \delta_{\mathbf p,\mathbf q}1$, with $\mathbf q=\mathbf 0$ to fix the integral at the term with $\mathbf ... | {
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Diagonalizability as a measure of uncertainty (discrete case) I have seen two characterizations of the problem in measuring a discrete variable of a state ψ exactly with each of two non-commuting Hermitian operators A and B:
(1) that the product of the standard deviations ( = √(<ψ|A2|ψ>-<ψ|A|ψ>2), & ditto for B) ≥ 1
(2... | If you have a situation where $[A,B] = iC$, and $\omega$ is any state of the C*-algebra containing $A,B,C$, then you have the relation
$$\Delta_\omega A\Delta_\omega B\geq \frac12|\omega(C)|$$
which is an answer to your first question, provided that, e.g., $[A,B] = i2\cdot\mathbf 1$.
Part two is basically the fact that... | {
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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... | In the mathematics used for physics dimensions are independent mathematical fields on which a variable can be assigned . Independent means that in the algebra used each projected on the other gives zero, is orthogonal. The example is the three dimensions we live in which are assigned orthogonal directions and the field... | {
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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... | Antimatter is simply matter with an opposite charge in each particle. It will (probably) look and behave exactly the same as regular matter.
However, no one has made enough antimatter to actually test that it does look the same. The major obstacles are the energy cost and the handling problems. Antimatter has to be bui... | {
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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... | Nobody is "doing the normalization".
Normalization is not even necessary. We often normalize for convenience, since that means that the Born rule for $\lvert \psi \rangle$ being the state $\lvert \phi \rangle$ reads
$$ P(\psi,\phi) = \lvert \langle\psi\vert\phi\rangle \rvert ^2$$
which is certainly easier to recall/wri... | {
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Why is kinetic energy defined as $(1/2)m v^2$? What is special about $(1/2)m v^2$ that makes physicists believe that it is a representation of kinetic energy?
| It's the work done to accelerate a particle from rest to a final speed $v$, i.e. the energy "put in" to initiate motion.
Work $W \equiv \int_0 ^{v} \,F \, dr$, with $F = ma = m\frac{dv}{dt} = m \frac{dv}{dr}\frac{dr}{dt} = mv\frac{dv}{dr}$, so:
$$W = \int_0 ^{v} \,F \, dr=\int_0 ^{v} \, mv'\frac{dv'}{dr} dr = \int_0 ^{... | {
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Sign of the totally anti-symmetric Levi-Civita tensor $\varepsilon^{\mu_1 \ldots}$ when raising indices I am confused with the sign we get when we want to raise or lower all indices of the totally anti-symmetric tensor of any rank. Take the metric to be mostly plus ($-+\ldots+$). Then is it
$$\varepsilon^{ijk}=\varepsi... | Sean Carroll's Spacetime and Geometry has a thorough discussion of this, and, even better, this discussion is in the lecture notes that turned into the book (see Chapter 2: Manifolds).
In full generality (at least for any right-handed coordinate system), we start off with the symbol $\tilde{\epsilon}_{\mu_1\cdots\mu_n}... | {
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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... | There are none. The reason is that the mainstream extensions of the Standard Model leave its gauge group intact at LHC energies and only add matter to the spectrum.
Such a modification will not lead to new hadronic states. Exotic particles with masses comparable to quark masses are mostly excluded (unless there is som... | {
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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... | When we discuss power in the general physics sense, we mean the rate at which energy is transferred from one system to another, or possibly one form to another. The sign convention your professor specified is very common, and yields the power consumed by the device, taking energy out of the charge flow system and putti... | {
"language": "en",
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Is gravity a force? If gravity just emerges from the curvature of spacetime, is it actually a force?
Why is it one of the 4 fundamental forces of nature?
| It could be or it could not be. It's really not clear. You still need some sort of means to communicate with space-time and tell it to curve. This is where gravitons could potentially come into play as the force mediator, and that would technically make gravity a fundamental force. It is certainly expected to be quite ... | {
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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... | When pitch of a voice is changed, both the wavelength and frequency change. For example, a higher pitch will have a higher frequency (of course) but a smaller wavelength.
Okay, that being said, the independence of the propagation speed of a wave to the properties of the wave itself it an model to use in many circumstan... | {
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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 ... | Yes, a rotating magnet emits radiation, exactly like a pulsar does. The solution to the Maxwell equations is known (but not very well known, actually). The analytical expressions for the electromagnetic fields $\mathbf{E}(t, \mathbf{r})$ and $\mathbf{B}(t, \mathbf{r})$ are very complicated. About the total angular m... | {
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How can I prove that $\langle\Omega\vert \phi(x) \vert\Omega\rangle \langle\Omega\vert\phi(y)\vert\Omega\rangle=0$ for a scalar field? From Peskin-Schroeder, p.212:
The term
$$ \langle \Omega | \phi(x) | \Omega \rangle \langle \Omega |\phi(y) | \Omega \rangle$$
is usually zero by symmetry; for higher-spin fields, ... | It's a bit more involved than creation and annihilation operators. What is meant is that the field has no vacuum expectation value, and in a way this is by construction. You may think about why $\langle x \rangle = 0$ for a harmonic oscillator (or better yet, an an harmonic one). It's because $x\to -x$ is a symmetry of... | {
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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... | The shell theorem assumes a continuous distribution of matter in the shell.
If you came infinitesimally close to a real, physical shell you would discover that it, too, is made of particles. As you passed through the shell one of two things would happen:
*
*You could crash into one of the particles and experience a ... | {
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Supermassive Black holes at centers of galaxies Why there is super-massive black holes at the center of our galaxy and other galaxies ?
| Because at the centre of the galaxy, there is much higher star density, and thus, much higher chances for having huge stars.
These stars will inevitably collapse, forming black holes. These black holes if located at the center of a galaxy, are able to easily gain more mass from nearby stars. Increasing their mass furth... | {
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Baryogenesis via Leptogenesis Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta L=N_f[N_{CS}(t_i)-N_{CS}(t_f)]$ since $(B-L)$ is anomaly free. Both the violations (i.e., $\... | When right handed neutrinos are introduced, they imply $L$ violation through their Majorana nature. Their decay into lepton and Higgs doublets
$$N\,\longrightarrow l\,\Phi^\dagger$$
violates the lepton number (since $N$ has zero lepton number being Majorana). These decays take place out of thermal equilibrium, therefo... | {
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Which Symmetry class and what kind of topological invariant for $2D -p+ip$? What kind of topological invariants are there for $2D-p+ip$ topological superconductor and to which symmetry class it belongs to?
| All topological insulators can be classified according to their symmetry classes. There is time reversal symmetry ($T$) , charge conjugation symmetry ($C$) and the combination $S=T*C$ symmetry. The $T$ and $C$ symmetries can be either positive or negative, i.e the energy spectrum may change sign under the symmetry oper... | {
"language": "en",
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What would happen to matter if it was squeezed indefinitely? I hope that this is a fun question for you physicists to answer.
Say you had a perfect piston - its infinitely strong, infinitely dense, has infinite compression ... you get the idea. Then you fill it with some type of matter, like water or dirt or something... | Presumably, it's going to be similar to the Big Bang in reverse, which is also what happens at the singularity of a black hole or any situation where matter is continuously compressed.
(Beyond a certain point, we don't really know.)
| {
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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 ... | There are formulations of classical general relativity that do not utilize the concept of the curvature of spacetime, which are equivalent to the traditional formulation that interprets gravity as the curvature of spacetime.
As with anything else, the framework that one chooses to do calculations in is a matter of circ... | {
"language": "en",
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Changing of spin for electron? Can we change the spin of electron by applying magnetic field from $\uparrow$ to $\downarrow$ configuration?
| A magnetic field consists of photons. Photons are spin $1$ particles, which means for a given $z$ axis a measurement of spin can yield $+1$ or $-1$. If a photon collides with an electron, we know that spin must be conserved. Let's assume the electron is in a spin up state $\uparrow_e= + \frac{1}{2}$ and the photon in a... | {
"language": "en",
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Moving electric charges I just wanted to double-check these three statements, as I'm not entirely sure I understood them completely:
1) A stationary electric charge (let's say a proton) produces electric field.
2) A moving non-accelerating proton produces also magnetic field.
3) An accelerating proton produces electrom... | For all of these points it is important that you ask 'relative to what' because the idea of an electric and a magnetic field was shown by Maxwell to be a different way of looking at the same thing. So if we were in the frame of reference of a charged particle moving past another charged particle (which would look like ... | {
"language": "en",
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Gravity and bottomless pits Assuming that someone is theoretically able to make a hole through the center of a large planet, and then jumps down the hole, what will happen? Given my understanding of gravity and energy, my estimate is that in the absence of any resistive forces, the person would fall right through to t... | You are correct about what you believe would happen.
Here's an important fact:
Consider yourself positioned at a random location within a solid planetary sphere. Let that point define a radius from the center of the sphere to you. Any matter that lies beyond that radius has a ZERO net gravitational pull on you. In othe... | {
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What kind of object is the Landau--Lifshitz pseudotensor? I understand that it's called a pseudo-tensor because it's not a tensor. Wikipedia says
most pseudo-tensors are sections of jet bundles, which are perfectly valid objects in GR.
Refer Here
Is the Landau-Lifshitz pseudo-tensor a section of a jet bundle?
| Because the Landau-Lifshitz pseudotensor behaves as a tensor only with respect to restricted coordinate transformations, it would be considered as a part of the jet bundle within the manifold when used to this end only.
| {
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Why are Majorana fields usually used to introduce gravity in the Rarita-Schwinger Lagrangian? When first introducing the gravitational interaction for a spin-3/2 Rarita-Schwinger field, Majorana fields are usually used (see for example here at chapter 4, or in Ramond, (6.4.112) ).
Why is this? What are the advantaged o... | In this context, the word "Majorana" doesn't mean that it is the "real one-half" of the ordinary simple Dirac spinor. It means that it is any half-integer field with a reality (Majorana) condition!
For example, in the Chapter 4 of the DAMTP lectures, the field introduced is a standard spin-3/2 field with one spinor in... | {
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What does 'channel' mean? I see many plots like the following that graph counts per channel,
I know what a 'count' is, but I don't know what a 'channel' is. Could somebody please explain to me? My guess is that it is that each channel represents a bin in the histogram, and so channel 453 would be the 453$^{\textrm{rd}... | In this case a "channel" is a separate register in the data acquisition (assuming the data comes from a MCA or other ADC driven collection device).
Each channel represents a discrete range in some input to the data acquisition system (generally time or charge) which is linked through the physics of the detector to som... | {
"language": "en",
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When is a unitary operator a quantum gate? Quantum gates we use like X, Y, Z, H, CNOT, etc. are all unitary. When can an arbitrary unitary operator be considered as a quantum gate?
| Quantum gates are all unitary transformations on a state of qubits. Any unitary transformation can be considered a "gate", although the ones you mention are primitive ones from which others can be constructed. More complex ones are usually referred to as circuits. The two qubit gates, $\mathrm{H}$, $\frac{\pi}{8}$ and ... | {
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Why does the surface structure of a metal make it hydrophobic? I was just reading this article from phys.org describing water-repellant surfaces.
However the article doesn't go into enough details of explaining why a particular structure repels the water.
Can someone please explain why the water molecules react to a pa... | The article Gowtham linked to seems to be the one you want. Basically (if I understood correctly), if the material is already hydrophobic (water is more attracted to itself than the material), the surface tension of the water prevents it from filling small empty spaces in the surface which will remain filled with air. ... | {
"language": "en",
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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... |
I'm sure that there might be all sorts of engineering details,
Not really. An electric starter motor requires a large amount of power to turn the engine over. If the battery is nearly exhausted, it cannot provide the power to rotate the electric starter motor.
However, as long as there enough power from the battery... | {
"language": "en",
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Limit as $x_1 \to x_0$ for the propagator of the harmonic oscillator
Consider a non-relativistic particle of mass $m$, moving along the $x$-axis in a potential $V(x) = m\omega^2x^2/2$. use path-integral methods to find the probability to find the particle between $x_1$ and $x_1 + dx_1$ if the particle is at $x_0$ at t... | Ideologically speaking, the absolute value of the propagator squared
$$\tag{1} |K(x_f,t_f;x_i,t_i)|^2 \mathrm{d}x_f ~=~ \frac{m\omega}{2\pi\hbar\sin\omega \Delta t}\mathrm{d}x_f, \qquad \Delta t~:=~t_f-t_i~>~0,$$
is the probability that a harmonic oscillator starting at $t_i$ in position $x_i$ will finish within the po... | {
"language": "en",
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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 ... |
What is different here?
In some reference frames, your friend guesses the information and acts before you send it and in others, he guesses and acts after you send it.
But there is no causality problem since his action is caused by his guess rather than the received information.
In all reference frames, the guess pre... | {
"language": "en",
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How do I solve this Gaussian path integral? Suppose
$$
Z = \int \mathcal D[\phi^*] \mathcal D[\phi] \exp(\phi^*A\phi + \phi B\phi)
$$
where $A$ and $B$ are operators. I know how to solve a Gaussian path integral involving only $\phi^* A \phi$ but I don't know how to handle the other quadratic term.
| You just divide $\phi$ to the real and imaginary part, to make things clear:
$$\phi = f + ig, \quad \phi^* = f-ig, \quad f,g\in{\mathbb R}$$
Up to some totally universal normalization factor, the integration measure is simply
$$\int {\mathcal D} f \,\,{\mathcal D} g $$
and the exponent in the exponential may be writte... | {
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What are the dimensions, width and length, of a photon? Everyone is always talking about photon's wavelength. But what about its dimensions?
What is length and width of it?
And does it even have a point to think about such things? Or those dimensions are non-existent in such cases?
| The photon can be experimentally shown to not be point-like. The Young's slits experiment involves the interference of a photon with itself (the photon behaves in some ways like a particle, in some ways like a wave and in some ways like a probability distribution. in reality these are convenient models that we apply to... | {
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What do quarks look like? I've heard everything from zero-dimensional points, to squares, and I would love to know what they really look like, or if they have any physical shape.
| I've not studied this at all but I have a theory that they are shaped like a triangular pyramid, all four sides being equilateral. It is the least amount of lines to create a three dimensional object, and being the simplest form of matter, it would be simple... But like I've said, this is just an unstudied guess
| {
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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's no doubt the solar system is accelerating. The milky way galaxy rotates, and we're quite on the outside. Hence, there's a permanent acceleration vector pointing to the center.
However, this is a phenomenally small acceleration. If you'd try to measure it here on earth, you run into all kind of practical problem... | {
"language": "en",
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How do you determine the "phase" of a hydrogen eigenfunction? I've been reading the wikipedia article on the atomic orbitals of hydrogen. They have a nice collection of diagrams, such as this one for n,l,m = 3,1,1
This is apparently showing the wavefunction, not the probability density, and the blue area represents po... | If you are referring to a global phase factor $e^{i\phi_0}$ (with $\phi_0 \in \mathbb{R}$ a real number, NOT the azimuthal angle $\phi$ upon which the hydrogenic wavefunction depends) multiplying the whole wavefunction, then that has probably been simply taken to be 1, as this choice does not affect any of the physics.... | {
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Bra-ket of products I was trying to solve the following problem.
(Lifted from Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund)
I came across across a solution for the problem as follows
(Lifted from http://theochemlab.asu.edu/teaching/chm598/ch2soln.pdf)
The 4th l... | I will consider non-relativistic quantum mechanics in this answer. The wave function of a particle with spin can be thought of as living in the tensor product space $L^2(\mathbb R^3,\mathbb C)\otimes V$, where $V$ is the spin space (usually just $\mathbb C^2$). This tensor product vector space becomes a Hilbert space (... | {
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What was Einstein's 1923 Nature paper "The Theory of the Affine Field" about? After his divorce with Mileva, Einstein published a paper in Nature entitled "The Theory of the Affine Field." Allegedly it confused renowned scientists. Why? What did the paper accomplish? What was it about, really?
| It was Einstein's reaction to Eddington's ideas about a unified field theory based on a symmetric affine connection. Ultimately, it did not go anywhere.
Cf. Hubert F. M. Goenner: On the History of Unified Field Theories. There's also a second part.
| {
"language": "en",
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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... | Note first that there are three different sources of gravitational potential: the disk, the bulge, and the dark halo.
There are a few different models of the gravitational field of the disk, two of the more common potentials are:
*
*Kuzmin model:
$$\Phi(r,z)=-\frac{GM}{\sqrt{r^2+(a+|z|)^2}}$$
*Miyamoto-Nagai model:... | {
"language": "en",
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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?)
| The designation of different colors of light as warm and cool, in contradiction to their actual color temperatures, has to do with the items that we experience in ordinary life.
Most objects hat we encounter are not warm enough to emit detectable levels of visible light. As they warm up, they begin to emit more visibl... | {
"language": "en",
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Confusion with potential in simple pendulum I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.
If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$... | So you've seen that $\frac{1}{2} m \dot{\vec{x}}^2+ mgz$ doesn't describe everything. Now, you'll learn about how to go from a formula almost like this to equations of motion later, but let's ignore that for a bit. Let's say there's a potential $U(\vec{x})$ which is zero on the circle, and off the circle is equal to a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161791",
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"source": "stackexchange",
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Why does the mathematical constant $e$ enter into quantum mechanics so much? In A. Zee's book Quantum Field Theory in a Nutshell, he mentions on pages 11-12 the following formula which he assumes reader had encountered before:
\begin{equation}
\langle q | p \rangle ~=~ \frac{e^{iqp/\hbar}}{\sqrt{2\pi\hbar}}.
\end{equat... | One reason is because harmonic oscillation is so common in nature. An oscillation is called harmonic if the force is proportional to how far the system is from equilibrium. E.g. a mass attached to a spring in a uniform gravitational field. If you lift the mass a bit, gravity takes over and there's a force in the down d... | {
"language": "en",
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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".
| Hadronization - the process by which colored objects form uncolored hadrons - is poorly understood, but we know the basics. Hadronization is a long-distance process, because, contrary to e.g. gravity, the strong force gets stronger at large distances.
When a quark-antiquark pair is created from a high-energy collision,... | {
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Is a black hole really a hole in space? What if when a supernova occurs, instead of it condensing into a singularity it creates enough force to tear a hole into the fabric of space? Is a black hole just what is sounds like, a hole in space?
| No. Spacetime is smooth and continuous everywhere except at the central singularity. If you jumped into a big enough black hole you would cross the event horizon without noticing anything special happening.
The requirement for it to be a big black hole is because the tidal forces at the event horizon decrease with incr... | {
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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... | Your equation (2) is right, in principle: it is the standard coproduct of Lie algebras,
but it is irrelevant, and should have never been used for anything here. The language confused you. It should read
$$ \boldsymbol{J^a} = \boldsymbol{j^a} \otimes 1\!\!1 +1\!\!1\otimes \boldsymbol{j^a} .$$
If you wished to apply it ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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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... | It is a mnemonic notation that indicates that $\mathrm{d}s^2 = g_{\mu\nu}\mathrm{d}x^\mu\mathrm{d}x^\nu$ is the object whose square root is to be used as the infinitesimal line element, traditonally denoted $\mathrm{d}s$, when determining the lengths of worldlines $x : [a,b] \to \mathcal{M}$ by integrating the line ele... | {
"language": "en",
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"source": "stackexchange",
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If a Killing vector field is timelike, can it be set to $\partial/\partial t$? If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to $\partial/\partial t$?
| Comments to the question (v3):
*
*Given a manifold $M$, if a smooth vector field $X\in \Gamma(TM)$ does not vanish in a point $p\in M$, then one may choose a local coordinate neighborhood $U\subseteq M$ of $p$, with local coordinates $(x^1, \ldots, x^n)$, so that $X=\frac{\partial}{\partial x^1}$. This procedure is ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | While rare, there are a few uses of the method of images to gravitational problems. As lurscher says, the problem is finding equipotential surfaces. In most problems, such a surface doesn't exist, and hence the scare use of the method of images in GR.
One class of problems for which it does applies are the so-called Di... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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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?
| My current understanding is that the physical reality of vacuum fluctuations, particle-antiparticle pairs being created and then annihilating, is disputed. The Casimir effect is often cited as physical evidence but there's a few authors which have come to dispute that the Casimir effect is convincing evidence for the r... | {
"language": "en",
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Calculating electrostatic potential A continuous charge distribution is spherically symmetric and has a volume charge density
$$\rho(r) = \rho_oe^{−\alpha r}$$
I need to find the potential as a function of '$r$' i.e. $V(r)$.
It seems fairly straight forward. I can easily find the Electric field as a function of $r$ us... | No, that is the simplest way to solve the problem. As mentioned in the comments, this is in the absolute scale of things a very easy problem: the spherical symmetry allows you to even have an integral to calculate, and the exponential is not only exactly integrable, but easily so. If you allow general spherically symme... | {
"language": "en",
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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... | In the book "Physics of the Plasma Universe" Dr. Anthony Peratt puts candle flames near the bottom of "energy in electronvolts" portion of the 'plasma spectrum'. If you look at the chart below, you'll see candles flames about midway (ok, cosmologically) between the ends:
*
*solar bodies and laser radiation
*terres... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | The proper time, $\Delta\tau$, between two events is a conserved quantity in special relativity i.e. all observers will agree on its value. Since the definition of timelike is $(\Delta\tau)^2 \gt 0$, and the definition of spacelike is $(\Delta\tau)^2 \lt 0$, there can be no coordinate transformation that interconverts ... | {
"language": "en",
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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... | Assume for the sake of argument that this decay channel happens.
Now, ask yourself how you are going to prove it?
*
*How about we compute the rate for each channel and see if the real rate is the sum? This works when the added channel is a reasonable fraction of the dominate channel, but you're talking about compari... | {
"language": "en",
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What does $v=c$ in the Lorentz transformation for time tell us? For the simpler cases as boost in the x-direction, the time dilation formula following the Lorentz transformation for time is $$\Delta t'=\gamma(\Delta t-v\frac{\Delta x}{c^2})$$Now, we observe that as $v\to c$, $\gamma\to \infty$. And we also observe that... | Also, the fact that $\Delta t' \rightarrow 0$ if we formally let $v \rightarrow c$ can be interpreted as saying that no time at all passes for a particle moving at the speed of light. Photons cannot "age" or in any other way change over time.
| {
"language": "en",
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"source": "stackexchange",
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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 goes back to the history of the Hubble constant. It's easy enough to write most cosmological formulas in terms of this value, but measuring it was something of a challenge for a while.
For several decades, we were confident it was between $50$ and $100\ \mathrm{km/s/Mpc}$. Many results scale with this value (to so... | {
"language": "en",
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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 problem is equivalent with considering stationary air and both train and boy moving 30m/s relative to the ground (and air). As they move in the same direction relative to the air, there is no relative motion between them (the observer and source are neither approaching nor receding). So there is no reason to expect... | {
"language": "en",
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Are the Wigner and Husimi transforms injective? I am wondering if the Wigner function is injective. By injective I mean, that, for every density matrix $\rho$, there is a different Wigner distribution. The same question applies to the Husimi distribution.
If the dynamical group is $\mathrm{SU}(2)$, the Husimi function... | The answer is a resounding "yes", cf Ref. 1, provided by Groenewold in 1946, op cit, and countless emulators since.
The Husimi is completely equivalent, so, injective, to the Wigner d.f., and so the answer is ipso facto "yes" here too.
I do not understand your particular SU(2)-blindness attributed to the Husimi, but ... | {
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Pumping charged particles (of same charge) into a blackhole Would would happen if you started pumping charged particles of same charge into a black hole? Let's assume that you have an infinite number of those charged particles. What will happen to the event horizon and the singularity? Please give both perspectives ... | Well if you add charge gradually to a black hole, it will become more charged. If you started with a neutral Schwarzschild black hole, it will then become a Reissner Nordstrom one, and each time you throw in another charged particle the charge will increase.
As the charge of a black hole is increased (keeping it's mas... | {
"language": "en",
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Is there a formal proof for the superposition theorem? I was just wondering whether there is a formal prove for the superposition theorem in electric circuits? I tried searching it online but couldn't find anything sufficient. Most of the sources assume it follows from the definition of linear systems, but then how do ... | There are many proofs, the problem is that they become too mathematical and hence end up distracting electrical engineering students from core electrical engineering.
Very rigorous proofs involve assuming your circuits can be represented as planar graphs. Additional assumptions including no short circuits, independent ... | {
"language": "en",
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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... | I would not be surprised if a cord with a given breaking strength of 80N held 100N once. It should be regarded as trash after that though.
You see, they set the breaking strength as guaranteed to hold under the worst-case setup. Select a low-reduction knot (the rating not is the double figure-eight which is common but ... | {
"language": "en",
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What is the expectation value of the position times momentum operator? Should I write the expectation of the position times momentum operator as:
$$\langle xp\rangle = \langle \psi|x (-i\hbar \partial_x) |\psi \rangle$$
or
$$\langle xp\rangle = \langle \psi| (-i\hbar \partial_x x) |\psi\rangle$$
| in short the first way, but you can see this via using the position basis,
$$
<x|\psi> = \psi(x) , \ 1 = \int |x><x| \ dx, \ p|x> = |x> (-i \hbar \partial_x), \ <x|x'> =\delta(x-x') \ \rightarrow \\
<\psi|xp|\psi> = \int dx \ dx' <\psi|x><x| x p | x'><x'|\psi> = \int dx \ dx' \psi^*(x) x <x|p | x'> \psi(x') \\
=\int dx... | {
"language": "en",
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What is basically the difference between static pressure and dynamic pressure? What is basically the difference between static pressure and dynamic pressure?
While studying Bernoulli's theorem, I came before these terms. The law says:
When the fluid flows through a small area, its pressure energy decreases & kinetic e... | The quantity $\frac{1}{2}\rho v^2$ is called dynamic pressure for two reasons: because it arises from the motion of the fluid, and because it has the dimensions of a pressure.
It is not really a pressure at all: it is simply a convenient name for the quantity (half the density times the velocity squared), which repres... | {
"language": "en",
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Why the electromagnetic wave transmits momentum in the direction of the movement? Ordinarily a transverse wave does not transmit momentum, as it is the case of the well-known sea wave phenomenon. But the electromagnetic radiation has both fields transversal to the movement of the wave. Anyway, the electromagnetic wave ... | It's possible to prove that while the fields $E$ and $B$ oscillations are transverse to the direction of propagation of the e.m. wave, the momentum carried by the electromagnetic field moves along the direction of propagation of the field(in vacuum) since it is defined in units of area and time by the relation $$\vec{S... | {
"language": "en",
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Does all the theoretical work of astrophysicists have to be confirmed by the observations of astronomers? I am a chemist an I have some doubts about the work of astrophysicists.
I know that astrophysicists do a lot of theoretical calculations based in other theoretical work and also based in real measurements, which ar... | Theoretical physics, in general, does not have to be confirmed by observations. Theories are proposed as an effort to explain observations, so some consistency with observations is expected. However, it's not necessary to wait for observations. A theoretical astrophysicist can propose work that is consistent with curre... | {
"language": "en",
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If any, what would be the ideal modulation frequency for a phase-sensitive light sensing experiment in a non-dark environment? I have constructed some equipment for sensing a beam of light. The equipment is enclosed in a rudimentary darkbox to block out the majority of the ambient room lighting, but is still partially ... | From your description, it seems that your detection system is operating in a nonlinear region. Nonlinearities in the detection system will complicate things, so making sure the detector is operating in its linear range will be very important. If the detection is linear, separation of the ambient and signal beam effec... | {
"language": "en",
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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... | There is no universally accepted quantum theory of gravity.
Quantumly, the "shape" of a fundamental particle is a very fuzzy notion - we know that states are often not localized, so it is wholly unclear what it means to say "the electron is pointlike". The proper formal interpretation of a "pointlike particle" is simpl... | {
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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_... | What you're missing is that you're interested in $E < 0$. Such states are "bound" in the square well. The equation:
$ \frac{d^2 f}{dx^2} ~=~ - k^2 ~ f(x)$
is solved by $f(x) ~=~ A e^{i k x} + B e^{-i k x}$. If $k^2 < 0$ then you get another $i$ in this picture and you switch from sinusoidal behavior to plus/minus expon... | {
"language": "en",
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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... | Part of the issue you're forgetting is the dynamics of the situation. The surface fields are not perpendicular because of the movement and the physical delay in setting up the induced eddy current to produce a counter field. If the velocity is very low or static then the forces cancel, which is why eddy breaking does... | {
"language": "en",
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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... | Consider a volume element $dV$ at a certain point $\vec{x}$. Let the strain tensor at it be given by
\begin{equation}
e_{ij} = \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}
\end{equation}
Let us diagonalize the strain tensor at this point and let its diagonal entries be
$u^{(i)}$. Since the tr... | {
"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... | Any body above 0K emits radiation. Same is the case with black body, it absorbs radiation and it also emits, now the rate at which it absorbs /emits depends upon the surrounding.
| {
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"question_score": "13",
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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=-... |
She asked us if the body was accelerating or slowing down
Acceleration is defined as the time rate of change of velocity and, in this example, the acceleration is constant and positive.
So, the full answer is: the velocity of the body is always increasing while the speed is decreasing for $t<1$ and increasing for $t... | {
"language": "en",
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Proof of Lorentz contraction? The measurement of the flux of muons at the Earth's surface shows that many more muons are detected than would be expected, based on their mean half-lifetime of 2,2 microseconds. This is a good proof for the time dilatation as predicted by the special relativity theory.
QUESTION: does ther... | Imagine for each observer there is a grid in space that maps how far light travels in an amount of time.
You can measure an object at rest in this grid by how long it takes light to travel its length and back again (this is important to measure it both ways).
Since light speed is a constant, the object needs to change ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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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.
| It is by lepton number and charge, but you can't get energy/momentum to balance. In the $\nu_e$ rest frame there isn't enough energy to make the products. If there is a nucleus around, you can imagine the $\nu_e$ emitting a virtual $W^+$ making the $e^-$, the $W^+$ scattering electromagnetically off a nucleus to deal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167008",
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Proving and demonstrating vacuum in container without breaking it Let there be a hollow container made of glass or some other transparent material, roughly the size and shape of an apple. Let the walls be of sufficient thickness for the container to be safely evacuated to some reasonable degree, perhaps around $10^{-8}... | Why don't you just put a balloon inside? It will enlarge because the proportion of the pressure inside and outside the balloon will change.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167098",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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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?
| The singularity probably does not exist, as GR likely breaks down at those size / energy scales. When we have a full quantum description of gravity we may know what's really there.
By the way, the part of the black hole we fully understand is actually the vacuum solution - the Schwarzschild metric - which includes the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167282",
"timestamp": "2023-03-29T00:00:00",
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Is it possible to have a black hole in empty space? If the escape velocity of two very massive objects is near the speed of light, and those objects are orbiting each other (let's ignore the Roche limit for this exercise), is it possible that the combined mass of these two objects is great enough that their center of m... | No, that's not possible. Even if the two bodies could be compressed to be just larger than their Schwarzschild radius (they can't really, without collapsing further to black holes), their combined Schwarzschild radius, which grows linearly with mass, is twice their individual Schwarzschild radii. That means that even i... | {
"language": "en",
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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?
| The formula for gravitational time dilation1 is
$$\frac{t_0}{t_f}=\sqrt{1-\frac{2GM}{rc^2}}$$
For a sphere,
$$M=V \rho = \frac{4}{3} \pi r^3 \rho$$
So
$$\frac{t_0}{t_f}=\sqrt{1-\frac{8G \pi r^2 \rho}{3c^2}}$$
So the greater the density, the greater the time dilation.
Has any relation been observed or postulated to exi... | {
"language": "en",
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What types of fusion reactions happened in population III stars? I have read that, in smaller stars, such as our Sun, the fusion reaction that takes place is a proton-proton chain, or PP chain for short.
From what I have learned, in larger stars, a different process takes place, known as the CNO cycle, in which carbon,... | I think you already know the answer...
Pop III stars, by definition, are born from primordial gas that is basically Hydrogen, Helium with trace amounts of deuterium, tritium, lithium and beryllium; they initially contain almost no C, N, or O. Therefore the primary fusion in massive Pop III stars has to be (well, initia... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Normalization of wave function meaning...? I just have one question.
I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I doing this? I'm not using any of the math I get out of it later on. The only thing I... | Like gonenc pointed out your assumption that normalizing your wave function does not imply continuity. And yes you'll probably won't need the normalization factor in your further calculations.
The reason for you doing this could be consistency with the Interpretation of the wave function squared as a probability amplit... | {
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White, is it a colour or absence of colours? Our chemistry sir and we had an argument today at the lab, he says that white actually is not a colour, it is the abscence of colour, but we say that it is a colour and we gave the following point to substanciate our point that white is a colour:
When we see an object in red... | To add to Steeven's answer:
Any wavelength of input light will be perceived as lighter or darker in color depending on the intensity of the light. At high intensities, we only 'perceive' whiteness. I'm not sure whether the brain just ignores the overloaded cones (color-sensitive retinal elements) in favor of the rods... | {
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Solving for the density operator in the quantum Brownian motion master equation I want to solve for the density operator in the quantum Brownian motion master equation,
\begin{align}
\begin{aligned}
\frac{d\rho_S(t)}{dt}=&-\left(\frac{i}{\hbar}\right)\Big[H_S+\frac{1}{2}M\widetilde{\Omega}^2X^2,\rho_S(t)\Big]-i\gamma[X... | How come you took an expectation value of an operator and still got an operator instead of a c-number?
In order to get a c-number equation, you will get it for the matrix elements of the density matrix, so in position space this would be $$\left\langle x | \rho | x'\right\rangle \equiv \rho(x,x')$$
I'll give you an exa... | {
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Estimating divergence of set of vectors I have a set of points where directions and intensities of a flow are given (in 3D). Is it possible to estimate the divergence of the flow defined by those vectors? I only need a rough estimate and I can assume continuity and smoothness.
I expected this to be a common question, b... | The definition of divergence is
$$\textrm{div}\,\vec{F} = \lim_{V \to p}\iint_{S(V)} \frac{\vec{F}\cdot\vec{n}}{|V|}dS, \qquad [1]$$
where $\vec{F}$ is the vector field, $V$ is the volume surrounding the point $p$ where the divergence is calculated, $\vec{n}$ is a unit-length normal vector of the surface, $S(V)$, of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168628",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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