Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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The origin of femto, atto and zepto SI prefixes Do you know why the SI prefixes: femto, atto, zepto have been accepted by Scientific Community, if this triad of metric units, is neither greek nor latin?
| From http://www.exa.com.au/metric/ a rewrite of the NIST Constants, Units & Uncertainty home page
Prefixes ranging from micro to mega were first introduced in 1874 by BAAS as part of their CGS system. Later, 12 prefixes ranging from pico to tera were defined as part of the International System of Units - SI, which was... | {
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The physics behind The Great Flood The book of Genesis floats (pardon the pun) some interesting numbers when discussing the Great Flood. For example, it rained for 40 days and 40 nights, and at the end of that time, the entire planet was covered in water.
I think we can deduce how much water that would have had to be,... | The closest to a physical discussion of the Great Flood may be
http://www.talkorigins.org/faqs/faq-noahs-ark.html#flood
| {
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Einstein's equation: Black hole solution Let Einstein's equations satisfy $ R_{\mu \nu } = 0 $. Suppose we solve it numerically with the aid of a computer. Can we know from the numerical solution if there is a black hole in the solutions? For example, how can you know when you solve Einstein's equation if your solution... | The way to do this is to look for a closed trapped surface in the solution. This is a spherical surface such that all the null geodesics, both going out and going in, have area that is locally going down per unit affine parameter. When you find such a surface, you know that it is inside a black hole, and you can stop s... | {
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How does the curiosity rover get it's power?
Possible Duplicate:
Mars Curiosity Power System
I found a web page that said it uses Plutonium. I am sure it's not based on fusion or fission. What is the basic idea on which the power plant works?
| Curiosity uses a radioisotope thermoelectric generator.
A radioisotope thermoelectric generator (RTG, RITEG) is an electrical
generator that obtains its power from radioactive decay. In such a
device, the heat released by the decay of a suitable radioactive
material is converted into electricity by the Seebeck e... | {
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Why does inverting a song have no influence? I inverted the waveform of a given song and was wondering what will happen.
The result is that it sounds the exact same way as before.
I used Audacity and doublechecked if the wave-form really is inverted.
The second thing I tried was:
I removed the right channel, duplicate... | Inverting a waveform is the same as rotating your speaker around 180 degrees to face away from you. (Yaw or pitch - not roll!)
The changes in air pressure your ear detects is exactly the same.
| {
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Making or Demonstrating Principle of Electron Microscope is it possible to either demonstrate the principle or make a SEM ( electron microscope ) at home or lab as an enthusiast??
and how can i start?
| "Yes, you can!" © :-)
Check out this guy on YouTube, he has described everything in detail:
http://www.youtube.com/watch?v=VdjYVF4a6iU (and his related videos)
Basically he used an electron gun from a small TV-tube, using phosphor and photomultiplier to detect electrons. Image is shown on an analog oscilloscope.
Althou... | {
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Is it possible to describe the entire universe with the behavior of an $\mathbb{R}^n$ field? Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as disturbances/waves/ripples/tensions in an $\mathbb{R}^n$ f... | Try reading up on string theory.Here is a series of lectures with "string theory for pedestrians".
A particular quantum vibration mode of the closed
string describes a graviton, the quantum of the
gravitational field. A particular quantum vibration of
an open string describes a photon, the quantum of the
elect... | {
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Charge and the Dirac field In Zee's quantum field theory in a nutshell, 2nd edition, pg 550 he has
$Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\}$
showing clearly that $b$ annihilates a negative charge and $d$ a positive charge.
I would very much appreciate an explanation o... | This is a matter of convention.
You are totally right: the $Q$ operator you have written implies that $b$ annihilates a positive charge and vice versa.
The thing is that in QED one usually defines $Q$ in a slightly different way, namely:
$$Q=-\left| e\right| \int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p... | {
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Sinusoidal Wave Displacement Function I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused.
The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is $y(x,t) = A\cos(kx - wt)$.
However, I see a drawing of the wave and they always seem t... | sinusoida functions is a function containing sin like y= Asin(kx+wt) and cosinusoidal are the ones like y=Acos(kx+wt)
| {
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How does the Sun's magnetic field continue to exist at such high temperatures? The temperature at the surface of the Sun is apparently well above 5000 C; I'm assuming the layers beneath the surface may be even hotter.
At school, we learned that heating a metal beyond a certain temperature, specific to each metal, would... | The current answers point into the wrong direction. The right direction, in my opinion, is indicated in the comment of dmckee.
The problem is with your intuition that high temperature destroys a magnetic field. This is wrong as we can see in numerous experiments.
It is correct, however, that there is a temperature at ... | {
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Gravity on supermassive black hole's event-horizon
*
*$M =$ black hole mass
*Gravitation is about $r^{-2}$
*Schwarzschild radius, $r_{\text{S}}$, is $\propto M$
*So, more massive black holes have weaker gravitation at their event horizon.
Consider a black hole so enormous that the gravitation on its event horizon... | The horizon, for any static black hole, is the surface where the escape velocity is $c$. Thus, your notion that gravitation is weaker at the horizon for larger black holes is incorrect.
EDIT: Consider that the thrust required to hover goes to infinity at the horizon regardless, i.e., the proper local acceleration for... | {
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Why does the running of the gauge couplings show $\frac{1}{\alpha}$ > $\frac{1}{\alpha_w}$ at low energy? I thought the coupling constants were something like:
$\alpha \approx 1/137$
$\alpha_w \approx 10^{-6}$
$\alpha_s \approx 1$
And yet if you look at any pictorial representation of the running of the couplings you s... | I think you're confusing the weak structure constant with the Fermi constant. The Fermi constant is $G_F=1.166\times 10^{-5}\text{ GeV}^{-2}$ and it gives us the effective strength of the four-point interaction of fermions. This four-point interaction is of course mediated by the W boson and by looking at the relevant ... | {
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How to prove that orthochronous Lorentz transformations $O^+(1,3)$ form a group? Orthochronous Lorentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$)
$$ \Lambda^0{}_0 \geq +1.$$
How to prove they form a subgroup of Lorentz group? All books I read only give th... | Misha's answer is correct and complete.
However, let me give you the physical argument that explains why you do not find the proof in any book. The proper orthochronous transformations are spatial rotations and pure Lorentz transformations (or boosts). And it is clear from a physical point of view that these transform... | {
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Could this fountain, under the right conditions, technically be able to lift me up? There is a big fountain in a lake in my city.
I was talking with a friend and we were wondering whether it would be able to lift me up. I sent a few emails and obtained information about the fountain. The raw email reads in French:
No... | You should consider yourself a 160 lb bag of water. The criterion for lifting you up is that the up-momentum per second in the water is roughly larger than the up-momentum you need. From the height of 200 ft, 60 m, you know the velocity is more or less $\sqrt{2gh}=35 m/s$, and to lift you up at 100kg requires transferr... | {
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Loopy lightning What causes lightning to follow the path it does ?
picture from BBC news: http://news.bbcimg.co.uk/media/images/62891000/jpg/_62891901_untitled-1copy.jpg main page: http://www.bbc.co.uk/news/in-pictures-19597250
| I would put it down to coincidence: a cloud to cloud bolt concurrent with a cloud to earth bolt.
Have a look at this, where branching is also seen. Do not forget that in cloud to ground, a bolt starts from the ground.
Or this one, which shows following two branches in cloud to cloud:
| {
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What are distinguishable and indistinguishable particles in statistical mechanics? What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann distribution is used for solving distinguishab... | Since there is no way in which the molecules can be labeled, the particles are indistinguishable.
On the other hand, if the assembly is a crystal, the molecules can be labeled in
accord with the positions they occupy in the crystal lattice and can be considered
distinguishable.
| {
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Applications of the particle in a box and the finite square well What are some "real" world applications of the particle in a box (PIB) and the finite square well (FSW) which are discussed in an intro quantum mechanics class? For instance, I know that the PIB can applied to quantum dots and the FSW to the Ramsauer-Town... | A very important real-world application of quantum mechanics is the laser, in a multitude of ways. For start, the whole operating principle is of quantum mechanic origin, and there is a host of other quantum mechanical phenomena involved.
Specifically, in this case a good example is the quantum-well semiconductor laser... | {
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Spooky action appears to contradict Relativity of time order of multiple events It is well known that in special relativity observers can disagree on the time ordering of two events.
It is also well known that entangled particles exhibit so called spooky action at a distance.
Today I read in the New Scientist and on th... | There is nothing in QM that allows c to affect a and b instantaneously. An observer who can measure c and a will simply observe that they are correlated, but that can't happen until signals have arrived from both c and a. So no contradiction can be observed. C doesn't cause the collapse of a. Their entangled states jus... | {
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Mechanics Energy (Calculus) A particle moves with force
$$F(x) = -kx +\frac{kx^3}{A^2}$$
Where k and A are positive constants.
if $KE_o$ at x = 0 is $T_0$ what is the total energy of the system?
$$ \Delta\ KE(x) + \Delta\ U(x) = 0$$
$$F(x) = -\frac{dU}{dx} = m\frac{dv}{dt} = m v\frac{dv}{dx}$$
Integrating to get U(x) ... | For this particular problem, it is useful to note that the force function has three zeros:
$$F(0) = F(-A) = F(A) = 0$$
This means the potential has three stationary points. Looking at the potential function, we see that $U(0)$ is a local minimum while $U(-A) = U(A)$ are global maximums.
This suggests that a natural ch... | {
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What happens when we cut objects? What is the role of the molecular bonds in the process of cutting something? What is the role of the Pauli exclusion principle, responsible for the "hardness" of matter?
Moreover, is all the energy produced by the break of bonds transformed into heat?
| You can cut diamonds and you can cut cake. The mechanisms responsible for making a cut are as different as there are different kinds of solids. Cutting is a process that separates a piece of material into two pieces along a plane. Although some of the total work expended to make the cut actually does go into breaking c... | {
"language": "en",
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Is Heisenberg's matrix mechanics or Schrödinger's wave mechanics more preferred? Which quantum mechanics formulation is popular: Schrödinger's wave mechanics or Heisenberg's matrix mechanics? I find this extremely confusing: Some post-quantum mechanics textbooks seem to prefer wave mechanics version, while quantum mech... | It is partly a specialty thing. Non-relativistic QM mixes the two approaches quite often (as do relativistic QM), but quantum field theory leans very heavily towards Heisenberg, as well as the path integral formalism.
There are more approaches, but they tend to be scarcely used. The algebraic approach is getting some u... | {
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Equations for an object moving linearly but with air resistance taken into account? I know (from Kinematics) that for an object moving linearly with an acceleration and without air resistance the following equations can be used to determine v(velocity) or x(position of the object) at any time:
$v=v_0+at$
$x=x_0+v_0t+\f... | Let $F$ be the independent force acting on the object. Let $D$ be the velocity dependent force acting in the opposite direction of $F$. The net force accelerating the object is just the difference. We have:
$F - D = ma$
Since $D$ is velocity dependent, the equation is a differential equation for the velocity.
$\dot ... | {
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Number of unique 2-electron integrals Consider 2-electron integrals over real basis functions of the form $$(\mu\nu|\lambda\sigma) = \int d\vec{r}_{1}d\vec{r}_{2} \phi_{\mu}(\vec{r}_{1}) \phi_{\nu}(\vec{r}_{1}) r_{12}^{-1} \phi_{\lambda}(\vec{r}_{2}) \phi_{\sigma}(\vec{r}_{2})$$
I am told that for a basis set of size K... | The right formula is very similar to yours,
$$ \frac{4!}{8}{100 \choose 4}+3!{100 \choose 3}+2\times 2!{100 \choose 2}+1!{100 \choose 1} = 12,753,775 $$
I think that by comparing the coefficients in front of the (correct) binomial numbers, you may determine how you need to fix your calculation.
| {
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Why is there a factor of 1/2 in the interaction energy of an induced dipole with the field that induces it? In this paper, there's the following sentence:
...and the factor 1/2 takes into account that the dipole moment is an induced, not a permanent one.
Without any further explanation. I looked through Griffiths' el... | The force on a dipole placed in an electrical field is given by $\mathbf{F} = (\mathbf{p}\cdot \nabla)\mathbf{E}$ (see, e.g., Griffiths, 3rd edition, eq. 4.5). Recall that,
$$
\nabla(\mathbf{p}\cdot\mathbf{E}) = \mathbf{p}\times (\nabla\times \mathbf{E}) + \mathbf{E}\times(\nabla\times \mathbf{p})+(\mathbf{p}\cdot\nab... | {
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How do electrons repel? I understand the basics, protons have a positive charge, neutrons have no charge, and the electron has a negative charge. But looking at the lines of force from a proton, they flow outward and push each other away. But, the electrons flow inward or towards themselves. How does that make them rep... | The force experienced by a charge is $F=E\cdot q$. Let electron number 1 be in some point in space. Its field lines are directed towards it. Now put another electron near it. Since the second electron's charge is negative, the above product implies that the force the electron feels is in the opposite direction than tha... | {
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What is an extreme deep field image (XDF) and how is it captured? NASA recently took this Extreme Deep Field image (XDF) that is the area of only small fraction of the dia of moon and contains 5,500 galaxies. Nasa says this was capture by extreme long exposures so it can capture the smallest of galaxies. My question by... | The adjective "deep" primarily means "a high resolution". The telescope just focused on a particular small region of the sky and took the sharpest picture it could.
There are no stars (from the Milky Way) in the XDF (or almost no stars, I am not sure) so the objects are bound to be far. In HDF, the "ordinary" Hubble De... | {
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Can Gases conduct Electricity? Liquid electrolytes ionize and hence a current can pass through them. So if a gas can ionize, can it conduct electricity too? If so, what are a few such gases?
| Gases do conduct electricity, as all materials do. However, they conduct electricity so poorly that we consider them insulators.
"Electricity" requires the movement of electrons. In a gas, these electrons are too dispersed to provided any measurable current.
The "lightning" example is slightly different. This refers ... | {
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Does the spectrum of Sol's emission change as it ages? A follow-up to my earlier question How would one navigate interstellar space? that just occurred to me; albeit on a different tack.
Sol is probably in a state of continuous flux. The change of state is probably over large timescales as compared to the life-span of ... | Each & every element has its own characteristic emission and absorption spectra (which we all know). As the star traverses its main sequence stage - the hydrogen atoms are actually getting used up to form helium atoms. As it enters the red giant phase, helium starts to fuse by the triple-alpha process.
The Hertzsprung-... | {
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How to properly bake a ultra high vacuum chamber? I need to get rid of water excess in my vacuum chamber, and for that there is the procedure of baking. In order to do that there are several things that one needs to consider, the power, heat load, type of heat tape to use etc. Since I've never done this before, I hope ... | The usual procedure involves
*
*Careful preparation for ultra high vacuum
*
*Do you reach a good high vacuum?
*Can all the equipment withstand high temperatures over a long period of time? If not you might to cool those parts while heating the rest of the chamber.
*Try to remove all materials that might have a h... | {
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Satellite Orbital Period I know I can calculate the period of a satellite orbit by Kepler's third law, but somehow it does not work out.
The sattelite is 20200km from surface of the earth.
*
*$r=$orbits radius=earths radius+satellites distance from surface of earth=20,200,000+6,378,000 = 26,578,000 m
*$G=6.67\cdot1... | Your formula and numbers look right to me. You can check (both your math and "all the calculators") by plugging in the numbers for a geosynchronous orbit (altitude of 35,786 km, or semi-major axis of 42,164 km): the period should be 24 hours.
| {
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Does the mass of the damper affect the transfer function in a vertical mass-spring-damper? Usually in system dynamics, I dealt with horizontal mass spring dampers. Now in my advanced class I am dealing with vertical mass spring dampers. So a spring is hanging from the ceiling with a mass connected, and then the damped ... | Gravity changes the equilibrium position, but not the motion around the equilibrium.
| {
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Calculating car's acceleration from change in angle of hanging object? The question essentially is based on a situation like this-
A car has a small object hung from the cieling on a string (apparently at an angle of 0 degrees to the ceiling).
The car is accelerating and the object is now hanging at a 30 degree angle ... | This is a neat example because the object makes its own force triangle - it's being pulled down by gravity and sideways by the car's acceleration. And the 45° angle means that the forces are equal.
| {
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Rotating hoop in Relativity What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the hoop change? (Note, I'm not intending to ask about optical effects, but rather what physically... | By symmetry, it'll look circular. Just look at it from above, along the axis. You can synchronize clocks along the rim by a signal from the center. Then have those rim clocks all emit signals simultaneously. In the rest frame, their signals will arrive at the same time as those of stationary clocks positioned around th... | {
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Do strong and weak interactions have classical force fields as their limits? Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
| I think there are really two separate issues here. One is the range of the forces, and the other is the existence of a classical limit.
Basically, being able to write down a Lagrangian density isn't the same thing as being able to describe the classical theory that is the counterpart of a quantized system. In particula... | {
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What is predicted to happen for electron beams in the Stern-Gerlach experiment? The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. What is theoretically predicted to happen f... | There is a bit of trouble with using electrons since the magnetic field of the apparatus will cause them to turn thanks to the Lorentz force. You could, of course, build a device to account for the turning, and still split the electrons by spin at the end.
| {
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Work Done by an Adiabatic Expansion I am given the information that a parcel of air expands adiabatically (no exchange of heat between parcel and its surroundings) to five times its original volume, and its initial temperature is 20° C. Using this information, how can I determine the amount of work done by the parcel o... | More clues? :-)
This is harder then the isobaric process because now the pressure is a function of volume. You need to write the pressure as a function of volume, then integrate it from the initial to final volume. For some clues see the Wikipedia article on adiabatic expansion. Although the question doesn't say so, yo... | {
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Would a spin-2 particle necessarily have to be a graviton? I'm reading often that a possible reason to explain why the Nobel committee is coping out from making the physics Nobel related to the higgs could be among other things the fact that the spin of the new particle has not yet been definitively determined, it coul... | A massive spin 2 particle must have five modes: helicity
$\pm 2$, $\pm 1$, 0. If a massless spin 2 particle has only helicity
$\pm 2$ modes without other modes and has a dispersion $\omega = c k$, then such a
massless spin 2 particle must be graviton (at least at linear order).
| {
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Hydrogen Hyperfine Structure: General Expression I was looking at the hyperfine structure for the hydrogen atom. I checked pretty much every textbook I knew but none of them gave me the general expression for the energy correction due to the hyperfine perturbation Hamiltonian.
All of them only treat the case when $\el... | The Hamiltonian for the spin-spin interaction is:
$$\Delta H_{SS} = \frac{\gamma_p e^2}{m m_p c^2 r^3} \Big( \frac{1}{r^3} \big(3(\vec{s}_p \cdot \hat{r})(\vec{s}_e \cdot \hat{r})-(\vec{s}_p \cdot \vec{s}_p) \big)+\frac{8 \pi}{3} (\vec{s}_p \cdot \vec{s}_p) \delta^{(3)}( \vec{r} ) \Big) $$
where $m$ and $m_p$ are the e... | {
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What are some of the best books on complex systems and emergence? I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory technical books.
| As how it's titled, Complexity: A guided tour is a guided tour to complexity sciences. There is no formula in the book, but it does discuss many results and give you pointers. The author is a student of Douglas Hofstadter. She has a talk here
FYI: @Chris Aldrich also shares many helpful links in Are there any theories ... | {
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Why does light of high frequency appear violet? When people are asked to match monchromatic violet light with an additive mix of basic colours, they (paradoxically) mix in red. In fact, the CIE 1931 color space chromaticity diagram shows this effect begins at about 510nm (greenish-cyan), where people mix in no red. F... | It's pretty hard to research but I think (not sure) that the short-wavelength spectra may appear deep violet because of a negative green cone response. This answer also explains the apparent brightness of violet.
| {
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How robust is Kramers degeneracy in real material? Kramers theorem rely on odd total number of electrons. In reality, total number of electrons is about 10^23. Can those electrons be so smart to count the total number precisely and decide to form Kramers doublets or not?
| I think Kramer's theorem is really only useful when you can write down a wavefunction for your system. It then tells you the degeneracy of the ground state of your wavefunction. If you have 1 mole of your material you couldn't write down a wavefunction for it so the degeneracy of the ground state would be meaningless.
| {
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Why are Euler's equations of motion coupled? Physical explanation I have a problem with one of my study questions for an oral exam:
Euler’s equation of motion around the $z$ axis in two dimensions is $I_z\dot{\omega}_z = M_z$, whereas it in three dimensions is $I_z\dot{\omega}_z =-(I_y-I_x)\omega_x\omega_y+M_z$, assum... | If you are familiar aircraft flight dynamics, then please remember an aerobatic maneuver so called "Immelmann turn". Let us take x,y and z axis for longitudinal, lateral and vertical coordinate axes fixed to the aircraft. Then, if we pull control a stick and let the aircraft turn in vertical plane around the y axis and... | {
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Do spacecraft engines suffer from carbon accumulation the way typical petrol/kerosene engines do? Just wondering whether the spacecraft engines/drives, or their booster rockets accumulate carbon the way car/truck engines do. What about ion/methane drives?
| Actually, it is a factor in some systems. RP-1 is a grade of kerosene specifically intended for use as rocket propellant, engineered specifically for reduced breakdown and coking at high temperatures which can otherwise cause problems for regenerative cooling channels, turbopumps, etc.
Also see page 115-116 in The Rock... | {
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Can a trajectory between planets accelerate a space craft? I read that if some spacecraft's trajectory is carefully planned, i.e. if it can slingshot (at loss of a better word) a massive body like a planet, it can gain speed. Is that correct ?
Does solar system actually lose some energy to such a space craft in this wa... | In order for this question to make sense you need to define which reference frame the spacecraft should gain speed in. Conservation of energy implies that the spacecraft gains no speed in the frame of reference in which the planet is stationary, but it can change its velocity (ie trajectory is changed). If you move tha... | {
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What is the difference between a spinor and a vector or a tensor? Why do we call a 1/2 spin particle satisfying the Dirac equation a spinor, and not a vector or a tensor?
| Spinor is a vector in the basis of not space-time, but its spin states;
in on sense, spinor is not a vector, since it will not transform as you transform the space (rotation, etc)
.
Generally speaking, tensors (including scalar, vector, tensor of rank 2,3,4...etc) are just mathematical objects (you lumped together) t... | {
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Same momentum, different mass The question is: if
*
*A bowling ball and ping pong ball
*are moving at same momentum
*and you exert same force to stop each one
*which will take a longer time? or some?
*which will have a longer stopping distance?
So I think I can think of this as:
$$F = \frac{dp}{dt} = m \... | Another way of looking at the distance is to look at the kinetic energies $\tfrac12 m v^2$, which will be greater for the less massive ping-pong ball if the momentum is the same.
The change associated with reducing the kinetic energy to zero will be equal to the force times the stopping distance, so if the forces are... | {
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Divergence of non conservative electric field I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field.
When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss (or Flux) theorem and get Gauss' law:
$$\mathbf{\nabla} \cdot \mathbf{E} ~=~... | As you've said, and just to be completely clear, in vacuum (neglecting, in other words, effects in macroscopic media like polarization), Gauss' law is the full, time-dependent expression of what you're calling the "first Maxwell equation."
The "derivation" of the Maxwell equations were originally formulated as differen... | {
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Why do green lasers appear brighter and stronger than red and blue lasers? This is mostly for my own personal illumination, and isn't directly related to any school or work projects. I just picked up a trio of laser pointers (red, green, and blue), and I notice that when I project them, the red and the blue appear to b... | A less scientific answer: It may also just happen that the green laser is more powerful than the others.
In fact, humankind always had great problems making a green laser diode, whereas the red and blue ones are readily available. The green pointers contain a full-fledged Nd:YVO4 DPSS laser oscillator with built-in KTP... | {
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Why is light called an 'electromagnetic wave' if it's neither electric nor magnetic? How can light be called electromagnetic if it doesn't appear to be electric nor magnetic?
If I go out to the sunlight, magnets aren't affected (or don't seem to be). And there is no transfer of electric charge/electrons (as there is i... | This image (taken from Wikipedia) demonstrates what an electromagnetic wave looks like.
Changing electric fields induce a magnetic field (this is how electromagnets work), and changing magnetic fields induce an electric field (this is how the charger on your electric toothbrush works). The result is that if one osci... | {
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Find magnetic scalar potential for superconducting sphere In regions where $J = 0$, the curl of the magnetic field $B$ is necessarily zero (since $\nabla \times B = \mu_0 J$). Therefore $B$ can be written as $B = -\nabla V_m$, where $V_m$ is a scalar function of position.
A superconducting ball of radius $a$ is placed ... | The boundary conditions you should use are that as $r\rightarrow \infty$, $\mathbf{B}\rightarrow B_0\hat{\mathbf z}$; and that at $r=a$, $\mathbf B \cdot \hat{\mathbf r}=0$.
| {
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Diagram-like perturbation theory in quantum mechanics There seems to be a formalism of quantum mechanics perturbation that involve something like Feynman diagrams. The advantage is that contrary to the complicated formulas in standard texts, this formalism is intuitive and takes almost zero effort to remember (to arbit... | There is an exposition of a diagrammatic representation of the terms in the quantum mechanical perturbation expansion here. Basically the diagrams are just used to represent the combinatorial properties resulting from eigenstate degeneracy.
(Just for fun there is also a diagrammatic approach to perturbation expansions... | {
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If nothing in the universe can travel faster than light, how come light can't escape a black hole?
Possible Duplicate:
How does gravity escape a black hole?
If nothing in the universe can travel faster than light, how come light can't escape a black hole? I mean, Einstein's relativity says nothing can travel faster ... | The essential idea to grasp here is that, regardless of the fact that light propagates at the "universal speed limit", gravity is curved spacetime.
Within the event horizon, the curvature of spacetime is such that there is no world line (path through spacetime), for light or any physical object, to the exterior of the ... | {
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limits of diamond anvils for high pressure research in this wikipedia article regarding diamond anvils, it mentions that the pressure peaks roughly at 300 GPa.
My question is why is this so? is the diamond crystal structure collapsing if higher pressures are applied (like 500-600 Gpa, where metallic hydrogen is expect... | The compressive strength of a perfect diamond cristal is in the range of 220–470 GPa, depending on the direction you compress. (X. Luo et al, J. Phys. Chem. C 2010, 114, 17851–17853; DOI: 10.1021/jp102037j)
To cite this article’s introduction:
Usually, diamond is used under nonhydrostatic conditions, such as a diamond... | {
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Mathematical definitions in string theory Does anyone know of a book that has mathematical definitions of a string, a $p$-brane, a $D$-brane and other related topics. All the books I have looked at don't have a precise definition and this is really bugging me.
| There isn't any mathematically precise definition. These are physical objects, and they acquire their definition in a given model which allows for calculations. The same physical object can appear in different models in different roles, so the strings have different mathematical definition in different limits of the fu... | {
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Long/short-range interaction A potential of the form $r^{-n}$ is often considered long-range, while one that decays exponentially is considered short-range.
Is this characterization simply relative/conventional, or is there a more fundamental reason?
| Graphing examples of each would rapidly convince you that the power law has a "long tail" whereas the exponential gets small rather quickly. That's the basic reason. But understand that it is possible to pick a distance from the origin and then to pick the constants in the potential such that the exponential will be ... | {
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What is the difference between weight and mass? What is the difference between the weight of an object and the mass of an object?
| The mass, strictly the inertial mass, relates the acceleration of a body to the applied force via Newton's law:
$$ F = ma $$
So if you apply a force of 1 Newton to a mass of 1kg it will accelerate at 1m/s$^2$. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface.
The we... | {
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Intuition for multiple temporal dimensions It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible... | I have been a self-guided student of theoretical physics for over 30 years. I don't have any formal training. I have been working on a model of our universe ever since I purchased and read Dr dr Michio Kaku book "hyperspace" in high school 25+ years ago. My model utilizes multiple dimensions of space time. It is still ... | {
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Where does Computer Science background students fit in Theoretical Physics I am basically an Electronics student - background in computer science (that's where I want to work). I applied for an internship in USA in a research institute where the group is focused in Theoretical Condensed Matter Physics, Chemical Physics... | Condensed matter physicists could always use some simulations, I'm sure. There's plenty of stuff where insight could be gained with a well run simulation. Depending on the place you're working at, you could have access to a supercomputer facility. The language people use for simulations vary, from Fortran, C, Python, M... | {
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How accelerometers sense constant velocity movements There is something I don't understand about accelerometers. I know it's possible to make an Inertial Measurement Unit (IMU) by using "three" accelerometers. So with that, I could calculate the $x$, $y$, $z$ coordinates of something in 3-D space.
The point that I don'... | It can't directly(Einstein was right)
What you can do is integrate all the accelerations you have measured upto that point in time to have a current knowledge of the current velocity.
This isn't very accurate because any small inaccuracies in acceleration will lead to increasingly inaccurate velocity, and so position, ... | {
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Force in tetrahedron edges I am looking for a formula that enables me to calculate the force in a tetrahedron edge such that it relates $F_b$ with $F_z$ through the beam thickness and length. I have the following assumptions:
*
*The beams are circular and hollow. So the have a radius $r$ and a thickness $t$.
*... | For there to be equilibrium, the cog has to be directly above the bottom vertex. The three beams joining there will support the same amount of compression each, and the vertical component of all three together must be equal to the loading. You will need a little trigonometry, and some properties of a tetrahedron you ca... | {
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What do the supercharges in extended supersymmetry do? What do the supercharges in extended supersymmetry do?
In ${\cal N}=1$ supersymmetry there are a certain number of fermions and and equal number of bosons. You can transform all fermions to the bosons (and vice versa) in a 1 to 1 fashion using a single supercharge,... | You need to be a bit careful about the counting of supercharges. In four dimensions, the smallest spinor representation is four-dimensional (over the real numbers), so $\mathcal{N}=1$ supersymmetry has four supercharges.
When there are more supercharges, there are simply more states combined into a single 'multiplet'.... | {
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How long will it take for a bullet to reach a Geostationary orbit? I'm curious to know this. Neglect air friction and imagine a bullet that were shot normal to the Earth's surface, from the Equator. I will have to consider the Coriolis effect and so I expect the path of the bullet will follow a spiral rather that a str... | $T = (R + H)(2H/(GM))^{0.5}$ for simple case without atmosphere. For GEO it's about 5 hours with zero velocity in GEO point and enormous shooting velocity.
But air resistance is proportional to ~$V^2$, so it would be hard for bullet to leave atmosphere ;)
Where does the question came from? Maybe you've just read "From... | {
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Equivalent spring equations for non-helical coil shapes? The compression spring equations are generally given for helical coil. What are the equivalent equations for alternative coil shapes, like oval?
| I'm guessing that the "equations that are generally given" you refer to the ones calculating deflection of a helical spring, based on the torsional deformation of the coil, such as what is found here. The following picture is taken from there:
As you can see, any cross section of the coil is subject to shear, as well ... | {
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Relativistic momentum I have been trying to derive why relativistic momentum is defined as $p=\gamma mv$.
I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one towards another in $x$ direction with velocities ${v_1}_x = (-{v_2}_x) = v$. After the collision these t... | Relativistic momentum is not defined as $p= \gamma m v$. For instance, this expression does not apply to photons, which are massless particles [*].
In the Lagrangian formalism of mechanics the momentum is defined as
$$p\equiv \frac{\partial L}{\partial v}$$
Using the relativistic Lagrangian for a free massive particle
... | {
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Can electromagnetic fields be used to deconstruct and reconstruct atoms? I was thinking one day and came up with a theory after reading about how scientists were studying anti-matter by using electro magnetic fields to separate matter from the anti-matter they made. It got me thinking would it be possible to use very ... | Electric strength =5.145175226 X 10^11N/C
Magnetic strength = 235125.6635 T
so Velocity of the electron =
E/B =2.188266.117 m.s^-1 = C/137
| {
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Bernoulli's equation and reference frames So I was thinking about this while driving home the other day.
I've never been quite clear on why when you drive with the windows down air rushes into your car. I thought this might be explained by Bernoulli's equation for incompressible flow, but I ran into what seems to be a ... | Bernoulli's equation is frame-dependent as the following paper shows it in a nice way
The Bernoulli equation in a moving reference frame
The essence of the argument is to realize that in a frame where the obstacles, around which the fluid moves, are not stationary, these surfaces do non-zero work. And one must account ... | {
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How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics? $$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
| In quantum mechanics, the likelihood of a particle being in a particular state is described by a probability density function $\rho(x,t)$.
Suppose my system is a 6 sided die. Then the expectation value for a given roll is
$$EV= \tfrac{1}{6} 1 + \tfrac{1}{6} 2 + \tfrac{1}{6} 3 + \tfrac{1}{6} 4 + \tfrac{1}{6} 5 + \tfra... | {
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Computational Science involve programming? I read what is computational science in Wikipedia but the explanation and understanding are not very clear.
So, I could you please give a simple example computational science project and what all basic skills a person should have?
Also,
*
*Does computational science invol... | *
*Some branches of computational science involve programming by yourself the needed algorithms for solving questions.
*Computational materials science would be a sub-discipline of computational science.
*I cannot say. You do not give details on your background neither details of the project.
| {
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How do bits get transferred over a copper wire? I've been a programmer for a while, and I've done a little bit of network programming, but I'm wondering, how do bits get transferred over a copper wire?
What counts for a 1 & what counts for a 0?
I don't know a lot of physics so explain to me as if I were a 8 year old pl... | You won't be surprised to learn it's just varying voltage levels in a circuit formed by the network cables. You also probably won't be surprised to find that the details are fiendishly complicated and far too involved to reproduce here. Even the voltage levels used depend on whether it's 10MHz, 100MHz or GHz cabling. G... | {
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Relative Velocity and Momentum The question is,
A $45.5~kg$ girl is standing on a $140~kg$ plank. Both originally at rest on a frozen lake that constitutes a friction-less, flat surface. The girl begins to walk along the plank at a constant velocity of $1.47~m/s$ relative to the plank.
(a) What is the velocity of the ... | Try this method for solving the majority of Momentum/Impulse Problems with these two simple equations. Michel Van Biezen on Youtube teaches this method. Sure beats m1v1 + m2v2 (initial) = m1v1 + m2v2 (final).
Given:
Girl- Mass of 45.5kg; Velocity +1.47m/s
Plank- Mass of 140kg
Questions:
QA Find the VELOCITY of Plank ... | {
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Statistics in physics What are the uses of statistics in physics? I am about to embark upon a study of statistics and I would like to know what the particular benefits I gain in physics.
| I can't vouch for your school, but I would imagine that the kind of statistics you do in a Statistics Major is different from the statistics used in thermodynamics. Thermodynamics is basically ensemble theory, permutations and expectation values.
I imagine that in a pure Statistics course, you will daily hear words lik... | {
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Photon energy - momentum in matter $E = h\nu$ and $P = h\nu/c$ in vacuum.
If a photon enters water, its frequency $\nu$ doesn't change.
What are its energy and momentum: $h\nu$ and $h\nu/c$ ?
Since part of its energy and momentum have been transferred to water, it should be less.
If water's refractive index is $n$, are... | A new solution to this controversy has just (June 2017) been published:
"in a transparent medium each photon is accompanied by an atomic mass density wave. The optical force of the photon sets the medium atoms in motion and makes them carry 92% of the total momentum of light, in the case of silicon."
(my emphasis)
http... | {
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How big of a lens or parabolic mirror would it take ...to heat a piece of steel so its glowing yellow (1100 C)? Assuming you had a cloudless day at a latitude of, say, San Francisco...
Basically I'm wondering if it is possible/feasible to be able to do basic metal working without a traditional forge, just using the pow... | For steel, the specific heat would be $c_p=0.5 kJ/kg K$, with a density of $
\rho=7000 kg/m^3$. Suppose you want to increase the temperature bij say $\Delta T=1100K$ of a piece of size $V=(15cm)^3$
Then you would need a total energy of.
$$E=\rho c_p V \Delta T$$
Which gives you typically $E=10^7 J$
Now, the power of th... | {
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Confused about unit of kilowatt hours So I am a little confused on how to deal with the Kilowatt hours unit of power, I have only ever used Kilowatts and I have to design a residential fuel cell used as a backup generator for one day.
The average power consumption of a US household is 8,900 kW-hr per year and 25 kW-hr ... | A kilowatt is a unit of power, which has the dimensions of energy over time.
A kilowatt-hour, then, has dimensions of energy.
As a simple example, if you wanted to charge up a battery so as to operate a 1,000-watt (DC) heater for one hour, you'd need one kilowatt-hour of energy (assuming the mythical world of perfectly... | {
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The requirements for superconductivity Which properties are sufficient evidence for a material to be not superconducting?
I am looking for a set of statements like
If the material is semiconducting, it is not superconducting
Edit:
I am not looking for a definition of superconductivity, or for introductional literatu... | I doubt that any such statement exists, as it would imply a very deep understanding of superconductivity we don’t currently have.
This holds especially as you apparently look for temperature-independent statements, whereas most metals can be made superconducting at sufficiently low temperatures, and all high-temperatur... | {
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DIfference in Pitch Caused by Water Temperature? I have recently been intrigued by the following question: What is the difference between the pitch of the noise of dripping water between hot and cold water? For example, would cold water create a higher pitched noise while dripping into a pot of water? Or vice versa?
| Taking into account some facts:
The speed of sound C is 343.2 m/s
In air the speed increases 0.6 m/s per degree Celsius
Source: http://en.wikipedia.org/wiki/Speed_of_sound
Also, the just-noticeable difference (jnd) in pitch depends on the tone's frequency. Below 500 Hz, the jnd is about 1 Hz for complex tones; above 10... | {
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exponential potential solution let be the Schroedinguer equation
$$ - \frac{d^{2}}{dx^{2}}y(x)+ae^{cx}y(x)=E_{n} $$ (1)
here a and c are constants.
i know how to solve it from http://eqworld.ipmnet.ru/en/solutions/ode/ode0232.pdf
but what is the condtion to get the energies ?? on the interval $ [0. \infty) $ or in oth... | To find the bound states for the potential
$$V(x) ~=~\left\{\begin{array}{ccc}ae^{cx} &\text{for}& x>0, \\ \infty&\text{for}& x\leq 0, \end{array} \right.$$
where $a,c>0$ are two positive constants, one should solve the time-independent Schrödinger eq. with the two boundary conditions
$$ \psi(x=0)~=~0 \qquad \text{and... | {
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Hubbard Model Hamitonian $$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$$ is defined to be a Hamiltonian for modelling the quantum random walk of identical particles on a graph (i.e., the Hubbard Model). A particle can make a transition from one verte... | http://arxiv.org/abs/1102.4006
if you want to do exact diagonalization, the paper above might be useful for you.
To obtain the matrix representation of the Hamiltonian, the basic idea is straightforward. First, enumerate the basis vectors; Second, act your Hamiltonian on each basis vector, see what basis vectors will b... | {
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Why are different frequency bands used in different countries? Why are different frequency bands used in different countries despite ITU's effort for a common frequency band use? There's got to be a reason behind this.
For instance, U.S.-based Verizon Wireless uses the 700 MHz frequency band for its LTE service while E... | The RFID Journal explains this succinctly.
The industry has worked diligently to standardize three main RF bands:
low frequency (LF), 125 to 134 kHz; high frequency (HF), 13.56 MHz;
and ultrahigh frequency (UHF), 860 to 960 MHz. Most countries have
assigned the 125 or 134 kHz areas of the spectrum for low-freque... | {
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Would a gauss rifle based on generated magnetic fields have any kickback? In the case of currently developing Gauss rifles, in which a slug is pulled down a line of electromagnets, facilitated by a micro-controller to achieve great speed in managing the switching of the magnets, does the weapon firing produce any recoi... | If the Gauss rifle shoots a projectile with exit speed of $v_1$ and mass $m_1$, then its momentum will be:
$p=m_1v_1$.
Because of momentum conservation law, the rifle will have the same momentum in opposite direction. If the rifles mass is $m_2$, the rifle will start moving in the opposite direction with end speed of:
... | {
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Can objects, animate or inanimate, be constructed out of basic particles? If all the elements are made of protons, neutrons and electrons, but some elements are much rarer and more expensive than others, would it be possible to break apart atoms of one element and make atoms of another element or molecules out of them?... | *
*In fact, according to modern physics matter consists of much more than only neutrons, protons, and electrons. Say for example, quarks that make up neutrons and protons, or pi-mesons that hold nuclei together(search on wiki "standard model").
*In principle, it IS possible to take apart atoms (' nuclei), rearrange t... | {
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Why can't "missing mass" (=dark matter) be photons? After a star lives and dies, I assume virtually all of its mass would be photons. If enough stars have already lived and died, couldn’t there be enough photon energy out there to account for all the "missing mass" (=dark matter) in the universe?
And if there were enou... | As a general rule, zero mass particles which travel with the velocity of light are not good for dark matter, because dark matter concentrates around gravitational attractors. It has to be particles with some mass that can be at rest in order to stay around a galactic center from the beginning. In addition they have to ... | {
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Physical intuition for higher order derivatives Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
| Higher derivatives of position are related to "generalized curvatures". In 3D, for instance, the derivative of acceleration is secretly related to the torsion of a curve. The hint is the Frenet-Serret (binormal, normal, tangent) triplet or the so-called repere mobile (a la Cartan). A higher dimensional extension of thi... | {
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What makes an equation an 'equation of motion'? Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint.
For example, in the Hamiltonian formulation of Maxwell's theory, Gauss' law $\nabla\cdot\mathb... | An equation of motion is a (system of) equation for the basic observables of a system involving a time derivative, for which some initial-value problem is well-posed.
Thus a continuity equation is normally not an equation of motion, though it can be part of one, if currents are basic fields.
| {
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How is the topological $Z_2$ invariant related to the Chern number? (e.g. for a topological insulator) This question relates to the $Z_2$ invariant defined e.g. for topological insulators:
Is it correct to relate $Z_2$ = 1 to an odd Chern number and $Z_2$ = 0 to an even Chern number?
If yes, is it also correct to think... | For a time reversal invariant bloch hamiltonian (such as in a $\mathbb{Z}_2$ topological insulator) the Chern number is always zero.
The topological invariant $\nu = 0,1$ classifies the insulator as trivial or topological. This can be found by counting the number of times the surface energy bands intersect the Fermi e... | {
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Do new universes form on the other side of black holes? I have four questions about black holes and universe formations.
*
*Do new universes form on the other side of black holes?
*Was our own universe formed by this process?
*Was our big bang a black hole seen from the other side?
*Are there solid reasons why th... | *
*No, physically, no new Universes ever get formed. In particular, the extended Penrose causal diagrams with new infinite regions just show the maximal extension of the spacetime that is possible mathematically, ignoring physical processes inside the black hole. In physics and reality, the extension is unphysical bec... | {
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Evaluating propagator without the epsilon trick Consider the Klein–Gordon equation and its propagator:
$$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$
I'd like to see a method of evaluating explicit form of $G$ which does not involve avoiding singularities by the $\varepsilon$ trick. Ca... | As far as my experience goes, the problem stems from writing the right solution for all reals to the problem:
$$
(p-m)G(p)=1.
$$
which reads:
$$
G(p)=\text{P.v.} \frac {1}{p-m}+c_0\delta(p-m)
$$
where $\text{P.v.}$ stands for principal value. The $\delta(\epsilon-\omega)$ function appears as it is the Kernel of $(\ome... | {
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What's the difference between space and time? I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the two concepts or how they are related.
How are the concepts of space, time,... | Suppose you move a small distance $\vec{dr}$ = ($dx$, $dy$, $dz$) and you take a time $dt$ to do it. Pre-special relativity you could say three things. Firstly the distance moved is given by:
$$ dr^2 = dx^2 + dy^2 + dz^2 $$
(i.e. just Pythagorus' theorem) and secondly the time $dt$ was not related to the distance i.e. ... | {
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Why does the moon sometimes appear out-of-place? Quite often I go out in the morning and I'm in Milton Keynes, so I would expect the moon to rise in the east and set in the west. Sometimes at about 2, 3, 4 o’clock in the morning the moon is low in the east. I was just wondering how that worked out?
| Well, let’s zoom out for a bit and imagine you're off of the Earth and you’re looking at the Earth and the moon from space. So you have the Earth as the bigger of the two bodies sitting let’s say, in the centre and the moon is in orbit around the Earth.
So the moon goes around the Earth and the moon takes a month to d... | {
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Averaging decibels Wikipedia:
The decibel (dB) is a logarithmic unit that indicates the ratio of a
physical quantity (usually power or intensity) relative to a specified
or implied reference level.
If I measure some physical quantity in decibels, then what is the preferred way to calculate the mean of the measur... | There are reasons more than "preference" for the averaging. You defined it that way usually because you can get more information from that, particular for those additive quantities.
Suppose you preform a set of measurement at a particular point in space, there are two cases: (a) get the averaged value (b) take the aver... | {
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Is H=H* sloppy notation or really just incorrect, for Hermitian operators? I saw it in this pdf, where they state that
$P=P^\dagger$ and thus $P$ is hermitian.
I find this notation confusing, because an operator A is Hermitian if
$\langle \Psi | A \Psi \rangle=\langle A \Psi| \Psi \rangle=\left( \langle \Psi|A\Psi\ran... | Hermitian in the sense used by physicists doing quantum mechanics is usually meant to be self-adjoint, or, equivalently, with real eigenvalues. That is, for some matrix representation of $A$:
$$ \left( A^{\dagger} \right)_{ij} \equiv \left(A \right)^{\star}_{ji} = \left(A\right)_{ij}$$
where the first equality is the d... | {
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Limescale formation at room temperature? There is a large metal container in form of a cube made of stainless steel. It is used for storing water in it for technical uses. The problem is that all joints at the bottom of the container have micro cavities and water leaks through them very slowly. I am thinking of a metho... | Use a solution of a suitable polymer. As the solution leaks it will dry in the outside air, solidify and block the holes. You might try Radweld.
| {
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Is there a way to formulate relativistic dynamics in a way that "hides" the finite speed of light? I'm not referring to the dimensional choice that makes $c=1$; rather I'm imagining something more about replacing all references that apparently involve velocities with the appropriate $\gamma$ factors or rapidity. In thi... | If you need equations without velocities, just with $\gamma$, just replace any $v$ by $c\sqrt{\gamma^2-1}/\gamma$ and you're done.
Incidentally, $\gamma$ isn't the only useful function of $v$ that takes values between $0$ and $\infty$. You could also use the rapidity $\eta={\rm arctanh}(v/c)$.
It's good to use $\gamma$... | {
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When is the right ascension of the mean sun 0? I understand that the right ascension of the mean sun changes (at least over a specified period) by a constant rate, but where is it zero? I had naively assumed that it would be zero at the most recent vernal equinox, but when I try to calculate the equation of time using ... | Im not entirely convinced that light-time is the culprit here. The Earths orbit is not circular, its elliptical, as the Earths orbital eccentricity is non-zero. Because of this, the Earths distance to the sun throughout the course of the year is not constant, and therefore the time delay due to lights finite speed wi... | {
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Are galactic stars spiraling inwards? Are the stars in our galaxy spiraling inwards towards the center, or are they in a permanent orbit?
And if we are heading towards the center then what is the rate of this process?
I started wondering this while watching this documentary: http://www.youtube.com/watch?v=zKE4Bt8ylhM
| All stars in our galaxy are in stable elliptical orbits around the galactic centre. But they are not all moving in the same direction with the same speed... meaning there is a random maxwellian distribution of velocities among the stars.
What this effectively means is (like the animation that Crazy Buddy posted) altho... | {
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How would natural (resonant) frequencies affect amplitudes? I read $y=A\sin(2\pi ft)$, where $A$=Amplitude, $f$=Frequency, $t$=Time and $y$=$Y$ position of the wave.
Since natural frequencies only take the most effect when they are close to the frequency.
How would one natural frequency and several natural frequencies ... | If you are driving a resonant linear system, which is characterized by a natural frequency $f_n$ and quality factor $Q$, with your specified sinusoidal input $y_{in}$ of amplitude $A$ and frequency $f$, the steady-state output $y_{out}$ will be:
$$ y_{out} = \frac{A}{1+j \frac{1}{Q} \frac{f}{f_n} - \left(\frac{f}{f_n} ... | {
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How to find out the maximum radius of a hole that can keep water stay in a container by water viscosity? Assume I have a inverse cone which holds 200ml water. I am going to cut the tip of the cone to create a small hole. How to calculate the maximum radius of the hole that the water will still stay in the container?
| If you have a water drop with radius $r$ then the pressure difference between the inside of the drop and the outside is:
$$ \Delta P = \frac{2\gamma}{r} $$
To calculate the hole size you need to work out the pressure at the bottom of the cone and equate this to the pressure calculated using the expression above. The pr... | {
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Why are so many forces explainable using inverse squares when space is three dimensional? It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance.
However, since volume is determined by three dimensions and presumably these phenome... | These physical phenomena (gravity, Coulomb force) are forces caused by an object you can consider pointlike. That is, for the inverse square law to hold, the object emits the force uniformly in all directions from one point.
That means that at any distance (call it $R$) from the object, you'll feel the same force as yo... | {
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Gaussian type integral with negative power of variable in integrand How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation arise in physics where this type of integral with negat... | In this form, you won't get it naturally in physics because the Gaussian factor $\exp(-t^2)$ appears in the normal distribution or the harmonic oscillator etc. but with the addition of $1/t$ or $1/t^2$, one gets a non-normalizable and non-integrable (divergent) modification of the original Gaussian. However, one could ... | {
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"answer_id": 0
} |
Why is lightning more rare during snow storms than rain storms? Lightning and thunder during a snow storm is uncommon. As far as I know, more uncommon than during a typical rain storm. Why is this? I speculate it might be one, or both, of the following two ideas, one having to do with a change in the dielectric, the... | The mechanism by which lightning is produced is complex and imperfectly understood, but we know moisture is important in two respects:
*
*Heat is released when water vapor in the air condenses into liquid drops, and this heat helps provide energy to the thunderstorm.
*Interactions between supercooled liquid water d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47312",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 4,
"answer_id": 0
} |
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