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How does one integrate the mass density over a closed Universe (a 3-sphere?) to obtain the total mass of that Universe? Is this the correct integral? $$M = R(t)^3 \rho\int_0^1 4 \pi r^2 \frac{dr}{\sqrt{1-r^2}}$$ where $R(t)$ is the radius of the Universe at cosmological time $t$. By making the substitution $r=\sin \chi...
I am reading a user's manual, and the word appears here. At first, I think "CW" means "center wave". But later, I find that the meaning of "CW" is "continuous wave". It makes me confused. Generally, Laser has a unique frequency. Properly speaking, it has a too small fluctuation of frequency, or line width, such that...
A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $R=4 \text{cm}$. The plane of the coin is tilted at an angle of $\theta=45^{∘}$ with respect to the horizontal plane. Find the coin's period $T$ in seconds, that is, the time it takes for the coin to go arou...
The question was asked about pressure vs. Volume increasing in an ideal gas as temperature is increased. My question then is this. What is the formula to determine how much volume and pressure will increase as temperature is increased? Let me frame the question this way. PV/T=P2V2/T2 this formula works for a controlled...
I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the self-interaction(The final result is we will get general relativity). How can we defeat this difficulties ? Can you please show me some pa...
I have a question about a linear FRW cosmology with $k=+1$. Assuming zero cosmological constant the first Friedmann equation can be written: $$\left(\frac{\dot R}{R}\right)^2 + \frac{kc^2}{R^2}=\frac{8\pi G}{3}\rho$$ where $R(t)$ is the radius of curvature of space and scalar curvature$$ k= \left\{ \begin{array}{rl} -1...
I always notice this weird thing and try to overcome it but cant. As shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right. But that doesn't happen. No matter what I do the handle ...
In two-dimensional motion, which conditions are needed to be satisfied so the conservation of energy law holds? (for example, simple pendulum motion)
In the Ising model the mean value of any particular spin is: $$ m = \left<s_i\right> = \frac{ \sum_{s_i}e^{-\frac{H}{T} }s_i} { \sum_{s_i} e^{-\frac{H}{T} } } .$$ I read in several sources that due to "translational invariance" $m$ is "independent of the site label $i$". That means that all spins have the s...
I have a simple question: Does gravity slow down a horizontally thrown baseball? Assuming when a baseball is thrown it has a vertical velocity as well, does it slow does the ball? Any help is much appreciated.
Why is there a size limitation on human/animal growth? Assuming the technology exists for man to grow to 200 feet high, it's pretty much a given that the stress on the skeletal structure and joints wouldn't be possible to support the mass or move...but WHY is this? if our current skeletal structures and joints can supp...
I went to a restaurant yesterday and while I was eating dessert, I saw a standard stainless steel spoon (note the alliteration!) balancing on a plate. It was balancing on its handle, and I started wondering, Why is that particular point the center of gravity for the spoon? Thanks.
Why the acceleration of free-falling bodies become zero after some time? My only idea would be that the closer to the core of Earth we are, the value of "g" the lower becomes (since the mass below the body is lower and consequently, its gravitational force is also lower) but it works on large scales, like hundreds and ...
I know we can't move at the speed of light, but if we were to travel on a photon how fast would we see other photons going? The speed of light is constant... So do photons see other photons moving at the speed of light?
The question is very simple: Why does the Moon or the Earth or any another planet revolve anti-clockwise? And can any planet (or satellite) revolve clockwise? What is the physical law for this phenomenon?
I am stuck on a few issues in this video. (Note: It is at the frame concerning this question.) In it, from what I understand (which could be wrong) we first apply the Hadamard gate to a qbit in the $\lvert 0 \rangle$ state. Then on that we use a controlled not on the output value, together with another input from anoth...
I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, how does this potential look like?
I know that it often occurs that we need to take a derivitive with respect to $\beta$ in statistical mechanics. However, I think it is poor style to use equations with both T and $\beta$ in them especially since in most of the theory we take $\beta = \frac{1}{T}$. I see this abuse of notation frequently in textbooks, h...
Can cosmic radiation (alpha radiation) transmute the material of a space craft, particular carbon, titanium and aluminum? Where can i find transmutation tables or formulas to calculate the possibility of a transmutation and the outcome?
Is there a proof that time is a 4th dimension? If it is, then why not measure it in units of the previous three? Logical right? How many seconds is a temporal meter?
Thanks in advance to anyone who takes the time to answer this, and apologies in advance for what is probably (yet another) question here due to unfamiliarity with The Math. I had a chance recently to visit the CMS detector at CERN (sheer luck) and it's made me curious to better understand how the Higgs field interacts ...
I dont get why a forward gear allows sliding a car backwards. Any ideas? So this is a car with an automatic transmission. The transmission is in the drive mode (move forward). Car is at the slope facing the hill up. I am in the car pushing the gas pedal very gently. The car is supposed to move forward going up the hill...
Is adiabatic quantum Hamiltonian of variable dimension possible? This is very hypothetical and I am afraid may not have enough merit to belong to this forum. I would still like to elaborate. Here is an example. Is adiabatic quantum evolution possible on a system which contains four spins when the evolution starts, thr...
Would it be possible with the "mostly magnetic wave" to have it behave in such a way that it would be undetectable by radio triangulation? I read about the monument at the CIA headquarters that was designed by an artist. Supposedly it's cryptography is very difficult to decipher, but some of it has been deciphered. One...
According to my understanding, at the smallest level sound is just a collection of particles colliding on a wave. So, assuming we can arbitrarily reduce the size of any human being, how small can we reduce someone while this someone can still "hear" normal size human beings talk coherently. EDIT: In other words, how s...
I want to know how to deduce the equation $\vec{\tau}=\vec{\omega} \times \vec{L}$, where $\vec{\tau}$ is the moment of force (also known as torque), $\vec{L}$ is the angular momentum, $\vec{\omega}$ is the angular velocity.
Are we (not) limited by our own speed through time (1 sec / sec) to measure highest possible speeds(c)? I fire a laser which hits a mirror and comes back and I precisely measure the time, and knowing the distance I calculate the speed.. but when I measured time, wasn't I limited by my own speed in time? Here I'm imagi...
Suppose I am calculating the (homogenous) electric flux through a straight line. How do I calculate the surface integral of a straight line? Is it simply a line integral, or is it more complex (I don't think the first is true because if the surface integral is a measure of area, but the line integral is a measure of le...
I am struggling with the following problem (Irodov 3.3): Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between the spheres $x \ll l$. Find the rate $\frac{dq}{dt}$ with which the charge leaks off each sphere if their approach velocity...
I was going thru Ch7 of Foot and trying to fill in the gaps. However I got stuck on (7.14). So Foot was working with a two level system with a small perturbation in the Hamiltonian resulted from an oscillating electric field $$H_I(t)=e\mathbf{r}\cdot \mathbf{E_0}cos(\omega t)$$. Now we assume that the new eigenstate fo...
I've been trying to model the Saturn V's velocity using Tsiolkovsky's ideal rocket equation, and in the process, I think I may have made a mistake with regards to the specific impulse? I've come up with the following equation, taking the change in gravity into account: $$ \Delta v(t) = I_\mathrm{sp} g_0 \left(\frac{R_\...
Related: Faraday's law in a ring The ring launcher is a standard introductory physics demonstration that I assume almost everyone has seen (if not, YouTube it). The explanation of why the ring is launched is explained on many websites. For example, here is the explanation from the Pasco’s website, which was exactly the...
I'm very primitive with my thought. So please help if you can in layman terms with an answer to this question. Here we go- by using a street power pole as the source responder, is it possible to read a speed of a traveling car by using two reflectors on the road which sonar back to the source? My thought is reflector ...
A particle of mass $m$, moves around a central force whose potential is $$V(r) = kmr^3 \; (k>0),$$ then $(c)$ if the particle is slightly disturbed from the circular motion, what is the period of small radial oscillation about $r=a$? I have the solution but I am not understanding it. It says that the equation of...
I am confused between these two quantities: Isentropic pressure and Total pressure. Are they the same?
On the Wikipedia I found that the Bohr radius is equal to: \begin{align} \boxed{r_b=\dfrac{4\pi\varepsilon_0\hbar^2}{m_e{e}^2}} \end{align} but while we have been learning Bohr's model we derived the equation for a radius of the electron orbit like they do it on the hyperphysics: \begin{split} &2\pi r = N \lambda_b\\...
Because of the lack of any materials to propagate sound, it can't spread in space. There's the air in the atmosphere, but its volume mass increases constantly (either linear or exponential, I don't know) - it means that atmosphere doesn't have a sharp edge that separates it from space directly. What happens, when an a...
How to calculate air velocity in a fan and what data should I know ? So if I have a fan motor, fan blade and a battery, what data should I get from these items ? I think I will need to know the number of turns per second. How can I determine it ?
I am developing an android based game. I have 10 soldiers uniformly spaced in the scene using some kind of formation. Example - banks of 3 3 and 4 or banks of 4 4 2 or banks of 4 2 and 4 etc... Now the user can translate any one soldier he has currently selected in any position in the 2d scene. WHat I want is other sol...
Suppose we take a spring and compress it in a clamp. There is a potential energy due to the compression of the spring. It is now placed into a bath of acid that will dissolve the spring but not the clamp. What happens to the potential energy? In a realistic situation one (weak) point on the spring could break, so it wo...
Relative velocity of sound. As I know that speed of sound in medium is property of medium. And independent of source motion but depend on motion of audience or observer and motion of medium. But it is not clear to me. Please explain it.
This is an extension of a Phys.SE question I asked earlier, Fourier transform of two pulses of light. I start with 2 Gaussians, represented by the equation $e^{-(t/a)^2}\times e^{2\pi i d t}*(\delta(t-\tau) + \delta(t+\tau))$ where a corresponds to the FWHM of the Gaussian. (FWHM $\approx 15,\ a \approx 9.$ d is the sh...
Is this correct? Are scalar fields defined as being invariant under $U^{\dagger}U$ transformations? If so, is this transformation also called the trivial transformation? Thanks for any help or comments
This was a problem on my final exam that has been really bugging me. Consider the quantum Harmonic oscillator prepared in an energy eigenstate, $\psi_n$(x). Calculate the expectation value of the potential energy, using the recurrence relation between the Hermite polynomials, $H_n(\alpha x)$ together with the orthogon...
How an $n$ dimensional space looks like? Is it possible that we are really in a space of dimension greater than 3?
Is the reason for the split believed to be spontaneous symmetry breaking? If so, did SSB occur because the Universe was cooling rapidly from extremely high temperatures?
So, I was solving this problem1 and I realized that the system given seems to be non-deterministic when analysed with classical laws. The situation is thus: A rope is wrapped for an angle of $\theta_0$ (symmetrically) around a fixed pole (the circle in the diagram). One end is fixed to a wall, and the other end is pul...
The headline question: Is it known how to construct an equivalent of the 3-D Ising Fixed point theory on an arbitrary 3-D manifold? Or any non-trivial d > 2 fixed point? The answer is maybe as simple as a careful conformal mapping of the action . I don't even know whether this is a hard question not. Let me try to expl...
Generally, metals are usually fairly conductive, but their oxides aren't. I know conductivity is just one attribute, but in general, should you expect a, say, diatomic bulk crystal's properties to be anything like the bulk properties of each element it's composed of? Or do all those properties get thrown out the window...
If I have a quantum system which I prepare in a certain state, this state then evolves unitarily via a Hamiltonian. Suppose an observer provokes a collapse of the wave function by a certain measurement, this means that it must be in an eigenstate of the measurement. What happens subsequent to that? Will it remain in...
The centrifugal force acting on a revolving particle with negligible size is $\frac{mv^2}{r}$. What if the size is not negligible? Say we are talking about a large homogeneous circular disc, so its radius is not negligible when compared to the radius of its revolution. For the sake of simplicity, assume the disc is pe...
So on the net (one forum) I stumbled upon this, and article by Nassim Haramein. Now, I researched this guy a bit, and I couldn't find any peer reviewed article (other than this in 'Physical Review & Research International', which tbh I've never heard of before). What he's saying is: We find an exact quantized expressi...
E.g. if I know that my topology is that of a hyperboloid, how much freedom do I have left for my choice of the metric? And the other way around: if my metric is some conformal factor times the unit hyperboloid how much freedom do I have left in my choice for the topology? Am I forced to conclude that the topology of t...
Let's say you spill 10ml of water on the kitchen counter. It forms a small puddle that would evaporate after a while (assuming room temperature and sane humidity). Would spreading a large, dry towel over the puddle cause the water to evaporate quicker? What I mean is a towel that's much larger than the diameter of the ...
I tend to believe that there are two elementary properties in electricity: Electric charge Coulomb's force I think that I can express any other entity in electricity using just these two (by means of other physical theories e.g. relativity). Am I correct, or there are properties which can't be expressed in terms of t...
A quantum computer with 10 qubits is classically equivalent to $2^{10}$ bits. How is this equivalence worked out? I understand that a single qubit is a vector in a 2-dimensional hilbert space, whose base we can label as $|0>$ and $|1>$. So, 10 qubits will require a 20-dimensional hilbert space. According to these not...
I have a question about deriving variation of metric under Weyl and coordinate transformations in Polchinski's string theory (3.3.16). Under transformation $$\zeta: g \rightarrow g^{\zeta}, \,\,\, g_{ab}^{\zeta}(\sigma')=\exp[ 2 \omega (\sigma) ] \frac{ \partial \sigma^c }{\partial \sigma'^a} \frac{ \partial \sigma^d}{...
Alright, so I've been messing around with turning air pressure into thrust, however I'm only a sophomore in high school, so my physics knowledge is fairly limited. (I've studied higher level physics, but have nothing official.) So, with that being said, I've been messing around with utilizing thrust from air pressure. ...
If as some people suggest, there is no collapse of the wave function (is there a standard name for this position), then must one rule out the many-worlds interpretation of QM?
Decoherence explains how a classical state appears once quantum information in a quantum state leaks out. But presumably that environment has its own quantum state which then leaks out to a larger environment. Does this mean that decoherence can only be understood locally, and not globally? For example if the entire un...
My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an uncertainty in its wavelength or the wave number? Is not a confined wave-train equivalent to a burst of successive pulse...
Car B rests at the bottom of a frictionless inclined plane. In order to travel a height of 0.6m and maintain a speed of 2 m/s at the end of the track it needs to start with 4 m/s. a) If car B perceives the speed through a fully elastic impact from car A, with what speed does car A have to hit car B if the mass o...
Condition: A cylinder with a piston are situated along Y axis. Piston receives an impulse (P1) along Y axis and transmits it to the cylinder through a gas medium with which cylinder is filled. The impulse received by the cylinder along Y axis is P2. Question: Is P1 = P2? Note: we are only considering the Y component ...
The free energy, $F$ of a thermodynamic system at a given temperature $T$, is defined as, \begin{equation} e^{-\beta F} = \mathcal{Z} = \sum_{\{\text{configurations}\}} e^{-\beta E(\text{configuration}) } \end{equation} where $\beta = 1/k_BT$ and $E$ is the energy of a certain configuration. Why the free energy is cal...
I can't understand something about emissivity. Emissivity is defined as the ratio of the radiant energy of an object, to radiant energy of blackbody at a temperature $T$. So, The vegetation has approximate emissivity of $0.99$ and concrete smaller than this like $0.95$. But in thermal images vegetation appears darker ...
The many-worlds interpretation of QM is a realist explanation as it makes the wave function of the universe real. That is it makes the probabilities of outcomes real outcomes. One could argue that this view is biased that realist ideas of reality are better by definition. But philosophically speaking idealist ideas of...
In our introductory physics class, we were being taught about charge density ($\sigma$). Our teacher told us that a spherical conductor has a uniform charge density while conductors like a cuboidal conductor have a greater charge density at the vertices. In general, charge density is greater than average in uplifted a...
Charging by induction seems very unintuitive to me. Let me explain: Consider a positively charged rod and a neutrally charged conductor. You can charge it by induction by earthing it and not lose charge on the rod. You can then use this potential difference in the spherical conductor as energy. This can be repeated man...
I've a questions about the difference between small and large gauge transformations (a small gauge transformation tends to the identity at spatial infinity, whereas the large transformations don't). Many sources state (without any explanation or reference) that configurations related by small gauge transformations are ...
I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I faced difficulties in penetrating the literature... I'd highly appreciate any help with the following question: My aim is to relate a certain (equivariant) linear sigma model on a disc (with a non-compac...
I don't want to play with physical laws in a frivolous way. Assuming that the nature of matter and energy is the same, can a high density of highly energetic photons produce a gravity force? We do know that radiation is affected by space-time distortions, or in another way "feels gravity". Why do photons can (or cannot...
I was thinking; what shape does a black hole have?. By 'Shape', I mean its form (e.g, circle , cylinder, sphere, torus, etc..). We usually think of black holes as if they're plugholes (e.g, a flat circular object), but what if they're spherical? A spherical black hole would make much more sense. I would imagine than a ...
Due to an experiment, I need a small heater (around 70 to 100 watts). I intend to use an incandescent bulb so it can act as a heater. What I wonder here is will a 70 watts Incandescent Bulb be equal to a 70 watts heater?
Analysis of data is integral in bridging the gap between theory and experiment. How much do the results of the analysis depend upon the choice between Bayesian and frequentist methods? For instance, consider experiments in particle physics. This paper by Louis Lyons states that particle physicists use a hybrid approach...
For example the eq 2.1 here with regards to Type IIB. Unless I am terribly missing/misreading something Polchinski doesn't ever seem to derive these low energy supergravity actions. I would like to see a beginner's explanation (maybe together with review paper for further information) to getting these actions from str...
I am implementing the Monte Carlo wave-function approach to dissipation problems. So far, I have simulated the quantum harmonic oscillator coupled to a finite temperature reservoir given in section 5A of the above paper. I must now implement the two-oscillator system, whose Hamiltonian I am told is of the form $$ H=\...
You can read everywhere about water's extraordinary property of expanding when frozen, thus the reason ice floats on liquid water. What other substances do this? There are claims of mercury, silica, germanium, bismuth, and antimony, but I've had trouble tracking down the data to back these up.
A small bead is sliding on a smooth vertical circular hoop of radius $a$, which is constrained to rotate with constant angular velocity $\omega$ about its vertical diameter. $\theta$ is an angle between the downward vertical and the radius to the bead. I've calculated that: Lagrangian for this motion is $L=\frac{1}{2...
We have a theory of a Higgs field that describes how a particle gets mass. Since mass and charge both are intrinsic properties of a particle, is there any similar theory for how particles get electric charge?
Jim Baggott's "Higgs" quotes David Millers' prize-winning one-page explanation of the Higgs mechanism (the one that evokes Margaret Thatcher crossing a room). I've heard that part many times, but not what follows: an analogy between the Higgs mechanism and lattice distortions in solid state physics: Lattice distortio...
I recently read (sorry but I don’t have a reference) that interference is not only about destructive and constructive interference but moving energy from destructive to constructive regions according to conservation of energy. The place where this really bothers me is when light is being transmitted through glass. As l...
A speedway turn, with radius of curvature $R$, is banked at an angle $\theta$ above the horizontal. If there is a coefficient of static friction, $\mu_{s}$ between the tires and the track, what are the maximum and minimum speeds at which turn can be taken? My solution: Since coefficient of kinetic friction, $\mu_{k}$ ...
If Lagrangian of the motion is $$\mathcal{L}=\frac{1}{2}m\left(a^2\dot\phi^2+a^2\dot\theta^2\sin^2\phi\right)+mga\cos\phi,$$ how can I show that total mechanical energy is conserved? I've read this: If the time $t$, does not appear [explicitly] in Lagrangian $\mathcal{L}$, then the Hamiltonian $\mathcal{H}$ is con...
The prerequisite for adiabatic quantum evolution of single photon or biphoton system is as follows. We have to prepare a single photon or biphoton quantum system which has a ground and a higher level energy state. Is that allowed in physics? If we consider a single photon quantum system, higher energy means higher freq...
(skip disclaimer) Hi, I have a question in Polchinski's string theory vol I p 90, after introducing the ghost fields $b_{ab}$ and $c^a$, it is claimed The equations of motion then provide a boundary condition on $b_{ab}$. They have a surface term $$ \int_{\partial M} ds n^a b_{ab} \delta c^b=0 \tag{3.3.28}$$ I simp...
I was wondering if the following steps would result in a net displacement on a spacecraft operating in Earth's magnetic field: Turn on a superconductor Use a linear actuator to shift some mass Turn off the superconductor Shift the mass back to its original position Repeat Would flux pinning allow pushing or pulling a...
Suppose I weigh about $75~\text{kg}$ and I am attached to a (non-elastic) rope which is attached to a carabiner which can take at least $20~\text{kN}$. Suppose furthermore that I reach terminal velocity before the rope is tight, a bit far fetched maybe, but pretend that I reach $530~\text{km/h}$. What force is being a...
I have come across a problem which is a homework indeed, but i tried to pack this question up so that it is more theoretical. What I want to know is: If I am allowed to write energy conservation for an atom which emits a photon (when its electron changes energy for a value $\Delta E$) like this (the atom is kicked bac...
Five dimensional empty AdS$_5$ space has mass $$ E = \frac{3 \pi \ell^2}{32 G}. $$ Is the above equation correct? Let's do some dimensional analysis to confirm. In natural units, in 5 dimensions $[G] = -3$ where $[...]$ is the mass dimension. Also $[\ell]=-1$. Therefore $\left[ \frac{\ell^2}{G} \right] = 1$. So the d...
I understand the lagrangian formulation of classical mechanics, to a degree. I can derive the Euler-Lagrange equations from the "least" action principle, and equivalently can determine the equations of motion from a given lagrangian. I can handle lagrangian exercises in textbooks with ease. I don't quite grok it, thoug...
I'm a developer. I tried (mostly for fun) to create a realistic physic engine. I try to sum all forces (here thrust) applying to an object in two composantes: an acceleration vector and the angular acceleration. I read a lot about torque and thrust but there is still some stuff that I can't figure out. Let's take a ex...
The de Broglie wavelength is given by $$\lambda\equiv\frac{h}{mv}$$ Now, if we have a small body, it's wavelength will be large when it is in motion. Similarly, a large body will have small wavelength. It can be seen from the equation. First of all tell me if I am right about these observations. I was studying electron...
Maybe this is more of an Electrical Engineering question, but does anyone know why iPhones looking green/red through a linear polarizer? I find it strange that the light coming out would be polarized... I mean I guess there's no reason it shouldn't be, but what is making it polarized, moreover, what goal does it serve?...
In minimal $\Lambda\mathrm{CDM}$, there is a parameter labeled $\Omega_\Lambda$, and current fits place it at around $\left( \Omega_\Lambda \sim 0.73\right)$. Meanwhile, $\Lambda$ enters the Einstein field equations as an offset to the Ricci scalar. The smallness of $\Lambda$ is a much-decried problem in physics today....
The question "Did NASA nuke Jupiter?" while debunked immediately (non-fissile isotope was used) arose many what-if questions. What would happen if a subcritical chunk of a fissile isotope, like Pu-239 was dumped down the atmosphere of Jupiter? We know fission bombs use a big conventional charge to compress the fissile ...
Is there a downloadable star catalog which not only includes positions, but also spectral class, size, etc.? A CSV file would be great for the sake of easiness.
My question is, whether this definition $E=E_0e^{-i\omega t}$ includes that it is a plane wave, since I am confused by the fact that we do not have any dependence on the position. So about what kind of electromagnetic waves are we talking if we use $E=E_0e^{-i\omega t}$?
Why is the force required to slide a magnet off a steel plate A LOT less than the force required to directly pull it off? The force required to pull the magnet can be: 20lb While the force required to slide the magnet can be: 1lb more/less. Why is that?
Can we get high energy from laser like fusion and fission reactions ? what is highest energy we can get from laser ?
I get water to my home from a nearby Tank A at a certain height above ground level. I have a 1" pipe through which I get this water to my home.. I leave this water into my well by connecting a 1" tube to this pipe. Reason for question: I have seen water pressure vary(lower- more flow) depending upon the height I hold ...