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How am I able to tell whether there is a light on in front of me even with my eyes closed? The usual darkness whilst eyes closed transforms into a not so bright glow when my closed eyes are in front of a light source? How am I able to intercept light when my eyes are closed?
I guess that, since the Z boson is more massive than both the electrons, they need to go pretty fast (so that their kinetic energy is large enough), but is annihilation a property of the electromagnetic force only? Can the weak force also cause annihilation?
Refraction: light changes direction of propagation when entering a material with a different refractive index. Does the direction of propagation of light change sharply and almost instantaneously (as shown in the diagram) or smoothly?
This question has been on my mind since I first learned optics. Where will the light ray go? First, I thought of it taking a U turn. But, I don't think that will happen. Now I have studied a bit about wave optics and I think that the light will go... everywhere? Can someone please explain it in realm of ray optics? I ...
Is there a way to see that Bertrand's theorem is true intuitively. I mean without getting into too much mathematics ?
The Einstein-Hilbert action is given by, $$I = \frac{1}{16\pi G} \int_{M} \mathrm{d}^d x \, \sqrt{-g} \, R \, \, + \, \, \frac{1}{8\pi G}\int_{\partial M} \mathrm{d}^{d-1}x \, \sqrt{-h} \, K$$ including the Gibbons-Hawking-York boundary term. A well-known derivation of the entropy of the Schwarzschild metric requires t...
Are the energy of the electric field and the energy of the magnetic field concentrated on their sources OR are they scattered in the environment where the fields arent zero? Can you base your answer on a formula so I can understand it better?
How is it possible to achieve waves which are spatially, but not temporally, coherent? Can this be done with a bandpass filter? Conversely, how is it possible to achieve waves which are temporally, but not spatially, coherent? Can this always be achieved with a pinhole?
In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to tunnel between two pieces of superconductor. With a potential difference $V$ across the junction, an alternating current should flow at a frequency $f$ given by: $$ hf = 2\times e\times V. $$ For a pot...
In Gasiorowicz's Quantum Physics, we determined the relation: $$L_z | l,m\rangle= \hbar m | l,m \rangle$$ I would like to determine: $\langle l,m_1 | L_x | l,m_2 \rangle $ I thought about expressing $L_x$ in terms of $L_{+}$ and $L_{-}$, which gives us: $$L_x= \frac12\left(L_{+}+ L_{-}\right)$$ We know that: $$L_{+}...
I have a question regarding coset space or homogeneous space $SO(n+1)/SO(n)$ which is simply $S^n$. I need some intuition regarding this result. As everyone knows that for a simple case of $SO(3)/SO(2)$, one can have $SO(3)$ as a group acting on $\mathbb{R}^3$ and $SO(2)$ as an isotropy group of $x\in\mathbb{R}^3$, the...
What is the difference between: $\nabla _{\sigma} $ and $ \nabla^{\sigma}$? I've been told that the first is the covariant derivative, however I'm just starting a course on spacetime geometry and am still a bit unsure of the notation.
The famous equation for mass energy equivalence: $E=mc^2$ It cannot conserve energy or momentum without some loss in one way or another. To elaborate further if I take $1kg$ of mass and I also take electromagnetic radiation with same energy as the $1kg$ mass and ensuring its accuracy using the above equation. Then use...
I can't understand the spectrum in the figure on page 19 from Argyres' lecture notes on supersymmetry: http://www.physics.uc.edu/~argyres/661/susy1996.pdf Argyres is considering a supersymmetric quantum mechanical system of an anharmonic oscillator, with a superpotential $W\sim x^3$. The plots of $W$ and $V$ make per...
I was interested in learning more about the status of our scientific understanding and technological instruments regarding extra solar spectroscopy. I am motivated by this almost 3 year old question/answer here at physics SE. Specifically: The composition of extra solar planet should be taken with a pinch of salt, the...
If two gravitational waves came in contact with each other what would happen? In another question entirely, what happens when a higher gravitational field interacts with a weaker one.
If we describe a photons with a wave packet, moving towards a potential barrier and E smaller than V, there is a finite chance that it will tunnel to the other side. In this process it is likely that it will arrive before a photon that does not tunnel, not because it exceeds the the speed of light, but because the fron...
Usually we say that equality of masses of particle and antiparticle follows from CPT-theorem. But do we need it for showing this equality? The first method to show that is following. The equation of free fields of an arbitrary spin $s$: all of them have Klein-Gordon or Dirac form (with some conditions of irreducibilit...
Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
Does it just mean "AC electric conductivity"? If so, why have a special name for it, and why mention optical specifically? The wikipedia page on it is very sparse. This (warning, PDF) document just says: The term “optical conductivity” means the electrical conductivity in the presence of an alternating electric fiel...
I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really illuminating in some aspects, I still feel that regardless of how hard I try there is something with relativity that preve...
Among two optical components. One is a Nd:YAG Laser 50/50 Beamsplitter and the second one is a Dielectric Mirror see pictures. Both of them almost looks like the same. If the specification is not mentioned on them. Is there a way we could differentiate them and know which one is a beam splitter and which one is a mirro...
I wanted to know if there is any relation between the color of light observed by the eye and the intensity of light transmitted by a material. Let us assume that I have a table of intensities of light transmitted at different wavelengths by a material for 2 materials. Is it possible to determine which material will app...
Question: A stick is thrown from a cliff 27 m high with an initial velocity of 18 m/s at an angle of 37 degrees above the horizontal. a) use the law of conservation of energy to determine the speed of the stick just before it hits the ground. Solution: \begin{align} E_\mathrm{T1} & = E_\mathrm{T2} \\ \frac12 m v_1^2 ...
I do not know what I should think about power divergences from loops. Most QFT textbooks tell us how to deal with logarithmic divergences from loops $\sim\ln(\Lambda^2/\Delta)$: we can set a counterterm $\sim\ln(\Lambda^2/\mu^2)$ to cancel the divergence at some scale $\mu$, then at any other scale this stuff in terms ...
I'm attempting to determine the half-lives of two silver isotopes (Ag-108 and Ag-110). A lab manual for a similar experiment may be found here http://web.vu.lt/ff/a.poskus/files/2013/06/NP_No08.pdf I have gathered my data, and I have counts/5 seconds on the y-axis and time elapsed on the x-axis. I have already subtract...
Suppose I have a 20x20x20 c"m plastic box where the top cover is open. On the top cover there is a fan ( 20x20 cm) which suppose to cool a cpu which is in the box . At the bottom there is a CPU which is getting warm. Now - in order to cool the CPU - I have 2 options : put the fan to suck air from the box towards out...
Question is what exactly title says that have we ever seen an atom through any means (microscopes/equipments.etc)? If not, how do we know they exists?
Acordding to Einstein's Relativity, while Space-man lives for 1 day(just a number for example , not an exact number calculated from the corresponding relative speed), Earth-man can live for 1000 years (just an example number too). But from the view of Space-man, while Space-man lives for 1 day, Earth-man lives for 1 ...
I' looking for an easy proof of Noether's theorem? I mean I know that the variation must be $ 0=\delta S = (EULER-LAGRANGE)+ (CONSERVED\, \, \, CURRENT) $ for the case of a particle $q(t)$. I know how to obtain it by I have doubts for the case of fields $ \phi (x) $, any hint? I have checked several books but I cannot ...
Provided that I have the instantaneous positions and velocities of two particles that can separate in 3D with respect to time. I would like to characterize the change in length. What could be a good formulation for that? Thanks.
In the case of the B-mode detected in BICEP2, at first they assumed there was no circular polarization and then the Q and U stocks parameter of the CMB is given by E-mode and B mode. If we have circular polarization too, what is relation between the B-mode and circular polarization? Does this B- mode include th...
To be more specific, what I mean is to measure it in a experiment. And if the answer is no, I want to know if it is principally impossible, or just impossible due to the technic limitation of our time. I am sorry I wan't clear enough at first. For most of the times, in the progress of experiment, the system does not ...
I've been learning about pressure and fluid dynamics, and I've stumbled onto a problem. Say you have a straw in a cup. The surface area of the water in the cup is much greater than that of the straw. So, I would expect Atm. Pressure × Large Area (of the cup) gives a much greater force than Atm. Pressure × Small Area (...
The $E$ string of a violin has a linear density of $0.5 g / m$ and is subjected to a $80\text{N}$ of tension, tuned for a frequency $u = 660 \text{Hz}$: What is the length of the rope? I know that in order to answer the question I have manipulate the equation: $$ \nu = \sqrt\frac{\tau}{\mu} $$ Getting this equation:...
As stated in the heading: Is $\frac{\partial}{\partial \Phi(y)} \Phi (x) = \delta(x-y)$ correct? Here denotes $\Phi(x)$ denotes a scalar field. And if yes, why? Any reference where I can read about this would be great.
As a homework I need to draw a hysteresis curve (preferably an interactive one) using Matlab or any other programming language. The problem is I have trouble finding a good algorithm to do so. I need something that can be implemented easily and in a systematic way. The Preisach model seems to be the best way, but I don...
I am not sure about the pressure existing in fluids.If the vertical pressure acts due to gravity and the atmospheric pressure since it also changes due to height also acts due to gravity then why is there horizontal pressure in a liquid. If there is then is it also equal to the vertical pressure at the point? If gravit...
In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they may be interpreted as Lie groups. My questions are: If we formulate a quantum field theory on a manifold which is also a...
What is the resultant focal length If a biconvex lens is cut into half and then the resulting 2 plano-convex lens arranged in such a way that the plane surface of one faces the curved surface of the other plano-convex lens considering the focal length of the plano-convex lens to be f.
One of the suggested diagrams for the Higgs production is the following: so basically an electron-positron pair annihilates and forms an (excited?) Z boson, which then decays into another (less excited?) Z boson and a Higgs boson. Why can't the electron-positron pair decay directly into a Higgs boson? Charge and lepton...
Why do we sometimes have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler with the smallest scale of 0.01 cm. This 0.01 cm is not our uncertainty of measurement, but we first divide it by $\sqrt{3}$ and then the result is our final uncertainty v...
Suppose a police car is standing by a wall. The siren light is rotating and it will hit the wall and reflect back to the car. Does the reflected light show a Doppler effect?
For example the core of the planet Jupiter, how to find out the magnitude of the force that compresses its core? and can that be thought of as the total force that holds the planet together?
Here is the wikipedia article. The basic idea is that the primordial density of microscopic black holes was high enough that many were able to form stable bound states before decaying through Hawking radiation (similarly to how unstable neutrons were able to form stable bound states with protons during BBN). These "hol...
Terminology question. Reading this, in the middle of the second page, when it says Left-handed quarks form 3 (3; 2; + 1 6 ) multiplets Qn (n = 1; 2; 3); What does this (3;2;+1/6) mean?
How do I calculate the velocity and acceleration of a stick that is vertically on my hand? How fast and far do I need to move my hand from side to side to keep balancing the stick? Assuming that we neglect friction force.
In a case where you vacuum your items in those airless bags (space bags), do they weigh more? Or is it just a feeling because of increase in density due to decrease in volume?
I read something explaining that gravitational waves actually repel space-time. It described the following. Mass bends space-time creating gravity. A massive object like the Sun, if it suddenly disappeared the space-time it bent would spring back up and the space it compressed (it's gravity well) would form a gravit...
The basic Randall-Sundrum model is given by the metric, $$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$ where $\sigma$ denotes the additional fifth dimension. Notice the brane is localized at $\sigma=0$; this 'slice' is precisely Minkowski s...
I am looking into Landau Levels and keep coming across a magnetic length defined as follows for a 2D system: $l_B=\sqrt{\frac{\hbar c}{e B}}$ I have seen numerous sources say this is: $l_B\approx 26nm \sqrt{B[Tesla]} $ But by plugging those numbers in I don't see how this is the case - the units are just plain wrong. T...
We can see that when a charge sphere is at rest & we are to put it in motion with any desired velocity than we will have to apply the same force for a longer time as if it were applied to the identical uncharged sphere to put it in motion with the same desired velocity.Here the due to electromagnetic fields associated ...
General relativity is the current model of gravity which has not yet been disproved. Are there still any anomalies such as the problem of Mercury's orbit during Newtonian gravity period that it failed to explain? If so are there other types of physics to be discovered?
In my quest for finding a good algorithm to draw hysteresis curve,I have found Jiles-Atherton model which seems to be a rather new model. But I have trouble understanding some of the variables/constants that are used in the formulation.There seems to be a rather similar question here. What I have trouble understanding ...
I'm writing up a lab report and have a question about the following formula $$N = N_0e^{-\lambda t}$$ $N$ indicates the number of nuclei left after a time $t$ and $N_0$ indicates how much there was to begin with. In the experiment, we used a scintillation counter (consists of a crystal and a photomultiplier tube) to de...
Lets assume we have a system of three particles in which three energy-levels labeled by $$E_1, E_2, E_3$$ are occupied. We want to write down all states that are symmetric (bosonic). One symmetric state is easily found by using a permanent, but how do I know that it is the only one? How many bosonic states are there if...
I understand that Planck's constant is essentially the ratio between the energy of a photon and its frequency. There are 2 things that im trying to verify: isn't the number that Planck's constant represents just an arbitrary result of the measurement system we use? As in, Planck's constant represents the ratio betwee...
I have a goal to educate myself up to the current level of knowledge we possess about the universe. I've tried textbooks, wikipedia, lectures, but i find each of them fundamentally flawed in different ways. Textbooks tend to be incredibly bloated, and I become unable to "see the forest for the trees" Wikipedia seems to...
$u$ is the e&m field energy $\frac{\partial u}{\partial t}=H\cdot \frac{\partial B}{\partial t}+E\cdot \frac{\partial D}{\partial t}$ Compared with thermo physics: $PdV,TdS,\mu dN$ ${H,E,P,T,\mu}$ are intensive variables ${B,D,V,S,N}$ are extensive variables But in microscopic level, there is no $H$ field. $B$ shoul...
I was reading http://en.wikipedia.org/wiki/Planck_time and noticed a reference to: http://phys.org/news192909576.html where it is stated that: 12 attoseconds is the world record for shortest controllable time This article is now almost 4 years old, is this still the record or is in the meantime this record broken?
If every time a particle's spin or momentum is measured, it gives a discrete answer (collapse of possibility states), how can they ever prove that prior to measurement it was in fact in a super-position of states? Is this solely a logical extrapolation from the wave-like interference patterns seen in the slit experimen...
Previously, I have calculated energy spectrum for 3D isotropic turbulent flow data which is equally spaced in all three directions and then to compute the energy spectrum, one performs Fourier transform and then accumulates energy located in different wavenumber bins and then gets the ($k^{−5/3}$) slope and it all work...
Is there a simple answer to this question ? see last line of this paragraph http://en.wikipedia.org/wiki/Fermionic_condensate#Fermionic_superfluids
I'm studying the refraction in optics. If a red light monocromatic beam of red light (700 nm) passes from air to water it becomes with a wavelenght of aprox 526 nm. So, my question is: How is going to see this beam a diver? Red (700 nm) or something more like green (526 nm)? (Let's suppose that the diver isn't wearing...
In the photoelectric cell my teacher says that the electron emission from the cathode depends on the frequency of the incident photon and it doesn't depend on the light intensity (I = nhU/ta , Right?) so if the light intensity increased the photoelectric current won't change . but what if this increase in the light in...
I have a question that arised by reading A Course in Modern Mathematical Physics by Peter Szekeres. He defines the galilean space $\mathbb{G}^{4}$ to be the space of events with a structure consisting of three elements: Time intervals $\Delta t=t_2-t_1$ The spatial distance $\Delta s=|\mathbf{r_2}-\mathbf{r_1}|$ Motio...
Last week in class we derived the formula for time dilation using light clocks and got $$t=\gamma t_0\quad \gamma=\left(1+\left(\frac vc\right)^2\right)^{-1/2}$$ So far so good. However, after class I was thinking of an alternate proof, but for some reason I got another result and I can't tell why. Basically you have ...
When one wants to include weak relativistic effects in classical equations, usually kinetic energy term is expanded into Taylor series about $p=0$. But the complete dispersion relation is $E=\sqrt{m^2+p^2}$, which has branch points at $p=\pm im$, thus its Taylor series diverges for any $p: |p|\ge m$. Does such divergen...
There are two points, $A$ and $B$ that move according to these laws: $$ \vec{x_a}= 20 -10 t $$ $$ \vec{x_b}= -15 +15 t $$ $A$ moves along the x axis, $B$ along the y axis. I have to compute the time $t_0$ when the distance between $A$ and $B$ (called $h$) is minimal. So the minimal distance is when $\frac{dh}{dt}=...
Is it true that a field of conformal dimension $h$ (integer or half integer) has $1-2h$ zero-modes on the sphere, if $1-2h \geq0$. This seems to be right for different ghost fields : $c$ has weight $-1$ and 3 zero-modes $\gamma$ has weight $-1/2$ and 2 zero-modes $\xi$ has weight $0$ and 1 zero-modes $\eta$ has weig...
If we can shield a charge from electrical forces by putting it inside a hollow conductor. Can we shield a body from gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ?
I would like to complete the following exercise: Prove that if the operators $P_i$ satisfy $P_i^{\dagger}$ = $P_i$ and $P_i^2$ = $P_i$, then $P_iP_j=0$ for all $i\neq j$. From $P_i^2 = P_i$ I conclude that $P_i(P_i - \mathbb{I}) = 0$, where $\mathbb{I}$ is the identity matrix. So $P_i$ is either $0$ or $\mathbb{I}$ ...
A guy who has a career in medical physics named Pierre-Marie Robitaille argues in two recently published papers in “Progress in Physics”, that the CMB is not from the big bang but from the oceans. The first paper is entitled WMAP: A Radiological Analysis. This work analyzes the WMAP images based on accepted standards ...
Suppose an observer $\mathcal{O}$ uses the coordinates $t$, $x$, and that another observer $\mathcal{O}'$, with coordinates $t'$, $x'$, is moving with velocity $\mathbb{v}$ in the $x$ direction relative to $\mathcal{O}$. Where do the coordinate axes for $t'$ and $x'$ go in the spacetime diagram of $\mathcal{O}$? $t'$...
There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete base. It is usually referred to as a statement about locality---if microcausality is broken then the "local" operators are no...
I want to simulate the vibration transmission between two colliding objects. I use a Finite Element Model to simulate the vibration on each object, but I haven't found any good mathematical model to transfer the vibration between two FEM models that collided and keep in contact. In the figure, a sphere is dropped in...
Resistance is $\frac{V}{I}$, and we get the unit $\Omega$. Another unit is $\frac{W}{A^2}$. How do you derive that unit?
Consider a system of two entangled harmonic oscillators. The normalised ground state is denoted by $\psi_0(x_1,x_2)$. The reduced density matrix of the second oscillator is given by: $$\rho_2 = \int_{-\infty}^{+\infty} dx_1 \int_{-\infty}^{+\infty} dx_2 \int_{-\infty}^{+\infty} dx_2' \,\psi_0(x_1, x_2)\psi_0^*(x_1, x_...
A ventilator fan mounted on the wall of an air tight room(except for an air intake with a given cross sectional area) is blowing air out of the room. If air displacement rate of the fan is given(CFM or m3/hr), is it possible to calculate the pressure differential that it can create between inside the room and outside t...
In a curved $(3+1)$ dimensional spacetime with metric components $g_{\mu \nu}$, the covariant derivative of a $4$ vector $\mathbf V = (V^0, \vec V)$ is given by $$\nabla_\mu~ V^\mu = \frac{1}{\sqrt{-g}}\partial_\mu (\sqrt{-g}~V^\mu).$$ I expect that this relation can also be used to derive the expression for divergenc...
$$ r(t)=R \left(\begin{array}{c}\cos(\omega t)\\ \sin(\omega t)\end{array}\right) , $$ $$ v(t)=\omega R \left(\begin{array}{c}-\sin(\omega t)\\ \cos(\omega t)\end{array}\right) $$ where the symbols have their usual meaning. Angular velocity vector is tangential to radius vector at a point. But I want to draw the graph ...
As far as I know, absorbing of the positive coefficient of $i\epsilon$ in a propagator seems to be a trivial operation without even the need of justification. In Peskin page 286, he did this: $$k^0\rightarrow k^0(1+i\epsilon)$$ $$(k^2-m^2)\rightarrow (k^2-m^2+i\epsilon)$$ In M. Srednicki's Quantum Field Theory, page 5...
It might be a very easy question for you, but I am confused and I need helps. In the simplest Hubbard model at one-dimensional lattice, I ignore the $U$ term and only remain the hopping term. $$H=-t\sum_{<ij>}{c^{\dagger}_{i} c_{j}}$$ where $c^{\dagger}_i$ and $c_i$ are creation operator and annihilation operator on si...
I am trying to do a tree level calculation of cross section in a process that involves sbottom exchange. There is a $ \widetilde{b} q \bar{q} $ vertex, where $q$ and $\bar q$ are quark and anti-quark of the same flavor. I have following questions: How is the color conserved in such vertices? The problem is that (s)qu...
I've been reading a set of notes (Chapter 13 of Caltech Ph 136 notes from 2004, by Blandford and Thorne) that draw an analogy between fluid dynamics and electromagnetism, identifying the magnetic vector potential $\mathbf{A}$ with the velocity flow field $\mathbf{u}$, the magnetic field with vorticity $\mathbf{\omega}$...
If quantum teleportation is performed into a black hole (by an electron for example), what happens to that electron? Let's say a hydrogen atom is very close to a black hole and the electron jumps into the next level of energy, which collides with the black hole, is the electron stuck forever? Is it prevented from enter...
If you try to block with your finger the flow of the water out of the faucet or a water hose, the water's speed increases. But while you're blocking the water flow out of the faucet by turning the handle, the speed doesn't increase. So what's the difference between the two ?
What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a convincing proof that it can be done at the level of path integral. How do we know for sure that Minkowski action and Euclidean...
In Peskin's QFT book page 294, he formally addressed the quantization of EM field, $$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$ Now that we have the functional integral quantization method at our command, let us apply it to the derivation of this expression. Consider the functional integral $$\int DAe^...
In Bose–Einstein condensation (BEC), how to prove the largest eigenvalue of the single-particle density matrix $$\rho_{ij}=\frac{\langle\Psi|a_i^{\dagger}a_j|\Psi\rangle}{N}$$ is $$\frac{1}{N}\sum_{i}{|\langle \Psi|a_i|\Psi\rangle|^2},$$ which is the condensate fraction f of the total particle number N in the thermodyn...
If this machine can build up high voltages of the order of millions of volts, can we use this voltage to generate a current of electrons? The building up of potential difference can result in an electric field. Can we not use this electric field to generate current?
I have to prove the identity $$ \left(\frac{\partial U}{\partial V}\right)_T=T\left(\frac{\partial p}{\partial T}\right)_V-p $$ I know how to do this using Maxwell's relations, but the assignment specified that I have to use Jacobian transformations. Reading many websites, pdf's, etc. has brought me no closer to the s...
I have been reading the notes on Supersymmetry by Martin. I am trying to understand gauge mediated symmetry breaking. From what I understand, there is a hidden sector where SUSY is spontaneously broken, there is a messenger superfield and there is a visible sector. There should be no direct coupling between the hidden ...
Reading about Dirac's equation in higher dimensional space-times I have read that the gamma matrices are $2^{[D/2]}\times{}2^{[D/2]}$. So, if we have $D=11$, for example, how is this formula supposed to be understood?
I am doing some simulations in COMSOL with the material $\rm GaAs$. The COMSOL built-in models require me to input the relative permeability and electrical conductivity of $\rm GaAs$. I have tried hard to search for these two electrical properties online, but no luck. Could anyone tell me these?
I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help. Here's the question: I tried to divide the string to 2 parts with $O$ as the mid-point of $AB$. Let $AO$=$T_{1}$ and $OB$=$T_{2}$, then $T_{2}-T_{1}=m\ddot x $. I don't know what to do nex...
Has anyone done any research about the upwind vehicle http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind? I think it is impossible but get a surprising number of disputes from some pretty educated people. It seems to me that if it were possible for a wind powered vehicle to go i...
Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values. For example, let's assume we are calculating: $\left<x=b\left.\right|e^{-\hat{H}T}\left.\right|x=a\right>$. Assume we can calculate this quantity via the p...
While i was studying about chaos theory, i stumbled upon this, When a ball confined in a square, and at the center is located a circle, is to bounce elastically, the path of the object deviates significantly. thereby causing chaos. I think this is equivalent to a sinai billiard. I couldn't understand the motion comple...
A bullet looses (1/n)th of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be? Logically, to me the answer seems to be infinity, as always a fraction of velocity will get reduced. But in my book the answer is n^2/(2n-1) (that comes from energy balance). What is...