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|---|---|---|---|---|---|
9332 | Does the AdS/CFT correspondence for thermal states really imply time evolution for evaporating black holes is unitary? | You always hear theoreticians proudly proclaim the AdS/CFT correspondence implies time evolution for evaporating black holes is unitary. But if you examine the argument carefully, you find AdS black holes can't completely radiate away because the outgoing Hawking radiation always fall back into the black hole in an asy... | What conditions must be met for a black hole to completely evaporate, and how does the cosmological constant affect this process? | 35,915 | cqadupstack-physics |
86705 | Does sound cancel itself out? | If there are two 10 x 2 x 1 foot rectangles in space and they are lined up so if they hit each other there will be no spots that are not hit in the front of the rectangle. Then they are pushed forward with the same exact same force, (this is space and there is no resistance) and they hit, will the tiny shockwaves of so... | If two identical sound waves traveling through two colliding 10 x 2 x 1 foot rectangles meet at high speed in a vacuum, what is the outcome in terms of energy transfer, and will they transform any energy into heat upon contact? | 26,535 | cqadupstack-physics |
113659 | The anapole moment, derivation from Dirac current density | Basically I am looking for a way to expand the electromagnetic interaction energy $W = A_{\mu}j^{\mu}$ (both $A$ and $j$ obtained from the Dirac equation) similar to the classical expansion in multipole moments, having in mind that there will be a term in the expansion called the anapole moment which is the only moment... | Given that the anapole moment is expressed in terms of the bilinear covariant \(\bar{\chi} \gamma^{\mu} \gamma_5 \chi\) and involves the electromagnetic field strength tensor \(\partial_{\nu} F^{\mu \nu}\), how can one derive the anapole contribution to the interaction energy \(W = A_{\mu}j^{\mu}\) in terms of \(\bar{\... | 25,524 | cqadupstack-physics |
36469 | Are the protons and neutrons in the nucleus arranged in any particular way? | I was wondering this: suppose you have two oxygen atoms. They will both have 8 protons and 8 neutrons in the nucleus (at least if they are the most common isotope). Now, will all those particles be arranged in the same way in both atoms? If they are, why would that be, and if not, does that affect the element's propert... | How do the arrangements of protons and neutrons in two identical oxygen atoms influence their chemical properties, and to what extent does the uncertainty principle limit our ability to determine the precise arrangement of these particles? | 20,240 | cqadupstack-physics |
85979 | How much extra distance to a CERN event horizon? | How much extra distance would a scientist have to travel to get to the event horizon of a mini black hole if they ever make one? | If a mini black hole has a Schwarzschild radius of 10 micrometers, how much extra distance would a scientist need to travel to reach its event horizon compared to the distance from the black hole's center to its event horizon? | 7,027 | cqadupstack-physics |
105156 | Gases at different pressures reaching uniform pressure | First of all, sorry if my question is dumb, I have very little understanding of physics. Also, English is not my native language. If two gases, initially with different pressures, are mixed in a closed vessel, do they (the mixture being treated as a single gas) generally reach uniform pressure? Now, atmospheric pressur... | When two gases at different pressures are mixed in a closed vessel, how does the final pressure of the mixture compare to the initial pressures of each gas, and what factors influence whether the resulting pressure is uniform throughout the vessel? | 35,244 | cqadupstack-physics |
32818 | PhD Research Areas in String Theory | I'm thinking of applying to do a PhD in String Theory, starting in September 2013. I'm gradually learning more about the subject through external reading, but still most papers are impenetrable! Could anyone give me a description of the areas of current String Theory research that would be accessible for a doctoral stu... | What are the top three open problems in current String Theory research that a doctoral student could feasibly tackle, and what quantitative metrics could be used to measure progress in these areas? | 15,942 | cqadupstack-physics |
90216 | Where does the loss in gravitational energy of the load go when a spring is pulled? | A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book): $$E=\frac12kx^2 $$ However, doesn't the load lose gravitational potential energy as it moves down? Where would this energy go? By conservation law, shouldn't the energy equ... | In a vertical mass-spring system, when a mass is pulled down by \( x \) meters, the gravitational potential energy lost by the mass is given by \( mgx \). If the spring stores energy according to \( E = \frac{1}{2}kx^2 \), how can we account for the total energy change in the system? Specifically, what is the relations... | 16,818 | cqadupstack-physics |
114902 | What is chaotic about Chaotic Inflation? | **Chaos** is defined as an aperiodic long-termed behavior, that is very sensitive to initial conditions. Now from this definition I can only conclude that the adjective 'chaos' is a _mere analogy_ , since there is nothing aperiodic (or periodic) during inflation. The inflaton follows a nice, smooth (often taken to be a... | Given that the inflaton during inflation follows a smooth potential and is characterized by the initial conditions \(\ddot{\phi} \approx 0\) and \(\dot{\phi}\) being small, calculate the potential energy \(V(\phi)\) at a specific value of the field \(\phi\) if the potential is modeled as a quadratic function:
\[
V(\p... | 12,138 | cqadupstack-physics |
29468 | Heuristics for specific heat capacities of solids | A didactic question publish in _The Physics Teacher_ (http://tpt.aapt.org/resource/1/phteah/v41/i1/p8_s1) asks which will melt more ice: 100g of metal at 100C or 100g of wood at 100C. (The particular metal is not specified. I have paraphrased the question.) The solution given is that the wood will melt more ice because... | Given that 100g of metal at 100°C and 100g of wood at 100°C can be used to melt ice, which material will melt more ice, and what is the underlying reason related to their specific heat capacities? Additionally, what factors contribute to the specific heat capacity of wood being higher than that of metals? | 15,009 | cqadupstack-physics |
26972 | What are some ways to (approximately) symbolically diagonalize Hamiltonian operator? | Specifically the Hamiltonian takes the form of $$\hat H = \frac{\Delta }{2}{\hat \sigma _z} + {\omega _1}\hat a_1^\dagger {\hat a_1} + {\omega _2}\hat a_2^\dagger {\hat a_2} + {g_1}\left( {{{\hat a}_1}{{\hat \sigma }_ + } + \hat a_1^\dagger {{\hat \sigma }_ - }} \right) + {g_2}\left( {{{\hat a}_2}{{\hat \sigma }_ + } +... | Can you provide a few symbolic approximation techniques to diagonalize the Hamiltonian $$\hat H = \frac{\Delta }{2}{\hat \sigma _z} + {\omega _1}\hat a_1^\dagger {\hat a_1} + {\omega _2}\hat a_2^\dagger {\hat a_2} + {g_1}\left( {{{\hat a}_1}{{\hat \sigma }_ + } + \hat a_1^\dagger {{\hat \sigma }_ - }} \right) + {g_2}\l... | 24,362 | cqadupstack-physics |
99149 | Wick's theorem for calculating OPE | I am trying to understand a calculation using Wick's theorem. Let $T(z)$ be the analytic part of a stress-energy tensor, and $\phi(z)$ a free boson field. Now, $$T(z)\partial_{w}\phi(w)=-2\pi:\partial_{z}\phi(z)\partial_{z}\phi(z):\partial_{w}\phi(w).$$ Using Wick's theorem, we know that $$:\partial_{z}\phi(z)\partial_... | Using Wick's theorem, if \( \langle \partial_{z}\phi(z)\partial_{w}\phi(w)\rangle = \frac{1}{(z-w)^2} \), calculate the expression \( T(z)\partial_{w}\phi(w) \) and show how it simplifies to \( 2\langle \partial_{z}\phi(z)\partial_{w}\phi(w)\rangle \partial_{z}\phi(z) \). What is the final result in terms of \( z \) an... | 14,360 | cqadupstack-physics |
96275 | What type of interferometry set up do I need to image a small structure at a distance? | Please forgive me, optics isn't my forte. I'm trying to work out how to image the surface structure of an object at a distance. Considerations are: * Monochromatic light- it must be imaged in the infrared. * Object size is around 1cm square, distance to the object up to 3m. * Preferable to not have to focus on th... | What type of interferometer would be suitable for imaging the surface structure of a 1 cm square object from a distance of 3 meters using monochromatic infrared light, and what key considerations should I take into account regarding resolution and exposure time? | 8,779 | cqadupstack-physics |
129629 | Examples of manifolds (not) being: flat, homogeneous and isotropic | I am looking for (at least) one example of the following manifolds: 1. Flat, homogeneous and isotropic 2. Curved, homogeneous and isotropic 3. Flat, non-homogeneous and isotropic 4. Flat, homogeneous and non-isotropic 5. Curved, non-homogeneous and isotropic 6. Curved, homogeneous and non-isotropic 7. Fla... | Can you provide examples of manifolds that fit the following criteria: 1) flat, homogeneous, and isotropic; 2) curved, homogeneous, and isotropic; 3) flat, non-homogeneous, and isotropic; 4) flat, homogeneous, and non-isotropic; 5) curved, non-homogeneous, and isotropic; 6) curved, homogeneous, and non-isotropic; 7) fl... | 26,470 | cqadupstack-physics |
114331 | What is chirality? | I actually wanted to make the title as "What is the difference between chirality and helicity"? But I didn't do that because I don't understand properly what chirality is. I have gone through this Wikipedia article: chirality to get the meaning of chirality? and what I get from there is that something is said to have c... | What is the relationship between chirality and helicity in particles, particularly how does the handedness of massless particles connect to their chirality? | 37,246 | cqadupstack-physics |
46463 | Does light shine better through a matt surface or a glossy surface? | I am currently designing a lighting solution for Phillips as part of my university degree. However I am stuck on a small problem, as stated above. If I was to have a strip of perspex, with the sides matt and the bottom polished, would I achieve more light through the polished surface or the matt surface. And why?? | If a strip of perspex has one surface polished and the other matt, calculate the percentage of light transmission through each surface when illuminated with a laser of a specific wavelength. Which surface would allow more light through and why? | 19,320 | cqadupstack-physics |
35826 | How does one make a particle with particular wavefunction? | I was always curious how scientists achieve a particle with particular wavefunction (of location and spins etc.) So how do they achieve it? Or is this impossible? | What experimental techniques can scientists use to generate a specific quantum state of a particle, including its wavefunction, spin, and position, and what are the limitations of these methods? | 18,358 | cqadupstack-physics |
111010 | High Current at first and then steady from a battery | I just came up with a question, When a battery is connected to a circuit, the current first suddenly peaks up and slowly goes down to a steady value. Why is it so? I have not actually observed this, but this question has been asked in exams, so it should be that way I hope. | When a battery is connected to a circuit, describe the expected changes in current over time, and explain how the internal resistance of the battery and the resistance of the circuit components influence these changes. Quantitatively, how would you model the current decay and the time constant in an RC circuit? | 3,638 | cqadupstack-physics |
87802 | Are there any stable (not metastable) string theory compactifications with a positive cosmological constant? | Previously, on Save us from swallowing baby universes, please!, I asked how we can be saved from false vacuum decay assuming we are living in a false vacuum. What if we are living in a stable vacuum after all, and string theory actually describes the world we live in? Are there any stable (not metastable) string theory... | What are the conditions required for string theory compactifications that yield a stable vacuum with a positive cosmological constant, and can you provide an example of such a compactification? | 2,280 | cqadupstack-physics |
19121 | Which symmetry is associated with conservation of flux? | Which symmetry is associated with conservation of flux (e.g., in electromagnetism)? For example, when working with Gauss's law in electromagnetism, net flux through an arbitrary volume element remains unchanged when the net charge is unchanged. | What mathematical relationship demonstrates that the flux through a closed surface remains constant when there is no net charge within that surface, as illustrated by Gauss's law in electromagnetism? | 6,890 | cqadupstack-physics |
24745 | Does the measure of proximity of two theories in "theory space" run? | From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the corresponding points in the high energy landscape of all valid theories can be far away from each other (and vice versa). This make... | What is the role of renormalization group flow in connecting effective quantum field theories at different energy scales, specifically in terms of their proximity in the theory space, and how does it account for the observed duality between short and large distances? | 35,545 | cqadupstack-physics |
126032 | Natural entanglement system | I'm beginner and amateur interested by the quantum physics. I would like to know if it exists entanglements systems at natural state or it requires mandatory an human intervention ? Is it possible ? Either no or yes, Why ? Thanks | Is it possible for quantum entanglement to occur naturally without human intervention, and if so, can you provide an example of a natural system where this phenomenon is observed? | 37,897 | cqadupstack-physics |
33195 | Classical and quantum anomalies | I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views: 1. Anomalies are due to the fact that quantum field theories (and maybe quantum mechanical theories with singular potential) must be _regularized_ and it can be possible th... | Can you provide examples of physical systems where quantum anomalies arise, and explain how these anomalies relate to each of the following aspects: regularization procedures in quantum field theories, ordering prescriptions for operators, the definition of Hamiltonians, and the emergence of central charges in conserve... | 5,516 | cqadupstack-physics |
79952 | Normal ordering and path integrals | What is the manifestation of normal ordering for creation/annihilation operators in the path-integral formalism? | How does the use of normal ordering for creation and annihilation operators affect the calculations of vacuum expectation values in the path-integral formalism? Please provide a specific example and calculate the vacuum expectation value for a given operator. | 3,435 | cqadupstack-physics |
67929 | Is the number-phase uncertainty relation classical? | For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications arising from the fact that $\phi$ can't be made into a single-valued and continuous operator (Carruthers 1968), but roughl... | What is the relationship between the uncertainty in the number of quanta ($\Delta n$) and the uncertainty in the phase of oscillation ($\Delta \phi$) for a harmonic oscillator, and how does this lead to the conclusion that $\Delta n \Delta \phi \ge 1$ holds true despite being a classical interpretation? | 35,667 | cqadupstack-physics |
45255 | How distorted does the Andromeda Galaxy appear to us due to the speed of light? | The Andromeda Galaxy appears to us at an angle to the galactic disk, i.e. we are not in the Andromeda Galaxy disc's plane, nor are we near the direction that the galaxy's pole points. Therefore, due to the geometry and distances involved, it would seem to me that we are seeing the 'far edge' a few thousand years later ... | What is the maximum angular distance that the Andromeda Galaxy could spin over a time period of 2,000 years, given its estimated rotational speed of approximately 210 km/s at the outer regions? Additionally, how does this rotation contribute to our perception of the galaxy's structure when viewed at an angle? | 3,543 | cqadupstack-physics |
106224 | Speed of light originating from a star with gravitational pull close to black-hole strength? | Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet. Since there is no event horizon, but a great gravity pull. Will the speed of light originating from this star be close to 0? A follow-up question: What will the speed of... | If a star is very close to becoming a black hole, what is the effective speed of light emitted from its surface as observed from a distance, and what will be the speed of light once it travels far enough to escape the gravitational influence of the star? | 34,081 | cqadupstack-physics |
32912 | Can extremely charged objects simulate some black hole effects? | If we had a positive point charge of incredible quantity, does there exist an imaginary sphere about it, such that regardless of the initial speed and direction of any electron, that electron could not escape spiraling into the positive point charge? Conversely, regardless of the initial speed and direction of a proton... | Consider a positive point charge \( Q \) located at the center of an imaginary sphere with radius \( r \). If an electron approaches the charge with an initial speed \( v_e \) and at an angle \( \theta \) to the radial direction, what is the minimum value of \( r \) (in terms of \( Q \), \( m_e \), and \( k_e \)) such ... | 32,493 | cqadupstack-physics |
109003 | Walter Lewin's lecture on Faraday's law | In Walter Lewin's lecture on Faraday's law, he does a demonstration with a solenoid where he shows that current is induced in a loop that surrounds the solenoid as the magnetic flux is changing. He claims that the induced current is the same regardless of the size of the loop of wire that he uses (since the magnetic fl... | According to Faraday's law, if a solenoid generates a changing magnetic field and induces an electromotive force (EMF) in two concentric loops of wire, one with a radius \( r_1 \) and the other with a radius \( r_2 \) (where \( r_2 > r_1 \)), how do you calculate the currents induced in each loop? Specifically, given t... | 2,024 | cqadupstack-physics |
129836 | Coupled Spring System (3 mass 3 springs) | Hello I am having trouble trying to find the correct model for this coupled spring system. The scenario is the following we have: Ceiling - Spring - Mass(1) - Spring(2) - Mass(2) - Spring (3) - Mass(3) End. I came up with the following system of differential equations in the 2nd order to model this problem. $x_1^{''}=[... | Given a coupled spring system with three masses and three springs, where the equations of motion are represented as:
1. \( x_1'' = \frac{-k_1 x_1 - k_2 (x_2 - x_1) - k_3 (x_3 - x_2)}{m_1} \)
2. \( x_2'' = \frac{-k_2 (x_2 - x_1) - k_3 (x_3 - x_2)}{m_2} \)
3. \( x_3'' = \frac{-k_3 (x_3 - x_2)}{m_3} \)
and linearized to... | 18,818 | cqadupstack-physics |
48157 | Scattering Processes in Scalar Yukawa Theory | I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through $H_I=g\int d^3x\psi^{\dagger}\psi\phi$. Suppose we want to compute the amplitude for scattering from an initial state $|p_1,p... | In the context of scalar Yukawa theory, when calculating nucleon-nucleon scattering amplitudes, consider the contribution of disconnected diagrams. Given a scattering process where the initial and final states are eigenstates of the free theory, what is the correct interpretation of the contribution from disconnected a... | 24,875 | cqadupstack-physics |
122148 | Calculating velocity change after impact? | Let's say there is no gravity here and objects won't crush. We have 2 rocks with $m=10\text{ kg}$. First rock has velocity $v_1=0\text{ m/s}$ and second $v_2=10\text{ m/s}$ (flying in leftward direction). The second rock hit first causing force for a time $t=0.001\text{ s}$. $F=ma \rightarrow F=\frac{mv}{t} \rightarrow... | If two rocks, each with a mass of 10 kg, collide in a gravity-free environment where the first rock is initially at rest and the second rock is moving leftward at a velocity of 10 m/s, and they collide for a time duration of 0.001 s, what will be the final velocities of both rocks after the collision, assuming an elast... | 29,597 | cqadupstack-physics |
80525 | How to derive the Bethe stopping power formula | I need the derivation of Bethe formula for stopping power, but I can't see the corresponding paper to this matter. > Application of Ordinary Space-Time Concepts in Collision Problems and > Relation of Classical Theory to Born's Approximation. E. J. Williams. _Rev. > Mod. Phys._ **17** no. 2-3 (1945) pp. 217-226. Can an... | Can you derive the Bethe formula for stopping power and explain its significance in the context of particle collisions, referencing E. J. Williams' paper published in 1945? | 32,632 | cqadupstack-physics |
114400 | Calculate orbit height from tangential velocity | Is it possible to calculate the altitude of a satellite orbiting a planet, just from the planet's mass and the satellite's velocity, assuming that the satellite is in a perfect circular orbit? If so, what would the equation be? I've derived the following equation: $G\frac{M}{v^2} = r$ , however I don't think it's corre... | Given a satellite orbiting a planet with mass \( M \) and traveling at a constant velocity \( v \) in a perfect circular orbit, can you derive the equation for the altitude \( h \) of the satellite above the planet's surface? What is the final expression for \( h \) in terms of \( M \) and \( v \)? | 30,225 | cqadupstack-physics |
90555 | Help in understand Magnetostatic Energy | $$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$ I can't understand this formula, what is the magnetostatic stored potential energy?! What does it show? Does it explain anything relative to magnetization? | What is the physical significance of the formula $$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$ in terms of magnetostatic stored potential energy, and how does it relate to the concept of magnetization in a material? Additionally, can you calculate the magnetostatic stored... | 15,797 | cqadupstack-physics |
89585 | XX coupling vs Heisenberg coupling | I am going through CURVATURE OF SPIN NETWORKS by Jonckheere et al. The first line of the abstract mentions XX coupling and Heisenberg coupling. What is the difference between these two couplings? | What are the quantitative differences in interaction strength and energy levels between XX coupling and Heisenberg coupling in quantum spin systems? | 6,285 | cqadupstack-physics |
135233 | Simple Relativity Question | I've been taking a course in modern physics and we've spent several weeks on relativity now, but I still am confused how to deal with this problem, which has shown up in several different ways throughout the course so far. Keep in mind that the units are SR, not SI. If an astronomer wants to travel to a planet that is ... | To determine the speed required for an astronomer to reach a planet 200 light-years away in 10 years from his perspective, how fast must he travel according to the principles of special relativity? | 15,077 | cqadupstack-physics |
111669 | Isotropy of Space | Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals $a^2\delta_{ij}$ at $x = 0$" May someone please illuminate the point. | What is the relationship between the three-tensor \( t_{ij} \) at \( x=0 \) and the metric tensor \( g_{ij} \) in terms of isotropy, and how can we express \( g_{ij} \) in relation to the scale factor \( a \)? | 9,552 | cqadupstack-physics |
102597 | Numerical: Work Power Energy | > _A particle moves along a straight line. A force acts on the particle which > produces a constant power. It starts with initial velocity 3 m/s and after > moving a distance 252 m its velocity is 6 m/s. Find the time taken._ Here are my attempts at solving it. | A particle starts with an initial velocity of 3 m/s and accelerates under a force that produces constant power. After traveling a distance of 252 m, its final velocity is 6 m/s. How much time did it take for the particle to travel this distance? | 24,787 | cqadupstack-physics |
89706 | How would I explain Ohm's Law in terms of Electrical Fields and Force? | In terms of current, resistance, and voltage, it's easy: Ohm's Law is the relationship between current, voltage, and resistance of a circuit. Boom, simple as that. How could I put this in terms of $E$ and $F$? I can sort of see a way to do it by relating the formulas $E=F/q$ and $I=q/t$ to Ohm's Law, $V=IR$, but I'm no... | How can I derive the relationship between electric field (E) and force (F) in terms of current (I), resistance (R), and voltage (V) using Ohm's Law and the formulas $E = F/q$ and $I = q/t$? Provide a detailed explanation. | 9,827 | cqadupstack-physics |
26764 | Why is Jupiter so sharply defined? | In photographs of Jupiter, the limb seems extremely definite. Being a gas giant, my naive self thinks that the atmosphere should have a more gradual cut off, creating a hazy effect similar to that on Titan. I am aware of Jupiter's immense size, so each pixel in the linked photograph is likely tens or hundreds of kilome... | What is the approximate altitude of Jupiter’s atmosphere where the transition to space occurs, and how does this altitude contribute to the apparent sharpness of its limb in photographs compared to atmospheres of smaller celestial bodies like Titan? | 4,113 | cqadupstack-physics |
43508 | What's the difference between the equivalence principle and curvature of spacetime? | Calculating using the equivalence principle only accounts for half the deflection of light, whereas the other half is from curvature of space-time. But isn't the equivalence principle the same thing as curvature of spacetime? Deflection of light has two parts: The first part is falling people measure the deflection. Wh... | What is the total angular deflection of light as it passes near the Sun, accounting for both the effects of the equivalence principle and the curvature of spacetime, and how can this be quantitatively measured? | 20,151 | cqadupstack-physics |
106167 | Origins of many-particle interactions | The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion \- it is assumed that the potential energy is a sum of pairwise interactions: $$U(r_1,...,r_N) = \sum_{ij}u(r_{ij})$$ with $r... | What are some specific examples of three-particle interactions in chemical systems, excluding catalyzed reactions? | 34,296 | cqadupstack-physics |
133675 | Invariant interval and gravity | Gravity is inversely proportional to the _distance_ between objects. Do we use Euclidean distance or the invariant interval for that distance? Using the invariant interval makes everything a bit more complex: An object that is one lightyear away, is also one year "younger" when we observe it. Does that temporal distanc... | How does the inclusion of temporal distance impact the calculations of gravitational interactions between two objects in different galaxies, considering their respective distances from an observer on Earth? Specifically, can you calculate the gravitational force between two objects that are both 25 million light-years ... | 25,086 | cqadupstack-physics |
38452 | 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 repel? Wouldn't they be mor... | Considering the electric forces between protons and electrons, how do the attractive forces between the negatively charged electrons and the positively charged protons result in the stability of an atom? Specifically, if we assume a hydrogen atom, what is the magnitude of the electrostatic force acting between its sing... | 35,528 | cqadupstack-physics |
14128 | When is many-body perturbation theory valid? | I'm calculating expectation values (thermal, time-independent) using many-body perturbation theory, but I'm unsure how to work out what values the parameter I'm expanding the perturbation series in can take. I read that it's when the matrix elements, $\langle i | H_{pert} | j \rangle$ where $H_{pert}$ is the perturbati... | For a one-dimensional fermionic Hubbard model with a Hamiltonian given by
\[
H= -t \sum_{\langle l,m \rangle} (c^\dagger_l c_m + h.c.) + U \sum_l (n_{l\uparrow} - 1/2)(n_{l\downarrow}-1/2),
\]
how can I determine the maximum value of the interaction term \( U \) for which many-body perturbation theory remains valid?... | 21,036 | cqadupstack-physics |
123408 | How to replace $T$-product with retarded commutator in LSZ formula? | I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: $$A(q_1) + B(p_1) ~\rightarrow~ A(q_2) + B(p_2)$$ and proceed to write down the $S$-matrix element using the LSZ formula,... | Why can the time-ordered product \( T \varphi^\dagger(y) \varphi(x) \) be replaced by the retarded commutator \( \theta(y^0-x^0)[\varphi^\dagger(y),\,\varphi(x)] \) in the context of elastic scattering when the momenta \( q_1 \) and \( q_2 \) are in the forward light cone? What is the underlying mathematical reasoning ... | 19,498 | cqadupstack-physics |
130035 | The inverse square law of sound through solids? | We all know about the inverse square law of sound. In short the power of the wave will get evenly spread on an ever increasing spherical expansion and this will dissipate the power of the wave at a rate of inverse squared to the distance travelled.  But... | How does the intensity of sound traveling through a solid medium, like wood in a rectangular table, change with distance? Can you provide a mathematical relationship or approximation that describes this phenomenon, and is it similar to the inverse square law observed in air? | 32,880 | cqadupstack-physics |
88389 | Why is it easier to walk diagonally upstairs | Try it yourself on a set of wide steps! Work is given by $$\int_C \mathbf{F} \cdot d\mathbf{x}$$ where $C$ is a path integral. In this case I think $\mathbf{F}$ is a rotational vector field because the stairs are essentially a set of discontinuities. This would mean that the integral is path dependent. Here is why this... | If you were to climb a staircase with a height of 3 meters consisting of 15 steps, calculate the work done against gravity if you climb directly upward compared to taking a diagonal path that ascends the stairs. Assume that the force applied is equal to your weight. Would the work done be the same in both cases, and ho... | 26,602 | cqadupstack-physics |
97971 | Implementing a transformation as $UaU$ and not $UaU^{-1}$? | I know one associates to each symmetry transformation a unitary/antiunitary operater...etc. But equation 3.123 in Peskin and Schroeder (PS) says that parity is implemented as $(\mathbf{p}$ is the three momentum) $$P a_{\mathbf{p}}^sP = \eta_a a_{\mathbf{-p}}^s \tag{1}, $$ where $P$ is the operator implementing the pari... | In the context of quantum field theory, how does the parity operator \( P \) transform the particle annihilation operator, and why is the relationship given in equation \( (1) \) not expressed in the standard form \( P a P^{-1} \)? Specifically, explain the significance of the equation \( P a_{\mathbf{p}}^s P = \eta_a ... | 26,582 | cqadupstack-physics |
99943 | What Does it Mean for an Extra Dimension to Have Size? | Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very small and "hidden" from us. He uses an analogy of looking across a parking lot at a telephone wire. From our vantage poi... | What is the physical significance of describing additional dimensions as "small" in the context of string theory, and how might one quantify the size of these dimensions compared to the three familiar spatial dimensions? | 5,574 | cqadupstack-physics |
80216 | The Emperor's New Mind or Shadows of the mind? | OK - I have never posted on this site before, and I hope this question isn't closed as "request for reference" but here goes: I'm a software guy who likes to dabble in math, physics and cosmology. Have read "The History of Time" and some books about information theory. Last night, I started reading Penrose's The Empero... | What are two key concepts presented in Roger Penrose's "The Emperor's New Mind" that are necessary for understanding the advancements made in "Shadows of the Mind"? | 33,538 | cqadupstack-physics |
112048 | What is the exact cause of flow separation in a viscous fluid? | I recently got into a lengthy debate about the exact nature of boundary layer separation. In common parlance, we have a tendency to talk about certain geometries as being too "sharp" for a viscous flow to remain attached to them. The flow can't "turn the corner" so to speak, and so it separates from the body. While I t... | What is the critical adverse pressure gradient that leads to boundary layer separation in a given viscous flow over a flat plate, and how does it compare to the effects of normal shockwaves on flow separation? | 9,085 | cqadupstack-physics |
69271 | A kind of Noether's theorem for the Hamiltonian | How can I (conveniently?) show that an invariance of the Lagrangian and Hamiltonian (i.e. the kinetic as well as the potential energy are independently invariant) will lead to a conservation law **using only the Hamiltonian formalism**? Am I correct, that the invariance of a Hamiltonian does not need to lead to a conse... | If a Hamiltonian is invariant under a specific transformation while the corresponding Lagrangian is not, does this indicate that there will be no conservation law associated with that transformation? Provide a detailed example to support your answer, focusing on the implications of the invariance in both formalisms. | 20,396 | cqadupstack-physics |
3075 | Quantum mechanics of thermal radiation | What are the quantum mechanisms behind the emission and absorption of thermal radiation at and below room temperature? If the relevant quantum state transitions are molecular (stretching, flexing and spin changes) how come the thermal spectrum is continuous? What about substances (such as noble gases) which don't form ... | How does the emission of thermal radiation in noble gases differ from that in molecular substances, and what role do quantum state transitions play in the continuous thermal spectrum observed in both cases? | 26,827 | cqadupstack-physics |
11227 | Analyzing the motion of a ball rolling without slipping inside a hemispherical bowl | Consider a solid ball of radius $r$ and mass $m$ rolling without slipping in a hemispherical bowl of radius $R$ (simple back and forth motion). Now, I assume the oscillations are small and so the small angle approximation holds. I wish to find the period of oscillation and I analyze the motion in two ways, first using ... | In the scenario of a solid ball of radius \( r \) and mass \( m \) rolling without slipping in a hemispherical bowl of radius \( R \), you're getting two different expressions for the period of oscillation from two methods of analysis:
1. Using energy conservation, you found the period \( T = 2\pi\sqrt{\frac{7r^2}{5g... | 21,204 | cqadupstack-physics |
48607 | Why photo cannot be captured while facing toward the Sun / | When the Camera is facing toward the Sun and a person is standing to and We're capturing his photo , all we get is a black shadow even when we capture with the flash light or anything. Why does it happen ? | Why does a person standing between a camera and the Sun appear as a black shadow in photographs, even when using a flash? What is the role of light intensity and angle in this phenomenon? | 4,848 | cqadupstack-physics |
75882 | What is the difference between phase difference and path difference? | I have learnt that path difference is the difference between the distance travelled by two waves meeting at a point. If that is path difference,then how will one know what is phase difference and how can one calculate or determine it? | If two waves traveling a distance of 4 meters and 6 meters meet at a point, what is the path difference between them, and if these waves have a wavelength of 2 meters, what is the phase difference in degrees? | 23,144 | cqadupstack-physics |
100420 | Why viscosity is diffusive? | I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion equation: $$ \frac{\partial u}{\partial t} + a\cdot\nabla v - \nabla(\nu \nabla v )=f, $$ and thinking in Fick's law, it's no... | How can the concept of viscosity in fluid mechanics be understood as a diffusive process analogous to Fick's law, particularly in the context of the Navier-Stokes equation, and what implications does this have for stability in numerical methods like Finite Element Method with artificial viscosity? | 1,886 | cqadupstack-physics |
9625 | Mechanical energy problem - please help | Quite new to all this - simple question. "A ball starting from rest rolls down a hill and reaches 10m/s at the bottom. If the same ball starts rolling down the hill from an initial velocity of 5m/s, will it's velocity at the bottom be: (A) Less than 15m/s; (B) Equal to 15m/s; (C) Greater than 15m/s." The answer I have ... | A ball rolls down a hill starting from rest and reaches a velocity of 10 m/s at the bottom. If this same ball starts rolling down the hill with an initial velocity of 5 m/s, what will its velocity be at the bottom? Choose one: (A) Less than 15 m/s; (B) Equal to 15 m/s; (C) Greater than 15 m/s. Explain your reasoning. | 31,750 | cqadupstack-physics |
112815 | Photon dispersion in an optical fiber | What is the law of spatial dispersion of a photon in an optical fiber? Say I have a femto second photon ($\lambda$ around $700\,\text{nm}$) with gaussian shape ($\sigma = c\cdot 1\,\text{fs}\approx 3\cdot 10^{-7}\,\text m$). How will it look at the end when I send it through a 50 km long optical fiber? I guess it will ... | What will be the final width of the Gaussian pulse (σ) of a femtosecond photon (λ = 700 nm) after traveling through a 50 km long optical fiber, considering the dispersion effects? | 3,968 | cqadupstack-physics |
92411 | What exactly is regularization in QFT? | **The question.** Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? **Motivation and background.** As pointed out by user drake in his nice answer to my previous question Regulator-scheme-independence in... | What are the minimum properties that define a valid regularization procedure in perturbative quantum field theory, ensuring that all divergent integrals become finite while preserving essential information about the structure of the theory? | 8,756 | cqadupstack-physics |
101513 | Derivation of cylindrical line heat source problem? | I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is $$\theta(\eta)=C_{1}\int_0^\eta \\! \frac{e^{-u}}{u} \, \mathrm{d}u + C_{2}$$ and my boundary conditions are $-4\pi kh\frac{\pa... | Given a line heat source embedded inside a cylinder, the temperature distribution is described by the differential equation solution $$\theta(\eta)=C_{1}\int_0^\eta \frac{e^{-u}}{u} \, \mathrm{d}u + C_{2}$$ with boundary conditions $-4\pi kh\frac{\partial\theta}{\partial \eta}|_{\eta=0}=q_{0}$ and $\theta\to0$ as $\eta... | 3,990 | cqadupstack-physics |
127248 | Experiment with spring and two light sources emitting light in opposite directions | Two (almost massless) light sources connected with a (almost massless) spring emit light beams in opposite directions. What is the speed at which the spring extends? | If two light sources connected by a spring are emitting light beams in opposite directions, and the spring has a spring constant \( k \) and is initially at rest, what is the extension of the spring after a time \( t \) due to the forces exerted by the light sources? Assume the momentum is conserved and the light sourc... | 36,929 | cqadupstack-physics |
18142 | Gravitational torque about a bolt that a mass is hanging from | A uniform rectangle sign h=20.0cm high and w=11.0cm wide loses three of its four support bolts(at points p_1, P_3, and p_4) and rotates into the position as shown, with p_1 directly over p_3. It is supported by the bolt P_2, which is so tight it holds the sign from further rotation. Find the gravitational torque about ... | What is the gravitational torque about the bolt P_2 when a uniform rectangular sign with a height of 20.0 cm, a width of 11.0 cm, and a mass of 5.0 kg is supported at that point, with one corner directly above the other? | 11,259 | cqadupstack-physics |
74107 | What happens with time at the speed of light? | Say that by some means you could become massless, and therefore travel at the speed of light. I understand that the closer you get to the speed of light, the slower time appears to the person traveling. Like say you were traveling a 99.999 % of the speed of light, ever year for you would be 200 or so years for people n... | If a massless traveler were able to move at the speed of light, how much time would pass for them compared to an observer at rest after traveling for one year as perceived by them? What would be the total time elapsed for the observer at rest? | 8,913 | cqadupstack-physics |
69828 | Equivalence Theorem of the S-Matrix | as far as I know the equivalence theorem states, that the S-matrix is invariant under reparametrization of the field, so to say if I have an action $S(\phi)$ the canonical change of variable $\phi \to \phi+F(\phi)$ leaves the S-matrix invariant. In Itzykson's book there is now an exercise in which you have to show, tha... | How can I demonstrate that the Jacobian determinant in the change of variables from $\phi$ to $\chi = \phi + F(\phi)$ is equal to 1, ensuring that the S-matrix remains invariant under this canonical transformation? | 37,085 | cqadupstack-physics |
24338 | How fictitious are fictitious forces? | How fictitious are fictitious forces? More specifically, in a rotating reference frame i.e. on the surface of the earth does an object that is 'stationary' and in contract with the ground feel centrifugal and Coriolis forces? Or are these forces purely fictional and used to account for differences in observed behaviour... | In a turreted armoured vehicle sitting stationary on the surface of the Earth in the UK, how does the direction of the turret's rotation (east to west vs. west to east) affect the power required by the motors to maintain that rotation due to the influence of centrifugal and Coriolis forces? Quantify the difference in p... | 4,135 | cqadupstack-physics |
27455 | Any use for $F_4$ in hep-th? | In high energy physics, the use of the classical Lie groups are common place, and in the Grand Unification the use of $E_{6,7,8}$ is also common place. In string theory $G_2$ is sometimes utilized, e.g. the $G_2$-holonomy manifolds are used to get 4d $\mathcal{N}=1$ susy from M-theory. That leaves $F_4$ from the list o... | What is a specific application or theoretical framework in high energy physics or string theory where the Lie group $F_4$ is utilized, distinct from studies focusing on $d=4$ $\mathcal{N}=1$ supersymmetry gauge theory? | 321 | cqadupstack-physics |
104581 | Can we detect whether food has previously been heated in a microwave oven? | An acquaintance told me that she refuses to eat microwaved food because she read that the microwave _changes the molecules_ of the food somehow. Her statement is vague and her sources are dubious but I am curious. I know that microwaves tend to heat food unevenly, causing changes at the macro scale to the structure of ... | Are there any specific chemical or structural changes to nutrients in food that can be detected after it has been heated in a microwave oven, and what methods can be used to determine if food was microwaved? | 12,023 | cqadupstack-physics |
54571 | Beta decay for Ar-38, K-38, Cl-38 | I want to prove that $^{38}Ar$ is stable with respect to $\beta$ decay, that $^{38}Cl$ decays by $\beta^-$ and that $^{38}K$ decays by $\beta^+$. I know from Googling that this is true, and I also know that $^{38}Ar$ has the highest binding energy for mass number 38, thus its definitely stable with respect to $\beta$ d... | What experimental method could be used to demonstrate that $^{38}Ar$ is stable with respect to $\beta$ decay, in comparison to the $\beta^-$ decay of $^{38}Cl$ and the $\beta^+$ decay of $^{38}K$, without relying solely on calculating binding energies? | 462 | cqadupstack-physics |
131851 | Speed of light and distance | Our measure of distance (the meter) is defined in terms of how far light in a vacuum travels in a specific time. When light travels through another medium, we say it travels at a different speed. Why not say it travels at the same speed, and the distance in the medium is different that the distance outside? Is it only ... | If light travels at a speed of 3.00 x 10^8 meters per second in a vacuum, and its speed decreases to 2.00 x 10^8 meters per second when passing through water, how much time does it take for light to travel a distance of 1 meter in both the vacuum and the water? Show your calculations. | 972 | cqadupstack-physics |
44302 | Why does water make a liquid film? | Cut a narrow slit in a thin sheet of opaque material. Immerse the sheet in a liquid, such as water. After removing the sheet from the liquid, you will see a liquid film in the slit. The question is: why does water make a liquid film and not stay where it was originally? | What physical principles explain the formation of a liquid film in a slit of a thin sheet after immersing it in water, and how would varying the width of the slit affect the height of the liquid film formed? | 18,714 | cqadupstack-physics |
16035 | Water and superconductors | If you have seen my previous questions then this may make better sense. If you put an insanely powerful superconducter on the outside layer of a ROV that is underwater, would it form an outer layer around it of near nothingness, if the water is only H2O? What I mean is, since water is a polar molecule and in the scenar... | If a powerful superconductor is placed on the outer layer of an underwater ROV, would it create a significant region of reduced molecular motion or altered density around it due to the polar nature of water (H2O), and how would this affect the neutral buoyancy of the ROV? What are the potential physical principles at p... | 28,541 | cqadupstack-physics |
94756 | Why does adding milk to my coffee produce a fractal? | Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, "Why?" Oh dear, that is never a good question, so let's try "Why shouldn't they?" The obvious observations are that the water is very hot whe... | What physical principles and mathematical models can explain the formation of fractal-like patterns when milk is added to hot coffee, considering factors such as fluid dynamics, diffusion, and the initial conditions of temperature and rotation? | 6,147 | cqadupstack-physics |
133058 | Torque due to a magnetic field | We have two infinite perpendicular wires, each carrying a current "i" and the distance between them is l. If both the wires are free to move, how will they arrange themselves because of the torque exerted by the magnetic field produced by the two wires? | What is the angle between the two infinite perpendicular wires when they reach equilibrium, given that each wire carries a current "i" and they are separated by a distance "l"? | 16,624 | cqadupstack-physics |
6798 | What are the modern marvels in Physics that seem crazy but true? | What are the modern marvels in Physics which are crazy but true? Ideas which are ridiculed and dismissed in the beginning but passed the test of time? | What are three groundbreaking theories in physics that were initially met with skepticism but are now widely accepted and supported by experimental evidence? | 12,782 | cqadupstack-physics |
82658 | Møller scattering: twisted? | I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation? | What are the steps to calculate the transition amplitude for Møller scattering using the S-matrix formalism, and how can this process be visualized through the corresponding Feynman diagrams? | 22,091 | cqadupstack-physics |
37695 | What happens with photon when it is slowed down substantially? | In a dispersive media light's velocity can change substantially. Imagine we can slow it down to near 0 what the wave would look like? Frequency of light does not seem to change even at v=0 (at least 20m/s is observable), E=pc, and p=h/lambda, E=h*frequency. There is a duality, but that this mean the wave properties sho... | How does the expansion of the universe affect the frequency of light from the Big Bang, and what is the relationship between this redshift and the observable temperature of the cosmic microwave background radiation at approximately 3 K today? | 19,795 | cqadupstack-physics |
102313 | How does one detect a single photon? | I understand the double slit experiment up until the point that we begin "detecting" single photons. What does it mean to detect. You cant place a camera in the slit because that would capture the photon just like the photosensitive plates would. I've also heard that you can do the double slit experiment with electrons... | In the double slit experiment, when single photons or electrons are detected, what specific methods or technologies are used to ensure that the particles are observed without interfering with their paths, and how do these methods allow for the observation of wave-particle duality? | 13,285 | cqadupstack-physics |
101048 | Electric field produced by a charged ring | I have a question I couldn't find an answer for anywhere. There is a ring of radius $R$ which is charged uniformly with linear density $\lambda$, and I have to find the electric field on any point of the axis of the ring. So far so good, but this $\lambda$ includes both free and polarization charges, and the ring is in... | Given a uniformly charged ring of radius \( R \) with linear charge density \( \lambda \), and placed in a dielectric medium with relative permittivity \( \varepsilon_r \), how can I calculate the electric field at a point along the axis of the ring? Please consider both the free charge from \( \lambda \) and the effec... | 1,702 | cqadupstack-physics |
121270 | Why speed of Mangalyan is constant? | I have learned in school regarding the relationship between speed,acceleration and distance is $$v^2-u^2=2as $$ The initial velocity of India's Mars Orbiter Mission, MOM, is 32 km/s source and now the speed of MOM is 34.99 km/s source If we assume the acceleration is constant and put the values in the above formula the... | If the initial velocity of India's Mars Orbiter Mission (MOM) is 32 km/s and the final velocity is 34.99 km/s, assuming constant acceleration, what is the minimum distance traveled by MOM according to the equation \( v^2 - u^2 = 2as \), where \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is ac... | 21,852 | cqadupstack-physics |
22817 | Entanglement and relativity | Two observers A and B measure a quantum entangled state and obtain correlated results, even if their separation is space-like (each is out of the light cone of the other). A possible interpretation is that the observer who makes the first measurement (say A) collapses the quantum state, thus fixing the result of the ot... | What is the minimum separation distance (in light-years) between two observers measuring quantum entangled states in a way that their measurements are still space-like correlated, assuming they are both using classical communication to report their results? | 24,947 | cqadupstack-physics |
7911 | Why can different batteries with the same voltage send different currents through the same object? | According to an answer in this thread on Skeptics: > If you take one of the little 12V garage door opener batteries and short out > (directly connect) the two terminals with a piece of wire or something else. > You'll get a light current flow through the wire or metal. It may get a > little warm. This battery is only c... | How does the internal resistance of a car battery compare to that of a garage door opener battery, and how would this difference affect the maximum current that can be drawn when short-circuiting each battery? Additionally, what role does contact area play in the overall resistance and current flow during a short circu... | 13,219 | cqadupstack-physics |
34992 | What is the status of the Gennes - Alexander theory of Superconducting Micronetworks? | I have started reading the book Connectivity and Superconductivity which gives an introduction to the ideas of de Gennes-Alexander theory. My question is: how is this theory regarded experimentally? Besides the sophisticated math approach,does it give good experimental results? | What are the key experimental findings that support or challenge the predictions made by the de Gennes-Alexander theory in superconductivity? | 7,093 | cqadupstack-physics |
93358 | Magnetic field exclusion and retention in superconductors | I'm studying the behaviour of superconductors in different cases, and I can't understand this. We have a superconducting cylinder with a coaxial hole inside (vacuum). When the cylinder is cooled below it's critical temperature, and later a magnetic field is applied (case a), the superconductor will exclude the field ev... | In the context of superconductors, explain the difference in magnetic field behavior in the coaxial hole of a superconducting cylinder when cooled below the critical temperature after applying a magnetic field (case b) versus cooling the cylinder first before applying the magnetic field (case a). Why does the magnetic ... | 17,124 | cqadupstack-physics |
76494 | Star product of two commuting spinors | Ok so this might be a very stupid and trivial question but I have spent a couple of hours on this little problem. I am trying to derive a simple formula in a paper. We have a real commuting spinorial variable $y_\alpha$ ($\alpha = 1,2$) ($y^\alpha = \epsilon^{\alpha\beta}y_\beta$, $\epsilon^{\alpha\beta}=-\epsilon^{\be... | Can you derive the value of the $*$ commutator $[y_1, y_2]_{*}$ using the given $*$ product law, and explain the steps to handle the divergent integral that arises in the computation of $y_1 * y_2$? | 33,481 | cqadupstack-physics |
105363 | Lagrangian for a moving spring device |  How can I write the proper Lagrangian for such as system as the one shown in picture? Am confused about what is the suitable way to designate the coordinate. | Given two masses \( m_1 \) and \( m_2 \) moving in the same direction with velocities \( v_1 \) and \( v_2 \) respectively, derive the Lagrangian \( L \) for the system. Assume the kinetic energy \( T \) is represented by the standard formula \( T = \frac{1}{2} mv^2 \) and there are no potential energies acting on the ... | 38,219 | cqadupstack-physics |
13611 | Planck's Law in terms of wavelength | I am drawing a blank when it comes to equation transformation. Wikipedia gives two equations for the spectral radiance of black body: * First as a function of frequency $\nu$: $$I(\nu, T) = \frac{2 h \nu^3}{c^2}\cdot\frac{1}{e^\frac{h \nu}{k T} - 1}$$ * Then as a function of wavelength $\lambda$ : $$I'(\lambda, T) ... | How can I correctly transform the spectral radiance equation from a function of frequency, \( I(\nu, T) = \frac{2 h \nu^3}{c^2}\cdot\frac{1}{e^\frac{h \nu}{k T} - 1} \), to a function of wavelength and obtain the \( \lambda^5 \) term in the equation \( I'(\lambda, T) = \frac{2hc^2}{\lambda^5}\cdot\frac{1}{e^\frac{h c}{... | 11,115 | cqadupstack-physics |
80949 | Rank of the Poincare group | There are two Casimirs of the Poincare group: $$ C_1 = P^\mu P_\mu, \quad C_2 = W^\mu W_\mu $$ with the Pauli-Lubanski vector $W_\mu$. This implies the Poincare group has rank 2. Is there a way to show that there really are no other Casimir operators other than trying to build all possible combinations of generators an... | What is the rank of the Poincaré group, and how can it be determined without explicitly constructing all possible Casimir operators? | 193 | cqadupstack-physics |
27251 | What methods are there to deal with quantum spatiotemporal chaos? | By now, there has been enough grasp on quantum chaos for systems with a small number of degrees of freedom. The major tool used is periodic orbit theory to approximate the spectral distribution. Is there any suitable generalization to a quantum field theory with one spatial dimension whose classical analog exhibits spa... | What is the expected number of prime cycles in a one-dimensional quantum cellular automaton that is Turing complete, and how does this compare to the prime cycles in a chaotic classical system with the same dimensionality? | 11,747 | cqadupstack-physics |
72388 | Contraction and expansion after constricting flow though a pipe | If an orifice is placed inside a pipe with a smaller diameter than the rest of the pipe, fluid will follow a curved path in order to enter the orifice, and then expand. I was wondering at what distance would the diameter of the flow reach its minimum (the vena contracta) and at what distance after that would the diamet... | What is the distance from the orifice where the fluid flow reaches its minimum diameter (vena contracta) and what is the distance after that for the flow to return to the diameter of the original pipe, given a pipe diameter D and an orifice diameter d? | 19,351 | cqadupstack-physics |
126774 | 1D Smoluchowski diffusion equation in a linear potential | I am interested in solving a 1D Smoluchowski diffusion equation in a linear potential $U(x) = cx$ for a constant force $c$. This problem follows chapter 4 of the theoretical biophysics script by Schulten. The Smoluchowski equation reads \begin{equation} \partial_t p(x,t|x_0,t_0) = \left(D \partial_x^2 + D\beta c \parti... | Can you derive the time derivative of the function \( q(y, \tau | y_0, \tau_0) \) with respect to \( \tau \) using the substitution \( y = x + b\tau \), and explain how the term \( b \partial_y q(y, \tau | y_0, \tau_0) \) arises from that transformation? | 27,463 | cqadupstack-physics |
7555 | determination of voltaic cell voltage | if i understood this correctly, the determination of voltage for a specific voltaic (gallvanic) cell is determined only by the chemical correlation between the two metals. is this true? for an example , if i use iron instead of zinc in the example from wikipedia, i will get a different voltage? | How does the choice of metals in a galvanic cell affect its voltage, and what would be the expected change in voltage if iron is used instead of zinc in a typical galvanic cell setup? | 1,233 | cqadupstack-physics |
132606 | Hydrogen extraction efficiency of newish nano particle AA battery | The internet is ablaze with the new nano particle based extraction method of converting water to hydrogen. In 2002/2003 when I was 16 there was a similar craze about a lawn mower motor which supposedly ran on water. Indeed there were even conversion kits on the internet for vehicles. They didn't work because of a funda... | What are the theoretical limits for the efficiency of hydrogen production from water using nanoparticle-based methods, and how do these limits compare to classical electrolysis? | 34,908 | cqadupstack-physics |
127796 | What is the analogy of $|x\rangle$ in quantum field theory? | Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ $|x_a \rangle$ is an eigenstate of position operator $\hat{x}$. In QFT we have $$ U(\phi_b,\phi_a;T) = \langle \phi_b | U(T) |\... | In the context of quantum field theory, consider the position-space representation of the single-particle wavefunction given by $$ \langle 0 | \phi(\mathbf{x}) | \mathbf{p} \rangle = e^{i \mathbf{p} \cdot \mathbf{x}}. $$ If we interpret the action of the field operator on the vacuum state and relate it to position stat... | 7,296 | cqadupstack-physics |
108136 | What can I say about compatibility between predictions and results? | If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\\ \omega_{b_1} = 0.0707 \pm 0.0003~\text{rad/s} && \omega_{b_2} = 0.0700 \pm 0.0002~\text{rad/s} \end{align} And I got these experimental results: \begin{align} \omega_{... | Based on the theoretical predictions and the experimental results given for \(\omega_{p_1}\), \(\omega_{p_2}\), \(\omega_{b_1}\), and \(\omega_{b_2}\), calculate the percentage discrepancy for each measurement and determine if the experimental results fall within the uncertainty ranges of the theoretical predictions. W... | 7,559 | cqadupstack-physics |
132705 | Richter scale equation | According to Wikipedia, the equation for finding magnitude according to the Richter scale is $M_\mathrm{L} = \log_{10} A - \log_{10} A_0(\delta)$. However, it is rather ambiguous as to the effect of epicentral distance ($\delta$) on the equation. Other sources seem to suggest that the distance from the epicentre is tak... | How does the epicentral distance (\(\delta\)) influence the calculation of the Richter scale magnitude \(M_\mathrm{L} = \log_{10} A - \log_{10} A_0(\delta)\), and can you provide a specific example of how \(A_0(\delta)\) is determined for different distances? | 34,399 | cqadupstack-physics |
123698 | Ising formulation of the graph isomorphism problem | **Context** I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I mention it briefly. Given two graphs, $G_1$ and $G_2$ of same $N$ number of vertices, the Ising Hamiltonian is, $$H = H_A +... | Given two graphs \( G_1 \) and \( G_2 \) with \( N \) vertices each, and the Ising Hamiltonian defined as \( H = H_A + H_B \), where
\[
H_A = A \sum_v \left(1 - \sum_i x_{v, i}\right)^2 + A \sum_i \left(1 - \sum_v x_{v, i}\right)^2
\]
for \( x_{v,i} \) being binary variables, how many unique terms are present in \(... | 21,817 | cqadupstack-physics |
9756 | What is the extent of Earth's gravitational pull? | 1. Where the gravitational pull of Earth exist up to? 2. What distance from Earth it will be zero? 3. How do the skydivers fly at a same altitude? 4. Won't they feel gravitational pull? 5. What is the Earth's gravitational pull? | At what distance from Earth's center does the gravitational pull effectively become negligible, and what is the approximate value of Earth's gravitational acceleration at sea level? | 2,492 | cqadupstack-physics |
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