Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is this a kinematics paradox? You consider a shaft which can rotate freely (there will be of course a frame with ball bearing to hold the shaft firm and to allow it to rotate with low friction); fixed on this shaft there are two gears, one with radius $R$ and another with radius $2R$. Note that the two gears rotate tog... | It seems to me that what you see is what you get here - that arrangement of gears would lock up and the shafts would not turn.
In general, if a big gear drives a small gear then the smaller gear will rotate faster, and vice-versa. If you try to do both at once, then your effort will simply go into applying torsion to ... | {
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Is it correct to say that; an object moving at a constant velocity is moving in a straight line? I think it is correct because:
v = displacement/time, if the direction changes, the displacement changes so the velocity is not constant anymore.
Please correct me if I'm wrong
| Yes you are correct$^1$, to define an object's velocity we have to specify in which direction it is travelling and how fast - this defines a vector quantity. If we say the vector is unchanging, its length (the object's speed) and its orientation (which direction the object is travelling) must be constant in time which ... | {
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What should I read to understand the math behind waves? I'm learning differential equations and waves - following online courses and reading some textbooks - and I find that quite often, the use of Phasors, equations combining sinusoidal waves of different amplitudes and frequencies (the derivation of beats)...etc...th... | Berkeley Physics Course vol. 3 is all about waves:
https://www.amazon.com/Waves-Berkeley-Physics-Course-Vol/dp/0070048606
I personally prefer the chapters reviewing waves in the book Optics, from E. Hecht:
https://www.amazon.com/Optics-5th-Eugene-Hecht/dp/0133977226
Good luck with your studies! :)
| {
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Question on Ampere's Law and Solenoid Just came across magnetic field inside a solenoid and amperes law. Amperes law says that dot product of magnetic field and distance from current would give us the $\mu_p$ times the current enclosed. If we put an amperes loop inside a solenoid, would the magnetic field be zero as th... | There is a catch, Ampere's law has not said that the field would be zero. Instead, it says line integral of the field along a loop will be equal to zero; fields inside the solenoid can't be zero.
| {
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Problem in Derivation of Goldstein
In Goldstein, chapter three, third derivation, given as, Kepler's equation can be written as
${\rho} = e\sin({\omega}t + {\rho})$,
Now I have to prove that the first approximation to ${\rho}$ is ${\rho_1}$ given by
$$\tan({\rho_1}) = \frac{e\sin({\omega}t)}{1-e\cos({\omega}t)} $$
and... | I'm writing this in connection with najkim's answer above, just because I noticed something when some terms were simplified using the first identity
For the 2nd part, when najkim gets to the part
$\sin{\rho_2} - e \sin{\omega t}\cos{\rho_1} - e\cos{wt}\sin{\rho_1}=-\frac{1}{6}e^3 \sin^3{(\omega t + \rho_1)}$
The left h... | {
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Behaviour of clocks and measuring rods on a rotating frame of reference I'm reading "Relativity: The Special and the General Theory" by Albert Einstein. In the following extract:
Let us consider a space-time domain in which no gravitational field exists relative to a reference-body K. K is then a Galileian reference-b... | The Coriolis force is not mentioned above because the disk and the observer are all at rest in the rotating frame. As soon as something is moving in the rotating frame then the Coriolis force will become important.
In the mathematics of general relativity both the centrifugal and the Coriolis forces show up in the Chri... | {
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Why is the field quantization applied to the free particle? This post claims that there is no real photon (particle) with a plane wave solution well-defined momentum state).
It makes sense somehow to me. I can think of several arguments:
*
*The plane wave solution doesn't have well-defined probability as it exists in... | All models are wrong, but some are useful
Much of physics is inductive theories, which build description of complex phenomena from small elements. Neither photon, nor a point-like particle in free space (the basis of the Newtonian mechanics), nor a harmonic oscillator, nor plane waves exist. However, they are simple an... | {
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What is the point of a voltage divider if you can't drive anything with it? The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So w... | Oh, but you can. You can drive an high impedance input with it...including a buffer, which can then in turn be used to drive whatever you want. The more current you draw the more the voltage will droop, so you just make sure to draw as little current as possible. So that the output is, for example, 99.9% of what the di... | {
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Help with finding speed and coordinates Can you please help me with this I'm stuck?
A particle starts from rest at $t=0$ at the origin and moves in the XY plane with a constant acceleration of $a=( 2i+4j)\ \mathrm{m/sec^2}$
After a time of $3$ seconds has elapsed. find:
*
*the $x$ and $y$ components of velocity.
*t... | Since the particle is moving under constant acceleration and you are dealing with vector quantities, you can use the SUVAT equations in the two different directions ($i$ and $j$), to find the results you require.
These equations are derived from the definitions of acceleration
$$\vec a = \frac{d\vec v}{dt}$$
and veloci... | {
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Which equations of 5 string theories show that elementary particles formed by strings? It is commonly said that
"elementary particles are indeed formed by strings."
(from E Witten interview)
Which equations of string theory show that elementary particles are indeed formed by strings (2d string worldsheets)?
How to se... | "that elementary particles formed by strings?"
Elementary particles are described theoretically by the standard model a well developed and flexible quantum field theory, with the group structure of SU(3)xSU(2)xU(1).
The interest in string theories arises because this group structure can be embedded in the group behavio... | {
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Why is the plane wave ansatz appropriate for scattering cross sections of a localized particle beam? This question is a spin-off from this related question: Why does the Born approximation for the scattering amplitude depend on the potential $V$ everywhere in space, unlike classical scattering? This question deals wit... | If I'm understanding your question correctly, the answer is yes - assuming a plane wave solution would yield a wavefunction of the form
$$\psi_k(\mathbf r,t) = e^{i(kz-\omega_k t)} + f_k(\theta) \frac{e^{i(kr-\omega_k t)}}{r}$$
so a wavepacket solution would take the form
$$\Psi(\mathbf r,t) = \underbrace{\int d^3\math... | {
"language": "en",
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Can gravity slow down the expansion of the universe? If dark energy drives a repulsive force between galaxy clusters, proportional to their distance which makes space expand, which creates space between them, and gravity between the clusters has the opposite effect, if it tends to shrink, to annihilate space between th... | Yes, gravity can slow down the expansion of the universe. That's why if the universe's average density is greater than critical, it is forecast to collapse into a big crunch (see this section of the Wikipedia article on the Friedmann equations).
I don't understand your second paragraph very well, but it seems like a mi... | {
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Does seeing an object modify it state? I took a dive into the concept of information in physics and from what I have read, I which someone to confirm if looking at something really modify the state of that thing.(modify state here refers to any small change in the object "information arrangement")
| Seeing is a rather vague term. To literally see something we have to send a stream of photons at this object and then detect by our eyes some of the photons scattered by the object. In a more general setting photons may be replaced by electrons or more exotic particles and the detection can be done using a device more ... | {
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What is that which is magnetic force? I believe a magnetic field is caused by movement of charged particles.
But, what is it that is actually making the force between two magnets repel or attract to another? For repelling, I'm mentally visualizing a water balloon between two magnets. What is the water balloon composed ... | So permanent magnetic materials are termed ferromagnetic. It is a good question to ask what the nature of the force is between two magnets, but I believe the answer is: we don't know.
Take as a similar type of example: electric charges. We know that like electrical charges repel one another and unlike charges attract... | {
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If net force is 0, why does elongation occur in a rod? I was taught that stress is the restoring force per unit area (let us assume a rod). This stress is developed on order to resist the motion of the rod. My questions are as follows :
*
*If the rod is subjected to equal and opposite forces why is stress developed a... | Stress takes into account the restoring force only. And restoring force is the internal force produced by the body. It's the next external force that is zero. But since internal force is not zero, there would be a stress and thus a corresponding elongation. The body won't have acceleration since net external force is z... | {
"language": "en",
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Can Maxwell's equations be generalized to all fields? For having studied both classical and quantum optics, I regard Maxwell's equations as the grand "cheat sheet" from which (almost) all optical/photonic phenomena can be derived. Yet, I also know that wave-particle duality extends to all other fields and particles in ... | Maxwell's equations can be written as a massless wave equation and this is a special case of Einstein's energy-momentum relation in wave form. The general case is the Klein-Gordon equation, which is satisfied by any free non-interacting field.
| {
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How does light get energy when moving from one medium to another? It is said that the speed of light increases when moving from optically denser medium to rarer medium but
as light can be considered as a particle how does it get the energy to increase it velocity
| Light can be considered a particle, known as a photon, but the energy of each photon is not related to its velocity. Instead, it is given by the Planck formula,
$$
E=h\nu,
$$
where $h$ is Planck's constant and $\nu$ is the frequency of the light. Since the frequency of the light remains constant as it travels from one ... | {
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Delayed Choice Quantum Eraser variation results If we were to start with the delayed choice quantum eraser setup in the attached image, what would the interference pattern look like for the photons at D0 if D3 and D4 were eliminated (and the two beam splitters that feed them) and the beam splitter configuration between... |
if the beam splitter configuration between D1 and D2 was altered so that 75% of the photons from each slit to go to D1 and 25% of the photons from each slit to go to D2?
This behaviour is unphysical from any beam splitter.
Take a beam splitter with two input ports, $\rm in_1$ and $\rm in_2$, and two output ports, $\r... | {
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Why does mass-spring system tend or prefer to oscillate with natural frequency? Can you explain it theoretically rather the derived version of it? Why the mass spring system prefers to oscillate at natural frequency, why does it rather oscillate at other frequencies? Every object in the universe is always vibrating, i... | For an intuitive explanation, imagine pushing a child on a swing. Once the swing starts moving, you wait to push it again until it reaches the high point of its backwards motion. If you try pushing the swing when it is already swinging forward, it is not going to be as effective. If you try pushing the swing while its ... | {
"language": "en",
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Relativity without constancy of light speed Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive:
$$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$
$$t' = \frac{t+\kappa vx}{\sqrt{1+\kappa v^2}}$$
$\kappa = 0$ denotes Galilean and $\kappa < 0$ deno... | As stated in almost all the answers, $\kappa>0$ does indeed define a set of transformation that preserves the Euclidean metric, with the Lorentz group $SO(1,3)$ being replaced by $SO(4)$. Although this does make mathematical sense, there's an internal physical inconsistency, which shows that an universe with $\kappa>0$... | {
"language": "en",
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How do I interpret uncertainty in velocity greater than the speed of light? I just studied Heisenberg's uncertainty principle in school and I came up with an interesting problem.
Assume an electron which is moving very slowly and we observe it with a distance uncertainty of say $\Delta x=1\times10^{-13} \text{ m}$ if... | So when you become a particle (or nuclear) physicist , one of the first things you need to memorize is that:
$$ \hbar c \approx 200\,{\rm MeV\cdot fm}$$
where "fm" is a fermi ($10^{-15}\,$m), which is the scale of a nucleon.
Thus, if your position uncertainty is 100 fm, you can immediately estimate a momentum uncertain... | {
"language": "en",
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What exactly is enclosed current? In the realm of magnetostatics, consider the integral form of Ampere's law:
$$ \oint_C \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enclosed}$$
What I realized is when asked the question "what is the enclosed current enclosed by?"
The most common answer I get is "enclosed by the Amperian lo... | You can think of the currents enclosed by the Amperian loop $C$ as the currents that go through whatever surface $S$ -no matter how you deform it, as long as you don't rip holes in it- that is enclosed by $C$.
From a topological point of view, the Amperian loop $C$ along which you are computing the integral and the loo... | {
"language": "en",
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Fermion LSZ reduction / Greens function In Matthew D.Schwartz book, 'Quantum Field Theory and the Standard Model' page 227/8 he talks about Feynman diagrams in QED, specifically $e^{-}e^{-} \rightarrow e^{-}e^{-}$ u and t channel tree level scattering amplitudes.
He then proceeds to say that these two diagrams represen... | The LSZ reduction formula is a method to calculate S-matrix elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory. The time-ordering operator $T$ manhandle the fields so that fields at a later time are at the left of fields at an earlier time.
As the LSZ formula perf... | {
"language": "en",
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Why can't photons cancel each other? The textbook argument against photons canceling each other draws upon the conservation of energy. Does this mean that energy conservation is a "stronger" principle than superposition? Waves in other media than the EM field, e.g., sound or water, do cancel out---presumably by passing... | You need to careful when you talk about photons as waves because one photon is certainly not an EM wave, which is a superposition of many many photons. Indeed if you are talking about very high energy photons they will produce an electrons positron pair. In other words you can convert the energy of photons into the "ma... | {
"language": "en",
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Angular Frequency of a charged particle moving in a Magnetic Field I am trying to solve the Differential Equation in Mathematica but it is giving me error. How to find it's solution in Mathematica or in general.
$$y'''=\frac{\omega^2E}{B}-\omega^2y'$$
The above equation is for the angular frequency of a charged particl... | Though this question is perhaps better suited to the Mathematica Stack Exchange, I think this differential equation is simple enough to be able to solve such equations by hand before resorting to tools like Mathematica! The key thing that you need to notice in the above equation that makes it very simple to solve is th... | {
"language": "en",
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Magnetism through Relativity If relativity tells that from a moving charge's frame (observing current carrying wire) protons contract in length and its charge density increases making the charge experience a electrostatic force. In lab frame (observing current carrying wire and a stationary charged particle) the electr... | I think, from the viewpoint of the lab observer, the diameter of each electron is Lorentz contracted in the direction of motion, whereas the distance between every two successive electrons remains unchanged. This causes the charge density of the moving electrons to be unchanged, and thus there is no net electric field.... | {
"language": "en",
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Does dark matter follow all principles of regular physics? Is dark matter bound by all the laws of regular physics?
i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation.
What about Newton's laws of motion (since all of Newton's laws assume an interaction between particles)?
|
Is dark matter bound by all laws of regular physics? i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation.
Yes. The four things you mention are assumed to apply to dark matter. It does not need to violate any known laws of physics. The only way in which dark matter needs to differ fro... | {
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Why are aerodynamic / streamlined shapes always stumpy at the front? I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:
The usual explanation is that the ... | One way of looking at the problem is to consider the pressures over the surface. Streamlines curling outwards tend to indicate high pressure pushing water away, streamlines curling inwards indicate low pressure drawing water in.
A reflex curve at the front, as in your second image, gives high pressure across much of th... | {
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Difference between Mixed and Pure states Suppose that there is a system of two photons 1 and 2, each of which is in a mixed state $1/2|R\rangle\langle R| + 1/2 |L \rangle\langle L|$, where $|R \rangle$ and $\langle L|$ are two orthonormal pure polarization states. (So the composite state would be a product of two mixed... | There is no difference for measurement outcomes in the $\{|R\rangle, |L \rangle\}$ basis. However, you will see a difference if you look at a rotated basis e.g. consider the axes:
$$|+\rangle = \frac{1}{\sqrt{2}} \left(|R\rangle + |L\rangle\right) \\
|-\rangle = \frac{1}{\sqrt{2}} \left(|R\rangle - |L\rangle \right) $$... | {
"language": "en",
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Would a hypothetic very fast camera allow to visualize the variations of the amplitude of visible light? The fastest camera available so far is capturing 10 millions images per second.
https://www.shimadzu.fr/hyper-vision-hpv-x2
In the scenario of the currently known physics, but in the hypothesis where technology woul... | MIT effectively achieved a trillion frames per second by creating frames at successively later times in a train of identical pulses. They made some amazing photos of the propagation of a pulse of light.
See Femto-Photography: Visualizing Photons in Motion at a
Trillion Frames Per Second
| {
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Kirchhoff's Voltage Law does not hold for a free source RC circuit? Say I have a simple free source RC as depicted in the image below. The capacitor initially has a charge of Q on its positive plate and at time t=0 the switch is close. I use the mesh current as shown in the diagram and apply KVL to that loop.
But then... | K.V.L. does apply here. Your mistake lies in incorrectly substituting the current in the resistor for the time-rate-of-change of charge in the positive-plate of the capacitor. The $I$ in the expression is actually $I(t)$ and it relates to the charge on the positive plate of the capacitor. Notice that as the charge flow... | {
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What is the direction of the frictional force acting on a rolling wheel? Let's keep things simple and assume that the wheel does not slide. Assume you are in a car that moves with constant speed. Obviously, the wheels exert a tangential force to the surface on the road in the points of contact, P. According to Newton's... | As the wheel is rolling without slipping the frictional force on the wheel is zero. This is because friction acts when objects slide over each other or when objects try to slide over each other. however at the contact point the velocity of the wheel relative to the ground is zero so there is no slipping so no friction ... | {
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Origin of magnetic field of Earth I have a hard time understanding why does earth have magnetic fields.
My textbook reads:
"The Earth's core is very hot and molten, and the ions of iron and nickel are responsible for Earth's magnetism.
But how did it manage to create such huge magnetic fields?
| https://youtu.be/lWHxmJf6U3M
Watch this video, you will get a good enough idea of how the earth's magnetic fields have strengthened itself over time.
But the question as to how the fields originated in the first place, is still a question to be answered.
But I think that though with very low probability, it may have ha... | {
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"url": "https://physics.stackexchange.com/questions/573390",
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My question is about satellite motion and gravitation Our teacher told us today:
Suppose a satellite is moving around the earth in a circular orbit of radius $r$. Suddenly an external agent stops its motion so that its kinetic energy becomes zero but its gravitational potential energy remains the same. Assume there is... | The satellite will stop but the rotation of the Earth no. The satellite will fall vertically but the trajectory of the satellite will be an ellipse relative to the vertical point where the satellite was stopped because of the rotation of the Earth.
| {
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Heat energy change in adiabatic process We know that when a system gains heat energy from the surroundings through conducting walls of the container , then the temperature of the system also increase till it reaches an equilibrium value .
Whereas in an adiabatic compression of a gas where temperature increases but the ... | The equation $Q=C_X\Delta T$, where $C_X$ is the heat capacity under some condition $X$, e.g., constant volume, is useful in telling you how much the temperature of a gas rises if you heat it with incoming energy $Q$ under that condition.
However, there are other ways to increase the temperature of a gas; you can compr... | {
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Extra energy in dual mass-spring systems Below is a Dual mass spring system placed on a smooth surface(no friction), let us assume the spring constant as $k$ in this case.
Now if we create a small extension in the spring of value $x_o$, the two masses will perform simple harmonic motion(SHM) individually with amplitud... | Let $x$ be the magnitude of the maximum displacement from its equilibrium position of mass $m$ and $X$ be the magnitude of the maximum displacement from its equilibrium position of mass $M$.
Conservation of momentum for the system requires $m\dot x = M\dot X \Rightarrow mx=MX$.
For this system the natural frequency of ... | {
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How does a resistor reduce current in a circuit? I'm in year 10 and I just have a question about resistors. How exactly does a resistor reduce current?
From what I've read the current before a resistor is the same as the current after a resistor so how does the resistor reduce current?
I know that the electrons bump in... | Say we have a simple circuit consisting of a battery, a wire, and a resistor. The purpose of the resistor is to decrease the current in the circuit. How does this happen?
Firstly, a resistor is made of material that is less conductive than the wire. As a result, electrons aren’t able to move as quickly in the resistor ... | {
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Kinematic theory and dynamical theory of x-ray (or electron) diffraction. Why such names are given? Kinematic theory and dynamical theory of x-ray (or electron) diffraction. Why such names are given to scattering theories ? Does it have any connection to Kinematics (of Galileo) and Dynamics (of Newton) of general physi... | Kinematics doesn't really have much to do with Galileo anymore, and dynamics doesn't necessarily involve Newton. Instead, those terms are roughly defined as the following:
*
*Kinematics is the process of understanding how things move. It involves determining the trajectory of objects without necessarily trying to com... | {
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How would cooking change at 1km depth under sea? A chimpanzee has just returned to the surface after extended time at 1km depth, breathing trimix air. This brings the possibility of hyperbaric habitation, however how would the basic functions of cooking be affected in hyperbaric conditions?
Specifically, could we have... | Cooking under high pressure is totally possible, but some recipes would need to be changed.
Say the boiling point of water at this pressure is 150 C. That means boiling water will be far hotter than we are used to, and will cause more vigorous reactions and diffusion.
The most salient effect is that boiling water would... | {
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What are the equations of motion for this simple system? I have a cart of mass $m_c$ connected to a pole of mass $m_p$ and length $L$ with a frictionless hinge. The cart can slide frictionlessly on a horizontal plane. Let $x_c$ denote the horizontal coordinate of the cart center of mass, and $\theta$ the angle between ... | Given that the hinge exerts horizontal, H, and vertical, V, forces on each object, we can write force equations for the cart: F – H = $m_c$$a_c$ and for the pole: H = $m_p$$a_{px}$ and V - $m_p$g = $m_p$$a_{py}$. Since the pole is in a non-inertial system, I would not use a torque equation. However, we can say that ... | {
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How big should a star be to turn into a black hole? My initial calculations show that if the radius of a star $-$ with a uniform mass density of $\rho$ $-$ is greater than $\frac{c}{2\sqrt{\pi G\rho/3}}$, the star would collapse into a black hole. However, I could not find any reference to check the result. Can anyone ... | If a star is collapsing into a black hole, it is reasonable to conclude that its density is not constant. As a star runs out of fuel, its temperature decreases, which means molecules have less energy and can resist gravity less. This means the star will compress, and density will increase. So just because a star is cur... | {
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Frequency and intensity in photoelectric effect In the explanation of photoelectric effect it is written that intensity and frequency of radiation have different results i.e. higher intensity means greater number of emitted photoelectrons and higher frequency means greater kinetic energy of emitted photoelectrons.
But ... | What you just discovered is that if you keep the intensity of a light source constant and increased the frequency, the number of photons per unit area must decrease. What Einstein told us is that intensity alone is not enough to tell us whether an electron will be ejected from a solid. Increasing the intensity and keep... | {
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Why do motorcycles front wheels lift of the ground when accelerating quickly When motorcycles accelerate quickly they do a wheelie. Where is the torque provided to lift the motorcycle?
| Just like the force to accelerate the vehicle forward comes from the friction with the road, the torque on the vehicle comes from the same road friction.
Draw a free-body diagram with motorcycle. As it begins to accelerate, the only external forces are gravity (with a torque about the rear axle in one direction), and ... | {
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(Fundamental) difference of Seebeck effect for metals and semiconductors In which way is the Seebeck effect different for semiconductors from metals and why is it greater? What is the difference in the underlying physical principle?
My knowledge so far is: Bring two materials in touch, doesn't matter which, their elect... | I think the answer has to do with the relation between the Seebeck coefficient and the electrical conductivity's dependence on energy, known as the Mott Formula (https://en.wikipedia.org/wiki/Thermopower#Mott_formula).
In short, the model that leads to the formula yields to a Seebeck coefficient that is proportional to... | {
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Will table sugar twist polarized light? I recently saw this awesome video by Steve Mould where he explained that a sugar solution in water will turn polarized light in the clockwise direction.
The explanation basically boils down to sugar molecules (glucose) having a handedness (they are chiral) and that linearly polar... | I have successfully done this demonstration in my classes using table sugar. I place a polarizer on an old-fashioned overhead projector, hold a crossed polarizer above it to block the light, and then insert a beaker of sugar solution between the two. I usually use a solution of 1:1 sugar-to-water (by volume), basical... | {
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Lorentz Force on a Current Carrying Wire Does the Lorentz Force on a Current Carrying wire given by the equation
$$\mathbf{F} = I \int \text{d}\ell \times \mathbf{B}$$
constitute an action reaction pair? That is, if i have two arbitrarily shaped current carrying wires, is it true that force on any one of them due to th... | Yes this is true, for example Lets take 2 parallel infintite wires carrying a current $I_1$ and $I_2$ that located distance $d$ from each other
We know from biot savart law that magnetic field of wire at distance $d$ is $$\frac{\mu_0 I}{2\pi d}\hat \phi$$ so now we can calculate to Force of wire 1 on wire 2
by your f... | {
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Software for matrix-product state calculations Which software packages exist to either numerically or analytically do matrix-product state calculations? (Such as finding the ground state, time evolution, bond decimation, symmetries..) Which are under active development? What are their strengths and weaknesses?
There is... | Most of modern software can do (or has packages that can do) matrix multiplication, solve eigenvalue problems, etc. On the top of the head one could mention the Matlab and the numpy module of Python. But one needs to understand the underlying matrix algebra to use either of them.
| {
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What is the effect of radius in a planet's steady state temperature? Let's say there are two planets, without an atmosphere, sharing orbit and equal in every way except their size: planet 1 is 10x larger than planet 2.
Heat into the planet $Q_{in}$ from radiation is proportional to the cross sectional area, $\pi r^2$. ... | If you are talking about a steady state temperature, then both heat in and heat out depend on the emitting/absorbing area. In that case, for spherical objects and assuming heat can be readily transferred inside the object, then size will not be a factor.
The size will be a factor if things cannot reach a steady state b... | {
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Uniqueness of Spectral Decomposition In one of the papers (related to Quantum Computing) I am reading, I came across this statement which says,
An elementary result is that sets of orthogonal rank-one eigenprojectors of Hermitian operators
are not unique when the spectrum includes degenerate eigenvalues, and that uniq... | Consider the following matrix:
$$A=\pmatrix{1 &0&0\\0&2&0\\0&0&2}$$
I can decompose $A$ as the sum of projectors onto 1D subspaces as follows:
$$A = 1 \cdot\pmatrix{1&0&0\\0&0&0\\0&0&0} + 2\cdot\pmatrix{0&0&0\\0&1&0\\0&0&0}+2\cdot\pmatrix{0&0&0\\0&0&0\\0&0&1}$$
But this decomposition is not unique, because I could also... | {
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Relation between Green’s functions and connected Green’s functions I attempt to understand the $0$-dimensional QFT from these QFT lecture notes by Ronald Kleiss from 2019. The author defines the generating function $Z(J)$ and its logarithm in the following way.
$$Z(J) = \sum_{n\geq 0} G_n \frac{J^n}{n!}, \quad W(J) = \... | From the given expression for $C_n$ we can write,
$$C_n = \left[ \frac{\partial^n W(J)}{\partial J^n}\right]_{J=0},$$
where $W(J) = \ln Z(J) = \ln \left[\sum_{n=0}^{\infty}\frac{1}{n!} J^n G_n\right]$.
Then determine different $C_n$ s.
| {
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Can rockets fly without burning any fuel with the help of gases under extreme pressure only? Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of rockets?
If it is done to create a greater reaction force on the rocket then why can't we get the same lift with just adjusting the speed of... | It will produce thrust, but think about it this way:
You need to throw some mass out the back anyway. If you can get the mass to react with itself so that it heats itself up and increases its velocity, all the better.
| {
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Why Lenz's law works? When we move a magnet towards a coil, current is induced in it. Magnetic field too develops around it. Since there is interaction of both magnetic fields(that of magnet and coil), there is magnetic potential energy in field(gained from the work we do). This energy is going to do work on magnet (ei... | if the force is attractive, we only have to start the motion, then the attraction would accelerate it, the current would increase, and we get energy for nothing or a perpetuum mobile.
| {
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How is it possible that combustion of coal releases similar energy as TNT explosion while intuitively we would not expect that? According to Wikipedia, the energy released in a TNT explosion is 4 × 106 J/kg.
https://en.wikipedia.org/wiki/TNT
According to web, combusion of coal is around 24 × 106 J/kg.
https://www.world... | First, there is a key difference between the energy values of TNT and coal: you miss the oxygen needed to burn the coal.
Burning 3kg of coal needs some 8kg of oxygen and the oxygen is not included in the calorific value above. The oxygen is also the factor limiting how fast the coal releases its energy. It is limited b... | {
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A question on dimensional regularization Let us consider the vacuum energy of a scalar field in $d+1$-dimensional spacetime. We have the integral
$$I=\int\frac{d^d k}{(2\pi)^d}\frac{E_k}{2},$$
where $E_k=\sqrt{k^2+m^2}$ and $k$ is a $d$-dimensional vector. Now this integral is apparently divergent. We will employ the d... | Dimensional regularization (DimReg) is insensitive to odd divergences. DimReg replaces every even divergence by $1/\epsilon$, but it does give any info about odd divergences. Consider more general integral,
$$\int\frac{d^dk}{(2\pi)^d}\frac{k^{2n}}{(k^2+m^2)^A}\rightarrow I=\int_{0}^{\infty}dk\frac{k^{d-1}k^{2n}}{(k^2+m... | {
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Infinite Coulomb force when charges contact The Coulomb force between charged particles is inversely proportional to the square of the distance. Yet, why don't we observe the infinite force when the distance approaches zero? Say we can bring two positively charged glass rods and make them touch each other. We don't obs... | Coulomb force and gravitational force have the same mathematical form. Let's consider an analogous example with gravitational forces.
Consider two spherical planets with mass $M$ and $m$, with radius $R$ and $r$, respectively. The attractive force between them is $\frac{GMm}{d^2}$, where $d$ is the distance between the... | {
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How does the Sun generate its energy? We all know that the sun generates its energy from nuclear fusion in the core. The electromagnetic radiation produced slowly travels upwards, while constantly being absorbed and re-emitted by the charged ions, until it reaches the photosphere, where it can basically travel freely (... | When an ion absorbs and re-emits radiation, it will usually emit at a different frequency from that absorbed.
The characteristic nuclear frequencies are only present in the inner reactive core, before they get absorbed.
The emission frequencies from there on out are primarily dependent on the temperature of the ionised... | {
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How is the mixing of neutrinos related to eigenstates? Can someone please explain to me why the following statement is true:
"Neutrino mixing phenomena arise from the noncoincidence of energy-propagation eigenstate and the weak (interaction) eigenstate bases"
This is a statement from an article about sterile neutrinos,... | I think the best analogy is birefringence (for 2 flavors). You have 2 orthogonal states of polarization (subbing for flavor), $H$ and $V$, and say electrons only interact with $H$ and muons with $V$, and never the twain shall meet.
Until they start propagating, in a birefringent medium. It has two eigenstates (the fast... | {
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Weird projectile motion question The question is as follows:
A ball is thrown from a point $O$ towards a vertical wall in such a way that, after rebounding from the wall, it returns to $O$ without striking the ground. The ball’s initial velocity has magnitude $U$ and is at an angle $θ$ above the horizontal. When the b... |
How is at possible that a particle is projected with the same speed from the same point able to follow the same trajectory both ways but hit a different point on the wall?
Same speed isn't the same thing as same velocity. Two projectiles launched from the same point with the same speed but different angles will follo... | {
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Can someone help me on the second part of this derivation? Pt.1: A particle moves in one dimension under the action of a force F(v) per unit mass. Explain how you would compute the speed $v$ of the particle, and its position $x$,at time $t$.Suppose $F(v) =k(v_0+v)$, where $k$ and $v_0$ are two constants. Find $v(t)$ an... | *
*Part 1:
$$F(v)=k(v_0+v)$$
Per unit of mass:
$$F=ma\Rightarrow k(v_0+v)=\frac{\text{d}v}{\text{d}t}$$
$$\frac{\text{d}v}{k(v_0+v)}=\text{d}t$$
Integrate between $(0,0)$ and $(t,v(t))$ to obtain $v(t)$:
$$\int_0^{v(t)}\frac{\text{d}v}{k(v_0+v)}=\int_0^t\text{d}t$$
Then:
$$v(t)=\frac{\text{d}x(t)}{\text{d}t}$$
Integr... | {
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What is the pressure at a random point inside container of an ideal gas? In most textbooks and thermodynamic lectures, the pressure is defined as the force on the walls of containers due to the incassecant beating of gas molecules divided by the area of the wall. Now, suppose I take a random point inside the container,... | Many physical quantities are defined in terms of "what would happen if ..." For example we might define the electric field strength at a point as the force per unit charge that acts on a small 'test' charge placed at the point, but we consider the electric field still to exist at the point, even if we don't have a test... | {
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Fermat's Principle of Least Time - Analogy Confusion Question:
I was reading this analogy of Fermat's Principle of Least Time:
In Figure, our problem is to go from A to B in the shortest time. To illustrate that the best thing to do is not just to go in a straight line, let us imagine that a beautiful girl has fallen ... | Which path you must take to save the girl before drowning (so in the shortest time) depends on the difference between your running velocity and your swimming velocity. If this difference is zero then you have to go to her in a straight line AB. When the difference is tiny, this straight path will be a bit different fro... | {
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Why does this block move backwards? In the diagram given below is a mass $m_1$ placed on an inclined block of mass $m_2$. And the question is to find the distance moved by the wedge when m1 reached the lowest point. The solution was given that as there is no external force on the system the center of mass doesn't move.... |
My question is why isn't there an external force...
So in other words, why isn't gravity considered an external force here? This is confusing at first, because we only experience the forces caused by gravity. But gravity itself is not a force; it is an acceleration.
Mass m2 wants to accelerate with gravity, but t... | {
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Particle as wave, stable? I've started reading about the wave-particle duality but, after a few steps, reached a dead end:
*
*Schrodinger equation solutions for a free particle is a sum of terms of the form:
$$\psi(\mathbf{r}, t) = Ae^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}$$
however, a single element of this form c... | Free particules tend to disperse, this is true. However this is not a dispersion like the dispersion of some energy into space. This is a probabilistic dispersion.
Think of Brownian motion for example. A particle starting from a known position undergoes Brownian motion. If you look at the probability density, it tends ... | {
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Am I understanding the equivalence principle correctly? So Einstein stated that gravity and acceleration are the same things in a local reference frame (please correct me if I misstated that).
Here is what I think I understand and want you to verify if it is correct:
In Special Relativity, the faster you go, the more t... |
Because gravity and acceleration are the same thing, does that mean that the time dilation when near a gravitating mass is the same time dilation as when you are at a very high speed?
In some ways, yes. However, remember that what causes time dilation near a $g$-mass is the difference in $g$-potentials rather than $g... | {
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Where did this derivative term come from in this derivation? I am stuck in the way this textbook shows how Planck arrived in the conclusion that the energy of a particle must be discrete. I have done the following, assuming that the energy $\Delta E$ is discrete, we cannot integrate it, thus we use the sum as it follow... | There is the generally well-known identity
$$\frac{\mathrm d}{\mathrm dx}\ln f(x)=\frac{f'(x)}{f(x)},$$
which can be quickly deduced using the chain rule. Because of this identity, $\frac{f'}{f}$ is also called the logarithmic derivative of $f$. Now they just apply this identity to
$$\frac{\sum_{n=0}^\infty n\alpha e^{... | {
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Electric and magnetic fields boundary conditions For a perfectly conducting and perfectly dielectric interface, I understood that tangential component of electric field is zero and continuous. But I have read that the normal component of magnetic field is also zero. I have read this in the chapter of guided waves betwe... | There can be, so long as in addition to being constant, it is curl-free.
Ampere's law says that the curl of magnetic field is produced by a current density or time-varying electric field. Since neither is present just outside the interface, then the magnetic field is curl-free there.
Faraday's law says that a time-vary... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Randomness in parallel universes Suppose we have two completely identical universes (for instance in Tegmark's type III multiverse). In both of them, two identical men are sitting behind identical random number generators (RAN1 and RAN2), and they push the "search" button at the exact same time.
My question is: will RA... | Assuming that by RNG you mean a quantum mechanical random number generator, the two RNGs would only produce the same outputs if they are entangled. Otherwise the two outputs would be uncorrelated and completely independent. However, if they are pseudorandom, deterministic RNGs typical of the RAN1 and RAN2 RNGs, "comp... | {
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How do photons affect each other gravitationally? Photons are energy. According to general relativity they should bend space.
Assuming two photons pass one another in a large void of empty space how would they gravitationaly affect each other exactly? Would there be a change in their path, a change in color, both, ne... | Yes. It is possible to treat linearized gravity like a QFT, write the graviton propagator and study the scattering of two photon thought a graviton exchange.
The amplitude, given the momentum of the two photons $k_{1}$ and $k_{2}$, in the limit where the graviton propagator momentum $q \rightarrow 0$ behaves proportio... | {
"language": "en",
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Is it possible to break the second law of thermodynamics regarding entropy? The motivation behind my question is that it seems very unlikely that a chunk of metal would "randomly" reach escape velocity and fly away from the Earth, but it happens thanks to NASA and other space programs. If the second law of thermodynami... | The phrasing of the question confuses physical laws with human laws. Human laws are prescriptive: they tell you what to do, and if you don't comply, you are breaking the law. Physical laws are descriptive, they describe the way things are. If something doesn't behave the way a physical law says they should, that's not ... | {
"language": "en",
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Effect of velocity on gravitational force If I am aboard a spacecraft and have with me two identical metal spheres having rest mass $= m$, what happens to the gravitational force between these two spheres as the space craft velocity approaches the speed of light. According to Newton, $F = G*m1*m2/r2$. Does $F$ between... | The relativistic force transformation answers your question regardless of whether the force is gravitational, mechanical, or electrical. Therefore, if you place the masses a distance $d$ apart from each other perpendicular to the direction of velocity $v$, the $g$-force should reduce by the inverse of the traditional g... | {
"language": "en",
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Electric Potential Energy - How a charge can be brought from infinity to a point without accelerating it? Question:
My Book says:
ELECTRIC POTENTIAL ENERGY: Electric potential energy of a charge($q_o$) at a point(A) in the electric field due to any charge is given by the work done by an external force to displace $q_o... | That wording is poor. By definition, you can't take any object at rest and move it without imparting acceleration.
Further, since the electric field is a conservative field, the work needed to move the particle is both path- and acceleration- independent -- other, of course for the final velocity if you don't apply a ... | {
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Pair production in vacuum So , everywhere I have looked for pair production it is stated that it cannnot happen in vacuum . Most proofs I have seen for that , state that the conservation of energy and momentum cannot be true at the same time without a body with which the photon will interact in the first place . In mos... | Any two massive particles always have a center of momentum frame, where the total momentum is zero. So for simplicity, you may as well analyze the pair production in that frame, which implies the two particles have four-momentum $(\sqrt{m_e^2+p^2},\vec{p})$ and $(\sqrt{m_e^2+p^2},-\vec{p})$. Then by conservation of fou... | {
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Why does the charge reside only at the surface of a charged conductor? On the web and in my books, there are two possible reasons given for why the charge on a conductor resides entirely on the surface.
*
*The electric field inside a conductor is 0.
*The like charges repel each other until they are at the maximum po... | For an arbitrarily formed conducting mass the distribution of the charge is not equally distributed on the surface of the mass (metal}.
Take for example a metal cube and put electrons on it. It's not so hard to imagine that these electrons will be concentrated at the edges of the cube. I.e. around the eight corners.
Fo... | {
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Arc discharge and dielectric breakdown - are these the same phenomena? Arc discharge and dielectric breakdown - are these the same phenomena?
With the subtle distinction, arc discharge generally occurs in the gaseous state and dielectric breakdown in condensed matter.
| Dielectric breakdown occurs when a material which usually behaves as an insulator suddenly starts conducting current
on being subject to a sufficiently high voltage. It occurs when the electric field is increased so much as to pull the outer valence electrons away from their atoms. The electrons become mobile, and the... | {
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How can a massless string move if the net force on it is always zero? Lets say we have a frictionless and massless pulley with a massless string over it. There are two masses attached to it $m_1$ and $m_2$ where $m_2>m_1$.
So $m_2$ would an experience an acceleration down while $m_1$ experiences an acceleration up and ... | The fact that the question states an assumption of massless pulley and string is to “idealise the situation”. Lots of physics problems ask you to ignore factors that are not particularly relevant to the point of the question. Here, you are asked to consider the forces and motion of the masses only. From there you are ... | {
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Wave function of a proton and a neutron with and without isospin Suppose I have a proton and a neutron in an external harmonic oscillator potential well. Let us first neglect all interactions between the two: since they are distinguishable particles I conclude their Hamiltonian eigenfunctions to be:
$$ \Psi(r_1, r_2) =... | I think you're barking up the wrong tree here with the ideas about interactions. This isn't about interactions, it's just about symmetry.
Let A be one HO state and B the other.
If you consider the neutron and the proton to be non-identical particles, and let the first quantum number be a label for the proton, then the ... | {
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Is Einstein Equivalence principle a consequence of weak equivalence principle + covariance principle? I have been doing some thinking about the Einstein Equivalence Principle (EEP) and its formulation, namely:
The outcome of any local non-gravitational experiment in a freely falling laboratory isindependent of the vel... | The idea that the Einstein equivalence principle should follow from the weak equivalence principle is known as the Schiff's conjecture. In its original formulation it states that:
Every theory of gravity that satisfies the WEP and is relativistic necessarily satisfies the EEP, and is consequently a metric theory of gr... | {
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Is it possible to create negative ions without ionization? I read that the air purifiers that can create negative ions also increase ionization, in theory is it possible to create a negative charge/ negative ions without creation ionization similar to waterfalls, etc. ?
| If you are asking : "Can we create negative ions without creating positive ones?"
The answer is: No.
Whenever a neutral system is provoked to generate ions then equal amount of oppositely charged ions are created (always). This is simply the law of conservation of charge.
| {
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How does the newly unveiled Tesla battery have 5x the Energy Capacity and 6x the Power, but only 16% increased Range? I just saw some exciting news from Tesla regarding a new battery, but I'm quite confused. As you can see on the headline of this article and the accompanying Tesla infographic:
The claim is that the ba... | The confusion likely results from assuming that each vehicle will continue to use the same number of batteries.
If instead it used, for example, a quarter of the current number of batteries, each with 5 times the energy, the total energy would be scaled by .25 × 5, increasing the range by 25%.
| {
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Why doesn't static friction point down the incline on a ball rolling down an incline?
In the figure above in which the sphere rolls without slipping down an incline, why is static friction directed upward? Static friction is meant to oppose impending motion so it should oppose the object's tendency to slide, and gravi... | The easiest way to find the direction of static friction, is to first imagine how the motion would be like on a smooth surface. Find out what direction the point of contact is moving with respect to surface, and then apply static friction in the opposite direction. If there is no relative motion, then there will be no ... | {
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Solving wave equations with Fourier transform: where are the time-independent solutions? One typically solves waves (fields) equations in Fourier space. For example, the 1D wave equation
$\frac{\partial^2\phi(x,t)}{\partial t^2}-\frac{\partial^2\phi(x,t)}{\partial x^2} = 0$
in Fourier space becomes
$(\omega^2-k^2)\tild... | It seems to me that if you want time independent solutions, you have to all the way back to your wave equation before you start finding solutions. Your time derivatives are zero and you don't really have a wave equation any longer.
| {
"language": "en",
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"source": "stackexchange",
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Force on a relativistic laser source Consider a laser source emitting a laser beam in the horizontal direction. If we are given the power of the laser source, we can calculate the force on the laser beam.
Now consider that the laser beam is moving horizontally with a 0.5c. Would the force on the laser source change by ... | The laser source consists of a laser gun and a fuel tank.
Force on laser source = force on laser gun + force on fuel tank
Force on fuel tank:
change of momentum of fuel tank over time (depends on velocity)
Force on gun: $F`=F$ (does not depend on velocity)
Force on laser source: $$F'= F + changeOfMomentumOfFuelTankOver... | {
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Time evolution of the Gaussian packet I am trying to get the time evolution for the following initial condition:
$$ \Psi(x,0) = \left(\frac{1}{2\pi \sigma^2} \right)^{\frac{1}{4}} e^{- \left(\frac{ x-x_{0}}{2 \sigma}\right)^{2}} e^{i\frac{ p_{0} x}{\hbar}}$$
I have got the Fourier transform of this function,
$$\Phi(p) ... |
Or should I use...
No! You should not use flakey wrong expressions simply because they might get you to the right known answer by cancelling errors.
You should do the FT correctly, since you know it's wrong, as, for t =0, its inverse FT you start with
$$\Psi(x,0) = \frac{1}{\sqrt {2\pi\hbar}} \int_{-\infty}^{\infty} ... | {
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Two springs coupled via a catenary I can't wrap my head around this problem. Let there be two masses $m$ attached vertically to springs of elastic constant $k$, each mass is also attached to an end of a catenary of mass $m_c$ e length $l$, so that $m_c = \mu l$.
Let $l_1,l_2$ be the partial length of the catenary betwe... | The difference is in the coordinate system.
You are doing your calculation with $x=0$ as the point where the string is in its natural length. The equilibrium position, in that case, is $(m+m_c/2) g/k$.
However, your professor is taking that equilibrium position $x_o=(m+m_c/2) g/k$ as his origin $x' = 0$ in the shifted... | {
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Nomenclature of X-ray transitions-Siegbahn Notation A colleague wanted to understand the notation for X-ray transitions. The main query is about the labeling of alpha, beta and gamma, with K, L, M etc. What is the main distinguishing criterion to label a transition as K, L, M along with the Greek letters alpha, beta an... | It is based on intensity: K$_\alpha$ is the strongest line, K$_\beta$ the second strongest, K$_\gamma$ the third strongest. Yes, in this case it is from the next higher shell (from $2p$, $3p$, $4p$ etcetera).
For L$_\alpha$ and L$_\beta$, again L$_\alpha$ is the stronger one, but the intensities are more similar than b... | {
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If gravity is curvature of space why are more massive objects "heavier?" How does curved space explain why a denser object of the same shape and volume feels heavier?
| Gravity effects all objects the same regardless of mass. An object that is travelling on its natural path through space and time is in free fall. Free falling objects all travel along the same path regardless of their mass, as was demonstrated by Galileo (unless they are so massive that we need to take their own gravit... | {
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How to find the direction of the magnetic field in a toroidal inductor?
I drew sort of a picture down below (although the cell is supposed to be an ac supply). I don't understand which direction the magnetic flux?
This is because, the current-carrying wire has individual magnetic fields (using the right hand grip rule... | If you apply alternating current to the terminals of coil the flux also changes direction and instantaneous flux also can be found by using right hand rule.
| {
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Rotation which diagonalizes the Hamiltonian I stumbled upon the following question:
Given the Hamiltonian of a spin-$1/2$ particle
$$\hat{H}=\epsilon\begin{pmatrix} 0 & -e^{i\pi/4}\\
-e^{-i\pi/4} & 0 \end{pmatrix} = \frac{2\epsilon}{\hbar} \vec{S} \cdot \frac{\hat{y}-\hat{x}}{\sqrt{2}}$$
what is the rotation transfo... | Just use the standard exponentiation of Pauli matrices, knowing that $\vec S =\hbar \vec \sigma /2$ for the doublet representation, which halves the rotation angles,
$$
e^{-i{\pi\over 4}\vec \sigma \cdot { (\hat x + \hat y) \over \sqrt{2}} } =
\cos (\pi /4) -i \vec{\sigma}\cdot \frac{(\hat x +\hat y)} {\sqrt{2}} ~ ... | {
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Stokes law and speed at equilibrium It is stated that the equation leading to Stokes law describes an equilibrium state, such as the upwards force is equal to the downward force:
$$ 6\pi r\eta v = \frac43\pi r^3 (d_1 - d_2)g $$
Now $v$ is velocity, and velocity at equilibrium is $0$, and this is the breaking point of m... | The equilibrium state in this case just means that there isn’t a net force acting on the object—the net drag force on the object coming from Stokes’ law is equal and opposite to the gravitational force + buoyancy force on the object. As a result, it doesn’t accelerate, and its velocity is constant.
| {
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Surface tension on a film Why don't the surface tension of the film of soap solution ( or any other liquid) increases or decreases when we increase the area of the film manually by applying a force ??
Isn't it analogous to the increase in tension of the string on stretching it.
| It's because surface tension by definition is force per unit length. Or if to be expressed in terms of surface energy :
Then surface tension is surface energy change due to area change :
$$ \gamma = \frac {dE}{dA} $$
| {
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Can $Z$ bosons mediate short-range forces between electrons? The flavor quantum numbers and charge of $Z$ bosons should allow it to mediate between electrons without violating any conservation rules. So at very short displacement scales do electrons actually attract each other through mediating $Z$ bosons?
| SLAC E158 measured parity violation in polarized Møller scattering ($\vec e^-e^-\rightarrow e^-e^-$). The beam electron is longitudinally polarized. The 1st order diagrams include t and u channel photon exchange and Z$^0$ exchange. Their interference is parity violating, leading to a left/right asymmetry in the scatter... | {
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Measurement of force (statics) body 1 and 2 are pulling the balance by 20 N
what does the balance read?
same question but without 2.
for 1st question I thought the balance will read zero force because they are two opposite forces of the same magnitude but it's wrong. the correct answer is 20N I don't know why
| The net force on the spring balance is zero, but that is not what the spring balance is measuring. You could replace either person by a fixed wall. The remaining person is then exerting a force of $20$ N on a spring balance that is fixed at the other end, and so the spring balance will read $20$ N.
| {
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Why do we use Eigenvalues to represent Observed Values in Quantum Mechanics? One of the postulates of quantum mechanics is that for every observable $A$, there corresponds a linear Hermitian operator $\hat A$, and when we measure the observable $A$, we get an eigenvalue of $\hat A$ as the result.
To me, this result see... | I think that the best example to motivate a student is the spin.
Particles prepared so that their spins are +1/2 in a given lab z-direction, if measured by an apparatus tilted arbitrarily with respect to the prepared orientation, have spins sometimes +1/2 and sometimes -1/2.
But the expected value of the average of a g... | {
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"source": "stackexchange",
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Confusion about Lorentz Coordinate Transformation A normal Lorentz coordinate problem might say:
At $t=t'=0$, two coordinate systems $S$ and $S'$ have their origins coincide with the $S'$ system moving with speed $v$ in the $+x$ direction relative to $S$. If event 1 happens at $x=a$, $t=0$ in the $S$ system then when/w... | You have discovered the relativity of simultaneity. In the basic Minkowski diagram:
the $x$ axis marks the all the coordinates for which $t=0$, so that for the $S$ frame's observer (living at $x=0$), at the time $t=0$, all events on the $x$-axis occur simultaneously. That is, it is "now" in his version of space + time... | {
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If objects in motion experience time differently, how does my body stay synced when I move my legs or arms? If I move my swing my arm really fast, the matter in my arm should experience time slower than the matter in my body.
So how does my body still sync with each other?
And a more general question that derives from ... | The relativistic affects of time dilation become noticeable when speeds become high. Especially close to the speed of light. That means when we are talking about the relatively slow speeds in moving our body parts, relativistic effects become so negligibly small, that they can be ignored.
| {
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Many-world interpretation of double slit experiment Different interpretations of young's double slit experiment is available, I read Copenhagen and Feynman's path integral interpretation of double slit experiment; former uses the idea of wave function and later uses the idea of infinite paths and sum over the weight f... | I think that the many worlds interpretation, as long as it is just an interpretation and not a new theory with testable predictions, is based on the Feynman path integrals formulation, so the mathematics of the FPI should be the same for the many worlds too. See this answer of mine .
As a new theory I suppose it has no... | {
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Time for an object's afterimage to disappear at the event horizon My understanding is that as someone/something falls into a black hole, they would get dimmer and dimmer until disappearing entirely as they cross the event horizon. Most non-radiant objects would probably become invisible to outside observers well before... | If you look at my answer to What is the general formula for time-dilation due to velocity and gravity together? this explains the equation for the time dilation of an object falling radially inwards towards a Schwarzschild black hole. We end up with the result:
$$ \frac{d\tau}{dt} = \sqrt{1 - \left(1 - \frac{r_s}{r}\ri... | {
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1-dimensional Heat Equation I have to solve the following differential equation:
$$ \partial _t u(x,t) = D \partial ^2_x u(x,t) $$
with the initial condition $$ u(x,0)=\exp \left( -100^2 \left( x-\frac{1}{2} \right) ^2 \right) .$$
The $x$ and the $t$ Interval is [0,1].
The Boundary Conditions are $$u(0,t) = u(1,t) = 0.... | This equation does not require the Fourier transform, as a linear, homogenous PDE with well behaved accessory conditions, it can be solved via the method of separation of variables.
Seek a solution of the form
U(x,t)=T(t)X(x)
and substitute this expression into the PDE
T'(t)=DX''(x)=λ (where λ is a constant)
from here ... | {
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Why amplitudes are rational functions? In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
Tree amplitudes must be rational functions of Mandelstam
variables.
What is the reason for such a prop... | After the OP explained in the comments what exactly they're looking for, I will attempt an answer. There are a few separate facts that need explanation:
*
*Tree amplitudes are rational functions of Mandelstam invariants: This is an obvious statement, that I have explained in the comments, and I will repeat here to pr... | {
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"url": "https://physics.stackexchange.com/questions/584809",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
How to convince myself that capacitance cannot be a function of voltage? My textbook states that:
...The capacitance $C$ depends only on the geometrical configuration (shape, size, separation)of the system of two conductors. [As we shall see, later, it also depends on the nature of the insulator (dielectric) separatin... | It all depends on the capacitor you use. Varicaps or "voltage controlled capacitors", are common circuit components that change their capacitance when the applied voltage changes. They are used as tuning components in oscillators and similar circuits.
Varicaps are reverse-biased diodes in which the depletion layer thic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/584947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
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