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Is it possible to apply the variational method to the Brownian motion? I mean, one of the requisites on $y(t)$ is that it must be continuous and $\partial_t{y(t)}$ too, and in this case, $\partial_t{y(t)}$ is not.
Question goes: "An anvil hanging vertically from a long rope in a barn is pulled to the side and raised like a pendulum 1.6 m above its equilibrium position. It then swings to its lowermost point where the rope is cut by a sharp blade. The anvil then has a horizontal velocity with which it sails across the barn and hit...
I always use to wonder how the experimental physicists discover new particles every now and then whose dimensions/properties/mass/charge several order of magnitudes below that of anything that is visible/perceptible. So as engineers do, I guess they also set up a extremely complicated equipment and do some pretty compl...
Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to practical constraints that we are capable of observing the known particles in the current World. Also could you please e...
I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or conformal field theories, and of older approaches such as algebraic QFT, and the classic works of Wightman, Streater, etc....
Here are some depictions of electromagnetic wave, similar to the depictions in other places: Isn't there an error? It is logical to presume that the electric field should have maximum when magnetic field is at zero and vise versa, so that there is no moment when the both vectors are zero at the same time. Otherwise ...
About 1905 Einstein published a work about diffusion of hard spheres and Brownian motion. One effluence of that is the so called "viscosity equation" which was/is very important for determining the molecular weight of macromolecules by the viscosity of solutions. http://www.ias.ac.in/initiat/sci_ed/resources/chemistry...
As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence supporting a fourth dimension?
The planck length is defined as $l_P = \sqrt{\frac{\hbar G}{c^3}}$. So it is a combination of the constants $c, h, G$ which I believe are all Lorentz invariants. So I think the Planck length should also be a Lorentz invariant! But there seem to be some confusion about that, see e.g. the following paper Magueijo 2001: ...
Why is the Lagrangian a function of the position and velocity (possibly also of time) and why are dependences on higher order derivatives (acceleration, jerk,...) excluded? Is there a good reason for this or is it simply "because it works".
I am aware that momentum is the thing which is conserved due to symmetries in space (rotational symmetry, translaitonal symmetry, etc). I am aware that in some systems, the generalized momentum, $$p_j = {\partial \mathcal{L} \over \partial \dot{q}_j}$$ is not simply $mv$. One example of this might be a charged particl...
I know that the rotation period of the moon equals its revolution period. It's just so astonishing that these 2 values have such a small difference. I mean, what is the probability of these 2 values to be practically the same? I don't believe this to be a coincidence. It's just too much for a coincidence. What could ha...
Is the number of states in the Universe countable? What framework could be used to answer the question in the title?
In Weinberg: Gravitation and Cosmology chapter 2.10 (Relativistic Hydrodynamics) the speed of sound is derived as $v_s^2 = \left(\frac{\partial p}{\partial \rho}\right)_\sigma$ Here the derivative is taken isentropically, that is, at constant entropy $\sigma$ (this is because a sound wave travels so fast that its propa...
We've got a hot star in the middle of a gas cloud. We point a spectrometer at the star, calculating the following attributes of our line of sight at the star through the cloud: Total number of various elements and molecules (H, H2, C, O, N, CO, lots of ions of all of the above) along the line of sight (units are numbe...
A quick wikipedia search will reveal the many different approaches to the measurement problem in quantum theory. What I find strange is that they even make up all these weird hypothesis like true randomness, many worlds, bohm and other interpretations when there isn't any ToE they're working it out from. I'm just a lay...
Here is a scan from an old Soviet textbook for school children: It shows the table of quarks and antiquarks of different generations, colours, spins. The book also includes similar tables of gluons and their interactions with quarks and between themselves. They all are coded in this fancy cake-shape code. The standard...
I have read about the existence of a non-linear scrhödinger equation. What is its utility and application? And how can it be derived? Is it in a relativistic or non-relativistic context?
Dirac once said that he was mainly guided by mathematical beauty more than anything else in his discovery of the famous Dirac equation. Most of the deepest equations of physics are also the most beautiful ones e.g. Maxwell's equations of classical electrodynamics, Einstein's equations of general relativity. Beauty is a...
I haven't seen any reference which explains these things and I am not sure of all the steps of the argument or the equations. I am trying to reproduce here a sequence of arguments that I have mostly picked up from discussions and I would like to know of references for the background details and explanations. It seems ...
Let us consider the following Gedankenexperiment: A cylinder rotates symmetric around the $z$ axis with angular velocity $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\mathrm{i}\left(kx - \omega t \right)} $ gets scattered by it. We assume to know the isotropic permittivity $\epsilon(\omega)$...
Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and responded that he rather sees the single particle QM as the non-relativistic limit of a QFT. He elaborated that the energies enc...
I have a pot of vigorously boiling water on a gas stove. There's some steam, but not alot. When I turn off the gas, the boiling immediately subsides, and a huge waft of steam comes out. This is followed by a steady output of steam that's greater than the amount of steam it was producing while it was actually boiling. ...
just wondering if it is a distinction without a difference - it seeming a bit weird that one thing can decay into different things.
The way it is sometimes stated is that if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles."(Wikipedia) That is confusing to me, but it seems to be an amazing theorem. It has been interpreted as ruling out hidden variable theories, but there is still so...
Suppose a large neutron star were to be spun-up by a particular pattern of mass-accretion. The increased centrifugal force could presumably mitigate the increased gravity thus delaying gravitational collapse. How far could this process be taken?
sometimes I get "charged" and the next thing I touch something that conducts electricity such as a person, a car, a motal door, etc I get shocked by static electricity. I'm trying to avoid this so if I suspect being "charged" I try to touch something that does not conduct electricity (such as a wooden table) as soon as...
Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These theories are valid until a scale $\Lambda$ (ultraviolet cutoff), after this scale an effective theory need a UV completion, ...
One often comes across actions written with an extra auxiliary field, with respect to which, if you vary the action, you get the equation of motion of the auxiliary field, which when plugged into the original action lets you retrieve a more familiar looking action, without the auxiliary field. An example is: $$\begin{e...
So I think my algebra is wrong somewhere. Lets say you have an object that goes under SHM with some initial conditions (amplitude is 5m. The piston is at 5m at t = 0 and period is 20 seconds). Okay so $x(t) = A sin(\omega_0 + \phi)$. $\phi$ for us is 0. The frequency = $0.05 Hz$, angular frequency = $\frac{\pi}{10}$ an...
A continuous charge distribution flowing as a constant current in a closed loop doesn't radiate. Is it therefore true that as you increase the number of proton bunches in the LHC, while keeping the total charge constant, the synchrotron radiation decreases?
Stephen Wolfram's A New Kind of Science (NKS) hit the bookstores in 2002 with maximum hype. His thesis is that the laws of physics can be generated by various cellular automata--simple programs producing complexity. Occasionally (meaning rarely) I look at the NKS blog and look for any new applications. I see nothing I...
I have read Sean Carrol's book. I have listened to Roger Penrose talk on "Before the Big Bang". Both are offering to explain the mystery of low entropy, highly ordered state, at the Big Bang. Since the second law of thermodynamics is considered a fundamental law of nature, and since it states that in a closed system en...
Suppose I have the following double split experiment set up: a monochromatic electron source of low intensity, which we can model as emitting a single electron at a time with energy $T$. a diffraction screen at a distance $A$ with two macroscopic slits equidistant from the source with width $w$ and distance from the c...
The latest I read is 3 but that was in Oct. With Lene Hau of Harvard's "frozen light" and with quantum donuts, newer strategies for stabilization are appearing, but the problem of keeping the qubit in superposition for long enough to sample it seems boggling. https://www.sciencedaily.com/releases/2009/03/090309105026.h...
Can one construct a filter out of nothing but pure metal that will pass only right circular polarized radiation and reflect left circularly polarized radiation? What would it look like? A helical spring in a tube? What about a twisted metalic ribbon inside a circular conducting tube? An axial mode helical antenna tran...
I think that, by now, it's understood that the gluon propagator in QCD has a dynamically generated mass. Ok, so my question is the following: where does the extra polarization degree of freedom come from? Or, asking in another way: suppose you try to define an S matrix for QCD, apart from the usual problems for doing s...
What are the factors that affect the density of an atom?
I have searched the web for good answers to why refraction occurs when light moves from one medium to another with different density. I have limited background in physics and want to know if there is an easy way to understand this without having to go back to school for years. Most explanations come in some variant of ...
Why do we have an elementary charge $e$ in physics but no elementary mass? Is an elementary mass ruled out by experiment or is an elementary mass forbidden by some theoretical reason?
I heard the term the other day, but it seems strange to me. My understanding is that neutron stars are made up of neutrons; and neutrons (having no charge) shouldn't be magnetised.
I can understand that on small scales (within an atom/molecule), the other forces are much stronger, but on larger scales, it seems that gravity is a far stronger force; e.g. planets are held to the sun by gravity. So what does it mean to say that "gravity is the weakest of the forces" when in some cases, it seems far ...
The alkali earth metals form the two left-most column of the periodic table of the elements, other than hydrogen. See wikipedia articles: http://en.wikipedia.org/wiki/Alkali_metal http://en.wikipedia.org/wiki/Alkaline_earth_metal Now "alkali" means that these are in a sense the opposite of "acid". One of the ancient us...
This is more of a math question and one, furthermore, that I know the final answer to. What I am asking is more of a "how do I get there" question as this question was generated during a self study situation. So, for a flat plate with a meniscus on it at some contact angle the form is: a y''$/(1+(y')^2)^{3/2}$ + b g y...
I am wondering: The noble 'gases' are inert because they have closed shells and don't want to give that up. But the noble metals, such as Copper, Silver, Rhodium, Gold, don't seem to have this. For example, Rhodium has electron configuration $4d^{8}\, 5s^1$. To me, this looks very similar to the alkali metals, which we...
I'm in the process of working on a physics related game. I'm looking to find the maximum velocity of an object given it's mass and the force acting on it when it is traveling horizontally. I believe there must be a method of calculating this but I'm unaware of it. Is there a formula for this scenario? I'm unaware i...
Suppose I know that Selenium has electron configuration $[Ar] 4s^2 3d^{10} 4p^4$. How can I use this information to then come to the conclusion that its possible oxidation states are 6, 4, 2, 1 and -2? I understand the 6: Give up all s electrons to reach $Ar$ configuration I also understand the -2: Obtian two electrons...
Under the Lorentz transformations, quantities are classed as four-vectors, Lorentz scalars etc depending upon how their measurement in one coordinate system transforms as a measurement in another coordinate system. The proper length and proper time measured in one coordinate system will be a calculated, but not measure...
Is there a tutorial explanation as to how decoherence transforms a wavefunction (with a superposition of possible observable values) into a set of well-defined specific "classical" observable values without the concept of the wavefunction undergoing "collapse"? I mean an explanation which is less technical than that de...
I've been watching a video about dark mater and a lot of the mass is missing in our universe. Astronomers got to this by measuring the speed that stars orbit the center of the galaxy and when they did this it didn't match the amount of gravity/mass in the galaxy. However I thought that the mass of the black hole in th...
Recently, there was a rapid communication published in Phys.Rev.D (PRD 83, 021502), titled "Gravity is not an entropic force", that claimed that an experiment performed in 2002 with ultra cold neutrons in a gravitational field, disproves Verlinde's entropic approach to gravity. The neutrons experiment gave results cons...
This is from an experiment we did in physics class. We shone a sodium light at a convex lens on top of a sheet of glass - and this image was captured by a USB microscope. I know what causes the main rings - but what about the surrounding ones, and why are they different colours?
I don't know hydrodynamics, but I wonder how one would compute resonance modes of a cubic box of water which we shake. I believe the waves would directly depend on the height of water and the width and length of the box. Is it a bit like a waveguide for electodynamics?
In an interacting theory I expect there to be caustics, resonances, and other situations in which some observables would give an infinite experimental result. Of course, these are idealized states and observables -- if a real device's measurement results are quite accurately modeled by such an observable, and we create...
I was thinking of the noted 1980 paper by Sidney Coleman and Frank de Luccia--"Gravitational effects of and on vacuum decay"-- about metastable vacuum states that could tunnel to a lower energy "true vacuum" with catastrophic results. I suspect the answer is that if our vacuum is a false one, we wouldn't "see" the true...
Suppose an advanced undergraduate student has reached a moderate level of understanding on electrodynamics. Where should he focus on, to sharpen his problem-solving skills? Practicing integrals and/or other mathematical tools. Studying theoretical results. Working on the physical meaning and applications of ED equatio...
I have tried to answer the problem correctly, and I have found similar (and even an identical) problem in my textbook, yet I still can't seem to yield the correct answer with this specific problem. The example problem in my textbook: A crate is hauled 8m up a ramp under a constant force of 200 N applied at an angle of ...
This is in reference to the calculation in section 3.3 starting page 20 of this paper. I came across an argument which seems to say that the "constraint of Gauss's law" enforces gauge theory on compact spaces to be such that physical states over which the partition function sums over be gauge invariant. I would lik...
Is there a time + two spatial dimension representation of a Minkowski-space surface which could be constructed within our own (assumed Euclidean) 3D space such that geometric movement within the surface would intuitively demonstrate the “strange" effects of the Lorentz transformation (length contraction, time dilation)...
My guess at a list of them would be: spin foams, casual sets, non-commutative geometry, Machian theories, twistor theory or strings and membranes existing in some higher-dimensional geometry... Firstly, what have I missed? Also, if there is a string theorist or similar on here that could briefly shed some light on wha...
If the S-Matrix is the only observable, that rules out both generalized free fields and Wick-ordered polynomials of generalized free fields as interesting Physical models, because both result in a unit S-matrix. Neither possibility has been developed since the 1960s when these results were proved, and when the S-Matrix...
Could life on earth survive a large pole shift caused by an asteroid collision? I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational axis changes rather than its magnetic axis. This is listed in wikipedia as follows: Cataclysmic pole shift hypothesis The cata...
The only finite mathematical framework that incorporates both the standard model of particle physics and gravity under one umbrella that I am aware of is string theory. I would like to know whether there are any other mathematical possibilities exist which do not depend on supersymmetry and still consistent with the st...
I have a series of measurements of temperature and relative humidity (RH), together with mosquito capture data. Because mosquitoes are sensitive to desiccation, it's reasonable that RH may be useful in predicting their activity. But I recently heard of a value called saturation deficit or vapor pressure deficit which h...
So we have two particles (A and B) that are entangled. From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment. Particle A goes zooming off into outer space. 10 years later, Particle B becomes incorporated into my brain. The day after that, an alien scie...
W and Z bosons are observed/discovered. But as force carrying bosons they should be virtual particles, unobservable? And also they require to have mass, but if they are virtual they may be off-shell, so are they virtual or not.
This just started to bother me after reading yet another entangled particle question, so I hate to ask one myself, but... If we have two entangled particles and take a measurement of one, we know, with certainty, what the outcome of same measurement of the other particle will be when we measure it. But, as with all fun...
My question is the title of a 1991 paper by Richard Gott and Li-Xin Li: http://arxiv.org/abs/astro-ph/9712344 and is also a subject of his popular book, "Time Travel in Einstein's Universe" Ultimately with cosmology, the chicken and egg question reduces to "How can something come from nothing?" Gott and Li use the conc...
In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical representations don't differ at all with respect to observables. Gauge transformations are therefore manifestations of a...
The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is zero. Since QG is intended to be a theory of interaction with force particles called gravitons, one may begin to wonder...
In discussions around a recent Stack answer in What does John Conway and Simon Kochen's "Free Will" Theorem mean? which covered axiomatic quantum mechanics, Bell's Theorem and Random Fields (related to axiomatic QFT) the phrase "Heisenberg Cut" was used. The basic question is what does this mean? Having reviewed this d...
First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant speed in a straight line. Wikipedia — New...
I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
Why is the speed of sound given so much importance in Astrophysics? For example in gas outflow (and accretion) problems, we often calculate the sonic point (the point at which the outflow speed becomes equal to the speed of sound). Is it simply because speed of sound is a convenient number that can be used to scale dow...
Apologies in advance if this is too basic a question for Phys.SE. I don't want to dumb down this venerable institution. :) My wife and I just watched this TV ad for Kit-Kat where a crew of crane operators line their wrecking balls up to form an enormous Newton's Cradle. It left us wondering if the basic premise is feas...
Hi I have a doubt (I'm not very expert in statistical mechanics, so sorry for this question). We consider a gas of hydrogen atoms with no interactions between them. The partition function is: $$ Z=\frac{Z_s^N}{N!} $$ where $Z_s$ is the partition function of one atom. So we write $$ Z_s =Tr\{e^{-\beta \hat H}\} $$ and w...
There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions regarding this: 1) Does the fact that a manifold with a) asymptotic (space) curvature zero and b) local inhomogeneities with p...
I'm having trouble getting my head around the time dilation paradox. Observer A and B are at the same "depth" in a gravity well. Observer B then descends into the well. A will observe B's time as going slower than their own. B will observe A's time as going faster than their own. What happens if B were to ascend the w...
Of course there is pretty hot stuff too. For example Suns. But isn't the vacuum of space the perfect containment for heat? And shouldn't the rare collision with particles even heat up an object that floats around in space? Why aren't they hot from time to time? Is it because they loose their heat by radiant heat? And i...
I know about these different energy conditions in GR, namely strong, weak and null, but never really understood the full physical significance of them or for example how to 'derive' them or how compelling is a certain condition (for that particular one to be applied). I know that they exist because you need some constr...
Not long ago I submitted an article to PRE. One referee was in favor and two against (this not more than 3 months ago). Rather than pressing, I decided to submit it elsewhere. A single referee report was negative on the grounds that the article was unclear, though the details helped me revise the article. Is it all rig...
In string theory I came across the fact that there are difficulties in describing the coupling of R-R fields with world sheets in RNS formalism and it can be done in GS formalism only. Can someone explain the reason(s) behind that? Also, I think if you have a space time where you can quantize strings and you have non z...
I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.
The qubit is a big topic of quantum information theory. A qubit is a single quantum bit. Physical examples of qubits include the spin-1/2 of an electron, for example, see page 39 of Preskill: http://www.theory.caltech.edu/people/preskill/ph229/notes/chap5.pdf In quantum mechanics, two variables are called complementar...
With the impending landfall of Cyclone Yasi, we were pondering how much water would be dropped by storm after hearing them say there would be about a metre of rain falling. Assuming that this is the amount of rain falling on one square metre, and is constant across the main storm, and that the storm is a regular circle...
It is known from experiments that the dielectric constant of a solvent might decrease in regions where there is a strong electric field, for example, near a highly charged ion in an infinitely dilute solution. In such a case the dielectric constant of the liquid might be described as function of the distance from the i...
I would be glad if someone can help me understand the argument in appendix B.1 and B.2 (page 76 to 80) of this paper. The argument in B.1 supposedly helps understand how the authors in that paper got from equation 3.6 to 3.8 on page 18 of the same paper. These 3 equations form the crux of the calculation done in this ...
A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$. If initially the balls are randomly placed throughout the jar, and we are to shake this jar, generally one type of balls will tend to gather at the top. Why does this happen?...
I have a particle at rest. At $t = 0$ a periodic force like $F_0 \sin\omega t$ starts acting on my particle. Can such a force transport my particle to infinity when $t \to \infty$? Please answer this question without solving the mechanical problem, just by intuition.
I didn't have much luck getting a response to this question before so I have tried to reword and expand it a little: In early 2010 I attended this inaugural lecture by string theorist- Prof. Mavromatos entitled 'MAGIC strings'. In it he proposes that some string theory models may violate Lorentz symmetry at the Planck ...
Given a collection of point-particles, interacting through an attractive force $\sim \frac{1}{r^2}$. Knowing only $m_1a=\sum_i \frac{Gm_1m_i}{r^2}$ and initial conditions we can deduce the motion of the system. Consequently we can observe that three quantities remains constant A) center of mass of the system B) total e...
Knowing * earth spin and translation movement around sun, * sun have a big magnetic field, * a variable flux can generate a induced voltage (and current) into the circuit Would it be posible to receive in a coil that energy? Perhaps it's just enough to detecting the earth movement relative to magnetic field, or if i...
I think I am over thinking this question: A point charge of $-2\space\mu C$ is located in the center of a hollow sphere. The internal and external radius of the sphere is given by $6.5$ and $9.5\space \text{cm}$, the charge density is $7.35 \times 10^{-4}$. Plot electric field vs. distance from the center of the sp...
Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice
What would happen if instead of $F=m \frac{d^2x}{dt^2}$, we had $F=m \frac{d^3x}{dt^3}$ or higher? Intuitively, I have always seen a justification for $\sim 1/r^2$ forces as the "forces being divided equally over the area of a sphere of radius $r$". But why $n=2$ in $F=m\frac{d^nx}{dt^n}$ ?
In Lorentzian AdS space there are both normalizable and non normalizable solutions and we also know (at least for scalar fields in bulk) what do they correspond to in the boundary. But I saw the calculation only for scalar fields. Can someone please give me a reference where people have calculated these modes for a gau...
Given: A half wave plate freely floating in space. Circularly polarized light, falling perpendicularly to it. The plate changes polarisation of the beam to the opposite one. Therefore it receives angular momentum and starts to rotate. Where does energy comes from? What would happen with a single photon passing thr...
Rb83 is unstable and decays to Kr-83. Mode of decay is electron capture. Rb85 is stable. The nuclei Rb83 and Rb85 have the same charge, but Rb85 is heavier than Rb83. While gravity acts more strongly on Rb85, this is probably not the factor producing the stability of Rb85. So, why does the orbital electron fall into th...
Kostyas question for angular momentum and half wave plates Half wave plate and angular momentum made me think a little bit. It took me some seconds to "swallow" the answer. :=) Then I started to think further, whether such a plate, rotating in the right direction, could lead to a slightly shorter wavelength? And fu...
We have learned that Torque is equal to a force that is perpendicular to a radius (displacement); however, I just cannot grasp one of the study questions we received: A hammer thrower accelerates the hammer (mass = 7.30 kg) from rest within four full turns (revolutions) and releases it at a speed of 30.0 m/s. Assumin...

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