Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Suggested reading for renormalization (not only in QFT) What papers/books/reviews can you suggest to learn what Renormalization "really" is?
Standard QFT textbooks are usually computation-heavy and provide little physical insight in this regard - after my QFT course, I was left with the impression that Renormalization is just a technical, somewhat arbitrary trick (justified by experience) to get rid of divergences. However, the appearance of Renormalization in other fields of physics Renormalization Group approach in statistical physics etc.), where its necessity and effectiveness have, more or less, clear physical meaning, suggests a general concept beyond the mere "shut up and calculate" ad-hoc gadget it is served as in usual QFT courses.
I'm especially interested in texts providing some unifying insight about renormalization in QFT, statistical physics or pure mathematics.
| And I have written another pedagogical article about renormalizations and IR divergences. I created a Google research group "QED Reformulation" and I run a blog on this subject. It is an alternative view of the problem, and I think, it is much more physical than the mainstream one. It is always useful to see the problem from different points of view ;-).
P.S. Se also this.
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Is Dr Quantum's Double Slit Experiment video scientifically accurate? I'm fascinated by the fundamental questions raised by the Double Slit Experiment at the quantum level. I found this "Dr Quantum" video clip which seems like a great explanation. But is it scientifically accurate?
| The video is horrifyingly bad. It shows a single-slit electron pattern over here, and then puts a second slit in, and shows the pattern from the second slit over there. Then it says: what if you have both slits open at the same time?
In fact, since the pattern from the first slit is separated from the pattern of the second slit, NOTHING DIFFERENT happens when you open both slits at the same time. There is no interference. But the video shows multiple bands. This is wrong.
You only get multiple bands when the INDIVIDUAL patterns of each slit occupy the same area on the screen. Then, when you open both slits at once, you get interference within that common area.
What the video shows is complete nonsense.
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Books that every physicist should read Inspired by How should a physics student study mathematics? and in the same vein as Best books for mathematical background?, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.
In spite of the frivolous nature of this post, I think it can be a valuable resource.
For example:
Course of Theoretical Physics - L.D. Landau, E.M. Lifshitz.
Mathematical Methods of Physics - Mathews, Walker. Very nice chapter on complex variables and evaluation of integrals, presenting must-know tricks to solve non-trivial problems. Also contains an introduction to groups and group representations with physical applications.
Mathematics of Classical and Quantum Physics - Byron and Fuller.
Topics in Algebra - I. N. Herstein. Extremely well written, introduce basic concepts in groups, rings, vector spaces, fields and linear transformations. Concepts are motivated and a nice set of problems accompany each chapter (some of them quite challenging).
Partial Differential Equations in Physics - Arnold Sommerfeld. Although a bit dated, very clear explanations. First chapter on Fourier Series is enlightening. The ratio interesting information/page is extremely large. Contains discussions on types of differential equations, integral equations, boundary value problems, special functions and eigenfunctions.
| Paul Dirac - Principles of Quantum mechanics
Robert Griffiths - Consistent Quantum Theory
A. Zee - Quantum Field Theory in a Nutshell
V. Mukhanov - Physical Foundations of Cosmology
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Relativistic Cellular Automata Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics.
Google Scholar still gives more than 2.000 results when searching for "quantum cellular automata".
But it gives only 1 (one!) result when searching for "relativistic cellular automata", i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.
How can this be understood?
Why does the concept of QCA seem more
promising than that of RCA?
Are there conceptual or technical barriers for a thorough treatment of RCA?
| Check out Mark Smith's PhD thesis titled Cellular automata methods in mathematical physics, specifically Chapter 4: Lorentz Invariance in Cellular Automata.
The conclusion part of the chapter:
Symmetry is an important aspect of physical laws, and it is therefore desirable to identify analogous symmetry in CA rules. Furthermore, the most important symmetry
groups in physics are the Lorentz group and its relatives. While there is a substantial
difference between the manifest existence of a preferred frame in CA and the lack
of a preferred frame demanded by special relativity, there are still some interesting
connections. In particular, CA have a well-defined speed of light which imposes a
causal structure on their evolution, much as a Minkowski metric imposes a causal
structure on spacetime. To the extent that these structures can be made to coincide
between the CA and continuum cases, it makes sense to look for Lorentz invariant
CA.
The diffusion of massless particles in one spatial dimension provides a good example of a Lorentz invariant process that can be expressed in alternative mathematical
forms. A corresponding set of linear partial differential equations can be derived with
a simple transport argument and then shown to be Lorentz invariant. A CA formulation of the process is also Lorentz invariant in the limit of low particle density and
small lattice spacing. The equations can be solved with standard techniques, and the
analytic solution provides a check on the results of the simulation. Generalization to
higher dimensions seems to be difficult because of anisotropy of CA lattices, though
it is still plausible that symmetry may emerge in complex, high-density systems. The
model and analyses presented here can be used as a benchmark for further studies of
symmetry in physical laws using CA.
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Lightning strikes the Ocean I'm swimming in - what happens? I'm swimming in the ocean and there's a thunderstorm. Lightning bolts hit ships around me. Should I get out of the water?
| Here's a crude way to look at the problem:
Suppose there are $N$ wires. Each has resistance $R$, common potential difference $V$ and are connected in parallel. So the current through each wire is $I = \frac{V}{NR}$.
Let's imagine a hypothetical wire formed by sea water which has a length, $L$ and cross sectional area, $S$. There are approximately $\frac{2\pi L^2}{S}$ of those wires in a hemisphere of radius $L$. The resistance of such a wire would be $\frac{\rho L}{S} $, where $\rho$ is resistivity of sea water.
The number of such wires that can be connected to your body (with area $A$) is $\frac{A}{S}$.
So the approximate current that will flow through your body is:
$I = \frac{\frac{A}{S}V}{\frac{2\pi L^2}{S} \frac{\rho L}{S}} = \frac{AVS}{2\pi\rho L^3}$
Now assuming $L=100, \rho=0.25, A=1, V=100M, S=10^{-2}, \rho=0.25$
$I = 0.6 Amp$
The most important things to note are that $I \propto A$ and $I \propto \frac{1}{L^3}$.
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How does gravity escape a black hole? My understanding is that light can not escape from within a black hole (within the event horizon). I've also heard that information cannot propagate faster than the speed of light. It would seem to me that the gravitational attraction caused by a black hole carries information about the amount of mass within the black hole. So, how does this information escape? Looking at it from a particle point of view: do the gravitons (should they exist) travel faster than the photons?
| We can think of gravity at distance as an energy level. Then The question how gravity escapes black hole is irrelevant!
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How relevant is LHC to quantum gravity? Premise: the LHC is obviously mapping unseen territory in high energies, and therefore it's always possible to imagine far out results.
Excluding completely unexpected outcomes - is the LHC performing any experiment that could help with string theory or m-theory? For example:
*
*direct super-strings or m-theory predictions to be tested or confuted
but also
*
*measurements that would help "shape" string/m-theory into something more concretely testable or practical than the current blurry incarnation?
| This article from CERN Courier is about string-theory and experimental tests of it, and about LHC. It is not really technical but it also links to various references and articles.
And for more technical info, you can browse the list of String Theory Seminar of the TH department at CERN and search for "LHC"; very interesting.
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Common false beliefs in Physics Well, in Mathematics there are somethings, which appear true but they aren't true. Naive students often get fooled by these results.
Let me consider a very simple example. As a child one learns this formula $$(a+b)^{2} =a^{2}+ 2 \cdot a \cdot b + b^{2}$$ But as one mature's he applies this same formula for Matrices. That is given any two $n \times n$ square matrices, one believes that this result is true: $$(A+B)^{2} = A^{2} + 2 \cdot A \cdot B +B^{2}$$ But eventually this is false as Matrices aren't necessarily commutative.
I would like to know whether there any such things happening with physics students as well. My motivation came from the following MO thread, which many of you might take a look into:
*
*https://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics
| The concept that quantum mechanics undermines determinism. The Schrodinger wave equation evolution is completely deterministic. The results of measurements are probabilistic, but this does not mean that the various superposed states do not have causes. This is not the same thing as a hidden variable theory. The probabilities are deterministic.
T'Hooft has some interesting ideas on a determinism underlying QM (not the same thing as saying the wave equation is deterministic). I am not arguing that qm is in all senses deterministic, but it isn't completely non-deterministic either.
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Home experiment to estimate Avogadro's number? How to get an approximation of Avogadro or Boltzmann constant through experimental means accessible by an hobbyist ?
| Your best bet is to try to replicate the experiments of Perrin who first measured Avogadro's constant. This is a common lab in "Advanced Lab" courses in undergraduate or graduate courses, so you can probably find writeups and such via google.
The principle is to observe Brownian motion under a microscope and measure the diffusion constant.
Einstein's theory for Brownian motion relates the diffusion constant of a spherical particle to the temperature via the Einstein-Stokes law:
$D=\frac{k_BT}{6\pi\eta r}$
Here $D$ is the diffusion constant, $T$ is the temperature, $\eta$ is the viscosity, and $r$ is the radius of a small spherical particle. All of these properties should be measurable at least crudely with home equipment.
The way I did this in my lab course was as follows. We had access to a microscope with a CCD camera which allowed digital video recording, as well as samples of monodisperse polystyrene particles (which are commercially available, and labeled with their size).
Suspend the particles in water (the viscosity of water is well known) at room temperature and place on a slide (better, put a thermocouple in your sample).
Take video of the particles Brownian motion, and then using something like John Crocker, David Grier, and Eric Weeks's celebrated particle tracking code extract 2D (or maybe 3D?) particle trajectories (i.e. $x(t)$, $y(t)$.
Now plot the mean squared displacement of particles versus time. The slope of this curve is the diffusion constant, which then yields an estimate for $k_B$ via Stokes-Einstein.
To recover Avogadro's constant, you need the ideal gas constant $R$, which is measured through independent means; typically via macroscopic thermodynamic experiments which probe the slope in $pV=nRT$.
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What's the difference between helicity and chirality? When a particle spins in the same direction as its momentum, it has right helicity, and left helicity otherwise. Neutrinos, however, have some kind of inherent helicity called chirality. But they can have either helicity. How is chirality different from helicity?
| Helicity is easy to define; chirality is more subtle.
The helicity of a particle is the normalized projection of the spin on the direction of momentum. If the spin is more along the same direction of the momentum than against it, then the helicity is positive; otherwise it is negative.
Chirality is to do with the way the particle's properties transform when they are described with respect to one inertial reference frame or another. The difference between right-handed and left-handed is like the difference between contravariant and covariant 4-vectors, but now we are talking about spinors. For a massless spin half particle, the spin and momentum can both be extracted from a single spinor. When one transforms from one frame to another, one should use the ordinary Lorentz transformation for a right-handed spinor, and the inverse Lorentz transformation for a left-handed spinor. Thus chirality is an intrinsic property of such a particle, but one whose influence is only revealed in this subtle way. It influences how the spinor enters into the Weyl equation, for example.
Massive spin-half particles such as electrons have their spin and momentum described by Dirac spinors which are made of two Weyl spinors, one of each chirality.
What distinguishes a neutrino (treated here as massless) from an anti-neutrino is primarily its chirality. But whenever just a single 2-component spinor describes both the momentum and the spin, one finds that the helicity for such a particle can only take one value (and for the antiparticle it takes the opposite value). Thus the helicity and the chirality then have the same value, but it does not mean they are the same thing.
When a given type of particle can only have one helicity, one has a situation that does not respect parity (mirror-reflection) symmetry. This is at the heart of the breaking of parity invarience by the weak force.
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How do I figure out the effects of wind on flight? For a school project, I'm trying to make an automated flight planner, considering mainly the differences in flight paths according to wind.
Now I've heard that flying with/against the wind affects airspeed. But I really don't know any specific(even empirical) laws on determining by how much it does so.
What's more, I've also heard about gas savings through these effects. That I would have pretty much no idea of how to calculate but that's less important.
Basically if anyone can point me in the right direction to figure out how to figure out solid speed gains, I'd be grateful, even moreso if I can find out the theoretical origins of such laws.
(The only thing I found that I think is close to what I want is this, but I have no clue what the laws derive from)
| Wind speed affects ground speed, not air speed. The airplanes fly at a specified IAS (indicated air speed). Add the IAS with the wind speed in the direction of travel and you get the ground speed. Using simple algebra
$$ u_{ground} = u_{IAS} + u_{wind} $$
So to travel a distance $S$ with head wind takes $t_{A\rightarrow B}=\frac{S}{u_{IAS}-u_{wind}}$, but to return with tail wind $t_{B\rightarrow A}=\frac{S}{u_{IAS}+u_{wind}}$. Obviously $t_{A\rightarrow B} > t_{B\rightarrow A}$
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Are gauge choices in electrodynamics really always possible? If $B$ is magnetic field and $E$ electric Field, then
$$B=\nabla\times A,$$
$$E= -\nabla V+\frac{\partial A}{\partial t}.$$
There is Gauge invariance for the transformation
$$A'\rightarrow A+{\nabla L}$$
$$V'\rightarrow V-\frac{dL}{dt}.$$
Now, we can write:
*
*Coulomb Gauge (CG): the choice of a $L$ that implies $\nabla\cdot A=0$.
*Lorenz Gauge (LG): the choice of a $L$ that implies $\nabla \cdot A - \frac{1}{c^2} \frac{\partial V}{\partial t}=0$.
Now, I'm trying to mathematically prove that it's always possible to find such an $L$ satisfiying $CG$ or $LG$.
| Wikipedia on gauge fixing seems to imply that gauge fixing always works in abelian Yang-Mills theory, of which electrodynamics is the standard example. But that this does not always work in non-abelian Yang-Mills theory. There you have to restrict to submanifolds of the base spacetime to get the gauge fixing. Usually these go by the terms Gribov region and the like.
I'm not sure that I'm convinced by Wikipedia on the abelian theory since gauge fixing is merely a way of choosing a global section. But to choose a global section of a principal bundle simply shows that it is trivial, ie untwisted. Not all abelian principal bundles are trivial. For example the Dirac magnetic monopole is not trivial. Hence even here the technology of Gribov regions and horizons etc is useful.
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Utility of displacements potentials in geophysics In the elasticity theory, you can derive a wave equation from the fundamental equation of motion for an elastic linear homogeneous isotropic medium:
$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$
But in the seismology tradition, you introduce scalar and vector potentials for the P and S components of the displacements, derive wave equations for them and use them.
Now, in electrodynamics you can derive from Maxwell's equations the wave equations for Fields and for Potentials; but there you use the potentials because they compose a quadrivector. In geophysics what's the convenience of it?
| Also, adding to what j.c. states:
If you have a complicated constitutive relation between the electric field and the electric displacement field, e.g. nonlinear and in terms of a convolution (no instantanious reaction of the medium), it might be very complicated to find a representation in terms of potentials obaying a wave equation using a non-perturbative ansatz.
| {
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Best example of energy-entropy competition? What are the best examples in practical life
of an energy-entropy competition which favors entropy over energy?
My initial thought is a clogged drain -- too unlikely for the
hair/spaghetti to align itself along the pipe -- but this is probably
far from an optimal example. Curious to see what you got. Thanks.
| Blackbody radiation: anything hotter than its environment radiates energy thus increasing the entropy of the universe. Entropy wins :-)
The Sun :-) The Sun's energy does not increase the Earth's total energy!
In fact, the Earth radiates almost exactly the same amount of energy as it receives from the Sun. What we really gain from the Sun is that we use the sun rays' low entropy to power life on Earth, and the Earth radiates high entropy microwaves in the night.
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Searching books and papers with equations Sometimes I may come up with an equation in mind, so I want to search for the related material. It may be the case that I learn it before but forget the name, or, there is no name for the equation yet. In this case, I may be able to recall a reference book. Searching in Internet can be a fast way though.
However, there are cases that I get some idea and equations (maybe a modified one) myself. So I want to know whether there are any other people working on it before. Because of the vagueness, it is difficult to search it by keywords because I do not know the 'name' of this idea: it is either too board or no results.
I can try to search google scholar, arxiv and maybe the prola, but there is no support of equation pattern matching. For example, entering ∇⋅V in google give you no useful results (it is better if you input the 'divergence of potential').
Is there any good way to search papers in this case? It is even better that I can use the combination of equations and keywords.
Edit: Another reason is that Mathematician should have done some deep analysis on the related mathematical topics. Yet it is difficult to know their results because there is a gap between the terms used in physics and mathematics. It would be really useful if we can find and learn their results.
| There was a similar question at Mathoverflow. I think it contains some useful references and discussion so it's definitely worth checking out.
Usually I would post this as a comment under the question but probably nobody would notice it anymore. And seeing that the other answer is also quite short I hope this is fine.
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Is there a name for the derivative of current with respect to time, or the second derivative of charge with respect to time? This measurement comes up a lot in my E&M class, in regards to inductance and inductors.
Is there really no conventional term for this?
If not, is there some historical reason for this omission?
| Nope, not as far as I know. It's just "rate of change of current" or something like that.
I suppose it's possible someone has given it a name in some paper or textbook, but if so, it's not widely used.
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Is it possible to obtain gold through nuclear decay? Is there a series of transmutations through nuclear decay that will result in the stable gold isotope ${}^{197}\mathrm{Au}$ ? How long will the process take?
| Last time I did the sum, 201Hg to 197Au plus 4He did not need external energy:
200.970277 - (196.9665516 + 4.0026032) = 4.0037254 - 4.0026032 = 0.0011222.
Caveats:
*
*I did not check the error term of atomic weigths, and
*The first decay, alpha to 197Pt, should be awesomely slow. In fact
*201Hg is considered stable in all the listings.
But the point is that the external energy would be recovered in this case.
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Which experiments prove atomic theory? Which experiments prove atomic theory?
Sub-atomic theories:
*
*atoms have: nuclei; electrons; protons; and neutrons.
*That the number of electrons atoms have determines their relationship with other atoms.
*That the atom is the smallest elemental unit of matter - that we can't continue to divide atoms into anything smaller and have them retain the characteristics of the parent element.
*That everything is made of atoms.
These sub-theories might spur more thoughts of individual experiments that prove individual sub-atomic theories (my guess is more was able to be proven after more experiments followed).
| No experiments prove any theory. Experiments can only refute theories.
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Does the recent re-count of stars in elliptical gallaxies affect our understanding of the universal mass balance? I've seen several popular reports of a new count of low-mass stars in elliptical galaxies (here's one).
Edit: Pursuant to several correct comments I've changed the title to agree with the actual report which is that the recount concerns elliptical galaxies---and I don't know where I got the notion that it concerned dwarf galaxies---but I am leaving my comments below intact as they represent the way I was thinking before I was corrected. Note that we are in fact talking about relatively few very massive galaxies instead of many very light ones, but the questions are largely unchanged.
My first instinct was to dismiss it as mostly interesting to those who specialize in galactic dynamics, but then it occurred to me that there must be a lot of those galaxies, and I began to wonder about the baryonic-matter/dark-matter/dark-energy balance.
My guess is that this makes little difference to the matter/dark energy part of the equation because the total matter fraction is derived from large scale measurements of cluster dynamics. But even if I am right about the matter/dark-energy thing, that leaves the question of baryonic vs. dark matter fraction.
Can anyone shed some light on this?
Also, links to pre-prints or journal articles related to this measurement would be welcome.
| The fraction of baryonic matter to dark matter is not deduced only from galactic dynamics. It is also derived from big bang nucleosynthesis and from the higher multipole acoustic peaks in the CMB spectrum. I would say that the element abundance is a far more important indicator of the fraction between baryonic and dark matter.
Big-Bang nucleosynthesis
Theoretical overview of Cosmic Microwave Background anisotropy: 1.2. Results
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What's the difference between running up a hill and running up an inclined treadmill? Clearly there will be differences like air resistance; I'm not interested in that. It seems like you're working against gravity when you're actually running in a way that you're not if you're on a treadmill, but on the other hand it seems like one should be able to take a piece of the treadmill's belt as an inertial reference point. What's going on here?
| I think the most significant difference between work done on an inclined treadmill and work done on a real incline is the gain in potential energy on the real incline. There is no real delta mgz on a treadmill, whereas if you fell back to your starting height from a real incline, you'd certainly notice a large amount of stored energy being turned into kinetic energy!
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Mechanics around a rail tank wagon Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it):
Consider a rail tank wagon filled with liquid, say water.
Suppose that at some moment $t=0$, a nozzle is opened at left side of the tank at the bottom. The water jet from the nozzle is directed vertically down. Question:
What is the final velocity of the rail tank wagon after emptying?
Simplifications and assumptions:
Rail tracks lie horizontally, there is no rolling (air) friction, the speed of the water jet from the nozzle is subject to the Torricelli's law, the horizontal cross-section of the tank is a constant, the water surface inside the tank remains horizontal.
Data given:
$M$ (mass of the wagon without water)
$m$ (initial mass of the water)
$S$ (horizontal cross-section of the tank)
$S\gg s$ (cross sectional area of the nozzle)
$\rho$ (density of the water)
$l$ (horizontal distance from the nozzle to the centre of the mass of the wagon with water)
$g$ (gravitational acceleration)
My thinking at the moment is whether dimensional methods can shed light on a way to the solution. One thing is obvious: If $l=0$ then the wagon will not move at all.
| As the problem is initially described, the nozzle is located on the left bottom side of the tank with the nozzle exit facing downward. if this is the case, there will be no horizontal force to act as a thrust to start the tank in a horizontal motion. Any thrust that may be developed by the water exiting the nozzle will be in the opposite direction of the jetting water. That is, in a vertical upward direction.
Now if the nozzle exit was directed to the left or right of the tank in a horizontal direction, the exiting water will surly develop thrust to move the tank along the rail tracks. the amount of thrust created will be a function of the flow rate and nozzle size. the maximum head of water will not be greater than the height of the water in the tank. the fact that inside the tank the water travels internally in the left direction will create no external force to move the tank. any force applied for horizontal motion must be external.
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Is it possible to accelerate air to supersonic speeds? What would it look like? The speed of sound is the rate that disturbances in air propagate through it.
Is it possible to have a wind that itself is moving at supersonic speeds relative to stationary winds around it?
Or perhaps a fluid flowing through a pipe at a speed greater than the speed of sound within it.
If so, what would it "look" like? What kind of phenomenon would occur?
| The facility to accelerate wind to supersonic speed is called wind tunnel. Here is the pamphlet of a hypersonic (Mach 7 and 8) wind tunnel in Japan. It is explained how it works and you can even see some photos of hypersonic flow.
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Why doesn't air freeze? I am in no way experienced in the Physics field so this question may seem a bit silly but i'd appreciate an answer :)
Why doesn't air freeze?
| At the normal pressure, 99.9% of air (nitrogen, oxygen and argon) will solidify in 55K (where the oxygen does). Below about 15K also hydrogen (0.000524% of normalized air) solidifies leaving only helium which will be a liquid up to 0K (yet will change into a superfluid about 2.17K).
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Does a towel that's spread out cool faster than one that isn't? I was thinking about how they say those sails on top of some dinosaurs helped regulate their body temperature. If a dinosaur didn't have that sail, would it really make any difference?
If you heated up two towels (large ones) to 50 degrees Celsius, and spread one out, and shaped the other one into a ball, which one would cool faster?
| Heat loss is largely proportional to surface area, so your spreadout towel more more efficiently cool.
About those dinosaurs. It is know that elephants large ears do get used for cooling. With a good blood supply those sails certainly could have dissipated at lot of heat. That doesn't prove that that was their primary purpose however.
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Why are physicists interested in graph theory? Can you tell me how graph theory comes into physics, and the concept of small world graphs?
(inspired to ask from comment from sean tilson in):
Which areas in physics overlap with those of social network theory for the analysis of the graphs?
| One context in which graphs can be useful in physics is in the discrete representation of spacetime in quantum gravity, where events are represented by the nodes of a type of poset (partially ordered set) called a causet and causal relationships are represented by the edges. This is particularly suited to a graph-theoretic interpretation, since posets can be intuitively visualized as DAGs.
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Why CAN we see the new moon at night? I understand that the Moon's phases are determined by its position in orbit relative to the Sun. (See: Full Story on the Moon). The "shadow" is not cast by the Earth (a common misconception - this is actually a lunar eclipse), but by the moon's body itself.
It would appear that, in order for the moon to be a new moon, it would have to be somewhere between the Earth and the Sun. However, it would seem that, if we were looking at a new moon, we'd necessarily be looking at the Sun as well.
Why, then, can we sometimes see a new moon at night? Why doesn't it vanish at night for a half-month every month, between its last/first quarters?
| You can't see the moon during the new moon phase because the sun, moon, and earth are in a line in that order so the sun is lighting up one side of the moon and the side facing earth is shadowed and can't be seen./Users/randyhopkins/Desktop/Photo on 1-13-14 at 5.50 PM.jpg
| {
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Why does holding something up cost energy while no work is being done? I read the definition of work as
$$W ~=~ \vec{F} \cdot \vec{d}$$
$$\text{ Work = (Force) $\cdot$ (Distance)}.$$
If a book is there on the table, no work is done as no distance is covered. If I hold up a book in my hand and my arm is stretched, if no work is being done, where is my energy going?
| $F=ma$ means that every force is applied to a mass and produces an acceleration. Okay. Acceleration is $a=\frac{\Delta v}{\Delta t}$. If you put this $\Delta v$ into ${\frac{1}{2}m(\Delta v)^2}$ you discover the energy which have been necessary to let that mass accelerate. Since energy is neither created nor destroyed, it is the energy burnt by the one who applied the force! His/her/its potential energy (e.g. from food) has become kinetic energy of the accelerated body. Now, what about holding up 5 kg with your arm? No energy? Of course you spend energy. It is the same as above: you apply a force, equal and opposite to the gravitational force, so the object doesn't fall and doesn't rise and if you apply a force, for the reason above, you spend energy. Now one could object that there is no acceleration in this case. If no acceleration (opposite to the gravitational acceleration $g$) existed, the object would fall! We have two opposite accelerations (since two opposite forces) at stake ($\mathbf{F}=-\mathbf{F_g} \Rightarrow \mathbf{a}=\mathbf{-g}$). Which cancel. But if they cancel they both exist. So yes, you spend energy for holding the object up: to let this counter-acceleration exist. So you need energy to hold up a mass but no work is done if the object is at rest on your hand, since its kinetic energy is NOT varying. If you stop with your hand a falling body you cause a negative $\Delta E_k$ (you do negative work on it) but once it is stopped no more work, your energy is simply to cancel $F_g$ and keeping the body at rest.
| {
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Why do we think there are only three generations of fundamental particles? In the standard model of particle physics, there are three generations of quarks (up/down, strange/charm, and top/bottom), along with three generations of leptons (electron, muon, and tau). All of these particles have been observed experimentally, and we don't seem to have seen anything new along these lines. A priori, this doesn't eliminate the possibility of a fourth generation, but the physicists I've spoken to do not think additional generations are likely.
Question: What sort of theoretical or experimental reasons do we have for this limitation?
One reason I heard from my officemate is that we haven't seen new neutrinos. Neutrinos seem to be light enough that if another generation's neutrino is too heavy to be detected, then the corresponding quarks would be massive enough that new physics might interfere with their existence. This suggests the question: is there a general rule relating neutrino masses to quark masses, or would an exceptionally heavy neutrino just look bizarre but otherwise be okay with our current state of knowledge?
Another reason I've heard involves the Yukawa coupling between quarks and the Higgs field. Apparently, if quark masses get much beyond the top quark mass, the coupling gets strong enough that QCD fails to accurately describe the resulting theory. My wild guess is that this really means perturbative expansions in Feynman diagrams don't even pretend to converge, but that it may not necessarily eliminate alternative techniques like lattice QCD (about which I know nothing).
Additional reasons would be greatly appreciated, and any words or references (the more mathy the better) that would help to illuminate the previous paragraphs would be nice.
| Gell-Mann's Baryon Decuplet can get enhanced and it can be shown that the 3 Upper Quarks and the 3 lower Quarks are exactly the points of Gravity of the 6 Triangels. There ist no more Place.
There are also 6 Gluons double colored on the horizontal 1 Spin boson circle, but the multicolored 2 Gluons take the perpendicular places W+1 & W-1.
YouTube.com. Konstruktion Standardmodell
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On this infinite grid of resistors, what's the equivalent resistance? I searched and couldn't find it on the site, so here it is (quoted to the letter):
On this infinite grid of ideal one-ohm resistors, what's the equivalent resistance between the two marked nodes?
With a link to the source.
I'm not really sure if there is an answer for this question. However, given my lack of expertise with basic electronics, it could even be an easy one.
| Nerd Sniping!
The answer is $\frac{4}{\pi} - \frac{1}{2}$.
Simple explanation:
Successive Approximation! I'll start with the simplest case (see image
below) and add more and more resistors to try and approximate an
infinite grid of resistors.
Mathematical derivation:
$$R_{m,m}=\frac 2\pi \left( 1 + \frac 13 + \frac 15 + \frac 17 + \dots + \frac 1 {2m-1} \right)$$
| {
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How long a straw could Superman use? To suck water through a straw, you create a partial vacuum in your lungs. Water rises through the straw until the pressure in the straw at the water level equals atmospheric pressure. This corresponds to drinking water through a straw about ten meters long at maximum.
By taping several straws together, a friend and I drank through a $3.07m$ straw. I think we may have had some leaking preventing us going higher. Also, we were about to empty the red cup into the straw completely.
My question is about what would happen if Superman were to drink through a straw by creating a complete vacuum in the straw. The water would rise to ten meters in the steady state, but if he created the vacuum suddenly, would the water's inertia carry it higher? What would the motion of water up the straw be? What is the highest height he could drink from?
Ignore thermodynamic effects like evaporation and assume the straw is stationary relative to the water and that there is no friction.
| If we are looking at this from a purely suction related problem then superman the maximum height sumperman could lift water in a straw would be equal to the pressure being exerted on the water he is drinking. If drinking from sea level then he could lift or suck the water about 10 m. Theoretically he could create a complete vacuum in his mouth then the amount of lift is merely the differential pressures. We run into this limit all the time with vacuum pumps. However, if he is able to suck really quickly then the velocity of the air could allow for water entrainment beyond the maximum lift. He could not suck the water as one big slug but rather as droplets carried up the straw due to the wind velocity within the straw. In a more practicle case, vacuum pumps have been shown to lift water from over a couple of hundred feet above static water level using this method. But the rate of recharge within the well must be suffuciently low to ensure that the water does not "clog" your suction pipe. To put another way you need to have far more air than water going up your straw.
| {
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Can radio waves be formed into a pencil beam? Laser beams are said to have high "spatial coherence". This means that the beam is highly concentrated even at long distances (low spread).
Can this be achieved with radio waves (much longer waves) or is it due to laser's stimulated emission?
| It depends on how big a pencil you're thinking about. There's no fundamental reason why radio waves can't be collimated in the same sort of way that visible light beams are. In fact, some radar systems send out fairly collimated beams at radio frequencies.
If you want to make a radio-wave beam that is the same size as a typical laser beam, though, you're out of luck. You can't focus light of whatever wavelength down to a distance much smaller than a wavelength and expect it to stay there for very long. Making a reasonably collimated laser beam with a width of a millimeter or so isn't really a problem because the wavelengths of visible light are in the neighborhood of 500 nm, or about 2000 times smaller than the beam. Radio waves, however, have wavelengths that are measured in centimeters or even meters, and those aren't going to let you make a tight beam a millimeter across.
| {
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Is it possible for information to be transmitted faster than light by using a rigid pole? Is it possible for information (like 1 and 0s) to be transmitted faster than light?
For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.
The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.
Would this actually work?
| A simple explanation why the speed of sound can never be faster than the speed of light:
Consider two atoms $A$ and $B$. Give the nucleus of $A$ a slight push. As we know, this push will carry over to $B$, but why? It's due to their electrostatic repulsion. So for $B$ to even react, you first need at least an electromagnetic wave/photon travel from $A$ to $B$. This can of course not get there faster than the speed of light. The nucleus of $A$ itself can obviously not be faster, either, so even with brute force it's not possible to get a sonic speed $\,>\!c$.
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How does the temperature of the triple point of water depend on gravitational acceleration? Suppose I do two experiments to find the triple point of water, one in zero-g and one on Earth. On Earth, water in the liquid or solid phase has less gravitational potential per unit mass than water in the gas phase. Therefore, the solid and liquid phases should be favored slightly more on Earth than in zero-g.
In a back-of-the-envelope calculation, how does the temperature of the triple-point of water depend on the gravitational acceleration and, if necessary, on the mass of water and volume and shape of container?
Edit
Let's say I have a box in zero-g. The box is one meter on a side. It has nothing in it but water. Its temperature and pressure are just right so that it's at the triple point. All the water and ice and steam are floating around the box because it's zero-g.
Now I turn on gravity. The liquid water and ice fall to the bottom of the box, but the average height of the steam remains almost half a meter above the bottom of the box. So when gravity got turned on, the potential energy of the ice and liquid water went down significantly, but the potential energy of the steam didn't. Doesn't this mean that once gravity is turned on, water molecules would rather be part of the ice or liquid phase so that they can have lower energy? Wouldn't we no longer be at the triple point?
Several people have posted saying the answer is "no". I don't disbelieve that. Maybe the answer is just "no". I don't understand why the answer is no. Answers such as "No, because gravity doesn't affect the triple point," or "No, because the triple point only depends on pressure and temperature" simply restate the answer "no" with more words.
| There is no difference; phase transitions does not change gravitational potential.
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How cold does it need to be for spit to freeze before hitting the ground? What is the dominant form of heat transfer between warm water and cold air?
If a $100 mg$ drop of water falls through $-40 C$ air, how quickly could it freeze?
Is it credible that in very cold weather spit freezes in the half a second it takes to reach the ground?
| Consider a spherical drop of water, initial temp 40C, radius 3mm, mass 0.1g
To get it down to 0C, you need to remove 4.18 (J/gK) * 0.1 g * 40 K = 17 J
then, to freeze it solid, you need to remove latent heat of fusion 333 (J/g) * 0.1 g = 33 J
for a total of 50 J.
The heat conductivity equation is
$H=\frac{\Delta Q}{\Delta t} = k A\frac{\Delta T}{x}$
where $k$ is the thermal conductivity of water ($0.6 W/m\cdot K$), $A$ is the surface area, and $x$ is the thickness. Take $A=4\pi R^2$ and $x=R=3$mm, and you find that it would take 27 sec to freeze the drop of water in -40C.
Now in practice, the drop will be elongated, increasing $A/x$, and really only the surface layer needs to freeze, possibly eliminating 50-90% of the required latent heat of fusion, so in practice, I think it should be possible to freeze in about a second.
For a real answer, I think we need to go to Mythbusters!!
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Dynamic ferrofluid sculptures http://www.youtube.com/watch?v=UJJuq_pcyIQ
What exactly is going on in the video example? I understand the phenomena occurs because of magnetism but I am trying to figure out the mechanics behind this sculpture. There obviously is a magnet underneath but what is it doing? Is it moving? Is it getting some type of charge? Any insight is great!
| I think I can tackle the mechanics aspect. What you can see is an inverted metallic cone with a helical groove running down and around its surface. On zooming in, you the perforations in the cone's surface. There is a pump which pumps the fluid back to the top as it flows down. As the empty cone begins to refill, the fluid also starts to leak out of the sides. That is why you see that flowery pattern emerge from the bottom and travel upwards. Once the fluid reaches the top the cone is filled and at maximum pressure, when the pump is turned off and the cycle begins again.
So the purely mechanical aspect of this construction is very clever on its own and presumably substituting other fluids would yield different kinds of fountains.
The leafy structure is generated due to magnetic fields. I can't say how exactly.
PS: On further reflection it seems that one can have an electromagnetic pump rather than a mechanical one. Imagine a inductor running through the center of the cone. A sinusoidal current would generate a sinusoidal magnetic field within the inductor, which would alternately pull the fluid up the cone and then push it back down.
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Solving straight-line motion question for time I apologise in advance if this question doesn't appeal to the advanced questions being asked in this Physics forum, but I'm a great fan of the Stack Exchange software and would trust the answers provided here to be more correct than that of Yahoo! Answers etc.
A car is travelling with a constant speed of 80km/h and passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80km/h in 10 seconds reaching a constant speed of 100 km/h after a further 5 seconds. At what time will the policeman catch up with the car?
The answer in the back of the book is 32.5 seconds.
The steps/logic I completed/used to solve the equation were:
- If you let x equal each other, the displacement will be the same, and the time can be solved algebraically.
Therefore:
$$x=vt$$
As the car is moving at 80km/h, we want to convert to m/s. 80/3.6 = 22.22m/s
$$x=22.22t$$
As for the policeman, he reaches 22.22m/s in 10 seconds.
$$\begin{aligned}
x &= \frac12 (u+v) t \\
&= \frac12 \times 22.22 \times 10 \\
&= 111.11 \mathrm m
\end{aligned}$$
The policeman progresses to travel a further 5 seconds and increases his speed to 100km/h.
100km/h -> m/s = 100 / 3.6 = 27.78m/s.
$$\begin{aligned}
x &= \frac12 (u+v) t \\
x &= \frac12 \times (22.22 + 27.78) \times 5 \\
x &= \frac12 \times 50 \times 5 \\
x &= 250 / 2 \\
x &= 125 \mathrm m
\end{aligned}$$
By adding these two distances together we get 236.1m.
So the equation I have is:
$$22.22t = 27.78t - 236.1 $$
Which solves to let t = 42.47s which is really wrong.
| Your mistake is in the equation
$$22.22t = 27.78t - 236.1$$
Everything up to there made good sense, but if the police officer has already traveled 236 meters, you should add that to his distance traveled, not subtract it. You'll also need to account for the way the police officer only began traveling at full speed 15 seconds into the chase.
Anyway, it is much easier to do the problem by thinking about the relative speeds. During the first ten seconds, the car is going 80kph and the police officer is going 40kph on average. So the police officer loses ground at an average of 40kph for 10 seconds. We can think of this as 10 seconds' worth of loss, and ask how many seconds' worth of loss the police officer gains as he speeds up further.
In the next segment, the police officer gains ground at an average of 10kph for 5 seconds. He's gaining ground 1/4 as fast as he lost it earlier and does it for 5 seconds, so this makes up for 5/4 of a second's worth of loss, leaving 8 3/4 seconds' lost ground remaining.
Finally he gains ground at 20kph until he catches up. He's gaining here at half the rate he was originally losing ground, so it takes him double the remaining seconds' worth time, or 17.5 seconds, to finish the pursuit.
This method is much simpler to calculate, eliminating many opportunities for errors.
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Would you be weightless at the center of the Earth? If you could travel to the center of the Earth (or any planet), would you be weightless there?
| You would not be weightless at the center of the Earth. In other words, the Earth does not follow a geodesic. Let me explain.
The Earth is not spherical, it is an oblate spheroid. The acceleration of a uniform non-spherical body in a spherical gravitational field does not follow an inverse square law. The acceleration of the center of mass does not equal the acceleration at the center of mass. An accelerometer fixed at the center of the Earth would read approx 1.75 pgal (1.75e-14 m/$\mathrm{s^2}$), not zero.
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Is there a limit to loudness? Is there any reason to believe that any measure of loudness (e.g. sound pressure) might have an upper boundary, similar to upper limit (c) of the speed of mass?
| Yes - there is a sound pressure limit for undistorted sound. Over that limit we have a shock wave. It depends on the environmental pressure, but there is a theoretical limit to loudness which you can find here.
The limit is basically equal to the pressure.
Theoretical limit for undistorted sound at 1 atmosphere environmental pressure 101,325 Pa ~194.094 dB
The lower limit of audibility is therefore defined as 0 dB, but the upper limit is not as clearly defined. While 1 atm (191 dB) is the largest pressure variation an undistorted sound wave can have in Earth's atmosphere, larger sound waves can be present in other atmospheres, or on Earth in the form of shock waves.
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How is the classical twin paradox resolved? I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within SRT, others say that you need GRT. Now, what is true (and why)?
| The problem is the symmetry break caused by the traveling twin when he changes his direction. This break makes the two twins distinguishable from each other. Before the traveling one changes his direction, both think of their partner to be the younger one (because the time in your own system is always the fastest possible time). So IMHO this paradox has not much to do with general relativity - special relativity can of course not describe accelerated movements, but what really matters is that the twin reverses, not how he accelerates and so on.
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How does mass leave the body when you lose weight? When your body burns calories and you lose weight, obviously mass is leaving your body. In what form does it leave? In other words, what is the physical process by which the body loses weight when it burns its fuel?
Somebody said it leaves the body in the form of heat but I knew this is wrong, since heat is simply the internal kinetic energy of a lump of matter and doesn't have anything do with mass. Obviously the chemical reactions going on in the body cause it to produce heat, but this alone won't reduce its mass.
| I recently lost a good deal of weight and would say it seems the water mostly leaves through urination, not exhalation. Basically, I could tell when my weight was going to be decreasing because I'd have a lot of pee in the middle of the night, without having much to drink before bed.
As the other answers say respiration byproducts are co2 Whig is exhaled and water, which, I think, makes it's way to the bladder at some point.
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What temperature can you attain with a solar furnace? A solar furnace is a device that concentrates the sun's light on a small point to heat it up to high temperature. One can imagine that in the limit of being completely surrounded by mirrors, your entire $4\pi$ solid angle will look like the surface of the sun, at about 6000K. The target will then heat up to 6000K and start to radiate as a blackbody, reaching thermal equilibrium with the sun.
The question is: is there any way to surpass this temperature, perhaps by filtering the light to make it look like a BB spectrum at higher temp, then concentrating it back on the target?
| According to wikipedia, it can reach 3500-4000 °C
You can increase the temperature by choosing material which is black at visible light range and white at IR range.
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"Magnetic mnemonics" Over and over I'm getting into the same trouble, so I'd like to ask for some help.
*
*I need to solve some basic electrodynamics problem, involving magnetic fields, moving charges or currents.
*But I forgot all this rules about "where the magnetic field should go if the current flows up". I vaguely remember that it about hands or fingers or books or guns, and magnetic field should go somewhere along something, while current should flow along something else... But it doesn't help, because I don't remember the details.
*I do find some very nice rule and use it. And I think "that one I will never forget".
*...time passes...
*Go to step 1.
The problem is that you have to remember one choice from a dichotomy: "this way or that way". And all the mnemonics I know have the same problem -- I got to remember "left hand or right hand", "this finger or that finger", "inside the book or outside of the book".
Maybe someone knows some mnemonics, that do not have such problem?
| To get the right answer, you should use the right hand, which happends to be the right hand, it cannot possibly get simpler
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How fast a (relatively) small black hole will consume the Earth? This question appeared quite a time ago and was inspired, of course, by all the fuss around "LHC will destroy the Earth".
Consider a small black hole, that is somehow got inside the Earth. Under "small" I mean small enough to not to destroy Earth instantaneously, but large enough to not to evaporate due to the Hawking radiation. I need this because I want the black hole to "consume" the Earth. I think reasonable values for the mass would be $10^{15} - 10^{20}$ kilograms.
Also let us suppose that the black hole is at rest relative to the Earth.
The question is:
How can one estimate the speed at which the matter would be consumed by the black hole in this circumstances?
| Since I have much better answer from Vagelford -- I'll write my own version.
When matter falls on the black hole it gets fractioned and radiates. As far as I know (correct me if I'm wrong) one can estimate the radiated energy as $\simeq 0.05mc^2$. Where $m$ is the mass of the falling matter.
The Earth's matter is pulled by the black hole gravitation and pushed away by the radiation. Moreover, for the matter flow $J$ we have "negative feedback" system:
*
*bigger $J$ -> more radiation -> more matter is "pushed away"
*smaller $J$ -> less radiation -> more matter is "pulled in"
The equilibrium between those forces corresponds to
already mentioned Eddington luminosity:
$L (J/s) = 1.3\cdot 10^{21} \frac{M}{M_{sun}}$
Equating $L=0.05Jc^2$ and going to $r_{sh}(m) = 3000 \frac{M}{M_{sun}}$, I obtain:
$J (kg/s) = 100 r_{sh}(m)$
It is remarkable, that the "consumption speed" for the $10^{20} kg$ black hole ($r_{sh} = 148.5\mu m$, look here) will give you $1.48\cdot10^{-5}$ kg/s. Which is just order of magnitude larger than the estimate by Vagelford.
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Is it theoretically possible to shield gravitational fields or waves? Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves?
| One potential solution, related to a problem discussed by Kip Thorne, would be to construct an enormous array of resonant bar detectors that attenuate the amplitude of the GWs as they pass through. If it is big enough, and the frequency is correct, you could absorb all the energy.
A more active device would be like noise-cancelling headphones: an array of quadrupole oscillators that can be tuned to exactly phase-cancel the incoming GWs, effectively reflecting them back to the source.
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Why does my wife's skin buzz when she's using her laptop? When my wife uses her laptop, if I touch her skin, I can feel a buzz. She doesn't feel the buzz, but she can hear it if I touch her ear.
So I'm guessing it's a faulty laptop, and she's conducting an electrical current.
But why would she not feel anything, and what would it be that she would be hearing when I touch her ear?
More info:
The effect is only intermitent - it's pretty reliable in a single session on the laptop, but some sessions it won't happen and others it will.
I had the same sensation with a desk lamp that I had several years ago, with no moving parts (as far as I could tell)
The effect only occurs when I move my finger - if I'm stationary, I don't notice anything.
I was playing with my son, and noticed the same buzz. First I thought he was touching the laptop. Then I realised he had skin-to-skin contact with my wife who was using the laptop.
| This effect occurs very often when touching electronic devices that are connected to the power mains.
You can verify that it is the connect to the power mains: unplug the power adapter and all other connections to other devices connected to the power mains and try again. The effect will be gone away.
It can best be felt also by the person touched if you touch with one finger only and move the finger (you can feel the difference on conducting surface areas of the device also).
What you are feeling is inducted power mains frequency so its probably 100 Hz (if you have a 50 Hz power mains or 120 Hz if you have 60 Hz power mains).
You can see this inducted voltage if you hold single-endedly the tip of a oscilloscope.
| {
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Tricky spring on a surface question I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it.
This is the scenario:
I have a spring that is on a flat surface, the springs details are like this:
spring constant = 100N/m
height = 0.1m
mass = 0.5kg
g = 10m/s^2
there is nothing attached to the spring.
The initial force exerted on the surface is 5N.
I compress the spring halfway until the force exerted on the surface is double, now 10N and then let it go.
The (simple) oscillation starts, and at one point the force exerted on the surface will be 0N (weightless).
I need to find out how much time has passed after letting it go, and reaching weightlessness.
as in:
10(N)---time--->0(N)
p.s. not homework, read comments.
| I assume for simplicity that the spring constant has a quite a high value so that the settling down of the spring under its own weight is insignificant.
Designations:
$x$-vertical displacement of the center of mass of the spring from its equilibrium position.
$l$-vertical displacement of the top of the spring from its equilibrium position.
$m$-the mass of the spring.
$k$-the spring constant.
$g$-gravitational acceleration.
First of all let's highlight the following relation: $$x=\frac{2}{3}l$$ Its derivation is elementary but too long to present here.
The next step is write down the equation of the conservation of energy:
$$m\frac{\dot{x}^2}{2}+\frac{3}{2}kx^2+mg(x_0-x)= \frac{3}{2}kx_0^2=const$$ $x_0=x(0)$ is an initial displacement of mass center of the spring from its equilibrium position. After differentiating with respect to $t$ we get the equation of the motion of the center of mass of the spring:
$$\ddot{x}+\frac{3k}{m}x-g=0$$ According to initial conditions $x(0)=x_0= \frac{2}{3}l_0$ and $\dot{x}(0)=0$ the solution of this equation:
$$x(t)=\frac{g}{\omega_0^2}+\left(x_0-\frac{g}{\omega_0^2}\right)cos(\omega_0t);\omega_0^2=\frac{3k}{m}$$ At the moment of the departure from the ground the following holds:
$$-mg=kl=\frac{3}{2}kx$$or $$x=-\frac{2g}{\omega_0^2}$$ Minus sign indicates that a vertical coordinate is above the equilibrium. Thus, the time we are looking for is:
$$t=\frac{1}{\omega_0}arccos\left(-\frac{3g}{-g+x_0\omega_0^2}\right)= \frac{1}{\omega_0}\left(\frac{\pi}{2}+arcsin\frac{3g}{x_0\omega_0^2-g}\right)$$ The formula has a meaning if
$$x_0>\frac{4g}{\omega_0^2}$$ I would point out the assumption at the top of the post! For the given data this is probably not a good assumption. But as a first approximation maybe it fits.
| {
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How Does Hubble's Expansion Affect Two Rope-Tied Galaxies? Suppose we have two galaxies that are sufficiently far apart so that the distance between them increases due to Hubble's expansion. If I were to connect these two galaxies with a rope, would there be tension in the rope? Would the tension increase with time? Is the origin of the tension some sort of drag between the expanding space and matter?
| Against all the above opinions:
The rope will shrink
and maintain the normal tension between atomic structure
A space expansion scenario is dual (almost) to a shrinking matter scenario.
Unless we have a way to decide I will support my point.
Already explained here:
A relativistic time variation of matter/space fits both local and cosmic data
and here:
Cosmological Principle and Relativity - Part I (arxiv astro-ph 0208365)
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Vortex in liquid collects particles in center At xmas, I had a cup of tea with some debris at the bottom from the leaves. With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin. At first, the particles were dispersed fairly evenly throughout the liquid, but as time went on (and the vortex slowed, although I don't know if it's relevant) the particles would collect in the middle, until, by the time the liquid appeared to almost no longer be turning, all the little bits were collected in this nice neat pile in the center.
What's the physical explanation of the accumulation of particles in the middle?
My guess is that it's something to do with a larger radius costing the particles more work through friction...
| I think the leaves congregate in the center as the tea decelerates due to the flow pattern established by the initial rotation. In effect the flow pattern in the tea will be a toroid flowing up the centre and down the outside effectively driving the denser particles (tea) at the bottom on the fluid into a pile in the middle.
See http://en.wikipedia.org/wiki/Tea_leaf_paradox
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Basic Spin or Double Cover Experiment We know that Spin is described with $SU(2)$ and that $SU(2)$ is a double cover of the rotation group $SO(3)$. This suggests a simple thought experiment, to be described below. The question then is in three parts:
*
*Is this thought experiment theoretically sound?
*Can it be conducted experimentally?
*If so what has been the result?
The experiment is to take a slab of material in which there are spin objects e.g. electrons all (or most) with spin $\uparrow$. Then rotate that object $360$ degrees (around an axis perpendicular to the spin direction), so that macroscopically we are back to where we started. Measure the electron spins. Do they point $\downarrow$?
| I'm surprised to encounter this old question without what I'd consider the correct answer: that the change of sign of a spinor under one rotation has been experimentally observed!
The experiment was performed using a neutron interferometer. A beam of polarized neutrons is divided, steered, and recombined by diffraction on slabs of perfect silicon crystals. Neutrons traveling down one arm pass through a region of where the direction of the magnetic field rotates; the neutron spin follows the field adiabatically, so neutrons on this arm get rotated by $2\pi$ radians. When the beams recombine, they are still completely polarized, but the interference pattern is consistent with the rotated beam having picked up a phase factor of -1.
The textbook I have at hand lists the first references for this experiment as Rauch et al. Phys. Lett. A 54 425 (1975); Werner et al. Phys. Rev. Lett. 35, 1053 (1975); Klein and Opat, Phys Rev D 11, 523 (1975); Klein and Opat, Phys Rev Lett 37, 238 (1976).
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Your favorite Physics/Astrophysics blogs? What are the Physics/Astrophysics blogs you regularly read? I'm looking to beef up my RSS feeds to catch up with during my long commutes. I'd like to discover lesser-known gems (e.g. not well known blogs such as Cosmic Variance), possibly that are updated regularly and recently.
Since this is a list, give one entry per answer please. Feel free to post more than one answer.
| John Baez's Stuff
It is more mathematics, but a lot of physics/mathematical physics related "stuff" also.
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What is the difference between a complex scalar field and two real scalar fields? Consider a complex scalar field $\phi$ with the Lagrangian:
$$L = \partial_\mu\phi^\dagger\partial^\mu\phi - m^2 \phi^\dagger\phi.$$
Consider also two real scalar fields $\phi_1$ and $\phi_2$ with the Lagrangian:
$$L = \frac12\partial_\mu\phi_1\partial^\mu\phi_1 - \frac12m^2 \phi_1^2
+\frac12\partial_\mu\phi_2\partial^\mu\phi_2 - \frac12m^2 \phi_2^2.$$
Are these two systems essentially the same? If not -- what is the difference?
| they are equivalent from a physics point of view and can be mapped into each other.
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Two slit experiment: Where does the energy go? In Physics class we were doing the two slit experiment with a helium-neon red laser. We used this to work out the wavelength of the laser light to a high degree of accuracy. On the piece of paper the light shined on there were patterns of interference, both constructive and destructive. My question is, when the part of the paper appeared dark, where did the energy in the light go?
| Try integrating the power in the resulting interference pattern; you will find that energy is indeed conserved. In the case where the slit is illuminated by a plane wave and observed in the far-field, this is very easy: the interference pattern is simply the Fourier transform of the pattern of slits, and conservation of energy is then given by Parseval's theorem!
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Why are snowflakes symmetrical? The title says it all. Why are snowflakes symmetrical in shape and not a mush of ice?
Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and couldn't find an explanation.
| K Libbrecht has a nice paper that answers your question in considerable detail and has some nice pictures-- his homepage:
http://www.its.caltech.edu/~atomic/publist/kglpub.htm
Scroll down to the article in American Scientist in his publications list
"The Formation of Snow Crystals," K. G. Libbrecht, American Scientist 95, 52-59 (2007). View pdf.
the pdf is here
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Solar heating of an object in air I need a solution to the heat equation that shows temp increase in an object, e.g. a cube or sphere, in sunlight. The object is assumed to be exposed on all sides except one. It is a solid object with a certain surface emissivity and heat capacity. In other words, I don't care what is inside the object. It absorbs some light from the sun and heats up, and heat is radiated and convected in air so that it reaches an equilibrium temperature. The solution presumably uses the parabolic PDE and the Neumann boundary condition. A Matlab formulation would be great!
| To the extent that convection is important, LOL. Temperature differences drive the fluid flows, which drive the heat loss. It would be a lot easier with a sphere than a cube, but the real problem is relating surface temperature with heat loss. If you put it in a vacuum, so you only had radiative losses, it would be easily tractable.
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What happens to an astronaut who's floating in a spaceship (in space) when it begins to move? I feel this is somehow a stupid question, but I don't know the true answer. What happens to an astronaut who's floating in a spaceship in space when it begins to move? Will the astronaut not move until he smashes onto a wall in the spaceship? Or will he move with the spaceship due to gravity? Or does it depend on the speed/acceleration of the spaceship; if it's too fast, the astronaut will smash onto a wall and if it's enough slow, he'll move with the spaceship?
| Dear huy, when a spaceship is flying to the Moon or when the International Space Station is orbiting the Earth, both the spaceship and the astronaut are moving by the same speed, so the relativity velocity is zero. Moreover, gravity determines the acceleration of all of them. The principle of equivalence implies that when the previous sentence holds, all effects will proceed exactly as in the absence of gravity and acceleration.
However, rockets have to be accelerated to get them to the speed. When they're accelerated, astronauts are pushed to their seats and their faces get deformed by the inertial force that is pushing them from one direction and the force from the seat or wall that is pushing them in the opposite directions. Astronauts should be able to withstand the acceleration of several $g$ - multiples of the Earth's gravitational field. They're trained on the Earth - in centrifugal gadgets, the vomit comet (even Stephen Hawking tried it), and otherwise.
If a spaceship accelerates by a big acceleration, it's a good idea to fasten your belt because indeed, the astronaut body floating inside the spaceship has absolutely no reason to accelerate at the same moment. It will continue to float by the same speed, so if the spaceship accelerates, the relative position of the astronaut and the spaceship will accelerate, too. The astronaut will hit the wall much like when he falls - by a constant acceleration - from a wall on Earth. The gravitational force of the spaceship or the astronauts are unmeasurably tiny; they make no effect. Even the gravity of Mr Everest is hard to measure or perceive by "ordinary tools".
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Will tensile strength keep a cable from snapping indefinitely? Trying to secure a wall hanging using magnets; me and a coworker came up with an interesting question:
When the hanging is hung using 1 magnet, the weight of it causes it to quickly drag the magnet down and the hanging drops. Using n magnets retards this process; causing it to fall more slowly, but does there exist a number of magnets m such that their combined strength will prevent the hanging from slipping, entirely and permanently?
Because this doesn't make for a very good question; we worked at it and arrived at a similar one; but slightly more idealized:
A weight is suspended, perfectly still, from a wire in a frictionless vacuum. If the mass of the weight is too great; it will gradually distend the cable, causing it to snap and release the weight; but will a light enough weight hang there indefinitely, or will the mass of the weight (and indeed the cable) cause the cable to snap sooner or later?
| Your two questions are not really related, in my thoughts.
The first one is about friction of some magnets clutched to a ferromagnetic wall.
The second is about failiure of some "wire".
Both are strange and unnessecary mixtures of idealized classical
mechanics and some real world problem.
So, first Question is really:
does friction (at rest) last forever?
and second:
does a "wires" stability against rupture last forever?
And answer(s): Yes in a surrounding of appropriate idealization, no in real world.
Georg
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How to avoid getting shocked by static electricity? 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 possible, in the belief that this will "uncharge me".
*
*Is it true that touching wood will uncharge you?
*How and when do I get charged? I noticed that it happens only in parts of the years, and after I get out of the car...
| Carry some metal in your pocket. When you suspect you are carrying an electric charge, take the metal (a coin?) out of your pocket and touch it to something grounded.
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Polarization of the gluon 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 so, would it be unitary? How?
In the case of a Higgs mechanism, it is clear that the extra degree of freedom comes from "eating" the Higgs, as they say. But and where does is come from in theories where the mass is dynamically generated?
| The asymptotic states of QCD are gauge invariant. They can include mesons which are quark-anti quark bound states and glueballs (which are roughly speaking bound states of gluons) but not gluons themselves. It doesn't really make any sense to say that the gluon propagator has a dynamically generated mass as this is a very gauge dependent statement and gluons are not asymptotic states with a well defined mass. Glueballs are massive and can have various spins, but there no puzzle regarding counting degrees of freedom because one is not starting with a perturbative state with fewer degrees of freedom and adding an additional degree of freedom as in the Higgs mechanism. This is not to say that the mass generation for glueballs is obvious. As a matter of fact, proving that pure glue QCD has a mass gap will win you a million dollars from the Clay Institute.
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R-R fields in RNS formalism 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 zero R-R fields, then you need to use GS formalism to quantize strings there. It seems to me that these two are related and again my question is- why is that? Do we always need to use GS formalism there?
| The easiest way to write the curved background action is to covariantize the vertex operator. But in the RNS version of the superstring, to write the RR vertex you need to break worldsheet supersymmetry and mix ghost and matter fields. You can look at that famous paper by Friedan, Martinec and Shenker if you don't know how it is done:
Conformal Invariance, Supersymmetry and String Theory
Without supersymmetry as a guiding principle, is very difficult to write the right action and no one really knows how to do it.
In the Green-Schwarz or pure spinor version, there is not much problem to do so. See, for instance:
Ten-Dimensional Supergravity Constraints from the Pure Spinor Formalism for the Superstring
The GS superstring has problems to be quantized and this is usually made in the light-cone gauge, but it is not always that this gauge exists. So, I guess that the the real known way to treat a superstring in a RR background as a quantum CFT is with the pure spinor action.
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What would happen if $F=m\dot{a}$? 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 $F=m\frac{d^nx}{dt^n}$ ?
| It is because the evolution of mechanical system is fully determined by initial coordinates and speeds. Therefore, your equation must be of second order, otherwise setting initial accelerations and "speeds of increase of accelerations" would be necessary.
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Homework about spinning top I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 m.
Could somebody help me derive some equations to help with this? Or to get me in the right direction? I have been trying to derive some sort of equations from $E=\frac{I \cdot \omega ^{2}}{2}$ but I cant get anywhere without ending up at radius = radius or mass = mass.
I need the final angular velocity.
| You should be able to calculate the work done by pulling the string.
You should also be able to write down an equation for the amount of work necessary to accelerate an object with a given MOI to some arbitrary angular velocity.
That should be a good start.
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Does Wick rotation work for quantum gravity? Does Wick rotation work for quantum gravity? The Euclidean Einstein-Hilbert action isn't bounded from below.
| I am a firm believer of notion of wick rotation. As Lubos nicely pointed out, the most clear indication of wick rotation comes from quantum cosmology. In fact, many new recent results in different models of quantum gravity such as loop quantum gravity$^1$ (LQG), causal dynamical triangulation$^2$ (CDT), non-commutative geometry$^3$, Horava-Lifshitz Gravity$^4$, causal sets$^5$, and eventually in superstring M-theory$^6$, strongly indicate that at the very high curvatures near or at the Planck scale (totally non-perturbative quantum gravitational system) the signature of spacetime is not Lorentzian anymore and turns into a quantum version of 4-D Euclidean space which is timeless, acausal and devoid of any dynamics or evolution, describing elegantly the so called No-Bondary Proposal of Hartle-Hawking.
Cheers
$^1$See M.Bojowald, J.Mielczarek, A.Barrau, J.Grain, G.Calcagni
$^2$See Ambjorn, Coumbe, Gizbert-Studnicki, and Jurkieiwcz
$^3$See Lizzi, Kurkiv, D'Andrea, and others
$^4$See Horava, Melby-Thomson, and Kevin Crosvenor, as well as the K. Crosvenor lecture at the GR21 conference 2016
$^5$See L. Glaser and S.Surya, as well as Glaser, D.O'Connor and Surya; forthcoming
$^6$See C.Hull, Edward Witten, Robbert Dijkgraaf, Ben Heidenreich, Patrick Jefferson, and Cumrun Vafa 2016
| {
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Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory? I was hoping for an answer in general terms avoiding things like holonomy, Chern classes, Kahler manifolds, fibre bundles and terms of similar ilk. Simply, what are the compelling reasons for restricting the landscape to admittedly bizarre Calabi-Yau manifolds? I have Yau's semi-popular book but haven't read it yet, nor, obviously, String Theory Demystified :)
| We can have compactifications over 7D manifolds with a $G_2$ holonomy, or an 8D manifold with an $SO(7)$ holonomy. We can have orbifolds, or flux compactifications. We can have warped compactifications like $AdS_5 \times S^5$.
| {
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Mathematical background for Quantum Mechanics What are some good sources to learn the mathematical background of Quantum Mechanics?
I am talking functional analysis, operator theory etc etc...
| You will have more than enough math for the first two semesters of quantum mechanics if you are taking functional analysis in a mathematics course.
The immense majority of quantum mechanics books will have the requisite math in an appendix. That is true whether or not you want the more sophisticated mathematical treatments (for instance Von Neumman's classic text), or the less rigorous nuts and bolts.
So while you may have to look elsewhere for the theory of distributions (eg the proper way to handle the Dirac delta function) for the most part you don't really need to know it in order to do the physics, or rather it just clutters notation.
This more or less also holds true for Quantum field theory (where eg you need to know some group theory) and again most texts will discuss the necessary material, although of course depending on how far you get it will lead into active research areas where knowing some esoteric maths sometimes does come in handy.
| {
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Colder surface radiates to warmer surface When radiation from a colder source arrives at a warmer surface there is some debate about what happens next. To make the question more concrete lets say that the colder source is at temperature 288K. The warmer surface is at 888K and has emissivity of 1.
3 possibilities
*
*We ignore such radiation because it cannot happen.
*The radiation is subtracted from the much larger radiation of every wavelength leaving the hotter surface.
*The radiation is fully absorbed and its effect is to be re radiated at characteristic temperature of 888K (plus infinitesimally small T increase due to radiation absorption).
I would have thought that 2. and 3 are more plausible than 1.
Both 2 and 3 satisfy the Stephan Boltzmann equation.
3 however seems to imply that the radiation from colder object is transformed into much higher quality radiation and a possible second law of thermodynamics infringement.
| The option three is valid -- the outgoing radiation is only dependent on the radiating object. Second law of thermodynamics is not violated since it must be applied to the whole system (and so to the net radiative exchange).
| {
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Resistance between two points on a conducting surface Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$
Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$.
Ie. it is approximately a 2D-surface (a rather thin disk).
What is the resistance between these two points?
Let $r,l\gg d$, (ie a 3D volume), is the resistance $0$ ?
Clarification:
A voltage difference is applied between two points a distance $d$ apart, inside a material with resistivity $\rho$, and the current is measured, the proportionality constant $V/I$ is called $R$. The material is a cylinder of height $l$ and radius $r$, and the two points are situated close to the center, we can write $R$ as a function of $l$, $r$ and $d$, $R(l,r,d)$, for small $d$.
The questions are then:
What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow \infty} R(l,r,d) $$
What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow 0} R(l,r,d) $$
| I think the answer is infinite because of the singular nature of a point. If we assume a steady state situation then the divergence of the potential is zero, by symmetry in a full 2D model the current density J will scale like 1/r. This implies the voltage scales like log(r), which diverges as r goes to zero. In the 3D case its even worse, as J scales as 1/r**2, and thus voltage scales as 1/r, which diverges even faster as r goes to zero. Note that we can compute restance, by fixing the current, and computing the voltage difference. The problem is that the voltage difference doesn't converge in the vicinity of a point current source/sink.
| {
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Should you really lean into a punch? There's a conventional wisdom that the best way to minimize the force impact of a punch to the head is to lean into it, rather than away from it.
Is it true? If so, why?
EDIT: Hard to search for where I got this CW, but heres one, and another. The reason it seems counter-intuitive is that I'd think if you move in the direction that a force is going to collide into you with, the collision would theoretically be softer. You see that when you catch a baseball barehanded; it hurts much more when you move towards the ball, rather than away from the ball, as it hits your hand.
| The only possible reason I can see is that the earlier, one faces the punch the less amount of momentum he would face. A punch builds its momentum during its journey towards destination and it reaches its maximum at the end of it. It the target comes close then he would naturally encounter less momentum and hence less force for the change of momentum.
Force $F =\frac{(mv - 0)}{\delta t}$ =$\frac{mv}{\delta t}$ if the target lean towards the punch when its seed is v
Force $F\prime = \frac{mV - 0}{\delta t}$ = $\frac{mV}{\delta t}$ if the target does not move and the punch reach its maximum speed V.
Since $ V > v$, $F\prime > F$
In both cases most of the transferred momentum will be absorbed and carried by the target's muscles and he will feel the pain.
It explains why the punch will be less if the target moves towards the punch.
| {
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Difference between electric field $\mathbf E$ and electric displacement field $\mathbf D$ $$\mathbf D = \varepsilon \mathbf E$$
I don't understand the difference between $\mathbf D$ and $\mathbf E$.
When I have a plate capacitor, a different medium inside will change $\mathbf D$, right?
$\mathbf E$ is only dependent from the charges right?
| $\mathbf E$ is the fundamental field in Maxwell equations, so it depends on all charges. But materials have lots of internal charges you usually don't care about. You can get rid of them by introducing polarization $\mathbf P$ (which is the material's response to the applied $\mathbf E$ field). Then you can subtract the effect of internal charges and you'll obtain equations just for free charges. These equations will look just like the original Maxwell equations but with $\mathbf E$ replaced by $\mathbf D$ and charges by just free charges.
Similar arguments hold for currents and magnetic fields.
With this in mind, you see that you need to take $\mathbf D$ in your example because $\mathbf E$ is sensitive also to the polarized charges inside the medium (about which you don't know anything). So the $\mathbf E$ field inside will be $\varepsilon$ times that for the conductor in vacuum.
| {
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Has every possible interaction between elementary particles been observed? There are some interactions that are forbidden by conservation laws, e.g. an electron cannot turn into a positron by conservation of charge and a photon cannot turn into a positron electron pair by conservation of momentum.
My question is if every interaction (between say up to 3 or 4 particles) that is consistent with all known conservation laws have been observed.
| There are some extremely important reactions that have never been observed directly. My favorite example is p-p fusion,
$$\text{p} + \text{p} \rightarrow \text{d} + \text{e}^+ + \nu_e$$
which is the rate-determining step for the main fusion process in the Sun and all other small stars. But it is utterly impossible to observe this reaction in anything like today's accelerators, because the cross section is so tiny. It's only important in the Sun because there's such a large, dense collection of hot protons. (In fact the smallness of this cross section is the reason all the stars haven't burnt out yet.)
Other examples would be any reactions of two photons, or two neutrinos, as Ted Bunn said.
| {
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References about rigorous thermodynamics Can you suggest some references for rigorous treatment of thermodynamics? I want things like reversibility, equilibrium to be clearly defined in terms of the basic assumptions of the framework.
| There are many presentations that are mathematically rigorous – but they have different underlying philosophies and conceptions of what thermal physics is or should do. So it'd be best if you read as many of them as possible to find those that are closer to your own philosophy, and maybe use them to be critical about your own philosophy, too.
Besides the texts given in the other answers, I'd add these:
*
*C. A. Truesdell: Rational Thermodynamics (2nd ed., Springer 1984). It is very rigorous in presenting thermodynamics in terms of primitive notions and general principles, both from a physical and from a purely mathematical points of view. It also discusses different ways thermodynamics can be presented, with their relative merits. And it gives plenty of historical remarks. Even if you don't agree with Truesdell's points of view, his insights can help you better understand and sharpen your own point of view.
*G. Astarita: Thermodynamics: An Advanced Textbook for Chemical Engineers (Springer 1990). As the title says, this is applied and gives plenty of concrete experimental examples, but at the same time is mathematically rigorous and draws from Truesdell's book above.
*I. Müller: Thermodynamics (Pitman 1985). Similar in spirit to Truesdell's, but with different assumptions motivated by different conceptions about physics.
*I. Müller, W. H. Müller: Fundamentals of Thermodynamics and Applications: With Historical Annotations and Many Citations from Avogadro to Zermelo (Springer 2009). Same philosophy as the previous book, but with additional historical remarks.
| {
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Electricity takes the path of least resistance?
Electricity takes the path of least resistance!
Is this statement correct?
If so, why is it the case? If there are two paths available, and one, for example, has a resistor, why would the current run through the other path only, and not both?
| The statement is correct if you interpret it to mean that there is a larger current in the path that has a lower resistance, when both paths have the same voltage across them. (This doesn't mean that the path with higher resistance has no current, just less current - as Ted Bunn's example shows)
You can understand this by thinking of the analagous situation of a a long pipe that diverges into two branches and re-converges back again. Suppose that the pipe is filled with water and there's a pressure difference (say using a pump) between the two extreme ends of the pipe. One of the branches is just like the rest of the pipe while the other branch is lined with, say, wheels that add to the resistance and make the water flow slower in that branch.
The pressure difference across both branches are the same (just like the voltage between two parallel electrical resistances is the same) but the water flows at a faster speed in the branch without the wheels, just like there's a larger current (rate of flow of electrons) in the path with lower resistance.
| {
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How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace? How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace?
| The full superspace terms are the "most general ones" but you may convert the chiral and antichiral terms to the full superspace form, too. In particular,
$$\int d^2\bar\theta = \int d^2\theta\, d^2 \bar\theta\, \theta_1\theta_2$$
and similarly for its complex conjugate. Sorry if a sign is wrong. Note that $\theta_1\theta_2$ may be written as $\epsilon^{ab}\theta_a \theta_b/2$ up to a sign if you happen to be annoyed by the explicit components.
The fact that chiral superfields only depend on $\theta$ but not $\bar\theta$ doesn't matter: it just means that it is a more constrained field. But you may still imagine that it's a function of the full superspace that just happens to have a special form.
Once you convert the action to an integral over the full superspace, you may proceed just like you would proceed for the full superspace, D-term-like terms. I am actually a bit unfamiliar with this thing - so I would convert the action to the components (no superspace at all) and proceeded just like in non-supersymmetric theories. Of course, the resulting conserved quantities wouldn't be nicely organized in supermultiplets - which they can be in a supersymmetric theory.
| {
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Do senior physicists actually conduct research? Senior physicists constantly complain they spend too much time on administration, teaching, getting grants, serving in committees, peer-reviewing articles, supervising, etc. . Do senior physicists conduct research by getting their post-docs and graduate students to do all the intensive work for them?
| Physics is top sport. When sports(wo)men age, they generaly discover that it becomes more and more difficult to compete. Some keep training and stay in the game till late age, but sooner or later they discover that the golden years are long past. No problem: these seniors carry a wealth of knowledge, and a position as coach, sports events organizer, etc. provides a natural second career.
Does a coach contribute to the results of his/her team? Sure (s)he does!
| {
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How does one build up intuition in physics? How does one build up an intuitive gut feeling for physics that some people naturally have? Physics seems to be a hodgepodge of random facts.
Is that a sign to quit physics and take up something easier?
Thanks for all the answers. On a related note, how many years does it take to master physics? 1-2 years for each level multiplied by many levels gives?
| I think the intuitive sense (your 'intuitive gut feeling'mentioned above)that one develops for physics starts with a passion for the subject itself. In my case that's where it all started. As a child, I recalled asking my father why his airplane flies. Later, when I was able to study physics, I could recall some relational experiences such as scuba diving (gas laws), airplane flight (Bernoulli's principle), list goes on. In all instances, I recall thinking oh yes, this makes sense, and from yhere I could extrapolate to another scenerio for example; fluid flow in tunnels as related to Bernoulli's principle. It gives you a sense of being part and parcel of the whole physics experience which is extremely gratifying. As I progressed through my graduate curriculuum to a PhD, the main areas of physics; Newtonian mechanics, quantum, statistical mechanics and electromagnetic theory seemed to be intricately linked together to explain the structure of the universe along with processes occuring within. This is not a 'hodge-podge of random facts' as you mention. By studying physics and getting the feel and understanding of physics, one doesn't neccessarily have to memorize equations, they just come naturally.
| {
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Do all light rays from a point passing through a thin lens converge at the image? I have often seen diagrams, like this one on Wikipedia for a thin convex lens that show three lines from a point on the object converging at the image. Do all the other lines from that point on the object that pass through the lens converge at the same point on the image?
*Updated question: * to say, "from that point on the object"
| No broadly speaking. Yes in a narrow context. Chromatic dispersion guarantees that it is impossible to construct a lens which will be free of caustics and other optical aberrations for all wavelengths. Individually lenses can be engineered to provide nearly arbitrary precision for narrow bands of wavelengths. However any (traditional, i.e. non-metamaterial) optical device is diffraction limited, in that the minimum size $d$ of an object that a wavelength $\lambda$ can resolve is:
$$ d = \frac{\lambda}{2n \sin \alpha} $$
where $n$ is the index of refraction and $\alpha$ the half-angle subtended by the object at the aperture of the device.
What this limit also says about the convergence of light-rays is that any pencil of rays coming from an object of size $ d' \lt d $ will fail to converge at a single point on going through the device.
So the answer to your question is "yes", as long as the device is used within its operating range!
| {
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How to build a laser in the garage? So I wonder if it is any how possible to build laser at home. A powerful one to melt brick.
| I believe that the answer to your question is no. Of course if you order all special components like resonator mirrors, high voltage power supply, etc., then it doesn't matter where you build the laser. But you cannot build a laser with items from a DIY-shop.
And just a remark - there is no way to melt a brick with a laser. Ceramic plates are very heat-resistant and they are used when you need to block a high-power laser beam (not a trivial task).
| {
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What percentage of physics PhDs leave physics? What percentage of physics PhDs leave physics to become quantitative analysts, work in computer science/information technology or business? Is physics that bad that so many people leave? Was it worth it?
| @Tim van Beek To look at it in another way, a lot of people get into physics with the aim of walking away from it after the undergrad, grad or phd. For instance, people may choose to go into environmental science. And a lot of physics phds go into biology because the problems there today are much more interesting than they are in physics. And lets face it. Biology has a lot of catching up to do!! :P
| {
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Physics for mathematicians How and from where does a mathematician learn physics from a mathematical stand point? I am reading the book by Spivak Elementary Mechanics from a mathematicians view point. The first couple of pages of Lecture 1 of the book summarizes what I intend by physics from a mathematical stand point. I wanted to find out what are the other good sources for other branches of physics.
| You might try, now in paperback,
Th. Frankel: The Geometry of Physics, An Introduction, Cambridge U.P. (Cambridge), 1997.
It's a course in differential geometry, actually, but one oriented towards physics, with succinct but comprehensive enough developments of physical theories (mechanics, electromagnetism, thermodynamics, Yang-Mills ...). It's a bit like Burke's Applied Differential Geometry (which I like too), but longer and more systematic.
| {
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List of freely available physics books I'm trying to amass a list of physics books with open-source licenses, like Creative Commons, GPL, etc. The books can be about a particular field in physics or about physics in general.
What are some freely available great physics books on the Internet?
edit: I'm aware that there are tons of freely available lecture notes online. Still, it'd be nice to be able to know the best available free resources around.
As a starter:
http://www.phys.uu.nl/~thooft/theorist.html
jump to list sorted by medium / type
Table of contents sorted by field (in alphabetical order):
*
*Chaos Theory
*Earth System Physics
*Mathematical Physics
*Quantum Field Theory
| Quantum field theory
Fields, by W. Siegel
Quantum Field Theory, by Mark Srednicki
Superspace, or One thousand and one lessons in supersymmetry
by S.J. Gates Jr, M.T. Grisaru, M. Rocek and W. Siegel
| {
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Where should a physicist go to learn chemistry? I took an introductory chemistry course long ago, but the rules seemed arbitrary, and I've forgotten most of what I learned. Now that I have an undergraduate education in physics, I should be able to use physics to learn general chemistry more effectively. What resources, either books or on-line, are useful for physicists to learn the fundamentals of chemistry? I'm not enrolled at a university, so official courses and labs aren't realistic.
Please note that I am not looking for books on specialized advanced topics, but a general introduction to chemistry that takes advantage of thermodynamics, statistical mechanics, and quantum mechanics while requiring little or no prior knowledge of chemistry.
| Oregon State University offers a pretty complete gen chem sequence online, as well as organic and inorganic. (No P-chem yet.) There are condensed lab courses for the gen chem sequence, three days each, taught on campus in Corvallis.
I took the first two gen chem courses, as well as the associated labs. I really, really loved them. Happy to answer any further questions. Will take the last gen chem course this summer.
BTW I've already got a bachelor's degree (in computer science), so I may have some idea of where you're coming from.
| {
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The Galileo thermometer: why do the bubbles float in the middle of the tube? If the water were uniform temperature, it would have uniform density, so a bubble should either be all the way at the top (if it's lighter than water) or all the way at the bottom (if heavier). But in reality you don't see this neat separation. Sometimes you see bubbles hovering in the middle.
Is this because the water temperature is not uniform? Does this mean that with time, if the room temperature stays constant, all bubbles will neatly separate along the top and bottom?
| Although I could be wrong, I think the reason is that the density of any fluid, including water, increases very slightly with depth.
There is a well-known relation between pressure and depth,
$$\Delta p = -\rho g \Delta y$$
which says that at the difference in pressure between any two points in the fluid is proportional to the difference in height between those two points. Now, we usually think of a liquid as being incompressible, so that its volume remains the same at any pressure, but in reality this is not true. Liquids do undergo a very slight decrease in volume as the pressure rises. So since the water pressure at the bottom of the tube is higher, the volume of a given amount of water will be slightly smaller at the bottom of the tube than at the top, and therefore the density at the bottom will be a little higher.
If the density of one of the glass bulbs just happens to fall in the range between the density of water at the top and the density of water at the bottom of the tube, then the bulb will come to equilibrium in the middle, at the point where its own density happens to be equal to that of the surrounding water.
Incidentally, Wikipedia reports that the liquid used in a Galilean thermometer is usually not water, but something else that has a more drastic variation of density with temperature. But the argument I've outlined above applies equally well to any normal liquid.
| {
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I need help with finding distance traveled How do I find the distance traveled of an object if the speed is not constant?
| It depends on whether you mean to find the final displacement,
$$\mathbf{D} = \int_{t_0}^{t_1}\mathbf{v}\:dt,$$
or quite literally the distance traveled. Think of the difference between the two in this way: if you travel from New York to London and back again, do you consider the length of both legs of the journey, or just the difference between your initial and final destination? In words, did you travel (roughly) 11,000 km, there and back, or (roughly) 0 km, since you wound up where you started? The former is the distance you traveled, the latter is the magnitude of your displacement.
If it's the total distance traveled you want, then the formula is
$$S = \int_{t_0}^{t_1}v\:dt,$$
where $v$ is the magnitude of your velocity velocity vector $\mathbf{v}$. Note that this is in general different from the magnitude of the displacement $D = |\mathbf{D}|$, unless the motion is always in one direction.
If you know the velocity as a function of time, then you're done. But if you're given the trajectory but not the velocity, that becomes a bit more tricky. Consider the Pythagorean theorem or distance formula:
$$\Delta s^2 = \Delta x^2 + \Delta y^2.$$
It is also correct in three dimensions for infinitesimal displacements:
$$ds^2 = dx^2 + dy^2 + dz^2.$$
Therefore:
$$\left(\frac{ds}{dt}\right)^2 = \frac{dx^2 + dy^2 + dz^2}{dt^2} = v^2.$$
Or:
$$S = \int_{t_0}^{t_1}\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2}\:dt.$$
You can also find lengths of curves that are not given in terms of time, but by some other parameter, even one of the coordinates (just replace $t$ with that parameter above, e.g., if you have a curve as a function of $x$, then replace every $dt$ with $dx$, and be mindful of $dx/dx = 1$).
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Snell's law starting from QED? Can one "interpret" Snell's law in terms of QED and the photon picture? How would one justifiy this interpretation with some degree of mathematical rigour? At the end I would like to have a direct path from QED to Snell's law as an approximation which is mathematically exact to some degree and gives a deeper physical insight (i.e. from a microscopic = qft perspective) to Snell's law.
| Sure. Start with QED, obtain Maxwell's equations, do the paraxial approximation and finally use Fermat's principle.
| {
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Gravity theories with the equivalence principle but different from GR Einstein's general relativity assumes the equivalence of acceleration and gravitation. Is there a general class of gravity theories that have this property but disagree with general relativity? Will such theories automatically satisfy any of the tests of general relativity such as the precession of mercury or the bending of light?
| I don't know that there's any general class of theories that compete with GR. If a competitor doesn't agree with experimental tests to date it wouldn't be viable.
The vast majority of tests of GR have been tests of the Schwarzschild metric. It's possible to tweak that metric so that it's compatible with quantum mechanics (unlike GR) yet is still confirmed by every experimental test of the Schwarzschild metric to date, including the anomalous perihelion precession of Mercury. Also the black hole information loss paradox vanishes. Tweaking the metric, as long as it's still a smooth curvature, doesn't necessarily deny compatibility with the equivalence principle.
| {
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What prevents the accumulation of charge in a black hole? What prevents a static black hole from accumulating more charge than its maximum? Is it just simple Coulomb repulsion?
Is the answer the same for rotating black holes?
Edit
What I understand from the answers given so far, is that maximum charge is a moving target. You can add charge to a black hole but Coulomb repulsion guarantees that you will do so in a manner than will increase "maximum charge value". Is this correct?
| Coulomb repulsion it is. Specifically, if a black hole has a lot of charge, then particles with a high charge-to-mass ratio will be repelled. Anything that falls in will contribute "more mass than charge," heuristically, keeping the charge-to-mass ratio of the black hole from getting too big.
| {
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Coriolis effect on Tsunami The Japanese tsunami, moving at about 700 km/h, affected areas as distant as Chile's coast, 20 hours after the earthquake. How does the Coriolis force affect tsunami? Also, I saw an image of a boat caught within a large whirlpool. Is the whirlpool's rotation due to Coriolis force?
| I don't believe the Coriolis force has much effect on a tsunami because it does only affect moving masses. Coriolis force in fact isn't a force but a movement pattern looking as though a force were involved. It is a result of inertia "driving" the moving masses towards a constant direction in space and at the same time the earth's rotation taking place.
However, while a tsunami travels across the globe there is little water moving, instead what actually is moving is its energy. By contrast, in hurricanes there is actually a huge amount of air moving which is affected by Coriolis force.
UPDATE:
Raskolnikov supplied us with sources that suggest Coriolis force has an effect which I do not question. However, I think it's negligible, although the wave recordings on the images presented to us show a curved trajectory. Deepak Vaid suggests this is due to ocean currents which I find not very convincing as they move at negligible speeds compared to that one the tsunami moved at.
I think the curvature of the trajectory we see on the images is an illusion due to the map projection just as in the image below showing the geodesic (straight line) between Japan and Chile:
This is the aforementioned image mapped onto a sphere.
http://www.youtube.com/watch?v=yoDFmHn4aLQ
The NOAA map in gnomonic projection
| {
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Readings of the detectors at Japan and Izu-Bonin-Mariana Trenches Given the relevance of this subduction system, I would expect that a wide range of detectors (temperature, vibration, seismometers, whatever) are deployed in the depth of these trenches. What would be the canonical source at which one could access the readings of these detectors?
| The idea of seafloor observatories making their data available freely and online is a vision and there are observatories being proposed by several of the major oceanographic institutions. Search for the term "seafloor observatory."
You might also take a look here, or contact the researchers:
Realtime Data from the Deep Sea Floor Observatory (off Kushiro-tokachi, off Muroto, off Hatsushima)
| {
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Can a nuclear reactor meltdown be contained with molten lead? If lead can absorb or block radiation, would it be possible to pump molten lead into a reactor core which is melting, so that it would eventually cool and contain the radiation?
Is there something that can be dumped into the core that will both stop the reaction (extremely rapidly) AND will not combine with radioactive material and evaporate into the atmosphere, thus causing a radioactive cloud?
| The heat of vaporization is not a temperature, but a capacity for holding heat (whose units are btu/lb, or some equivalent to that) which is at the boiling (vaporization) temperature of a substance. Yes, water does have one of the highest heats of vaporization of any substance around, the Fukushima reactors have not melted yet, and so it does make sense to put lots of water on them right now to cool them down to avoid a run-away meltdown. My suggestion deals with a hypothetical, in which say not enough water was put on a reactor, not enough heat could be taken away, and the core actually melted into a pool of molten liquid radioactive nasty. (pray that don't actually happen). My thought was to take something like liquid silica (sand) that might dilute such a liquid mass such as to stop the heat generating and nuclear reactions from taking place. Water could not do that. Once the molten nasty is diluted no longer producing so much heat and radioactivity, one would then entomb it in more sand and cement.
What I am also wondering about is if anyone in the nuclear community has actually thought out the worst case scenario so far, and what actual plans are out there to deal with a total runaway meltdown?
| {
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For an accelerated charge to radiate, is an electromagnetic field as the source necessary? For an accelerated charge to radiate, must an electromagnetic field be the source of the force?
Would it radiate if accelerated by a gravitational field?
| The radiation, if considered classically, is independent for the reason Mark Eichenlaub gives. But considered quantum mechanically, it is not independent.
In short, photons are bosons. So the presence of radiation of a particular polarization and frequency will increase the probability of the particle radiating that polarization and frequency.
This is a topic I'd not seen before. I'll look around and see if I can find a reference to the effect.
An accelerated electron produces "synchrotron radiation". An example of the electromagnetic field altering the emission of such radiation would be "stimulated synchrotron emission". Stimulated emission was described by Einstein and is the physics behind lasers. An example paper combining these ideas:
Phys. Rev. Lett. 66, 2312–2315 (1991), J. L. Hirshfield and G. S. Park, Electron-beam cooling by stimulated synchrotron emission and absorption
http://prl.aps.org/abstract/PRL/v66/i18/p2312_1
| {
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Rigid body dynamics joints I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ragdoll physics for my first person shooter game.
| Probably too late for the OP, but for the sake of the next generations or anyone searching about something related to this topic, I'm dropping this link:
http://www.gamasutra.com/resource_guide/20030121/jacobson_01.shtml
This article actually contains everything you need to know about programming cool ragdoll physics engine. Code samples included!
This article is actually one of the turning points in my life, will it be yours as well? :)
| {
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Why does nuclear fuel not form a critical mass in the course of a meltdown? A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?
| If you read Wikipedia page about corium, they say that critical mass can be achieved locally.
But if you are concerned about a critical mass allowing a nuclear explosion, the difficulty in nuclear weapon design, as told here, is to achieve the criticality fast enough. If you do not achieve criticality fast enough, your material heats and its interaction with neutrons decreases, slowing the chain reaction down. And that is with pure ²³⁵U. So basically what happens if criticality happens in a melting nuclear reactor is the release of a lot of heat and radiation, but not in an explosive manner as in an atomic bomb.
| {
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What is the most energy efficient way to boil an egg? Starting with a pot of cold tap water, I want to cook a hard-boiled egg using the minimum amount of energy. Is it more energy efficient to bring a pot to boil first and then put the egg in it, or to put the egg in the pot of cold water first and let it heat up with the water?
| Break egg into vacuum vessel, lower pressure until egg boils (sorry don't have a phase diagram for eggs handy)
| {
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What is energy in string theory? Facts agreed on by most Physicists -
GR: One can't apply Noether's theorem to argue there is a conserved energy.
QFT: One can apply Noether's theorem to argue there is a conserved energy.
String Theory: A mathematically consistent quantum theory of gravity.
Conclusion -
If one can apply Noether's theorem in String Theory to argue there is a conserved energy, String Theory is not compatible with GR. If one can't, it is not compatible with QFT.
Questions -
Is the conclusion wrong? What is wrong with it? Is there a definition of energy in String Theory? If yes, what is the definition?
| Within GR, there is a conserved stress energy pseudo-tensor. It is called a pseudo-tensor because it is not a tensorial quantity, it's transformation properties allow you to make the stress-energy of the gravitational field vanish at any point. This quantity can be derived by using Noether's prescription on the Einstein-Hilbert action, and it was proposed by Einstein as the correct stress-energy of a gravitational field. It has been controversial, because of its non-tensorial property, but it is the correct thing. If you integrate to find the total charge, you find sensible total masses in asymptotically flat space time, but the objects are defined relative to boundaries at infinity.
String theory has exactly the same type of stress-energy definitions. These are on the worldsheet, and not in space-time, and so are asymptotic S-matrix energy and momentum. The global/local issues in string theory exactly match the global/local issues in General Relativity, and your argument is actually one that supports an S-matrix/string description.
| {
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Can D and H form an 'in materials' version of the electromagnetic tensor? In analogy to the electromagnetic tensor, with the components defined as the electric field $E$ and magnetic field $B$ as such:
$F^{ab} = \begin{bmatrix}
0 & -E_x/c & -E_y/c & -E_z/c \\
E_x/c & 0 & -B_z & B_y \\
E_y/c & B_z & 0 & -B_x \\
E_z/c & -B_y & B_x & 0
\end{bmatrix}$
Can one form a relativistic tensor from the electric displacement field $D$ and magnetizing field $H$ like so:
$\bar{F}^{ab} = \begin{bmatrix}
0 & -D_x/c & -D_y/c & -D_z/c \\
D_x/c & 0 & -H_z & H_y \\
D_y/c & H_z & 0 & -H_x \\
D_z/c & -H_y & H_x & 0
\end{bmatrix}$
and thus obtain an "electromagnetic tensor" that can be easily used to handle the effects of fields in materials?
Since $D = \epsilon_0 E + P$ and $H = \frac{1}{\mu_0}B - M$, this is equivalent to asking if $P$ and $M$ can be used to form a relativistic tensor.
| The answer is "yes". One has
\begin{equation}
\bar{F}^{ab} = \bar{\epsilon}_{abcd} F^{cd}
\end{equation}
where
\begin{equation}
\bar{\epsilon}^{0i0j} = \epsilon^{ij}
\end{equation}
and
\begin{equation}
\bar{\epsilon}^{ijpq} = (1/\mu)^{kr}
\end{equation}
up to a factor $c$ here and there :-) .
Here $i,j,k$ and $p,q,r$ are spatial indices such that $\hat{k}=\hat{i}\times\hat{j}$ and $\hat{r}=\hat{p}\times\hat{q}$.
See A.O. Barut, Electrodynamics and Classical Theory of Fields and Particles.
| {
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Are regular light bulbs better for the eyes than CFLs or "tube lights"? I've heard that regular light bulbs with a filament are better for the eyes. Is the spectrum of one worse than the other? If so, are there any regulations for their use in industrial settings for worker safety?
| The "warmer" white-color of the filament (incandescent) bulb is usually considered more relaxing than the "colder" white of tubes and certain white LEDs.
However, the main ergonomic drawback of tubes is that many of them flicker. Some people are more sensitive to this than others. Some tubes have high-frequency modulators which greatly reduce or remove this effect. There is a very slight emittance in the UV-spectrum from tubes as well which could affect people wiht a photosensitive condition.
Since tube-lighting is used in virtually all offices and industries I don't think there are any particular regulations limiting their use.
See the wikipedia entries for tube lighting and color temperature.
| {
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A Basic Question about Gravity, Inertia or Momentum or something along those lines Why is it that if I'm sitting on a seat on a bus or train and its moving quite fast, I am able to throw something in the air and easily catch it? Why is it that I haven't moved 'past' the thing during the time its travelling up and down?
| Barring the affects of air resistance and such, just think of the object as also "part" of the train moving at the same velocity as you. Essentially there is no way to distinguish between an object at rest or moving at a constant velocity.
| {
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The Heisenberg limit is not a limit? This new Best-ever quantum measurement breaks Heisenberg limit
PHYSICISTS have made the most accurate
quantum measurement yet, breaking a
theoretical limit named for Werner
Heisenberg.
Nature, DOI: 10.1038/nature09778
When an experiment breaks a theoretical limit we have to reassess what we are accustomed to know.
Is it the case with this experiment?
At what level ?
| The use of the term "Heisenberg Limit" is somewhat misleading for outsiders (that is non-quantum Interferometers). If we recall the Heisenberg Uncertainty Principle is a limit on simultaneous measurement of two complementary variables. In the case of (quantum) metrology one is only interested in the measurement of a single variable to high accuracy, and this does not (directly) conflict with the HUP.
In the case of interferometry the variable of interest is $\Delta \Phi$ the phase difference between two waves detected in two arms. In basic interferometry there were some limits as to how accurately this could be measured:
Quantum Shot Noise : $\Delta \Phi = 1/N^{1/2}$
Heisenberg Limit : $\Delta \Phi = 1/N $
Here the N corresponds to how many quanta are required for the given accuracy, so the second is more accurate when it can be achieved, as was eventually done using entangled states, and perhaps squeezed light. If you cannot use these features of QM one gets just the Quantum Shot Noise accuracy.
Well a few years ago it was noticed that the assumption behind the Heisenberg limit calculation was that the Hamiltonian was quadratic in its (key) variables: this corresponded to the assumption of linearity amongst the measuring quanta. If the Hamiltonian could be made non-linear then an improvement on the Heisenberg limit would be possible.
This interaction between the measuring photons is discussed in the given paper, in Arxiv form here.
| {
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Will Earth Hour do damage to power supply system? There is always a debate around Earth Hour every year, and the opposite side of Earth Hour usually claims that
The (sudden) decrease and increase of the power usage in the start and end of Earth Hour will cause much more power loss (than the save of power), and even do damage to the power supply system.
Is this statement true? To what extent?
Thank you very much.
| The grids can take turning the lights off, by experimental observation: everyday all over the world the lights come up at about the same time for each geographical region, and turn off at about the same time due to the similar sleep schedule of millions.
Total black out might overload the system, but the percentage of people who take part in the game is small so even then dangers are minimal.
| {
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What future technologies does particle physics and string theory promise? What practical application can we expect from particle physics a century or two from now? What use can we make of quark-gluon plasmas or strange quarks? How can we harness W- and Z-bosons or the Higgs boson? Nuclear physics has given us nuclear plants and the promise of fusion power in the near future. What about particle physics? If we extend our timeframe, what promise does string theory give us? Can we make use of black holes?
| Allow me to answer your question with some quotes:
*
*"The energy produced by the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine." —Ernst Rutherford
*"There is not the slightest indication that nuclear energy will ever be obtainable. It would mean the atom would have to be shattered at will." —Albert Einstein
*"There is no likelihood that man can ever tap the power of the atom. The glib supposition of utilizing atomic energy when our coal has run out is a completely unscientific Utopian dream, a childish bug-a-boo." —Robert Millikan
*"Radio has no future." —Lord Kelvin
*"The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.... Our future discoveries must be looked for in the sixth place of decimals." —Albert. A. Michelson, 1894
*"There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." —Lord Kelvin, 1900
Also, I couldn't find a good quote for this one, but it was widely believed that number theory was an abstract mathematical discipline with no practical application. Now it is the basis of all modern cryptography.
Basically the idea I'm trying to get across is that it's impossible to predict the future applications of basic research.
| {
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Nature of tetragonal distortion in Jahn-Teller effect I am wondering: If I have a regular octahedron as my starting point, oriented along the x-y-z axis, and now Jahn-Teller suggest I elongate or compress along the $z$-axis, what happens along the other axis? I expect that these move in the opposite direction, but by how much? Say my displacement in $z$-direction is $\delta$. Is the displacement in $x$- and $y$-direction then $-\delta$, or do I have to find $\delta_x = \delta_y$ so that the total Volume is conserved?
| Very generally, Jahn-Teller distortions are indeed volume conserving, and there is an "elastic" cost associated with moving the atoms that make up the octahedron from their equilibrium positions, so if you stretch along the $z$-axis, say, then you have to compress along the $x$- and $y$-axes in such a way as to minimize an elastic energy that goes as $\delta x^2+\delta y^2$. Symmetrically compressing the axes is the best way to minimize that.
| {
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