timo

Err... I might have misunderstood you, but: - The only thing leptons and quarks have in common is their spin: 1/2. - The striking property allowing to cast the spin-1/2 particles (the SM fermions) into the two distinct groups "leptons" and "quarks" is their color charge. Leptons carry a color charge of zero and therefore do not interact with the QCD gauge field (the gluons).

The interesting point about quantum computers is that due to their different operation mechanism they allow for algorithms that are not possible with classical computers. These algorithms can, for some applications, way outperform classical algorithms. I think that´s just one example. Another one is, iirc, related to doing fourier transformations and related tasks like frequence filtering very effectively.

That depends on if the mirrors reflect the wavelengths that the solar panel uses. Generally, I´d think "yes". As a quick check you can try to find out what wavelength the solar panel uses. If it´s the wavelength of visible light, then it will definitely work.

how about [math] K = \{ \left( \begin{array}{cc} \frac{1}{4} & \frac{-1}{4} \\ \frac{-1}{2} & 1 \end{array} \right) \, r, \ r \in R \} [/math] ? Note: I didn´t check your math but I assumed you did calculate the elements of M_22 that map onto 0 of R^4, which I think is the definition of the kernel.

Ok, here goes the first violation against the rules, a no-nomination post: Last time, staff wasn´t allowed to nominate, even though the rules didn´t say so. What´s the take on that this time?

What are T, d, l, "gradient" and "y-intercept"? I think you should post the whole problem so that it´s able to see what you´re talking about.

Interestingly, that question doesn´t really make sense. You can compare it with a classical example: I travel to some other city by car. I can either take the highway or some shortcuts using smaller roads. When I arrive via the highway, the distance I travelled is bigger than it had been had I used the smaller roads. At which point on the highway did I travel additional kilometers? Of course, there is no such point. The highway simply is the longer route. The different aging of the twins is pretty much the same thing. They took different paths from A to B, so the time they experienced on the way can differ. From a more theoretical point of view: At which two point on their respective paths through spacetime would you compare who is older? A quite natural aproach is taking two point that have the same time coordinate in some coordinate system. The question that you encounter then is: Would those two points have the same time coordinate in some other coordinate system? The answer to that question is: They do exactly if they also have the same space coordinates, too. In other words: If you compare the ages at the point where the twins meet, then you are comparing the same points on their path through spacetime for all coordiante system. If you´re comparing the ages when they don´t meet, then you´re comparing two pretty much arbitrary points (the points compared depend on the coordinate system chosen) on their path and can get pretty much any result you want. To compare it with my previous example: Assume you wanted to find out where I have to drive the extra-kilometers when using the highway. So you decide to compare the kilometers already traveled not at the destination town but somewhere along the route. Which points on the routes do you compare with each other? You could chose some comparison like "I compare points at which you taveled an equal distance to the north". But that is not a better choice than comparing points with an equal distance travelled to the west or comparing points at which you have an equal altitude over the ocean surface. My personal problem with this "second interpretation" is that I´m not understanding what you´re saying. You´re saying that you want to leave all the maths unchanged but want to alter the interpretation of the results? Are you saying that a stone doesn´t always fall down because if I turn myself head-down I see it falling up and therefore the coordinate system where my feet are on the ground is a prefered one (it is my prefered one, for sure )?

Perhaps you shouldn´t over-interpret the energy bands. From a more abstract point of view they are merely a nice way to describe the possible energy levels for electrons in a periodic potential - but a very practical one for describing certain effects nonetheless. Determining the energy eigenstates for multi-particle systems is a problem with an awesome complexity and can, in practice, only be done with very strong simplifications. In the case of the energy bands, the simplification used is that the electrons are in a static periodic potential and do not interact with each other (more sophisitcated models might include electron-electron interaction and slight deviations periodicity staticity, though). These conditions are quite well fulfilled by single-crystals and, given that the model still works, also sufficiently for polycrystals. Both, single- and polycrystals are solid states. It seems unlikely (to say the least) that periodicity of the ions is sufficiently satisfied in a fluid or a gas (I would spontaneously expect the energy-eigenstates to be bound to a single ion rather than being spread out over the whole crystal). Since the conditions are very different, I´d expect the resulting distribution of the energies not to be band-like. Ok that was mostly just speculation from my side and I should note that I´m not a solid-state physicist. I mostly responded because to my knowledge no one else on this forum (at least no one that posted here during last year) is, either. But I hope it still helps you a bit. Two questions from my side: 1) Why are you interested in energy-bands? While it´s refreshing to see that people can ask questions about something else than quantum gravity it´s a bit surprising for me that you do. 2) What´s your background on QM? I think energy-bands belong to the part of solid-state physics that, at least from the theoretical side, can only be understood from a QM perspective.

You are very, very vague. What do you already know? What is you mathematical background? Why are you interested in black holes? Is there any specific thing about black holes that interests you? How scientific can the information be? Generally, any physics textbook on general relativity should include a section about black holes. Assuming you have enough background knowledge and/or time to read into it, that could be a start.

It is a particle's potential energy divided by its charge - in other words a potential. Dividing the potential energy by charge removes the charge-dependence of the values so voltage is only dependent on the outer conditions and has the same value for all particles affected. You do, in general, need two values to differ. Since only differences in values matter, it is physically irrelevant where you set voltage=0. You simply set one point to zero, arbitrarily (there might be conventions in electrical engineering, though). In electrical circuits it usually means the difference from one end to the other of the part of the circuit that´s currently considered - which can either be a single part of the circuit like an LED or the whole circuit. Potential energy (voltage times the electric charge) can be transformed into kinetic energy resulting in movement. This is also true for electrical charged particles (e.g. electrons) in an electric field (electric potential). The kinetic energy of the moving particles can then go into other form of energy, e.g. warmth by friction in a wire (resistance), light in a lightbulb or mechanical energy in an electric motor.

And now ... can you make a "newest style" with both, the avatar and the name on the left? Because that´s where I usually start reading . I personally wouldn´t mind any bad wrapping so if it´s possible to have a user-selected non-default style with both on the left, I´d probably use that for me.

We have pretty clear evidence that gravity exists, but that´s of course not what you were asking. Since gravity affects mass in large quantities, it seem natural that it should affect mass in smaller quantities to a proportionally lesser extent. This would then of course include scales at which we currently use quantum mechanics to describe the behaviour of particles. I can imagine that all arguments for the gravitational field to be quantized indeed relate back to all the other interaction-carrying fields also being quantized, but that already seems like a good reason to investigate that possibility (relating different effects back to common mechanisms and stuff).

I´m not sure what you wanted to say with that. 0/10 = 0, hence for N people with a reputation of 0 giving you points, your new score will be 0 + N*0/10 = 0, making the system a bit redundant.

You do. When writing a post, click to "go advanced", then "manage attachments" und "additional options". In the new window, you can upload files. @mamakosj: But I think you shouldn´t use the SFN webspace for non-SFN use.

In the original design proposed by YT, the amount of new points is decided by the number of points of the persons who gave you points on a linear scale (their points / 10, iirc), hence it can´t start at zero.

I´m not sure what you mean by "how". The photons interact with a charged field creating a particle/antiparticle pair of charged particles that can then interact with the other photons involved. Schematically, a feynman diagram could look like the one I´ve attached, where the outer wavy lines are the photons (you can pick for yourself which two lines are the incoming and which two are the outgoing) and the inner square is some charged particle (electron, myon, tauon, quark, W) running in a loop (or equivalently two particle/antiparticle pairs if you consider going in opposite direction of the arrow as an anti-particle).

To emphasize which would probably be the first real hindrance: I think most giverments reserve the right to shoot down planes (which includes shooting things up to this height) exlusively to themselves and do not grant their citizens the right to do so, too. Sadly, these weapon restrictions exists regardless of the clear evidence that weirdos attacking you with a plane is a realistic threat to your personal safety.

The reason is that photons interact with electric charge. Since photons are electrically uncharged, they don´t directly interact with other photons.

If you encounter the problem with copying from WP in diploma theses (it doesn´t clearly come out of your OP) then I think something is really going wrong with your supervision.

Mathematics, because it gives +3 to defense.

Afaik, Thermodynamics was originally an empiric branch of physics meaning it was a model trying to describe observations. Modern thermodynamics is based on statistics which indeed makes entropy a statistical variable. Little simplified description of entropy: If you have a gas in a container you cannot realistically expect to know where each particle is and where it´s heading; a particular state describing the state of each single gas molecule is called a microstate. But you can possibly measure more global properties like the pressure or particle density in different parts of the container; that would be a macrostate. Since you cannot tell in which microstate the system will be, you simply assume that all microstates are equally probable. This is, in fact, just an assumption whose only real justification is that you wouldn´t know of any mechanism that would make one microstate more likely than the other. However, this does not mean that all macrostates are equally probable. Different macrostates can have different numbers of microstates that would lead to them, therefore the relative probability of macrostates is equal to the number of microstates that would lead to them (if each microstate has a probabilily of p, then a macrostate with N microstates leading to it would have the probability N*p). Entropy is simply a measure for the amount of microstates leading to a particular macrostate (it´s proportional to the logarithm of the number of microstates). Tracing this description back, you´ll see how the empiric "systems will most likely be in the state with maximum entropy" becomes a statistical "systems will most likely be in the most likely state" statement. I would therefore say that the 2nd law is not empirical in nature, except if you call the assumption of equal probabilities of microstates as empiric (I'd not call it so). It´s not a fact either, given that there´s some assumptions coming in. @V8: Perhaps you should open a seperate thread about that in an appropriate section. Two rather unrelated questions in one thread might lead to confuse overlaps.

The term is WIMP without and H and stands for "weakly interacting massive particles". The term, however, is also generic to some extent. It refers to electrically uncharged (hence not interacting via photons but at most via the "weak force" and of course gravity) massive particles - where I think (but do not know for sure) "massive" also means a relatively high mass. But it doesn´t necessarily mean a specific particle and isn´t bound to a specific exotic physics model. As a follow-up question: Does anybody know for sure if warm dark matter (meaning light particles) is still an option or is it ruled out by now?

Well, the main problem I see is that I think the classical picture (neutrons as little hard balls with definite momentum and position) breaks down in the case of a neutron star. A remarkable property of a neutron star is that the gravitational force that tries to collapse the star to a single point in space is not countered by electromagnetic interaction (the repulsion of the electron clouds around different molecules) but by a mixture of a Quantum Mechanical principle called "Pauli exclusion principle" and the energy-dependence of the different QM states of the star's radius (the boundary condition). In other words: I think you need QM at least for understanding why the whole thing is even stable. The model you use for describing a system often also depends on what you actually want to know about that system - you can almost never model a realistic system completely. For the question why a neutron star is stable (i.e. the countering of gravitational interaction and "QM repulsion") there is a relatively simple model giving reasonable results. I could probably put down the maths of that either here or on the sfn-wiki if you´re interested in that. But I´m not sure to what extend that covers your original question. Some points in short: - I don´t think a classical model is appropriate for neutron stars. - Temperature is not necessarily a measure for the kinetic energy of the particles in the sample. You can apply temperature to systems like a set of spins and their orientation in a magnetic field that don´t even have any kinetic energy at all. - By pure intuition I would assume that realistically, a neutron star won´t have T=0K. It would probably not even have a uniform temperature - but that´s both just guesses. -- Some properties, like the stable radius, can be approximated reasonably well with models that use T=0K, I think. @Martin: Sry, but for any information on the topic that is beyond the simple model in which the pressure of the compressed fermion gas counters the gravitational attraction, I´d have to look it up somewhere, too (and you´d possibly know the better sources, though).

Well, a key point in your statements that you might have overlooked/underestimated is the term "every". Starting a statement with "every" means that if there is at least one counter-example, then the statement is wrong. If you´re altering the statements to "some x must know quite some y", then I´d probably say the statements are all right (medical research, cell biology, quantum chemistry, mathematical physics, not sure about the last one). But that´d be completely different statements.

The new design obviously encouraged some people to post a whole lot (although seemingly in some hidden forums I cannot access - I can´t see his posts), replacing YT as top poster: Top Poster: smart (4,294,967,295) btw.: That information which is located on the front page (right box) seems rather uninformative to me, even when it displays correctly.