timo

I think that's an idea that's only good at first glance - I'll gladly be proven wrong, though. I don't even have the time to read all the papers I'm interested in from my field alone. Let's face it: I don't even understand all of them. So I somewhat doubt that you'll find many (or any) papers for which you find 2+ people interested in and capable of understanding. The idea of presenting a paper for discussion might be interesting in the lines of experts presenting some work to a laymen (not necessarily meaning non-scientist but people from other or even fields) and being able to answer questions. Anyways, why not simply propose a paper for discussion, ask if someone is interested and to what extent they understood it and see if whatever sort of discussion arises. Apart from some time there seems to be nothing to lose, and you don't need a seperate forum for it (and you can also link the thread from here so that it doesn't vanish in the specialized sub-forums that interested people possibly don't look into).

Multiply with the denominator, (then) solve as normal.

You will not get answers here without showing that you put some effort into getting them yourself - except maybe by someone who does not know the forum rules. If you don't know what a normal is, then there's no need to even comment on Q1 and Q3. If you understand what it is, they are likely to become redundant.

2) The normal is (in this case) the line orthogonal to the surface. What is so hard to understand about that?

When constructing sensible equations for the gravitational field there is one degree of freedom left over; say an integration constant. This constant can not be directly linked to any known physical entity but does affect the physics. Since it is (read: seems generally considered) somewhat unsatisfactory to have a physically non-further-specified mathematical possibility affect actual physics, one sometimes assumes this constant is caused by some yet-unknown physical entity or mechanism which is then called "dark energy". I don't understand most of what you say. Some general remark: It is usually quite meaningless to compare forces without any given scope (typical silly statements often found are "the electromagnetic force is much stronger than the gravitational one"). You question seems to have a scope at some point at least: For the rotation of galaxies you can completely forget dark energy influence. It would probably be consistent with being interpreted as creation of new space. Not sure about new time because as far as I know you already talk about space expanding with time, not about spacetime expanding with ... well, what? That said, I do not know if that actually is a common interpretation. The expansion is not explained by or attributed to mainstream particle physics. In some quantum gravity it would probably be related to the creation of something, but probably real and not virtual stuff.

I think the best idea would be walking into a nearby university's library (preferably the library of the physics department), grab a few books with promising titles (both, specialized books and books which are part of a course), and browse them for an afternoon. Then, get yourself the book(s) that suited you best. For a non-professional level any textbook intended for (ongoing) professional physicists should be good enough when it comes to accuracy of the content (it probably also is for all professional sub-professor levels, too). So simply sticking to personal preferences (of writing style and content) seems like a good strategy. Of course this only works if you live close to a university where you can just walk in as an outsider.

I'm wondering whether this [half-filled conduction bands or more generally mobile electrons] isn't what qualifies a substance as a metal - not the (mixture of) atoms contained. It would be my spontaneous understanding of the term (no need to tell me that Wikipedia has an article called "metal", btw). In that case the answer to the question is probably "no, metals cannot be gaseous".

I said that saying the legal ways to obtain guns were unproblematic and that it was only the illegally-obtained guns that are a problem is -in the context of the question whether people should be allowed to have/carry/buy guns in principle- short-sighted. That is because legal and illegal market are probably not independent.What I did not say, but in effect did mean, is that there would be much less guns illegally bought if there was no legal market. You already mentioned scenarios. Guns are not drugs that a farmer or wannabe-gangster can grow in his backyard. And despite knowing little of US reality I claim that the problem with assault rifles illegally smuggled in from some east-block state is negligible compared to attacks with ordinary pistols. EDIT: To make that clear: Above is not a conclusive statement about my attitude towards legal private gun ownership (but for the record: I value the freedom/right not to be treatened with guns above the freedom/right to own guns). I just say that I think the statement "the legal market is unproblematic" is not correct. This attitude comes as a surprise to you?

A council of Tailban leaders recently came to the conclusion: No. You probably meant "legally acquire firearms", the question is quite a no-brainer otherwise. Dunno. Where do the guys selling guns to criminals on the black market (wouldn't that make them criminals, too?) get them? Saying that criminals [people attacking or threatening other people with guns in a way not allowed by the law] get their guns from the black market so legally selling guns is fine sounds a bit like blindly preferring electrical motors over diesel motors because they consume electricity instead of fossil fuel.

I think in the scientific context "warping" is used for a change in spacetime curvature - if at all. There is no spacetime curvature existing/relevant for your question. Yes. |v1|=0, |v2|=c => |v3|=c. Note that the thread particularly is about one of the velocities being c.

That's not really the same statement with different words. You'd probably call the body temperature of the jogger a scalar, but it certainly isn't the absolute value of the displacement. Doesn't that contradict your statement that distance is the absolute value of the displacement vector, i.e. the absolute value of the vector (0 km,0 km,0 km) ? It is confused. Hint: The question does not ask for "distance", which can be a lot of stuff (including the magnitude of displacement). It asks for "distance travelled".

I dunno, of course. But from the fields of knowledge I listed above that I'd expect a Mechanical Engineer to lack, I'd think an Electrical Engineer at least knows a few more of. Namely field theory approaches (the EM field) and relativity. You do know what a scalar potential, a vector potential and the 4-potential (for the EM field) is, right? I cannot judge lab-courses; my knowledge about applied or experimental physics is extremely limited. In any case, and that might not have come across properly in my previous post, chances of being accepted will probably depend on 1) the field and approach (theory vs. experiment) you are going for (which is where the list of possibly lacking or possible additional skills comes in), 2) how specialized Masters courses are in your country (I just dunno for any country), 3) to what extend the programs are laid out such that missing skills can or must be obtained (dunno either), 4) the amount of competition (how many possibly better-suited candidates are there?). I certainly don't want to discourage anyone. There's no loss in trying and not being accepted, in any case. I just find it unfair to tell everyone "sure, you can do it; everyone can do everything" just because it is a nice thing to say and somewhat sociologically correct - irrespective of possible reality. That said I might be completely wrong and switching subjects is just as easy as staying in the same field. I merely meant to mention a few possible problems I can imagine because I think/hope it's more constructive than a virtual pat on the back. If you know relativistic electrodynamics and have taken a physics course in QM then you meet most of the fields that came to my mind above (statistical physics might be the least important of those, but that again depends on the field and approach), so you are probably quite well prepared (on paper and in reality). Same goes for gokul.er137: If you write research papers in physics then you are at the level that a physics student is after the masters program - the professor you are working with could also have told you so, I think.

1) The increase in lifetime is perfectly accounted for by boosting the rest frame to a different frame. I do not think someone yet saw a need to account it to something different. That would, of course, not mean that it's impossible or principally wrong to try to do so. 2) If in the rest frame you'd increase the mass of the muon, the lifetime would -in very first approximation ignoring the state of the intermediate W boson- decrease. That's because the volume of possible final states increases and hence the decay becomes more likely. So: Yes, by mindlessly rearranging formulas it trivially could: Obtain the Gamov factor from the mass increase (simply from [math]m_\gamma = \gamma m_0[/math]). The factor equals the ratio in decay times (due to [math]t = \gamma \tau[/math]). But conceptually it seems a step backwards because the effect is not similar to the effect a "real" increase in mass (i.e. increase in proper mass) would have; neither quantitatively, nor even qualitatively. Plus, it would be a very "black-boxed" approach this way - it completely ignores any mechanism for decay.

It's not related to car safety. I also do not know what a "student" is; can be anything from younger than high-school to a PhD student. Anyways, how about something like http://www.myphysicslab.com/dbl_spring1.html Note: - An experimentally well-behaved alternative setup is to connect a 3rd spring on the right and fix it to a wall. Also, all interesting effects happen with springs with equal spring constant, too - a case that makes things a bit easier. - The problem can be solved analytically (I do not remember the details atm, though); it's possible to compare the experimental results with analytical predictions. Either the full position(time) or velocity(time) or distance(time) data if you can measure them, or just the qualitative behavior (masses oscillating in phase, in opposite phases or a mixture). - It might sound a bit boring but the math, and how it translates to reality, is somewhat interesting. Also, in the case you are actually interested in physics, understanding what an equation of motion is, what a solution is and what a starting condition is is quite a fundamental thing in physics beyond school level. - The math is not too rough, but if you just need an experiment and don't want to bother learning stuff beyond high school level, then it's probably not a good idea.

As always in such questions I'd use the relation to the complex exponential function [math]e^{ix} = \cos x + i \sin x[/math]. From that it follows that [math] \sin x = \frac{ e^{ix} - e^{-ix} }{2i} [/math] [math] \cos x = \frac{ e^{ix} + e^{-ix} }{2} [/math] Rewriting [math] A \sin cx + B \cos cx [/math] that way and realizing that appearing terms like [math]( B + iA )[/math] can, like any other complex number, be written as a magnitude times a complex phase [math]( B + iA ) = \sqrt{A^2 + B^2} \exp ( i \underbrace{ \tan^{-1} \frac AB}_{=:\delta} ) [/math] you pretty much have the result. That way of solving the question assumes you know the relation of exp(ix) to the trigonometric functions, know complex numbers and know the exponential function. But on the plus side you don't have to remember or look up all the trig identities.

I think all programming languages and environments keep their source codes as normal ASCII files. So you can program with notepad if you want, what you save is the source code. What you then do with the source code depends on you and the programming language. The two typical options are running it via an interpreter installed on your computer or compiling it into an executable file and then running the compiled executable. A compiled file does not need the compiler anymore so in theory you could copy it to another machine and run it there. However, the target machine and the machine you compiled on need to have similar architectures for this to work, making this type of spreading software more typical in the Windows world. I know it is cool having created an "independent" "real" program rather than just a script for some interpreter. But in practice the actual advantage is not really that great - I personally see having to compile as a disadvantage since at least c++ compilers can be somewhat slow (during my diploma thesis I could go for a 20 minute coffee break if I had to compile and had touched some core files since the last compilation - and that happened about once a day on average and not necessarily at coffee time).

From the most basic principles: - Having something float does a priori not need energy, so that is possible. - Lifting something needs energy, regardless of how advanced the method is. Presumably quite a lot for a whole city. - Having to lift all goods and people going into the city doesn't sound too smart energy-wise, either. In practice, energy consumption will of course be much worse than the E=mgh minimum because the mechanisms may not be fully efficient. Additionally, it's not clear if you find magnets strong enough, either. Living conditions in a city with a super-high magnetic field in it may be strange, too. And thousands other technical issues. I tried finding a picture online but didn't. Anyways: In theory, just putting balloons on the city would seem much more efficient for lifting it than pushing from below with superconductors. The idea is not new but dates back to the days when balloons were invented. Somehow, the difference between theory and practice (which in practice is often bigger than in theory) somehow prevented this idea to become the mainstream solution for modern city design. So from the principle of superconductivity there is nothing that speaks against the idea. Only due to the interplay of this principle with reality it is pretty much impossible. EDIT: Oh, and reading insane_alien's post: I was having a design with an artificially-created magnetic field on the ground in mind, not one using earth's magnetic field (in which case the strength of the field might or might not be a limiting factor even in theory).

I'm not sure it is a frame. You cannot define a unit vector in time direction, for instance. I'd find it interesting to see how far one can get without that, though.

Without wanting (because of limited time) to say too much: The usual meaning of time dilatation and length contraction is a local (instantaneous) property. The ratio of the twins agings is the time change experienced integrated over the trajectory. The ratio happens to be the same as the ratio for the local ratio of measured time distances because in the frame chosen to discuss the problem the magnitudes of the velocities of both twins are constant. But conceptually, the local property and the integrated property are really different things. Now to answer the question: With the times you compare the aging of both twins, i.e. the time passed in their frames of reference, i.e. an integrated quantity. The distances passed in either frames are zero by definition so it's not a useful integrated quantity to compare. I wouldn't know what sensible observable to construct from the length contraction (size integrated over time ?!?) but I think its ratio is just the inverse of the time ratios, anyways.

You'd better invest it in some Nigerian scammer ring, anyways. Their stories are in accordance with the known behavior of nature (not the human nature, though), at least.

When I start walking east on earth there is, mountains and oceans apart, nothing that stops me traveling further forever. We would probably agree that earth is not infinitely large, though. An interesting observation: I'd think the only reason why you think this cannot be the case for the universe is that on earth your are used to think of it as a sphere from the beginning while for the universe you are not. It somehow makes the people who denied that earth could be spherical seem less confused in retrospective; they even had additional arguments against it (you'd fall down on the lower side).

Dunno. I call it "product". It's the multiplication version of the sum sign, so [math] \sum_{X=a}^b X = a + (a+1) + \dots + b [/math] and [math] \prod_{X=a}^b X= a \cdot (a+1) \cdot \dots \cdot b [/math] X, a and b can of course be any integer-valued expression, i.e. a number, a variable or a term. And as always, someone wrote something in Wikipedia: http://en.wikipedia.org/wiki/Multiplication#Capital_pi_notation Something in that direction, yes (I do not fully understand your question). But looking at it a 2nd time you'd have to catch the error one step further ahead in the "definition of the factorial" step. When a=n, then (a-n)! = (a-n)*(a-n-1)* ... * (1) does not hold true anymore. 0! is 1, not 0*...*1. For your proof that would mean the following: - You have proven that for n=1, your expression works. - You have proven that if your expression works for n=x, then it also works for n=x+1 - if x is smaller than a. => So rather than the usual conclusion that your expression is correct for all n>1 you now can say that your expression is correct for all n from 1 to a.

- Perhaps that's exactly what you wanted to avoid, but I find [math] \frac{a!}{(a-n)!} [/math] a rather obscuring way to write [math]\prod_{k=a-n+1}^{a}k[/math] or simply "product of all integers from a down to a-n+1". Also, the factorials don't work for negative exponents. - Way too many parentheses for my taste. - Actually, you can see the problems with n>=a directly from your proof if you properly catch the division by zero in the step you called "cancellation". - The correct notation (your steps were fine just what you wrote down is not according to standard syntax) for your first step is [math] \frac{d^{n+1}y}{dx^{n+1}}= \frac{d}{dx}\left(\frac{d^{n}y}{dx^{n}}\right)[/math]. What you wrote would mean [math] y' \cdot \left(\frac{d^{n}y}{dx^{n}}\right)[/math] - Apart from the division by zero and the notation mistake that's a nice, simple, correct and nicely presented (perhaps a few too many steps for my personal taste) proof by induction.

It's more like 64 MB.

1) You'd have to ask yourself to what extent infinite mass (or an infinite amount of anything) makes sense. 2) Idealized vacuum has a constant density [sidenote: I am not interested in being told about imagined quantum effects]. I do not see why a sensible definition of an infinite mass would be would exclude its density to be non-constant. Either take a stone and make it infinitely heavy -> the density is still not constant but remains zero outside the stone. Or take a finite density over an infinite volume and set the density zero in some finite sub-volume -> again, a non-constant density. 3) Why should an infinite mass not have a temperature? In the simplest case, temperature can be thought of being defined in the thermodynamic limit. This involves the number of particles going to infinity which implies the total mass of the system going to infinity. 4) "no time" seems just as wrong. 5) "one state", too. Take an object of infinite mass (again assuming such a thing could be properly defined) but finite size and place it somewhere else. Two distinct states. My guess is that with "infinite mass" you mean something like a system with a reduced amount of degrees of freedom. In that case, some of your comparisons might become true. If there's only one state (zero degrees of freedom) then you cannot define a temperature, for example.