timo

Assuming "identical in every way except one is denser" also implies that the denser one has a higher total mass (the only other possibility would be having a different diameter) the denser one will hit the ground earlier than the less dense one. That is because the motion of the denser object is less influenced by friction with the atmosphere that hinders the free fall Capn and yourdadonapogos assumed (they probably didn't catch the "in an atmosphere"-part).

LHC has a proton-proton mode and a lead-lead mode. As I said, all new elementary particles are looked for in the proton-proton mode which is targeted for 14 TeV center-of-mass energy. The lead-lead mode is kind of a seperate experiment (also having its own detector, if I remember that correctly) and operates at a cms energy way above the 14 TeV (something like 1000 TeV I think, but the correct number should be rather easy to find).

2) I don't think so. The tenor I've heard is that if there is a Higgs boson, LHC will confirm it. 3) "Accurateness" of the results at LHC is strongly dependent on electronics, software and analysis algorithm. For the electronics part, many critical parts were constructed explicitely for LHC. I would not be surprised if today's top-level electronics developed elsewhere was inferior for LHC usage than the parts specifically designed for it (it's not that the LHC parts were developed in some backyard garage, there's whole research groups at universities dedicated to building parts of LHC. For the software and analysis methods: You throw away most of the data (~90% I think) coming from the detectors. What is thrown away at this stage is gone for good. If your criteria for keeping data - which must be fixed before building the detector (they are so-called "hardware triggers", i.e. built into the detectors)- were bad then you might miss crucial data. For the data kept at this level at least some part (still a huge amount of data) is saved. So if at some later stage you come up with some idea, say something like "there should be a new particle which should have shown up on LHC", you could in principle just reanalyze the data. 3a) I would assume at least parts are interchangable. I would assume that overall the design is mostly fixed, though. 4) I think the problem is not that magnets you have are not sufficiently powerful to guide the beam around a bend but that by guiding a beam around a bend the beam loses energy; the more curved the bend the more energy lost. The next collider planned ILC won't have any bends but will just accelerate the particles in a straight line, btw. 5) Dunno. But I guess it's not much. 6b) Higgs particle is searched for in proton-proton collisions as are all searches for new particles. 8) Dunno STS 125. But I think you might be heading towards the statement that LHC wanted to create/investigate conditions at the big bang. The whole "recreate (condition at) the big bang" is, in my opinion, mostly a commercial slogan to get people interested in the project.

Nothing till now (I've not checked the numbers, though) except the last step: [math]\bigtriangledown h = 10((3y-8x+28)\hat{x} + (3x-6y-17)\hat{y}) = 10 \left( \begin{array}{c} 3y-8x+28 \\ 3x-6y-17 \end{array} \right) \stackrel{!}{=} \vec 0 = \left( \begin{array}{c} 0 \\ 0 \end{array} \right)[/math].

It is not true that matter-antimatter reaction have to turn into photons only. Depending on the type of matter and anti-matter I think it is usually not even the case that the majority of reactions does. Past and future particle physics experiments like Tevatron and ILC look at the reactions that are not purely photonic (for Tevatron they should be mostly hadronic, for ILC they probably are mostly leptonic with potentially a sufficiently high rate of supersymmetric particles and Higgs bosons.). There is only one example where the statement with "photons only" is true: Electron-positron annihilation with both particles being slow (meaning their kinetic energies are small compared to their rest masses). The reason you can only get photons there is that to create new particles you need the energy for their rest mass. Since electrons are -with the exceptions of photons that actually are produced and gluons that cannot exist as free particles- the lightest particles and the kinetic energy was supposed to be negligible this reaction simply does not have the energy for any other reaction product than photons. Admittedly this only example is also the most important one as it is -to my knowledge- the only particle-antiparticle reaction that is used in applications, namely positron emission tomography. In short: The statement that matter and anti-matter must react to photons only is wrong. I think this misconception is so widespread because there is one prominent special case where it is true. EDIT: My statement why e+ e- is photon-only above is incomplete/wrong. I forgot the neutrino-antineutrino mode which, however, should be strongly suppressed by the weakness of the weak interaction at the energy considered.

I think the dominant term that drives the moving of the shadow is the rotation of earth around an axis through earth, not the rotation of earth around the sun. It would be interesting to see if you can make a measurement that precise that after your substracted the term for earth rotation around itself you get a remainder that indeed gives stems from the rotation of earth around the sun. What values did you measure and what calculation did you do to get to your result, btw?

No, I don't see it. Mostly because I have no idea what the z-pinch effect is. I'm currently not fit (and not interested, either) to really read the WP article or even make some serious approaches understanding it (looking up literature or simply doing a calculation of my own). Spontaneously, I see nothing that states that there is an effect in the order of magnititude such that it would prevent two electrons to repell each other. I don't know to what extend the effect is tied to plasma conditions, either - two electrons certainly do not make up a plasma.

[math]F_e® = Gm_e/r^2, G_e := Gm_e/r_e^2 \Rightarrow F_e® = G_e \frac{r_e^2}{r^2}[/math] (expand the former equation by [math]\frac{r_e^2}{r_e^2}[/math] to see it). Same for the force by the moon. The only and supposedly (see also D_H's comment) striking problem is the choice of Y.

It's (vaguely) akin to asking whether an object moves to the left or not. In different reference frames the velocity to the left has different values. I do not know what answer to the question "does an object move to the left or not" you prefer, but similarly to the motion of an object to the left, the magnetic field created by a charge depends on the reference frame (as you already noted) and I think the answer is pretty much the same for the motion-to-the-left question and yours.

I'm afraid I didn't read all of the long text but only up to the calculation. I wonder where the value for Y comes from?

I see this as a question of fundamental research vs. applications considering that there's nothing really LHC or fusion research specific in the question ("no immediate application to be seen" and "could be damn helpful if we had the application" are generic arguments). In the short run, investing in applications always look better - especially to politicians . On the other hand, you'd not even think about applications if the fundamentals for them hadn't been laid out some time ago. No real opinion on the topic, except that fusion never really conviced me of being a good idea. http://en.wikipedia.org/wiki/Superconducting_Super_Collider

No I wouldn't. I didn't add an explanation, after all. For the graphs: The two axes represent possible choices for the two variables x and y. Usually, then you draw a graph for an f(x) type function, you draw possible values of x on the horizontal and the corresponding f(x) on the vertical. Since in the plot I have two variables I have already used up the horizontal and the vertical axis for possible values of the variables. So if you want to draw a picture of the function you must use some other approach, the common ones being - Drawing a fake 3D plot with the value of the function at the f(x,y) as z-coordinate. Often looks nice but is usually not particularly helpful for any other thing than having drawn a nice picture. - Fixing one variable to a number and then drawing something like e.g. f(x,5), the values of the function when y is 5, in the conventional way. Perhaps just draw several of those graphs e.g. one for y=1, one for y=2, ... . - Using colors to indicate the value. Different colors then represent different values. That's pretty bad for reading off exact values but sometimes nice to get a feeling for the function. The (approximate) translation from the colors to the actual numbers is given on the right-hand side. In this case, you can see that the values tend to decrease as the values of x and y increase, for example (do not mistake equal colors for equal values, that might just be because the number of colors is limited!). Anyways: Don't take the pictures too seriously. They are just supposed to visualize something and not particularly important for anything else. Look around for a calculus tutorial covering functions with more than one variable - either in a book or on the internet, the stuff is so folklore that you can probably even trust the internet here (except if you are a mathematician). THE keyword you are looking for for this question is the gradient but seeing you already opened other threads on related (i.e. f(x,y) stuff) topics you are probably best adviced to read up a few basics somewhere.

The question asks for derivatives of a R²->R function. EDIT: Here's a colored plot of the function. Not sure if that helps you understanding; you'll have to solve the question analytically, anyways.

If the term is not used in english then it probably simply was a mistranslation of mine, not the usage of a less-frequently-used term. "Eigenzeit" is the german term for it (@booker: The -non-mathmetical- justification there is that it is the time that an object experiences; its "own time"); I simply assumed that the "eigen" prefix also translates to english (like for eigenvectors). That would depend on the non-given context, I think. It does not matter for the sake of the argument that you can compare the ratios or behaviours of two different time parameters.

Tex-mode is done with putting the math code between [ math] and [ /math] tags not Dollars leading to [math]P(x_1,x_2,...,x_N) = e^{-\beta V(x_1,x_2,...,x_N)} / Z[/math], [math]V(x_1,x_2,...,x_N)=\sum^N_{i=1}{1 \over 2}\lbrace(x_{i+1}-x_i)^2+v(x_i)+v(x_{i+1})\rbrace [/math], [math]v(x)={x^2 \over 2}+{\lambda \over 4}(x^2-\delta)^2 , x \in {\bf R}[/math]. For the question: I only have some basic knowledge about Monte-Carlo methods. I do not know what "hybrid Monte-Carlo" is. What exactly is your problem? Have you written a Monte-Carlo and it does not work? Does it work but you want to use this "hybrid Monte-Carlo" technique? What is or would be your algorithm? I do not believe that statements about correlation time can be made independently of a concrete algorithm (not that I think I could say much about them if you had presented one, but your post/question seems incomplete to me).

Electrons are not made of leptons, they are leptons (similarly to a Mercedes not being made of cars but being a car).

Most experiments on Dinosaur behaviour.

I see three quirks in that statement: 1) It's supposedly not what the majority of people mean when they say "relativistic mass". I'd think most people actually do mean the energy and define it via m=E/c². I have not heard your definition before. To be honest: I am not convinced that many others have, either. 2) Taking your statement literally your RE wasn't even properly defined. I assume that for the v=0 case one has to think of a limit, though. 3) What would the so-defined quantity be good for?

It's more like relativistic mass really just being another word for the energy, despite the "everything is relative" crowd not liking it.

The problem with your question is that in any widely-accepted theory that has photons (i.e. quantum theories of the electromagnetic field) there is no handle for gravitation. If you come from pure Relativity, then energy and momentum density contribute to a term that creates curvature of space (the energy-momentum tensor) - although for a universe with only a single photon you could probably make that term vanish by taking the limit to a state where the photon has zero energy. A more simple answer that you are probably looking for: The sources of gravitation are energy and momentum. A photon has both. That said, I'd like to re-emphasize that photons are the result of quantum mechanics (a special quantized base of the electromagnetic field) and that we do not have a theory of quantum gravity. While it would violate many of the guidlines in modern physics I am not even sure that we have a convinving (=experimental) evidence against the statement that gravity only works by/on gluons, for example.

No

Non-polymorphic is faster and takes up less memory? I don't think it is a good idea in the sense that I think it's the best way (though I prefer it over using "+" and over not being able to paste different objects into an output in one command at all). But I don't really see a problem with it, either.

Or the masses of particles or the lifetimes of radioactive isotopes or the center of mass energies of colliding particles or the elementary charge or the amount of people believing that "everything is relative" or the number of beer cans in a six-pack or ... . Velocities being dependent on who observes the motion is not a big deal. It is true in non-relativistic physics, too. In fact, it if you take the standpoint of differential geometry velocties actually are absolute and independent of an observer in relativity (at least the time-likes). Thinking "the physics model is called 'relativity' therefore everything must be relative" seem like a certain path never to understand the theory. The constants (under changes of the coordinate system=observer) in the theory are very, very important for understanding it so in that respect the name "relativity" is really an extremely bad choice of a name (can't think of a respect in which it was a good name, either).

I thought the boom comes from passing from v(plane)<v(sound) to v(plane)>v(sound), not from being in the later state?

Continuous and discontinuous with what parameter?