timo

See http://www.scienceforums.net/topic/51059-the-official-sfn-starcraft-2-thread/

Imagine there's a group selling you bullshit and making a good penny with it. A group of men and women who just want to rip you off. What if that group is completely ruthless and won't just take a few bucks but aims to totally control your mind and life. What if this group was faced with opposition from people who prefer not having themselves, their friends or their fellow citizens brainwashed? - How would such a group portray itself? More importantly: would they lie about their intentions? And if they had to send a message on a science forum, would it make any sense? - Who read this far to risk seeing the end of this post? Maybe we're all trans-dimensional beings of pure energy. I don't think conspiracy theories mixed with ridiculous phrases provide a good starting point for discussion.

I was of course completely aware of that which is exactly why I proposed trying it out ok, I screwed that one up.

Wasn't there some famous experiment by some famous scientist (Galileo?) proving that two balls heavy enough so that air resistance becomes negligible roll down the same speed? Perhaps you should simply try if they really roll down with different speeds. Seeing you are new: Welcome to sfn. Here's an alternative answer: If you [can] ignore resistance the two balls will roll down the slope with the same speed. That's what theory says. I was serious about trying it out, though.

I still don't really get your point. Perhaps this helps: The 2D and 3D plots without a time axis are more sensible than the 1D plot without a time axis, I think we agree there. They also give some information that might be helpful (e.g. in the 2D plot: how far did the stone fly till it came down again?). But they do not contain all of the information about the motion (e.g. not how long the stone flew). So they are not a complete graphical representation of [math]\vec x(t)[/math], but a helpful visualization.

I could probably ask the same about your question. Anyways, - What I said is that a plot without a time coordinate still carries some information in 2+ dimensions (look at the plots, they tell you something about what is happening, right?). In 1D, the respective plot is always just a line segment which carries little to no information. So no one plots line segments. - I don't get your point about parametric equations. In 1D you describe a path as x(t), where x is a 1D vector. In 2D you describe a path as [math]\vec x(t)[/math] where [math]\vec x[/math] is a 2D vector (which also can be written as (x,y)(t) or (x(t),y(t)) or x(t), y(t) ). In 3D you describe a path as as [math]\vec x(t)[/math] where [math]\vec x[/math] is a 3D vector (which also can be written as (x,y,z)(t) or (x(t),y(t),z(t)) or x(t), y(t), z(t)). In other words: There's no difference, except for the dimensionality of the position vector. Hope that's more clear and helpful.

From the 2D and 3D plots, the motion can be understood rather well without a time coordinate. Try that with the 1D plot.

The time it takes the ball I throw to you to reach you depends on 1) it's speed and 2) the distance from the point at which I stood when I threw the ball and the point where you stand when you catch the ball. Where you stood when I threw the ball or where I stood when you caught it does not matter. Perhaps it helps your understanding to know that relativity is completely irrelevant for the point I am trying to make. My point is almost trivial. The reason why you are confused -and I only understood that after reading Swansont's comment which looked very strange at first- is that you are making additional assumptions that you do not mention and which are wrong. MAJOR EDIT/REWRITE: Goomadeed, ignore the above, I overread the bold part in your following statement There is two answers: 1) Light moves at c absolutely. That does not rule out that it moves at some other distance relative to some other moving object. That is the easy answer. And also the one above by Swansont. 2) Now the tricky part: Considering the light source as static and the objects as moving is somewhat arbitrary. Couldn't you just watch the scene from a different perspective where object 1 is static and the rest moves? Then, the light takes t1 = d1/c to reach object 1 where d1 is the distance of object 1 to the source. Or an angle where object 2 is static and the rest moves. You'd have t2=d2/c, then (the speed of light, c, is the same in both cases by definition). And since in your construction, in the perspective where the source is static, the distance of the source to the objects at the point of emission was equal, you'd expect d1=d2 and hence t1=t2. So obviously, a constant c is not possible by that reasoning. That was your reasoning, right? Problem is: the assumption that d1=d2 seems so obvious that you'd never question it (except if you already know Relativity, of course). But it's wrong. To allow for constant c you must allow that in different perspectives distances are measured differently. It gets worse: in relativity you allow that different perspectives measure time intervals differently (as a matter of fact, t1=t2 would indeed not mean that the light arrives at the two objects simultaneously). It gets even worse: relativity allows for distances and time intervals to convert into another. What might be 1 second for A could be 1.1 second and 100 kilometers from the perspective of B (except that the numbers probably don't match). This mixing is not completely arbitrary but well defined, its rules are the Lorentz transformations. You'll understand that I won't start explaining Relativity now (your example would be a very bad starting point anyways because it approaches it from the direction where it looks ridiculous) so just a few more or less random comments: * If you stay within my point 1) you get the correct result and you didn't need Relativity for it. * Unequal distances for seemingly the same ... "distance" ... seem completely ridiculous. There's two things to do about it (in my opinion): 1) accept that it's unintuitive but experimentally proven and live with it. 2) Learn Relativity by the math, not by examples and so-called "thought experiments". Physical Relativity is not intuitive so you can as well go with math which not intuitive but rigorous rather than so-called examples which are neither. I doubt that there's any other way to learn relativity than to learn the math, then develop an intuition for the math, then try applying to actual problems.

Relativity says that the light pulse travels at c, regardless of the motion of object 1 and object 2 (that's only expected: when I throw a ball towards you, why should the ball suddenly change its motion just because you start running?). It also tells you that the light pulse travels at c regardless of the motion of the source (that's the unexpected part which seems illogical to you because you're used to think that velocities did add up). It definitely does not say, that a light pulse takes the same time from A to B as it takes from A to C, regardless of A, B and C. In other words: since the two objects are not the same distance from the light source, a direct consequence of the light traveling at c is that is will not arrive at the same time.

I actually wouldn't be too surprised if your answers were pretty close to my previous ones (except for the post count obviously and the zero books per month maybe). Answer ">100 posts" probably should have been "<100 posts", btw.

I'd also advice spending more time on the writing. Professionals (i.e. people with more experience than you) spend weeks writing a publication - after having finished the work. Someone is going to read what you wrote (in the best case, at least) and you should not waste other people's time because you felt that working over your publication for the fourth time is boring.

For dark matter: The additional value is that the amount of god needed is specified and that god has some very simple properties (some mass density and an electric charge of zero). We have yet to figure an efficient mathematical structure that includes the god element. Or to phrase it differently: Scientists do a bit more than to look at an effect then say "that's because of XYZ". You are free to call this additional work (making the numbers match) worthless -some people who always hated math in school might even agree- but it's what makes it different. On the sociological side the advantages are somewhat more obvious: you're not risking eternal damnation for trying to picture dark matter or disagreeing with its prophets. EDIT: To be fair, the down-sides of the scientific approach should also be mentioned: "Dark matter did it" does not work as a generic answer to all questions .

For dark matter: The additional value is that the amount of god needed is specified and that god has some very simple properties (some mass density and an electric charge of zero). We have yet to figure an efficient mathematical structure that includes the god element. Or to phrase it differently: Scientists do a bit more than to look at an effect then say "that's because of XYZ". You are free to call this additional work (making the numbers match) worthless -some people who always hated math in school might even agree- but it's what makes it different. On the sociological side the advantages are somewhat more obvious: you're not risking eternal damnation for trying to picture dark matter or disagreeing with its prophets.

My sister was being told from the very beginning (though it's not so very clear what "the very beginning" is, given it turned out not to be the super important point that everyone bothered about all the time). It never was a real issue which I -from my experience, though- do not find too surprising, considering it's not a real issue. I can certainly understand that you're drawing that conclusion from your experiences. For me, combining it with mine, it's really just an additional argument to tell children from the very start. Let me comment on some semi-randomly picked statements of your post, too: I completely disagree with the inherent notion that only someone with a certain amount of gene-match can be considered part of the family (hell, some people even consider their dog being part of the family). Oh, I agree on the 2nd sentence. The point about being honest about adoption from the very start is that being adopted is natural from the very beginning then and that there's no reason for the adopted child to feel like an outsider. I also find it strange that you call your brother (in the sense that you legally have the same parents and probably were raised together) your half-brother; would never occur to me to call my sister that (even though technically she'd probably qualify as a quarter-sister). Is that due to the context of the thread (i.e. to emphasize that he's adopted) or is that what you normally label him?

What's "F" and "C", by the way? The standard thermo cryptography I know defines F as the free energy but I don't see how this would make sense in this context (where a natural choice seems to be F=0 for T=0).

I can't think of anything special happening. Mayhaps you'd approach the heat capacity of an ideal gas; assuming free practically non-interacting particles for [math]T\to \infty[/math] doesn't sound like the worst be to me (especially when no actual setup is provided). @Dalemiller: The letter you use to describe it is completely irrelevant. What's meant is the heat capacity, irrespective of whether volume of pressure is held constant. The background is that at zero temperature a tiny increase in energy can provide a significant increase in temperature, formally being a heat capacity of "infinity" (huh, sounds very scientific, doesn't it?). There's also no limit on temperature and the assumption that on some finite temperature the object's molecules "wiggle at c" is problematic (i.e. wrong) for several reasons, the simplest being that a molecule cannot move at c in the first place.

I am, therefore I exist.

1) The stuff responsible for an (accelerated) expansion is "dark energy" (provided it exists), not "dark matter" (which is supposed to be responsible for a different effect and arguably much more likely to exist). 2) The idea of taking into account the effect of mass on time is, to my knowledge (but I am not in the field), not so bad. In fact, about two years ago there was a colloquial talk at my university where the speaker was talking about exactly that. He threw away the standard assumption that the distribution of mass is homogeneous at the relevant length scales. I don't remember what he exactly did instead (probably something Monte-Carlo over a density distribution pushing experimental results through this filter) but he claimed that his results were compatible with the assumption that there is no dark matter. However: That sounds like a great result. And it has not become the standard argument, yet (as far as I know, at least). So it's probably not as easy as it sounds (though I definitely like the idea to replace the assumption of a homogeneous mass distribution with something better). I'll see if I can find the name of the speaker, but I doubt it. EDIT: Hah, we have an archive: Prof. David L. Wiltshire, University of Canterbury, Neuseeland, "Gravitational energy as dark energy: towards concordance cosmology without Lambda". And as a service: http://www2.phys.canterbury.ac.nz/~dlw24/universe/ EDIT2: Removed a comment since I figured out it wasn't the OP I was quoting.

There is a function giving 1 for x>=0 (or x>0, I am not sure if there is a standard definition because for the usual applications it doesn't matter) and 0 else. It's called "step function", I think and usually denoted by [math] \theta(x) [/math]. The function you are looking for would simply be [math] x \cdot \theta(x)[/math], then. Neither the absolute value nor the step function are linear functions, so I'd go as far as to say that they cannot be rewritten in terms of linear functions. Beyond that, I don't fully understand what you mean. It's obviously trivial to write a subroutine that serves as the functions you look for so it's probably not what you are looking for.

I think that is just a plot by Germany and Japan who want their top scientists back.

Of course popular science books can be educational - they just don't teach you science. You can still learn a lot of interesting anecdotes from them, probably even anecdotes about science or how other people do science. But people tend to mistake being told nice little anecdotes and comparisons as having understood the real science. There's a joke: A physicist and a businessman sit in a plane and figure they both read "A brief history of time" by Steven Hawking. The physicist says "oh, I really liked the book. but there's a few things I didn't quite understand". The businessman replies: "No problem. I'll explain them to you". (though perhaps it's only funny when you are a physicist and hang around on science forums) There is absolutely nothing wrong with reading popular science books. If you enjoy that, then go for it. You just sounded so damn serious about having to get the worlds best PhD and completely focusing on it that I thought you should know that the time you spend reading those books could technically be better invested in learning something real. For the record: I'd strongly advice going for what interests you, not what you think might benefit your career most. In Germany, the average school book lasts one or two years. How many do you expect to need per year? Not to mention that you could simply borrow one in your library or maybe ask in your school if they have one left over that they can borrow to you [same for university for more advanced stuff]. As a matter of fact: Perhaps you should ask you math and physics teacher about learning more advanced stuff for yourself. I think a good physics teacher should support such an endeavor (and also be able to gauge your skill - possibly better than you can yourself).

Hi MUTANT, welcome to sfn. There's a few points that are wrong in your post and I hope you don't mind me correcting them. - Neutrinos are not believed to travel faster than lightspeed. - The term "tachyon" simply means a particle with the property to travel faster than lightspeed so saying they do travel faster than the speed is somewhat redundant. There is no tachyon known to actually exist. In other words: It's a bit like saying that white horses with a single horn on the center of their head exist: unicorns. - Massless particles do travel at exactly lightspeed, not faster as you seem to assume.

I think claiming a successful invention before having actually built a working version may be premature. In practice, the step from theory to practice is larger than in theory .

No, that's not what I meant. What I meant is that you have no idea what alex is trying to discuss here.

I'd skip the pop-sci books - what are they supposed to be for? If it's just for fun then go ahead of course - it'll just not speed up your education. And there are pop-sci math books. I've read at least two myself (one named something like "Fermat's last theorem" and something about game theory - the latter completely sucked). Since money is not an issue, why don't you simply buy textbooks used in school levels or university levels above your current one? I definitely recommend something printed over something online. Getting a recommendation should be easy; just go to the appropriate institution and ask (or send a mail). If you feel bored with the stuff you currently learn in school and are interested in math/physics then I'd definitely like to encourage you to look into stuff beyond what you currently do. You are certainly not way over your head to go for learning something more advanced; but start with something slightly more advanced rather than trying to jump into research papers. As for reinforcing what you learned: At least for physics that is very easy: Get your hands on some exercises and try solving them. For low-level math that also works nicely.