timo

I don´t really get what you´re doing but maybe this helps: You seem to map (B,C) -> Z and want the inverse Z -> (B,C). As the number of combinations (B,C) |{(B,C)}| is about 1 million while |{Z}| = 1001 the map (B, C) -> cannot be injective. Therefore it cannot be bijective. In the case that Z is not limited to an integer in the range of 0-999 (1000 elements is easier to talk about and the extension to 1001 is not too hard) but to 1 milion elements, a bijection can be made rather easily by: (B, C) -> Z = 1000*B + C with the reverse Z -> (B, C) = (Z div 1000, Z mod 1000).

There are no boundaries of the universe (at least in mainstream physics). "The universe expands" means that the distance between two points in space increases with time. Consider the plane {(x,y) : x,y real}. This plane is infinite. Let the distance between two points P1=(a,b) and P2=(c,d) be defined by d(P1, P2) = t*sqrt[(a-c)² + (b-d)²]. The distance between those two fixed points increases as the time t increases. Therefore one could argue that the plane expands. Also, the distance between any two point is zero at t=0 (which is the big bang, then). But the plane still doesn´t have any boundaries. If you want to have an example of an expanding finite space without boundaries take a sphere with radius time.

One reason why no information should propagate faster than light is causality. Two events are considered causally connected if there is a non-spacelike (no faster than light contributiuons) connection curve between them. The interesting feature about those causally connected events is that they will have the same time ordering in any coordinate system (except under time-reversal, of course). Therefore, distinguishing "cause" and "effect" makes sense as the cause will always come before the effect. When nothing can propagate faster than light, all efects will have causally connected causes. If you allow for ftl propagation, you can have effects with non-causally connected causes. In this case you can find a coordinate system in which the effect happens before the cause which is weird, at least. Distinguishing cause and effect is not an invariant (under coordinate transformations) statement anymore. And invariant statements are kind of a holy cow in a physics which states that all coordinate systems are equaly correct.

[math] \begin{array}{rcl} a &=& b + c \\ &=& (b + d) - (d-c) \end{array} [/math] Source: \begin{array}{rcl} a &=& b + c \\ &=& (b + d) - (d-c) \end{array} Your answers look good. Especially part b) which gives the classical result as one would expect at such low velocities.

Or you could place a mirror close to the sun, send a beam of light there and have it reflected back to a point about 10 meters from you. After you send out the ray you calmly walk over to this point and wait for the light to arrive. It´s ftl travel in the exactly same sense. Only disadvantage here is, that many people in this forum won´t consider it scientific enough as it uses neither multiple dimensions nor exotic matter nor magnetotachyonic stringgravity fluctuations.

I do not understand the following statement: I also didn´t get the connection to string theory but this might simply be because my knowledge about it is very limited (nonexistent might fit better).

I think so, yes. A base always spans the space as being a base implies that each vector can be written as a linear combination of the base vectors. But you could have a set of vectors spanning the space which are not a base (if you were given a 4th vector, for example).

It´s a base for P_2 so it spans P_2.

I do not really understand why you added the zeroes in an additional collumn. Simply wrinting p1, p2 and p3 in a matrix and taking the determinant would have been enough. For b: What you are looking for is a set of coefficients a, b, c which satisfy a*p1 + b*p2 + c*p3 = 1 + 1t + 1t². The solution should be straightforward. EDIT: I can only guess what you did to solve b so I cannot comment much on it. I think you solved the equation system I mentioned above so unless you did some error in the computing it should be correct. Just plug your coefficients to the equation above and check if your results are correct.

Which directly leads me to the point why I was a bit disappointed about this thread: Why didn´t YOU say how you derived your result? I mean: It´s ok if you ask for help on homework and it´s great that you already have some results and just want them checked. But for the future (or here, "I used length contraction" is quite a lose description of how you derived your numbers) it would be great if you´d add the steps that led you to your results. Imho there are a lot of people in this forum who can tell you if your calculations are correct with just one look at your steps. But I´m not sure if all of them want to search for a pocket calculator just for a "your numbers are correct/incorrect" answer. At least, I don´t want to (and I wouldn´t even know where my calc is ). You have to multiply one of the lengths by the length contraction factor and divide the other one by it. Dunno if your numbers are correct.

Also, a hypoglycaemy (lack of glucose) is much more dangerous (you can fall unconcious which alone is a life threatening state) than a hyperglycaemy (excess of gloucose; you get nervous, the veins are damaged in the long run).

^^ It´s either "ich bin eine Nase" (I am a nose) or "ich bin ein Hase" (I´m a rabbit)

What do you think would be the implications for string theory if a supersymmetric theory is proven?

I do not know what your infinite sum is supposed to be. A complex number z can be written as z = a+bi = r*exp(it), r>=0 (radius), 0<=t<pi (angle), r and t being reals. Multiplication of two complex numbers in the latter representation then is z1 * z2 = r1*exp(it1) * r2*exp(it2) = r1*r2*exp(i(t1+t2)). Therefore z^n = r^n * exp(int). And the n-th root of a complex number is all complex numbers z' = r' exp(it') for which r'^n = r (only one solution due to restrictions r'>=0, real) and exp(int')=exp(it) (n solutions due to periodicity of exp(ix) and restriction 0<=t'<2pi). The angle-part is the one dave mentioned (|z|=1 <=> r=1). EDIT: No, it isn´t. I didn´t read carefully enough. Dave mentioned z=1, not |z| = 1. You have to add a "t/n" summand to the phase in Dave´s solutions to go from z=1 to |z|=1. Nevertheless, the point is: Find n angles t' for which n*t' mod 2pi = t. Sidenote: The sum of all n-th roots of a complex number must be equal to zero for n>1 due to symmetry arguments, anyways.

a) very bad title for your thread b) how´s "gravitational field" defined in your class? c) gravitational force is given by F = G*m1*m2/d² with d=900 km, m1 being mass of the earth and m2 being mass of the astronaut. Neither m1 nor m2 nor G is zero. Hence, F is non-zero. If the answer to b) was "there is no force due to gravity", then you´ve got your answer. d) although it isn´t asked for (teachers tend to demand answers that aren´t asked for explicitely): The astronaut experiences weightlessness because gravitational force and centrifugal force cancel out.

I think it´s kind of funny that in the german press it was said that they were accused of robbery, drinking alcohol and "sexually attacking" (in lack of a better translation) a 13 year old boy, not of having sex with each other.

They are not. However, a neutron can decay to proton + electron + antineutrino.

You are probably talking about Hydrogen Fuel Cells which run on (big surprise) hydrogen which reacts with oxygen and leaves water as an exhaust gas. You certainly picked the wrong subforum for such a question. It´s rather engineering or perhaps chemistry but certainly not modern theoretical physics where your thread fits in.

Sidenote first: "invents the planets" sounds quite funny I do not know who named Pluto. Neither do I know why the name Pluto was chosen. Nevertheless, according to wikipedia Pluto is a god: http://en.wikipedia.org/wiki/Pluto EDIT: Had I read the 2nd line of the link I just posted, I had read that Pluto is named after this god. I tend to believe wikipedia more than physics teachers (mainly because I know of the quality of their education and their average competence ).

In many languages (ok, I can only say that for french and german) objects which are genderless in english do have a genderspecific pronoun. In french all objects are either male of female. The genders of objects vary from language to language. But in case of the planets I´d think they have gender of the god(ess) they are named after. At least in german it´s: Mercury : Male Venus : Female Earth : Female (ok, not a godess) Mars : Male Jupiter: Male Saturn: Male Urrectum: Male Neptune: Male Pluto: Male

Your political compass Economic Left/Right: -1.25 Social Libertarian/Authoritarian: -3.85

Nice drawings. I really like those more than those unpersonal computer generated ones.

http://en.wikipedia.org/wiki/Higgs_Boson ^^ now, that wasn´t too hard, was it? The Higgs field is part of the so-called "standard model of elementary particle physics" (SM). This field is nessecary to allow massive (mass-like term in the lagrangian) exchange particles like the Z boson without violating "gauge invariance" which is a fundamental assumption of the SM. As those massive exchange particles have been observed either the Higgs field must exist or the SM, which stood every experimental test very well so far, is flawed. The Higgs has not been found experimentally, yet. But a lot of people believe that the chances of finding it at the "Large Hadron Collider"(LHC) experiment are extremely good. Afaik, finding the Higgs was even the main reason to build LHC.

Insurance companies tend to base their fees on statistics. So I´d say: Yes, it´s either the non-representative sample of the people you know or your insufficuently objective perception. Oh, and: It´s not nessecarily the rest of the world that´s different from the people you know. Only the area where the respective insurance company operates in (at this point wanted to guess that you´re from the US but I figured out it´s actually written in your profile ).

[math] 3*10^{-30} g/cm^3 [/math] You could just take any point as r=0, that´s not the problem. The prob is that the equation you want to use is only valid for a special metric in a special coordinate system. You could as well try to solve the Kepler problem by saying "hey, I know gravitational force in Newtonian mechanics is F = m*g, g = (0, 0, -9.81)m/s²". Try "Robertson-Walker metric" and "Friedmann universes" for cosmological predictions of GR. What do you mean by "an equation which only uses density" ? EDIT: Oh, and the equations for the effect of mass on spacetime are called "Einstein equations".