AlphaNumeric

Told you this would happen

Classically, like Newtonian dynamics, has angular momentum obeying the equation [math][L_{i},L_{j}] = \epsilon_{ijk}L_{k}[/math]. Quantum spin obeys the equation [math][s_{i},S_{j}] = \epsilon_{ijk}S_{k}[/math]. So they have the same mathematical form and so they are called 'spin' in both cases. I doubt you recognise the equations I've just posted, but I don't have time to explain them.

But given you don't want any kind of indepth answer and all you want is a yes or a no, your project is going to be pretty crap. You don't enter into a discussion, you just ask the same question again and again. Also, no school project is going to involve giving you a highly complex, very mathematical, topic like closed time-like curves. Guest gave you a formal definition of closed time-like curves on SciForums and you don't understand it. All your posts just ask the same thing. You are not making any attempt to do the research yourself and if you did, it would be completely over your head. You don't understand that closed time-like curves are not related to antimatter (antimatter doesn't require curved space-time) and you will no doubt ask another inane question on that. Basically, if this is your method of doing school projects I imagine you're pretty crap at science.

We gave you the answers on both forums. You asked hundreds of times the same question. Initially you get answers which were indepth, because a simple yes or no isn't enough, but you continued asking again and again and eventually, after the dozens of threads you started, we got tired of your display of ignorance and unwillingness to accept the answers and you got banned. And they haven't given straight forward answers here, they have said "Depends" and "We're not entirely sure". Why are you obsessed so much with ctcs?

Just to let everyone know, ps3 is known as Wolv1 on SciForums and Deuce2 on PhysOrg. Myself and the posts known as Rpenner and Prometheuse (on PhysOrg) and BenTheMan (a mod on Sciforums and a poster on PhysOrg) have all answered the thread starters questions multiple times. He just asks the same questions again and again and again. He was banned from SciForums for repeatedly ignoring the answers we provided and spamming several people's PM boxs with the same questions. The aforementioned people are either physics graduates or current postgraduates, so it's not like he's asking questions to people who don't know. He will continue to ask these questions and I'm willing to be he's already PM'd a few of you. Don't bother replying, he'll just ask the same question rephrased again and again. We can't work out why he's got such an obsession with it.

An email was forwarded to my department 2 or 3 days ago containing a link to an LHC guy's presentation about the damage and it said that the collider will be offline till after 2009. So that means it won't be up and running for about another 15 months

But technically our theories never predicted infinities, the "Oh, we've got to renormalise this system" procedure means divergent quantities are a step on the path to the actual quantum field theory predictions, which are not infinite. It's fair to say (though it is somewhat of an assumption) that Nature is consistent, not 'it removes infinities' or however you wish to phrase it. When you work through the field theory calculations and end up get you prediction, you shouldn't have had to deal with actual infinities, just large finite quantities. [math]\infty - \infty[/math] is not something which appears in quantum field theory but you do get [math]\left( \frac{A}{\epsilon} + B + C\epsilon + \ldots \right) - \frac{A}{\epsilon}[/math] for [math]1>>\epsilon>0[/math]. The [math]\epsilon>0[/math] condition means your algebraic manipulation is well defined and then you take the limit [math]\epsilon \to 0[/math] after you've done that. String theory takes a step towards not even having to consider these divergent quantities because, at least on heuristic grounds, it doesn't have the same UV behaviour as particle based theories. With scattering processes described by Feynman diagrams which are now 2 dimensional Riemannian surfaces, not branched graphs, there is no frame independent notion of an interaction point in space-time between two strings. The worldsheet 'smooths' this interaction out over a region (well, that's somewhat of an arm wavey description but the technicalities aren't important), removing the divergent quantities which might be seen as 'embarrassing infinities'.

The proof claims that x^p + y^p can be divided by (x+y) to give an integer. That's clearly false. x=3, y=4, z=5 are pairwise coprime and p=2 gives 3^2 + 4^2 = 5^2 but x+y = 7 and clearly 7 doesn't go into 5^2. Therefore the logic employed in the first paragraph is wrong and kills the 'proof'.

Perhaps you can try to say that again. This time think before you type so that your post is coherent.

I was going for elementary particles only (or what we currently think are elementary). There's tons of bound states of matter and it's antimatter versions, some we call particular particles, others are a little more open to opinion like positronium, the bound state of an electron and a positron. Unstable obviously. Fair point. I'm familiar with Weyl/Dirac representations etc but I've never used them in regards to the neutrino, only within SUSY string constructions and that's a little departed from considering the phenomenology of the particles.

Axioms : 1. a + (-a) = 0 for all a 2. a*(b+c) = a*b + a*c for all a,b,c 3. 1*a = a for all a We have that (1+(-1)) = 0 by axiom 1 therefore (1+(-1))*(1+(-1)) = 0 1*(1+(-1)) + (-1)*(1+(-1)) = 0 by axiom 2 1+(-1) + (-1)*1 + (-1)*(-1) = 0 by axiom 2 and 3 (0) + (-1) + (-1)*(-1) = 0 by axioms 1 and 3 -1 + (-1)*(-1) = 0 +1 + (-1) +(-1)*(-1) = +1 0 + (-1)*(-1) = 1 (-1)*(-1) = 1 Therefore minus * minus = plus , from the general axioms you get in things like rings and fields.

Except that axes are 1 dimensional entities and if you made them complex numbers then they would have to be 2 dimensional! So you would have to plot a 4 dimensional graph, because your axes would become 2 dimensional planes. This is why it's often so much more difficult to do complex analysis, it's hard to conceptualise the extra degrees of freedom.

I really don't like that. Yes, it's a nice way of viewing extensions of our space-time but the way those links extend space-time is not how string theorists do it or anyone else who works in extra dimensions. The extra dimensions are curled up and small but strings still move through those spaces like we move through the space we see. I think you are making reference to Godel's work incorrectly. In mathematics, pre-Godel it was thought that any statement which can be constructed within some logic system would be either provable or falsifiable. Godel proved that there's always constructable statements which can be true but it is not possible to prove so, hence the label 'undecidable'. In maths you are given all your axioms and you work from there. You know the rules of the game. In physics it's a different story. You are trying to discover the rules of the game. And no number of tests can prove that you've deduced a particular rule correctly, only increase your confidence you're at least close to the 'real' rule. You can never prove there isn't some additional caveat in Nature which will result in your rule not being completely squared with Nature. For instance, quantum field theories were developed in the 1930s initially and people saw that Nature obeys a particular rule, there was no CP violation (see Wiki if you don't know what I mean). Loads of tests on on QED, no CP violation. Physicists said "Nature is invariant under CP symmetry". More tests done. No problems. Then in the 60s someone saw that the weak force didn't obey that symmetry. The caveat was found and the rule this shown to be not universally true. That is why there's a "It's not a proven fact" methodology in physics. There's no 'The Rules Manual' to check.

You would have to generate the entire matrix A first. Let B = A^2, then [math]B_{ij} = \sum_{k} A_{ik}A_{kj}[/math] so to know say the entry in the first row and first column of B, ie [math]B_{11}[/math] you need to know the entirety of the first row and first column in A. Clearly if you only know the [math]A_{11}[/math] entry in A you cannot compute [math]B_{11}[/math]. Unless you are doing HUGE, and I mean where n > 1000, matrices, just doing A first and then doing B won't take you long. I've run Mathematica routines which do a coordinate transformation on a rank 3 tensor in 12 dimensions (so there's [math]12^{3} = 1728[/math] entries in the tensor and each one is the result of summing together 12 products of matrix multiplication) and on a 2.4Ghz machine it takes seconds. So if you're doing anything which decent sized matrices, just do the routine again with [math]B_{ij} = \sum_{k} A_{ik}A_{kj}[/math] in the middle of the two Do loops.

Except that P and C are not 'symmetry' and 'antisymmetry', they are 'parity' and 'charge' and relate to how you could consider a system with it's chirality swapped or matter exchanged with antimatter and see if the evolution is analogous to the original system. As was discovered in the 1960s, doing both of these and considering weak decay processes results in a different time evolution from the original weak decay system.