Recent content by kakaz

Yes exactly - it is the same. So it is vary strange, because such situation, requires some very precise relation for mater and energy of Universe to follow. It is amazing coincidence to be seen in reality. So it is very strange...

That is good point! At least locally: YES. So for small distances and not very large mases and energies, our universe is Euclidean. But there is other one point of view we may say the same: at cosmological scales, there is doubt if our universe is expanding ( hyperbolic geometry) or...

I will not agree. Nature choose some kind of space-time as flat. When there is no matter, no energy, no other disturbances, then there is an Euclidean metric - and obviously that is the choice. Why? I do not know: but I assume that answer would be interesting... In mathematics Euclidean...

I understand. In 3-dimensional space, there are 2 different families of representation od SO(3) - gerenal group of rotation. One family has spin which is natural number whils second one family has multiplicity of 1/2. This is mathematics, not physics. Question of Your friend may be, rephrased...

I will wrote for You once more what I wrote last time: You do not have any forces in order to have pressure in system. You push with some force system with fermion particles. You want to lover of volume in such gas for example. But as the whole energetic states are occupied, then after You...

Ha! This is the Question! If You think about curved spacetime in GR Theory, Then You will see that Euclidean metric is flat. It is not by taking other spaces/metrics relative to Euclidean, but it is somehow real thing: differential of x^2 is linear function with constant coefficients (...

Ok, now I accept. Sorry for disturbing. Of course You may suppose whatever You like about Platonism. But Gödel theorem refer to systems with countable number of axioms. It has also form first level theory which is rather limitation in context of whole Platonism. relation between Platonism and...

I cannot catch the point: why unproved statements has to lead to contradictions? The meaning of Goedel theorem is quite opposite: You may state whatever You like, about Your Unprovable Theorem of Choice, for example that is is true or false and You always find model in which Your Choice will...

So maybe I ask once more, with better defined question: Do You know any database of finite presented structures, like algebras, groups, monoids etc. when I may look for my structure in order to check if someone else use it in other than my situation? There are some databases in the wild: huge...

There is general theory: theory of metric spaces, where You may assume that metric, that is the mathematical form used for measuring distances is general, function of Your choice. Function may be treated as metric if has following properties: \rho(A,B)>0 \rho(A,B) = 0 \iff A =B...

Reality is stranger than fiction ;-) So let's begin with some hints. As You've may seen, fermions has spin which is multiple of 1/2, whilst bosons has spin given by natural numbers. What is that mean? When You consider wavefunction of composed system which consists of many particles ( bosons...

Maxima gives me following eigenvalues for Your matrix: [[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]] First vector are eigenvalues, second one - multiplicity.

You may compute covariant derivative for any covarinat tensor, and in this case for A_i. As expressions are in spherical coordinate system then subscript i must agree with names of coordinates, so then i \in {r,\theta, \phi}. You may treat it as usual as with {x,y,z} . The proper use of...

Good observation! Of course in typical situation, You have right: You do not need any additional element other than generators of a group. But in my situation there is a strange and interesting gain when I add L: as I wrote every element of R[M] may be expressed as : Z = aI + bS +cT +dL * I...

Structure You describe is very general, but it also is algebra. So probably You should ask for software which works in general algebra and finds ( construct is probably better word) solutions. I assume that You know some algorithms for solving equations You show? If Yes, You probably may...