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Sorry but is is looking that way. Also, if you want to discuss ideas about the aether and extensions of relativity etc. I am happy to do so. However, I refuse to get involved with any rant about the moderators and how they are like the church and you are like Galileo.

You mean in the "pseudoscience and speculations section" or as a class of theories that predict gravitational birefringence? To the first one, no they solidly belong in the modern physics section. To the second part, I guess they do as QED on a curved space-time is a low energy limit of string theory.

That is a problem. In any canonical approach one needs to cut space-time into space and time. This is the origin of the problem. Time usually plays a distinguished role. Even in quantum mechanics, time is not a hermitian operator. That is why path-integrals are the best way to proceed with a relativistic quantum field theory. Something related you might be interested in is multisymplectic geometry. It is the geometric setting for covariant Hamiltonian field theory. The idea being to formulate a classical theory with does not use the space-time cut. However, as far as I know due to the issues with Poisson brackets no canonical or deformation quantisation procedure exists.

You mean the underlying space(-time) is continuous? (usually a manifold). Then yes. Yes, ok. Discrete as in a discrete set (a set with the discrete topology)? Things like causal set theory live in the category of sets. (Avoid calling collections of "theories" a category. A category has specific meanings and I am not sure if these collections are categories) You can leave the category of sets completely and have "point-less geometry". Noncommutative differential geometry is of this kind. I honestly don't know where LQG sits. There are people here who know more about it than I. Don't know. Martin will refresh our memories.

Special and General relativity would presumably break down at that so of scale. Quantum gravity effects would become important. So you question is good and is a big question in research right now. Riogho is indeed correct, people do consider a version of special relativity with a fundamental minimum length called double special relativity.

10th grade, that make you 15/16? I guess you are after more of a popular science account? My be the books by Hawking? If you are looking for a text book I don't know what to recommend. Can't say I have found a book on special relativity that I like.

Rights to do what?

Is there any need for a classical aether? Relativity and quantum field theory don't seem to need it. Wouldn't trying to reintroduce it make things more complicated than needed? As far as I can tell, any modern papers discussing the effects of the classical aether tend to be flawed and as such not many people take the idea seriously. Things like Gasperini's scalar field or Jacobson and Mattingly's vector are as you said different. They are used to give a preferred direction in general relativity and break local Lorentz symmetry, but keep Einstein invariance (Diff M). To me these ideas seem more natural to investigate than a classical aether, at least we can understand the geometric objects involved.

That a joint degree in mathematics and biology? If so that would put you in a good position to mathematical biology stuff such as evolutionary biology as you stated. The biologists I personally know are very ignorant of mathematics.

This has been posted on other forums in exactly the same way.

I picked physics and mathematics; I currently hold 2 physics degrees and will finish PhD in mathematics soon.

Isn't that almost how we view it anyway? You should look up the idea of inflation.

1d is a path on a space. It is not necessarily "straight". See my other post. This is the correct way to describe a a "particle moves". (see also world-line) Two dimensional "objects" can be locally represented in a "graph" as you put it. Not always can you describe the whole object in one go in one graph. Same holds for 3d, or any d. (manifolds can always be seen as subspaces of some large dimensional flat Euclidean space. However, we usually like to discuss them in their own right and think about intrinsic properties of them) Space, our space is 3d right? You can walk right/left, forwards/backwards and then you can go up/down (use stairs or a lift for that one!). Space-time is then considered as 4d. But you should not really confuse the extra dimension with the time an actual observer measures. It is a little more involved than that.

Fourier series of periodic waves. Wavlets. Orthonormal basis on [math]L^{2}[/math] spaces (Hilbert spaces). (Bäcklund transformation transformations in soliton theory?) So, there is no problem decomposing waves into a "series" of infinite "basic" waves.

DH is absolutely right on this one. A line is not a fractal, but it is kind-of self-similar. (We need a metric I think to discuss this properly). A fractal is defined to be a metric space that has Hausdorff dimension strictly greater than it's topological dimension. Hausdorff dimension is a measure theoretic construction. I really suck at measure theory so you will have to read up on that yourself. But what I can say is that for Euclidean spaces [math]\mathbb{R}^{n}[/math] both the topological dimension and the Hausdorff dimension are equal to [math]n[/math] and so cannot be fractals.

I'd hate to try to explain my research to a journalist, even a well meaning one! I am interested in the idea of presenting research to the public as they fund a lot of good work. It is only right that we prove to them it is money well spent. No idea how I would explain my work in a meaningful way to almost anyone who does not work in the same field or something similar.

A particle is by definition 0D. Mechanics is really the study of paths in some configuration/phase/or other space. These paths are parametrised (usually, but not always) by [math]\tau[/math] which sometimes, but not always has the interpretation as time. To me more concrete, consider standard (conservative) Hamiltonian mechanics with phase space [math]T^{*}M[/math] which has natural local coordinates [math]\{q^{a}, p_{a} \}[/math]. A curve/path [math]\gamma[/math] is a map from [math]\mathbb{R}[/math] to [math]T^{*}M[/math]. If we give [math]\mathbb{R}[/math] the local coordinate [math]\{ \tau \}[/math] then a path is described (locally at least) by [math]\gamma : \mathbb{R} \rightarrow T^{*}M[/math] [math] \tau \mapsto \{q^{a}(\tau), p_{a}(\tau) \}[/math] This path is then interpreted as the trajectory of a particle in phase-space. The parameter [math]\tau[/math] is interpreted as time. I don't think we have the machinery need to continue yet; we need to understand vector fields, differential forms, Lie derivatives... What I will say is that in relativity a similar thing happens. The difference here is that [math]\tau[/math] can be interpreted as the proper time for a massive particle only. For massless particles it is "just" some parameter. To me, when doing mechanics anyway time is just a parameter that describes curves in some space. The physical interpretation (if there is a meaningful one) comes later.

Only you can decide that. I am not very familiar with either. So talk to the lectures involved?

"string theory" would be the encapsulating theory of strings, both bosonic, fermionic and super (both fermionic and bosonic). Not that I ever hear much about pure fermionic strings.

I wonder if you are mixing the ideas of a particle (0D) and it's phase-space? (or something similar like configuration space) Look up phase-spaces, and in particular how to do non-autonomous mechanics in double extended phase-space. In this set up energy (Hamiltonian) becomes another coordinate "dual" to time. So we have a space with local coordinates {q,p,t,-H} (minus H for a reason, but I forget). You can then formulate geometric mechanics on this space via symplectic geometry. (For those that know, contact geometry (extended phase-space) can also be used for non-autonomous mechanics, here we have the local coordinates {q,p,t} which is of odd dimensions. I rather use double extended, as we have a symplectic structure.) This is the closest thing I can think of to what you have been trying to say.

The ideas of space-time being birefringent is definitely not a new idea. It has been discussed in the context of QED on curved space-times by Shore and Hollowood recently, but the idea is older than that. There may well be other theories (LQG?) that also exhibit this phenomena. (I know Shore and Hollowood, they are to be trusted.) Multidimensional time has also been discussed in the literature. I am much less familiar with this I believe string theory "suggests" 2T physics (?) So Zephir, if you want to discuss any thing specific in a context of a theory we know (or a slight generalisation) then as swansont has said point us in the right direction with a reference or two. Also it is usually bad practice to compare yourself with a famous physicist/mathematician unless you really do have something in common with them. A sure fire way to spot a crack-pot is via him saying "like Einstein I... " or similar.

Please do so... Lorentz violation is interesting. Please formulate your ideas so we can understand and make comments.

really? Because I thought you could do a Fourier decomposition. Oh, wait, yes you can! ??????

Leave it out Zephir. We like to work within the set (category?) of accepted physics. You can of course push this, but only in a consistent way. Unless you can do this use another forum or post in the speculation section.

Ok, so what does axis/dimensions/directions (whatever) interacting mean? I am very unclear on this. Unless you simply mean it takes two numbers to (at least locally) to describe points on a 2D (topological) space? (As an aside, people don't talk about axis in geometry. Picking local coordinates is fine and probably what you really mean. Also, complex has a very specific meaning, so again I would avoid that term.)