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gizmo

Space-Time

Recommended Posts

gizmo

Here is an example if you're unfamiliar:

 

user posted image

 

Explanation

 

 

Click the link if you are confused by the picture.

 

 

I want to hear your opinions before I really say anything...

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Ravien

While this could be considered thread hijacking, since the OP didn't actually propose an idea or pose a question, I thought I would throw something out there.

 

I'm no physicist or mathematician, but I read in one of these threads that K^2 is, so perhaps he could help me understand this new paper I just read that proposes a unified theory of everything. Here's the abstract:

 

 

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.

 

And here's the actual paper for those who might be able to decipher it: Link to PDF

 

I get that it is unifying all quantum field physics and gravity in E8 248 point geometry, and in doing so opens up the potential for a Particle "table of elements" with many currently blank spots to be filled by further inquiry. But what I don't get is the layman's conceptualization of how this geometry of the universe gives rise to quantum effects. There's just too much high level maths being bandied about that is all greek to me, so if someone could explain the ramifications of this theory in english, that'd be cool. An explanation similar to the OP's linked image is an elegant way to convey space-time curvature, much as a wave-function is an elegant way of conveying quantum effects. String theory, despite being purely mathematical masturbation, also had a similarly elegant visualization which helped the laymen like myself to conceptualize it and understand the rudiments of it. So I guess I'd like a similarly elegant visualization of how this E8 geometry creates both space-time curvature and quantumness (not a word, I know tounge.gif ).

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gizmo

I read your post while listening to music and completely confused the f*ck out of myself.

 

But, I somewhat grasp the idea of space-time I want more info on it and thought some of the more intellectual people on this site might have some information towards it. I somewhat have a theory of traveling across the bent, curved plane of space-time but I want more info before I put out my theory and possibly make myself look like an idiot, haha.

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K^2

Ravien, I don't think this new geometry will work with QM. It still uses the conventional 4-space, and there are fundamental problems with it. QM is defined in relation to an absolute time-parameter, which contradicts one of the premises of General Relativity in a rather bad way. But of course, if this new geometry naturally gives rise to SU2 and SU3 sub-sets, it is worth looking into. I'll read the article when I'll have a little more time.

 

I am currently working on re-writing the General Relativity in a new framework which should consistently allow for both the principles of GR and to set up a wave equation that I already know to go to Dirac's eqation in the flat-space-time limit. I believe that equation to be the fundamental equation of Quantum Mechanics in curved space-time as well, but I'll have hard time proving it if I can't find an experiment that can be evaluated using such model.

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Ravien

Well in my opinion, since absolutely everything that can ever be observed on any meaningful scale (larger than quantum) can be described completely in 4-dimensions, then the additional dimensions which have been added whenever someone encounters coordinates with weird properties are crutches used to cover up mathematical weaknesses. Either they make up new dimensions, or introduce super-symmetry and have a fermion for every boson. But E8 has the unique property that the adjoint action of a subgroup is the fundamental subgroup action on other parts of the group. So both the fermions and gauge fields can be arranged in the Lie algebra and root diagram of a single group. It doesn't need more than 4 dimensions. This is hardly a weakness.

 

It's just messy for the universe to have dozens of special case dimensions for a few exceptions at the quantum level while it also has 4 super-ordinate and consistent dimensions for absolutely everything all the time. It seems far, far more likely that these extra special case dimensions are just the result of shoddy maths than they are the result of a shoddy universe.

 

If a single theory can unify GR and QM using only 4-space, then I'd have to say that's easily the most elegant and solution, and one Occam's Razor would approve of.

 

As for QM being defined by absolute time and GR having relative time, something has to give. Both cannot be true, unless there really are two completely different sets of rules for reality at different scales, which I think any scientist would agree is pretty unlikely. Since relative time has been irrefutably shown experimentally, and absolute time is merely a requirement for certain QM maths to be right, I'm erring on the side of absolute time being a crutch for incomplete QM understanding. At the end of the day, QM has to work with GR. There is only one reality.

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K^2

There is actually a pretty good explanation for extra dimensions that cannot be observed. If these dimensions are closed and are "small" compared to observable dimensions, it is expected that we would not observe them. It is the same as viewing a piece of string. On large scale, it can be considered 1D, while it is truly 3D when you get down to it. So it very well may be that our universe has more than 4 dimensions on the very fundamental level. But I agree, whatever we come up with must be possible to translate into equations that require only 4 dimensions, even if these equations are not quite as elegant. The equations I am considering do have such a property. Once I have the transformations worked out, I will be able to record the QM equations using only the 4 dimensions of GR. The trouble is that these equations will no longer be linear, which is something that you really want in QM. In the end, I would expect the equations with extra dimensions to be more useful simply because the math will be easier. Whether or not this has anything to do with how universe really works doesn't really matter. We will have equations that work in both cases, and whether you want to count the higher dimensions as reflections of true nature of universe or just a math trick, doesn't really matter.

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