Grounding the Kaluza-Klein Fifth Dimension in Reality

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby Yablon » Wed Jun 06, 2018 7:36 am

Dear SPF Friends:

A couple of weeks ago I posted a document comparing my recent research on hyper-canonical electrodynamics with Kaluza-Klein theory. I soon realized that what I learned from this earlier research could actually be use to "fix" all of the problems which have dogged Kaluza-Klein theory for a year short of a century, while maintaining the still-formidable benefits of placing Lorentz Force motion and the Maxwell Stress-Energy on a purely-geometrodynamic footing and possibly understanding the fifth dimension as a matter dimension.

At https://jayryablon.files.wordpress.com/ ... -klein.pdf you may download the complete first draft of a paper to memorialize this recent research. I have developed this to stand alone, entirely independent from my other recent paper. At 22 pages this is a short paper, for me. I am thinking about submitting this research for peer review in the near term ahead of my other paper, because it can be assimilated much more quickly and with a lot less study time.

Accordingly, I would very much appreciate any public or private comments or suggestions you can provide. If you private, send to yablon@alum.mit.edu.

Thank you,

Jay
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby lkcl » Sun Jun 10, 2018 3:47 am

jay, hi,

it was a long, long time ago that i tried to envision what 4D, 5D or 6D would look like, and i came up with the very simple idea that:

* to visualise 4D you would have a circle at every point in 3D space.

* to visualise 6D you would have a *sphere* at every point in 3D space. another 3D at every 3D point.

ironically i did not actually explore 5D, visually, but a "cylinder at every point in space" would make sense, geometrically.

i invite you to consider another possible geometric shape at every 3D point: a poincare sphere (there is a reason for that, which i will go into in a minute). imagine that at every 3D point, matter may also have 2 "angles": theta and phi. this would give us 5 dimensions.

question: what would give the *impression* that there were 5 dimensions... whilst in fact there were actually only 3? well, if light could get itself gravitationally and electro-magnetically trapped into extremely tight self-standing-wave patterns, that would do it, would it not? the photon would, on its circular loop (of radius equal to the compton wavelength) put out current-loops in a spherical pattern, but *only* on a spherical pattern (hence the addition of the 2D not 3).

i'd be interested to hear your thoughts on that.
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby lkcl » Sun Jun 10, 2018 5:04 am

from wikipedia:

Kaluza's original hypothesis was purely classical and extended discoveries of general relativity. By the time of Klein's contribution, the discoveries of Heisenberg, Schrödinger, and de Broglie were receiving a lot of attention. Klein's Nature paper [4] suggested that the fifth dimension is closed and periodic, and that the identification of electric charge with motion in the fifth dimension be interpreted as standing waves of wavelength {\displaystyle \lambda ^{5}} \lambda ^{5}, much like the electrons around a nucleus in the Bohr model of the atom.


it is not a coincidence that in dr randall mill's theory, the definition of a particle is that a photon is trapped in a circularly standing-wave pattern with itself.
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby lkcl » Sun Jun 10, 2018 9:17 pm

lkcl wrote:it is not a coincidence that in dr randall mill's theory, the definition of a particle is that a photon is trapped in a circularly standing-wave pattern with itself.


correction/clarification: *elliptically-polarised* photon trapped in a circular standing-wave pattern with itself where the current-loops go out at right-angles (obviously) and form a perfect sphere. still all "1 extra dimension" as far as "loops" are concerned though. still matches with the "cylinder" thing. which is absolutely fascinating.
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby Yablon » Wed Jun 13, 2018 7:52 pm

lkcl wrote:from wikipedia:

Kaluza's original hypothesis was purely classical and extended discoveries of general relativity. By the time of Klein's contribution, the discoveries of Heisenberg, Schrödinger, and de Broglie were receiving a lot of attention. Klein's Nature paper [4] suggested that the fifth dimension is closed and periodic, and that the identification of electric charge with motion in the fifth dimension be interpreted as standing waves of wavelength {\displaystyle \lambda ^{5}} \lambda ^{5}, much like the electrons around a nucleus in the Bohr model of the atom.


it is not a coincidence that in dr randall mill's theory, the definition of a particle is that a photon is trapped in a circularly standing-wave pattern with itself.

Hi Luke,

Let me use this to reply to all of your recent comments.

It is especially important regarding the issues you raise, to be mindful that the 5th dimension that I uncover in https://jayryablon.files.wordpress.com/ ... -klein.pdf is timelike not spacelike, and that the metric tensor first found at (3.11) decouples the timelike signature of the fifth dimension from the scalar field . So as I elaborate in the first full paragraph of page 22, the curling up of an extra spacelike dimension is off the table, to be replaced by whatever epistemology ends up attaching itself following deep analysis to the existence of two time dimensions. One question this raises is the following: take what we know about the probabilities that are endemic to nature because of quantum theory, whereby the "could have happened" separates itself from the "did happen" as time progresses, and see if there is an isomorphic mapping of probability theory onto a time plane rather than a time axis. For now, I will leave this to others who may find it interesting to pursue. A second question which I will pursue in the near term, is the "matter dimension" viewpoint which I elaborate upon in a recent thread / post at https://groups.google.com/forum/#!topic ... pDPRRKNkiA.

I have long had an intuitive problem with there being a fourth spacelike dimension, but only with the paper being discussed here have I become convinced of this. This is because as I prove in this paper, the usual KK theory is not generally-covariant in five dimensions at the Dirac level, without having the metric (3.11) with a timelike signature for the fifth dimension. And to me, any anyone who firmly believes in the Einstein did with GR, general covariance is a must.

Jay
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby lkcl » Wed Jun 13, 2018 11:23 pm

Yablon wrote:Hi Luke,

Let me use this to reply to all of your recent comments.


hi jay - sure!

It is especially important regarding the issues you raise, to be mindful that the 5th dimension that I uncover in https://jayryablon.files.wordpress.com/ ... -klein.pdf is timelike not spacelike, and that the metric tensor first found at (3.11) decouples the timelike signature of the fifth dimension from the scalar field . So as I elaborate in the first full paragraph of page 22, the curling up of an extra spacelike dimension is off the table, to be replaced by whatever epistemology ends up attaching itself following deep analysis to the existence of two time dimensions.


ok. so (summarising) there are still 5 dimensions but 2 of them are a time "plane", and you are looking for inter-relationships between the 2 time-dimensions, would that be about right?

if so, my hunch - but also based on those recursive time-dilation things you raised - is that it's not 2 time-dimensions, it's the fact that matter (energy / photons) go round a circular loop of length particle-wavelength and *meet itself*. as there's no friction with photons the only possible "slowing down" of matter is down to the massively (infinitely) repeated accumulation of the same photon meeting itself again and again.

so it may be viewed as being not {T1, T2] but [T, T+particle-wavelength] give-or-take a bit of time-dilation, where the time-dilation equations are where you'll end up with the "complicated bits" that i won't be able to help with specifically but will intuitively "recognise" if you know what i mean.

please please do look at dr randall mill's work (i can help guide you through the relevant bits) as it's the only accurate first-principles model of particles that makes any sense and is based on E.M "circular loops" WITH ZERO POSTULATED MAGIC CONSTANTS. the current distribution formulae, the mass formulae are all consistent and complete, the only bit i don't truly follow is the use of special relativity to give a mass correction figure.
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Re: Grounding the Kaluza-Klein Fifth Dimension in Reality

Postby lkcl » Thu Jun 14, 2018 3:18 am

basically the loop allows particles to do integration and differentiation over time (an approximation thereof, using that "area under the graph" thing where the buckets are "particle-wavelength" wide)....
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