• #1
BiGyElLoWhAt
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Main Question or Discussion Point

http://en.wikipedia.org/wiki/Kaluza–Klein_theory
##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche)
http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf [Broken] (this author makes some interesting arguments)
Also, a lot (if not all extensions) of this seems to stem back to the work of a physicist/mathematician that I'd never heard of until a few days ago, when I lifted up the rug to see what was hiding underneath.
http://en.wikipedia.org/wiki/William_Kingdon_Clifford
and a more rigerous derivation:
http://iopscience.iop.org/1751-8121/40/32/F03/pdf/1751-8121_40_32_F03.pdf

So, long story short, I'm a little perturbed... First off, I'm not sure I've heard a whisper of the name "Clifford", let alone a mention of his work. This would be insignificant if I felt his work was. Contrarily, would Einstein have been able to fromulate GR without the work of clifford? GR and cliffords union of space and EM seem analagous (if not identical in form).

Point number 2: With the Kaluza-Klein-Einstein collaboration (as well as Einstein's "independant" work), we see the union of space and time, as well as EM and time, and apparently somewhere in these papers theres the argument for mass being united (I missed the direct point, and only saw references). Why can I not find this union for the strong force? I honestly feel like if I keep following the bread crumbs (assuming I can find the next one) that I'll end up at some (obscure?) form of string theory. I don't really know what the dimensions in string theory actually represent, though... but I degress...

Can anyone provide some insight as to whether or not this is something that has been done? I really like the formulation of both GR (+temporal dimension - gravity) and I'm not sure who or what to credit it to (+scalar potential dimension - EM).
What's really surprising is the success (again, apparently, as the resources I've found are limited) this potential dimension had in being able to not only predict EM, but derive Maxwell's equations... and then we hang it up on the fridge until the kids go to bed, and pitch it when they're not looking.

On second thought, it might be 5D spacetime (kaluza/klein) that predicted EM and successfully derived maxwell's eq.'s.

Any word on why I'm struggling to find more?
 
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  • #2
Simon Bridge
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Can anyone provide some insight as to whether or not this is something that has been done?
Whether or not what has been done? You've mentioned a number of things that you seem to be confused or excited about (hard to tell which).

we see the union of space and time, as well as EM and time, and apparently somewhere in these papers theres the argument for mass being united (I missed the direct point, and only saw references). Why can I not find this union for the strong force?
... lets see, the unification of space and time would be the geometric representation of time as another space dimension. Mass, to my knowledge, has not been unified with space - but it has been "unified" with energy in the mass-energy relation. Einsteins early papers have a nice proof in them - forget which one but they are actually quite easy to read so have a look.
Similarly the strong force and space?? Perhaps you have been looking in the wrong place?

Wikipedia is a starting point:
http://en.wikipedia.org/wiki/Unified_field_theory
... don't know where else to send you because I'm not sure I understand you.
You question seems related to:
http://scienceline.ucsb.edu/getkey.php?key=1825
... you should be able to use these references as springboards for future searches.

Note: Who gets the credit is not as important as the model itself and future avenues of research ... though it does help with research grants and Nobel prizes...
 
  • #3
BiGyElLoWhAt
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Whether or not what has been done? You've mentioned a number of things that you seem to be confused or excited about (hard to tell which).
Both? =D
... lets see, the unification of space and time would be the geometric representation of time as another space dimension. Mass, to my knowledge, has not been unified with space - but it has been "unified" with energy in the mass-energy relation. Einsteins early papers have a nice proof in them - forget which one but they are actually quite easy to read so have a look.
Similarly the strong force and space?? Perhaps you have been looking in the wrong place?
I'm using this termonology pretty loosely. You introduce the temporal dimesnion, creating a 4-D space-time (albeit geometric) manifold. Gravity is no longer a force on this manifold. Now we add cliffords work in. You introduce the EM scalar potential dimension, extending space-time to 5-D. EM is no longer a force. That's where I stopped finding specifics. Although, recent readings from yesterday keep pulling up M-theory, and M. Kaku described it as the superiour Kaluza-Klein theory, so I'm relatively confident that the end point of my search is M-theory, I was just expecting there to be a more linear (or gradual) extension to this. So we go from 3->4->5 dimensions, then 10 is the next lowest number I seem to find that's along the lines of what I'm looking for, which is the logical extension of these manifolds. 1D at a time would be phenomenal. Chronologically, the next one I found was the bosonic string theory, which jumps straight from 5D->26D =/

Wikipedia is a starting point:
http://en.wikipedia.org/wiki/Unified_field_theory
... don't know where else to send you because I'm not sure I understand you.
You question seems related to:
http://scienceline.ucsb.edu/getkey.php?key=1825
... you should be able to use these references as springboards for future searches.
Well, I've been through ##\approx## all the wikipedia pages... Pulled up all the arxiv papers I could find that were relevant. I just cant seem to find the extension I'm looking for. Also, as for the mass: yea, there's mass energy, integrate force over distance, do some substitutions, and bam, 2 term kinetic energy, one term is rest energy i.e. mass energy. Several places I found cited a evidence for a 4th spacial dimension curled up inside matter which gives it mass, kind of like a singularity at some point in this 4th dimension different than the point (plane? volume? whatever.) in this 4th dimension that we percieve ourselves to exist in. I personlly don't see it, yet. On the other hand, I could also have misinterpreted it, I kinda feel like Quagmire from Family Guy in that episode where he discovers internet porn. There's just soo much, and I've pretty much been on the internet at work, at home, or on my phone if I'm out and about thumbing through links for 4 or 5 days now. I'm not going to claim to have interpreted everything 100% accurately.
Note: Who gets the credit is not as important as the model itself and future avenues of research ... though it does help with research grants and Nobel prizes...
In the grand scheme of things, I have to agree with you. However, it feels disrespectful to disregard someone who argueably was the first person to take the first step down the road that leads to modern theoretical physics. I am stronly leaning towards pursuing theory, and if I do something half as brilliant as what clifford did, I would want to be remembered. I don't think that theorists can come up with their theories by merely "putting in the hours". Expermintalists do the bulk of their work while in front of their equipment, but for theorists, all they need is some chalk or dry erase markers, a board, some intuition and tostino's. For people that come up with brilliant things such as extending the manifold used to model the universe, I'm inclined to say they never really stop working; the lightbulb never stops trying to light, even when they leave "work" to go home. Clifford did great work, and gave up what little life he lived (died at 33/34) to further our knowledge as a species. I think he should be remembered as more than a footnote.
This however is my opinion, and you can agree or disagree. It's irrelevant, again, in the grand scheme of things.
 
  • #4
PeterDonis
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a lot (if not all extensions) of this seems to stem back to the work of a physicist/mathematician that I'd never heard of until a few days ago, when I lifted up the rug to see what was hiding underneath.
http://en.wikipedia.org/wiki/William_Kingdon_Clifford
Two articles on Clifford algebras, which is what Clifford invented:

http://en.wikipedia.org/wiki/Clifford_algebra

http://math.ucr.edu/home/baez/octonions/node6.html

Clifford algebras are certainly used plenty in physics (for example, they play a fundamental role in how fermions are represented in quantum field theory), but I'm not sure how they relate to the other things you're talking about. See below.

a more rigerous derivation
I'm not sure how this relates to the other things you're talking about. It isn't describing Kaluza-Klein theory, or the souped-up versions used in string theory to make all the fundamental interactions (including weak and strong as well as gravity and EM) appear as geometry. It's talking about its own 5-dimensional theory.

You introduce the temporal dimesnion, creating a 4-D space-time (albeit geometric) manifold. Gravity is no longer a force on this manifold.
Ok so far.

Now we add cliffords work in. You introduce the EM scalar potential dimension, extending space-time to 5-D. EM is no longer a force.
How is a Clifford algebra used in this? All you do is write the 5-D metric and split it up into a 4-D piece and a 1-D piece. The 5-D Einstein Field Equation then splits up into the ordinary GR EFE plus Maxwell's Equations. This is all straight tensor algebra; no Clifford algebra anywhere.

Several places I found cited a evidence for a 4th spacial dimension curled up inside matter which gives it mass...On the other hand, I could also have misinterpreted it
We can't tell unless you give us the reference.
 
  • #5
BiGyElLoWhAt
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Hmmm... well im having trouble finding the sources again. You can read the first paragraph here http://www.britannica.com/EBchecked/topic/121527/William-Kingdon-Clifford
Which seems to suggest (as i found other places) that he did work in theoretical physics as well as his math stuffs. Ill try to find the articles i read before, but there was a lot and im not exactly sure how i got to all of it. Links within links and whatnot.
 
  • #6
BiGyElLoWhAt
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Well as this article suggests, it could have been his philosophy that led to his contributions to theory. http://galileospendulum.org/2011/12/19/w-k-clifford-the-geometry-of-physics/
According to this, he worked as a mathematician, but thought as a theorist. Also per this and wikipedia to name a few, he also hypothesized GR a large number of years before einstein did. Ill have to dig deeper here soon. Its 2am here though.
 

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