Theodor Franz Eduard Kaluza November 9, 1885 - January 19, 1954
In Kaku's preface of Hyperspace, page ix, we find a innocent enough statement that helps us orientate a view that previous to all understanding, is counched in the work of Kaluza.
In para 3, he writes,
Similarily, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and grvaity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained inthe fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.
Oskar Klein September 15, 1894 - February 5, 1977
Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, i.e. that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).
Thank you, Plato. I found the following enlightening:
ReplyDeletehttp://backreaction.blogspot.com/2006/07/extra-dimensions.html
Hi Steven,
ReplyDeleteYes, I see none of my comments are there either:)
Yes it has always been of "trying to understand" the "incomprehensible light" that such discussions about are immediately comprehended. Why I spend time to at least add perspective to something that seems alien and foreign in a mathematical sense, that what is mathematically spoken is phenomenologically understood.
Now so easy as to see this link that with Banchoff one can explore the 2d screen for what it represents of a 5d world(An image helps).
http://eskesthai.blogspot.com/2005/08/fifth-dimension-is-spacetime-fabric.html
Better yet, that if you are given so much energy with which you give the LHC process the onion(calorimeters) skin which covers the process will give you all the constituents of that energy "plus" some unaccounted for. Tests around the ring.
Where are those that are not accounted for, leaves you with some energy that has been lost as it is explained in Bee's assessment. This "is" a very real point of view.
So you get to the point where relativity becomes "a result of" this theoretical thinking. The result is the residue of something finer in distinction, that leaves elements in the bulk, as containing "all information" that will help with the complete assessment of our reality.
You may understand this or not, but I hope it helped.
Topology can become a interesting exploration into mathematics understood in the proper light?:)
Best,
Linked to current day point of view
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