On a Fractal Version of Witten’s M-Theory

Abstract

Starting from Witten's eleven dimensional M-theory, the present work develops in an analogous way a corresponding 5 11 + φ dimensional fractal version where E D mc mc 2 2 2 5 2 21 22 = φ  in astounding agreement with cosmic measurements and observations.

From the Heterotic String Quartet to the Cosmic Dark Matter, Dark Energy and Ordinary Energy Symphony

“…For sure the 26 must include our 3 + 1 = 4 classical spacetime or Einstein's 4D spacetime. In both cases it is reasonable to assume that we cannot see the remaining 26 4 22 − = dimensions and can regard them as compactified in one way or another similar to how we got used to think of the Kaluza-Klein 5D theory [22]. The next step in our simple scheme is to think of these 22 quasi dimensions as a sort of pre-quantum messenger particles [20][21][22][23][24].…”

“…In both cases it is reasonable to assume that we cannot see the remaining 26 4 22 − = dimensions and can regard them as compactified in one way or another similar to how we got used to think of the Kaluza-Klein 5D theory [22]. The next step in our simple scheme is to think of these 22 quasi dimensions as a sort of pre-quantum messenger particles [20][21][22][23][24]. Having accepted this move let us subdivide these 22 messenger particles to 6 plus 16 bosons [20][21][22][23][24][25][26][27].…”

“…Again an embarrassingly trivial rearrangement of the preceding equation clearly shows that a consistent description of the relevant bosonic filed requires 16 extra coordinates [13][14][15][16][17][18]. It is those 16 extra coordinates corresponding to 16 dimensions or bosonic pre-quantum particles which will play a crucial role in the next section regarding pure dark energy as distinct from dark matter and ordinary energy [20][21][22][23][24]. We note on passing, without going into detail, that the vital 16 extra bosonic spacetime dimensions need compactification and result in a gauge group 16 (1) U which when broken gives us the carrier of pure dark energy [11].…”

“…The essence of this theory is lucidly explained in many papers and text books notably by the creators of the theory, namely a group around Nobel Laureate David Gross [17,18] which is often fondly referred to as the "Princeton quartet" [17,18]. Never the less because we will present this theory in the next section with a minor twist here and there, we felt it pertinent to give here a brief account of the quintessential idea behind heterotic string theory seen from our "pure dark energy and dark matter" explanation view point [20][21][22][23][24][25][26][27].…”

“…Thus whenever we say particles here, we mean pre-quantum particle-like states which will result from symmetry breaking of a corresponding Lie group of certain dimensionality [15][16][17][18][19]. Something similar will be assumed with regard to the word wave with which we mean prequantum wave of the pre-quantum particle [19][20][21][22][23][24][25][26][27][28].…”