Thoughts on why space must have three dimensions

A few months ago I listened to an interview on National Public Radio with
physicist Lisa Randall. She is a top theorist on foundational theory of why
the universe is the way it is. That means strings, branes, and such. One of
the venerable questions is: why is space three-dimensional? It may seem
natural to have three dimensions of space and one of time, but
mathematically there can be any number of dimensions (think of specifying
points using 4, 10, etc. variables.) Physicists, including Lisa, say they
can't see why space *had* to have three dimensions. (Check out
http://arxiv.org/abs/hep-th/0506053 ) However, they have come up with
reasons why three large-scale dimensions would be more likely to expand out
of a larger set (usually thought of as 10 or 11) of original, perhaps tiny
dimensions. Below follows a statement adapted from my post to
http://www.radioopensource.org/the-holy-grail-of-physics/ in response to the
interview, and outlining my own efforts to answer this question.

I too have been working on the question, why are there three *large*
dimensions of space? (There are probably more, like a total of 10 or 11
space dimensions, but the rest are curled up very small or otherwise
inaccessible.) After extrapolating electromagnetic interactions to spaces of
other dimensions, I formulated some arguments:

1. In spaces with other than one or three dimensions, an oscillating charge
does not project the same *average* field along the axis of oscillation as
the rest value. That is due to two things: the combination of "projection"
of its retarded distance - where it would be had it continued at the
velocity it had when light left it - and the distortion of the field due to
Lorentz contraction, which weakens it to gamma^(1-N) the value it has at
rest. N is the number of large space dimensions. (We also must take into
account the Doppler shift of projection intervals. Heh, it's not quite as
complicated as it sounds.) Remember that the Coulombic electric field
intensity is given as E = qr^(1-N) due to field spreading. This amplifies
the effect of the oscillating charge's apparent position being close
(projected from approaching cycle) to a second "target" charge at rest. It
increasingly swamps the weakening effect of the gamma factor as N goes above
three and is incorrect when N = 2. That would impose a net force on a second
"target" charge unequal to that on the oscillating charge, and violate
conservation of momentum and energy. The one-dimensional case is ruled out
due to infinite potential energy as is the 2-D case (why didn't A. K.
Dewdney realize that about the 2-D Planiverse?)

2. Let two charges be connected by a reasonably rigid rod. Then, accelerate
the rod along its length. The combined force between the charges will be
derived from the sort of considerations given in (1.), as the projected
field of each charge catches up to the other charge. Then we must take into
account the extra force created by the action of acceleration on the
relativistic stress-correction to the momentum and energy of the rod. Only
in three dimensions of space does that equal in net the effective inertia
the charges should have given their potential energy. (In higher dimensions,
taking the integral of f = q1q2/r^(N-1), that potential w.r.t. infinity
is: -q1q2r^(2-N)/(2-N). )

I hope I can publish the full development of this before long. I don't think
anyone else has an explicit proof that N *must* equal three, only reasons it
was more likely to form, or oddities like being unfriendly to life,
distorted wave propagation (see Barrow and Tipler's _The Anthropic
Cosmological Principle_ for great discussion of this.)


Neil Bates


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Relevant Pages

  • Re: Thoughts on why space must have three dimensions
    ... mathematically there can be any number of dimensions (think of specifying ... In spaces with other than one or three dimensions, an oscillating charge ... That is due to two things: the combination of "projection" ... Let two charges be connected by a reasonably rigid rod. ...
    (sci.physics)
  • Re: Nobel Prize for David Thomson?!
    ... Charge is a quantity, simply a quantifier for our measurements, ... > due to the structure of the Aether in five dimensions. ... > primary angular momentum to produce the electron. ... > negative sphere allows for the existence of the anti-proton. ...
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  • Re: Nobel Prize for David Thomson?!
    ... Charge is a quantity, simply a quantifier for our measurements, ... > due to the structure of the Aether in five dimensions. ... > primary angular momentum to produce the electron. ... > negative sphere allows for the existence of the anti-proton. ...
    (sci.physics)
  • Re: Nobel Prize for David Thomson?!
    ... Charge is a quantity, simply a quantifier for our measurements, ... > due to the structure of the Aether in five dimensions. ... > primary angular momentum to produce the electron. ... > negative sphere allows for the existence of the anti-proton. ...
    (sci.physics.relativity)
  • Re: Thoughts on why space must have three dimensions
    ... interesting possibility is that dimensions are in fact com- ... If in that way one-signed charge were to ... would get to particles of such huge mass discrepancies (electron versus ... asking where the magnet is in the standard space. ...
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