Re: Thoughts on why space must have three dimensions


"Sue..." <suzysewnshow@xxxxxxxxxxxx> wrote in message
news:1151691713.235330.206580@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Neil wrote:
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:

....

Two charges are already connected by a mechanism whose
behavior you can't alter by invoking the rigid rod declaration.

No, *two* charges aren't "already" connected to begin with - it is long
accepted that the connecting rod contributes it's own term to the total
energy and momentum of the system. If they weren't connected, they'd fly
apart. When we connect them and try to accelerate them together, the
interaction between the charges *and* the effect of acceleration on the
stress in the rod both contribute to the effective inertia (m_eff = f/a_0
in motion parallel to velocity.) All I did was extrapolate this to spaces
with other than three dimensions, which don't behave the same since dE/dr =
(1-N)q^(-N).
Four angels from the head of a pin can nullify any such
construction and there are credible reports of three angels
accomplishing the task on occasion. :o)
Pointless fluff that makes no substantive contribution -
PS: scholastics never argued about that particular issue - it's like "Beam
me up Scotty" and "Play it again, Sam."


Orthogonality of force can't be achieved by adding any new axis
once the three have been employed. That is why three works nice.

There is nothing about force per se that requires three dimensions. It is
convenient for mathematicians that there is a cross product in 3-space, but
all such operations (even the analog of magnetism in other dimensions) can
be worked out - it is just more cumbersome to work with.

Also it makes this work:
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html

Well, once you already have 3-space, then the inverse square law for fields
follows, but what if there weren't three dimensions to begin with? Then the
field law for charges is: E = qr^(1-N). In 4-space, there is an inverse
cube law, etc. I found that inconsistencies arise if the field law is other
than E = qr^(-2), hence space needs to have three dimensions.

Two objects and their associated fields can occupy the same
space... but not at the same time which considering the finite
speed of light is the reason for transforming between temporal
and spatial axes.

Time-independent Maxwell equations
http://en.wikipedia.org/wiki/Multiple_integral
Time-dependent Maxwell's equations
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html
"Space time"
http://farside.ph.utexas.edu/teaching/em/lectures/node113.html
....
Interesting stuff, but doesn't single out 3-D space as being preferred, or
show why others couldn't exist etc.



.

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