[OT] How many dimensions? (WAS: Power over radio)

[Oleg Goldshmidt]

Shachar Shemesh <shachar at shemesh.biz> writes:

> Dotan Cohen wrote:
>
> Oleg, I understood that the universe has 11 or so dimensions, and that
> 5 or six can even be measured. But the wikipedia article that you
> link to claims only 3+1. I have googled a bit but found only very
> technical explanations, or baby facts with no explanations. Can you
> sum it up for someone who is familiar with relativity, but is not a
> physicist?  Thanks.

Ouch! We need a new list - science for Linux geeks or sth like
that. Mea culpa!

Essential disclaimer: I am not, nor have I ever been, a string
theorist.

> I'll do my best as another non-physicist, and then Oleg (or anyone
> else) can correct me where I'm wrong.

<Shachar's response stripped, but *only* because
anyone can find it in the archives - see below.>

I will not attempt to address any of the points that Shachar
mentioned, but the essence of his response is quite correct. Various
numbers of dimensions come from string theories, superstring theories,
membrane theories, and so on. We'll call them "string theories"
collectively. You mention 11 dimensions, there have also been theories
predicting 10, 26, 119 (or at least a hundred and something, I don't
recall the details, and there have been quite a few of those), or
whatever.

These are mathematical theories that start from various symmetry
considerations, and usually operate on mathematical constructs, be it
1-dimensional strings or multi-dimensional surfaces ("membranes", or
"branes" for short). Observable phenomena, e.g., particles, are
particular "resonances" or "eigenstates" corresponding to oscillations
of those strings or membranes, similar to different musical notes
corresponding to particular resonant states of a guitar or a violin or
a piano string. This is where "strings" and "membranes" get their
names from - they must be oscillating "lines" or "surfaces" to produce
particles we can observe.

Now, if a string or a membrane oscillates the oscillation has some
energy and, by relativity, this energy can be related to the mass of
the corresponding particle. Now you do the math to fit the
observations. E.g., a photon, that travels with the speed of light,
must be massless. It turns out that this can happen only if the
string/membrane/whatever world has so many dimensions (the value of
"so many" depends on the theory, it may be 11, or 26, or sth else).

How do these theories reconcile the 10/11/26/115/etc. dimensions with
the observed 3+1 of the "macro" world? They devised a notion that the
extra dimensions are "compactified", i.e., in the other dimensions the
world is so small that it cannot be measured, at least not at
attainable energies (and at the required energies it is not clear to
me if any theory predicts that Heisenberg's uncertainty principle can
be overcome).

Now, as Shachar wrote, this is all mathematics. To become physics,
these theories must make predictions that can be empirically
verified. Physics, unlike philosophy, is an empirical
science. Unfortunately, the zillion and a half of various string
theories predict observable effects at energies that are many orders
of magnitude higher than anything modern particle accelerators can
produce. In fact, the preferred method (beyond arguments related to
mathematical elegance) of picking "most promising" theories out of the
multitude is based on the minimal energy at which the theory predicts
an observable effect. Mind you, they pick the theory that predicts an
effect at the lowest energy as "promising" *not* because they think
chances are it will be correct, but because it will be the first to
check if and when they get enough billions or trillions to build an
accelerator that is 100 times more powerful than the current most
powerful one. This is part of the reason why these guys are so keen to
build more and more powerful "colliders".

So, to sum up, as far as physics, the empirical science, knows there
are 3 spatial and 1 temporal dimensions. There are a zillion and a
half complicated mathematical theories of various degrees of elegance
that predict various number of dimensions (there is indeed a subclass
that predicts 11), the extra dimensions must be "compactified" in
order not to spook the imaginative (or not[1])
non-mathematicians. None of these theories makes any prediction that
is practically verifiable at the current level of experimental
technology. If and when the relevant experiments are performed either
(some of) the theories will be rejected or we'll find out that the
Universe is more fascinating than we thought. Until then you are
welcome to retell your favourite version of theory vs. practice
witticism.

Now, if you'll excuse me, I have plans for tonight that are restricted
to 3+1 dimensions. ;-)

[1] Gauss said of one of his former students, "He became a poet, he
    didn't have enough imagination to become a mathematician."
 
-- 
Oleg Goldshmidt | pub at goldshmidt.org