Higher Dimensions in Physics and Mathematics! |

Pseudoscientists lean heavily on the assumption that their readers will know absolutely nothing about science or math. This is a pretty safe assumption, alas. And it requires no effort on the part of the pseudoscientist, because he also invariably knows no science or math either.

It is worth summarizing the ways in which the various concepts of "higher dimensions'' gradually diffused out from legitimate math and science, through hundreds of increasingly distorted, confused and muddled journalistic presentations and sensationalizations, into late 19th Century science fiction and 20th Century pseudoscience.

In the late 19th Century mathematicians became increasingly interested in the foundations of geometry. Our own universe has 3 space dimensions. But what would geometry be like if there were 4 space dimensions? Or 5? Or 10? Or an arbitrary number? Or an infinite number? Mathematicians worked a great deal on geometries with arbitrary numbers of space dimensions. |

Mathematicians also worked a great deal on "non-Euclidian'' geometries that violate one or more of the postulates of Euclid. In Euclidian geometry, parallel lines remain the same distance apart. One can imagine a geometry in which parallel lines eventually intersect, and a geometry in which parallel lines gradually separate further and further. Such spaces are usually described as "curved''— an example is the 2-dimensional surface of a sphere, on which lines initially parallel at the equator of the sphere intersect at the poles of the sphere.

Mathematicians had no idea
that
their
work would ever prove useful
to physicists, but some of it did have application in
the real world.
For hundreds of years physicists had worked in a
4-dimensional
framework, because it takes a minimum of 4 numbers to
specify an
event: 3 to specify its space location and 1 to specify
when it
happened. In 1905 Einstein found that, to be correct,
laws
of physics |

In 1915, Einstein found a more general description of gravitational phenomena, in which the density of matter directly determines the "curvature'' of 4-dimensional space-time. That is, his theory of gravity was purely geometrical. The amount of matter determines the type of geometry that exists in the surrounding space. Other matter travels along the straightest possible trajectory in this curved space-time. |

Later, physicists like Kaluza and Klein and Pauli tried to generalize Einstein's ideas to include the electromagnetic force. In order to include a number for "charge,'' the source of electromagnetic effects, in a purely geometrical theory, they had to add a new space dimension, since every number in a geometrical theory is a projection onto a coordinate. Thus, they wound up with a 5-dimensional theory (4 space dimensions, and time). These so-called Kaluza-Klein theories did not seem to lead anywhere, and were abandoned.

Physicists for centuries have worked in arbitrary spaces, usually called "phase space,'' in which various important physical quantities are interpreted as dimensions. For instance, in order to show the "state'' of a container of gas, one might plot a graph in 3 dimensions, the 3 dimensions being pressure, volume and temperature. To show the "state'' of a particle, a physicist might plot 4 dimensions, 3 of them being the 3 components of the momentum vector of the particle, and 1 being time. If it requires 100 numbers to specify a process, then a graphical description of the process would have to show "slices'' through a space of 100 dimensions. None of these would be required to have anything to do with actual space dimensions. |

In the late 1920s,
physicists
working
on quantum physics found that
the mathematics fell naturally into the framework of a
theory of
vectors in a space with a denumerably infinite number of
dimensions.
German mathematician David Hilbert had already worked
out the theory
of such spaces, which we call Hilbert Spaces. In quantum
physics,
each possible outcome of a measurement is a projection
along an
axis in an abstract space, having nothing to do with
space-time.
A bit later British physicist
P. A. M. Dirac pointed out that in general the space
used in quantum physics
needs an |

Multidimensional spaces have even proved useful in computer architecture. For example, networks of processors can be set up that are linked geometrically as surfaces would be in a multidimensional space.

The structure of all known physical laws demands that our universe have only 3 extended space dimensions. For example, the fact— established and confirmed by experiment consistently for nearly 400 years— that all long-range interactions, such as gravity and the radiation field of the electromagnetic force, fall off like the inverse square of the distance, demands that space be precisely 3 dimensional.

More confusion about higher
dimensions
was generated in the press
beginning in 1984, when physicists became excited about
so-called "string theory.'' Physicists have never been able to
work out
a theory of gravitation that is consistent with quantum
mechanics
and also has some feature that indicates it might be uniquely
correct!
String theory provided a geometrical description of quantum
processes that incorporated gravity very naturally. But three
other
forces besides gravity are known. Borrowing the idea of
Kaluza and Klein, physicists incorporated the other three forces
and their "couplings" by adding space dimensions— the only thing
you can do in a theory that is purely geometric. A typical
string
theory had 9 or 10 space dimensions
and 1 time dimension. The extra space dimensions had to be there
to incorporate phenomena other than gravity geometrically, but
they
could not
"actually'' be there or the theory would not have worked.
The solution was to curl these extra dimensions up
mathematically into tight
"wads'' no more than 10^{-35}
meters in length,
a process called "compaction." The extra dimensions would
thus be "compact," and indetectable.
At first it was hoped that such a theory would be unique, so
that
we would have confidence that this was the right way to go.
After
nearly 25 years, the "glitz'' of string theory has almost
entirely worn
off. Midway along, physicists began to realize that the five or
six
different string
theories that had been suggested all appeared to be different
limiting
cases
of a far more general theory, which is tentatively called
"M-Theory."
In M-Theory, strings are generalized into surfaces and
membranes,
and ordinary space-time coordinates no longer exist in general.
The space-time framework can still be up to
eleven-dimensional.
It is vital to realize that *no aspect whatsoever*— not
even the
most basic assumptions— of string theory has ever been tested
experimentally. Only in early 2007 was an experimental
test of of its three basic assumptions finally proposed.

So far,
physicists have no concrete idea as to what a unified
theory of all
quantum processes
and gravity might look like, but it is certainly
possible that such theories
will remain multi-dimensional. It is important to
realise that these
theories |

Harvard physicist Lisa
Randall, in her book |

A lesser-known alternative to string theory, which also provides a possible quantum theory of gravity, is so-called Loop Quantum Gravity. In this approach, first suggested at about the same time as the earliest string theories [mid-1980s], space-time is four dimensional but has a “grainy,” discrete structure at submicroscopic levels. At present (2011), loop quantum gravity still remains a very viable alternative to string theory, and some have suggested that the two different approaches might turn out to be different approximations to a single, more general theory.

In any case, no matter what new ideas and new information are forthcoming along these lines in the future, the statement that there are only three extended space dimensions available to macroscopic objects such as ourselves will remain true no matter how M-Theory or quantum gravity or whatever replaces them ultimately may develop, or what experimenting at scales of energy and distance we haven't examined in detail before ultimately reveals to us. Theories try to describe the world, they don't change it. Elephants don't lay eggs. Facts is facts.

Beginning in the last decade of the 19th Century, newspapers and magazines were full of completely confused accounts of "the fourth dimension,'' not to mention "vibrations'' and "energy,'' two hot topics of late 19th Century physics. When Einstein came along, the "fourth dimension'' became an even hotter topic, and acquired some curves too. Higher dimensions in pseudoscience are often even further confused with then-unrelated scenarios, such as "coexistent worlds,'' "parallel worlds,'' the "worlds'' reached in dreams and drug-visions, not to mention Heaven, Hell, and even other planets. Mindless journalistic publicity for string theories has over the past two decades touched off yet another wave of science-fictional and fantastical delirium involving "multiple universes," a delirium owing a lot to late 19th Century Theosophy, but essentially nothing whatsoever to advances in physics.

Pseudoscientists and fiction writers have always loved "higher dimensions.'' Almost any fantasy can be motivated by appeal to the "mysterious 4th dimension,'' or the famous "15th Akasic dimension.'' But it is important to realize that such concepts are not borrowed from either science or mathematics, and have no basis whatsoever in the verified descriptions and observed phenomena of the world we actually live in.

Create your own four-dimensional creatures here, seen only as two-dimensional slices as you interfere with the natural evolution of a pocket universe... or so it says.

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