Natural Science Forum / Physics / Relativity / June 2005

http://www.pbase.com/scalarp6/image/45314188/original

To Bjoern in particular and other Bjoern level veterans in
in general. Early this year I mentioned Brian Greene talking
about how spaces are turbulent in the microscopic plank realms
and why it is not compatible with General Relativity which
has smooth spaces and the core reasons for the interest in
M-theory. Bjoern wrote the following (dated Jan 20, you could
use search to get the thread if needed):

"I mean that what scientists mean when they say that
General Relativity is not compatible with Quantum Theory,
they do not mean that "spaces are in turbulence in the
microscopic Plank realms".

The problems are totally different. They are mainly
mathematical, not conceptual."

---------

I was supposed to discuss it last time but because we had so
many topics, I didn't pursue. Now let me do it as I re-read Brian
Greene book "The Elegant Universe" yesterday and I find it
puzzling how Bjoern or others can't agree with Greene
on the core of it.

Refer to this illustration:

http://www.pbase.com/scalarp6/image/45314188/original

And the following text (note how it is contrary to Bjoern comment
above since Greene is saying it is literal and not just
mathematical)

Brian Greene argued:

"The Need for a New Theory

General Relativity vs. Quantum Mechanics

The usual realm of applicability of general relativity is that of
large, astronomical distance scales. On such distances Einstein's
theory implies that the absence of mass means that space is flat,
as illustrated in Figure 3.3. In seeking to merge general
relativity with quantum mechanics we must now change our focus
sharply and examine the microscopic properties of space. We
illustrate this in Figure 5.1 by zooming in and sequentially
magnifying ever smaller regions of the spatial fabric. At first,
as we zoom in, not much happens; as we see in the first three
levels of magnification in Figure 5. 1, the structure of space
retains the same basic form. Reasoning from a purely classical
standpoint, we would expect this placid and flat image of space
to persist all the way to arbitrarily small length scales. But
quantum mechanics changes this conclusion radically. Everything
is subj ect to the quantum fluctuations inherent in the
uncertainty p rinciple-even the gravitational field. Although
classical reasoning im plies that empty space has zero
gravitational field, quantum mechanics shows that on average it
is zero, but that its actual value undulates up and down due to
quantum fluctuations. Moreover, the uncertainty principle tells
us that the size of the undulations of the gravitational field
gets larger as we focus our attention on smaller regions of
space. Quantum mechanics shows that nothing likes to be cornered;
narrowing the spatial focus leads to ever larger undulations.

As gravitational fields are reflected by curvature, these quantum
fluctuations manifest themselves as increasingly violent
distortions of the surrounding space. We see the glimmers of such
distortions emerging in the fourth level of magnification in
Figure 5. 1. By probing to even smaller distance scales, as we do
in the fifth level of Figure 5. 1, we see that the random quantum
mechanical undulations in the gravitational field correspond to
such severe warpings of space that it no longer resembles a
gently curving geometrical object such as the rubber-membrane
analogy used in our discussion in Chapter 3. Rather, it takes on
the frothing, turbulent, twisted form illustrated in the
uppermost part of the figure. John Wheeler coined the term
quantum foam to describe the frenzy revealed by such an
ultramicroscopic examination of space (and time) - it describes
an unfamiliar arena of the universe in which the conventional
notions of left and right, back and forth, up and down (and even
of before and after) l ose the ir meaning. It is on such short
distance scales that we encounter the fundamental incompatibility
between general relativity and quantum mechanics. The notion of a
smooth spatial geometry, the central principle of general
relativity, is destroyed by the violent fluctuations of the
quantum World on short distance scales. On ultramicroscopic
scales, the central feature of quantum mechanics-the uncertainty
principle-is in direct conflict with the central feature of
general relati vity-the smooth geometrical mo del of space (and
of spacetime).

In practice, this conflict rears its head in a very concrete
manner. Calculations that merge the equations of general
relativity and those of quantum mechanics typically yield one and
the same ridiculous answer: infinity. Like a sharp rap on the
wrist from an old-time schoolteacher, an infinite answer is
nature's way of telling us that we are doing something that is
quite wrong. The equations of general relativity cannot handle
the roiling frenzy of quantum foam. Notice, however, that as we
recede to more ordinary distances, (following the sequence of
drawings in Figure 5. 1 in reverse), the random, violent
small-scale undulations cancel each other out-in much the same
that, on average, our compulsive borrower's bank account shows no
evidence of his compulsion-and the concept of a smooth geometry
for the fabric of the universe once again becomes accurate. It's
like what you experience when you look at a dot-matrix picture:

and create the impression of a smooth image whose variations in
lightness seamlessly and gently change from one area to another.
When you inspect the picture on finer distance scales you
realize, however, that it markedly differs from its smooth,
longdistance appearance. It is nothing but a collection of
discrete dots, each quite separate from the others. But note that
you become aware of the discrete nature of the picture only when
you examin e it on the smallest of scales., from far awa y it
looks smooth. Similarly, the fabric of spacetime appears to be
smooth except when examined with ultramicroscopic precision. This
is why general relativity works on large enough distance (and
time) scales-the scales relevant for many typical astronomical
applications - but is rendered inconsistent on short distance
(and time) scales. The central tenet of a smooth and gently
curving geometry is justified in the large but breaks down due to
quantum fluctuations when pushed to the small.

The basic principles of general relativity and quantum mechanics
allow us to calculate the approximate distance scales below which
one would have to shrink in order for the pernicious phenomenon
of Figure 5. 1 to become apparent. The smallness of Plancks
constant-which governs the strength of quantum effects-and the
intrinsic weakness of the gravitational force team up to yield a
result called the Planck length, which is small almost beyond
imagination: a millionth of a billionth of a billionth of a
billion th of a centimeter (10^-33 centimeter). The fifth level
in Figure 5.1 thus schematically depicts the ultramicroscopic,
sub-Planck length landscape of the universe. To get a sense of
scale, if we were to magnify an atom to the size of the known
universe, the Planck length would barely expand to the height of
an average tree.

And so we see that the incompatibility between general relativity
and quantum mechanics becomes apparent only in a rather esoteric
realm of the universe. For this reason you might well ask whether
it's worth worrying about. In fact, the physics community does
not speak with a unified voice when addressing this issue. There
are those physicists who are willing to note the problem, but
happily go about using quantum mechanics and general relativity
for problems whose typical lengths far exceed the Planck leng th,
as their research requires. There are other physicists, however,
who are deeply unsettled by the fact that the two foundational
pillars of physics as we know it are at their core fundamentally
incompatible, regardless of the ultramicroscopic distances that
must be probed to expose the problem. The incompatibility, they
argue, points to an essential flaw in our understanding of the
physical universe. This opinion rests on an improvable but pro
foundly felt view that the universe, if understood at its deep
est and most elementary level, can be described by a logically
sound theory whose parts are harmoniously united. And surely,
regard, less of how central this incompatibility is to their own
research, lost physicists find it hard to believe that, at rock
bottom, our deepest theoretical understanding of the universe
will be composed of a mathematically inconsistent patchwork of
two powerful yet conflicting explanatory frameworks.

Physicists have made numerous attempts at modifying either
general relativity or quantum mechanics in some manner so as to
avoid the conflict, but the attempts, although often bold and
ingenious, have met with failure after failure.

That is, until the discovery of superstring theory."