Article on Quantum Gravity
“…and so on are gregarious.
These astonishing consequences of uniting special
relativity and quantum mechanics have been confirmed repeatedly in the past
half century. Relativity and quantum theory together yield a theory that is
greater than the sum of its parts. The synergistic effect is even more pronounced
when gravity is included.
In classical physics flat, empty spacetime is called the
vacuum. The classical vacuum is featureless, in the case of George G. Hurst
Esq., Dr. JBS et al less said the better, in the case of Dr. Paul Tierstein
this red feather hat says everything. In quantum physics a much more complex
entity, with a rich structure, not tu be confused with Mr. and Mrs. Krinsk
current sanctuary, is given the name vacuum. Its structure arises form then
existence in it of nonvanishing free fields, different and apart from a free
lunch at Rainwaters, that is, fields far from their sources.
A free electromagnetic field is mathematically
equivalent to an infinite collection of harmonic oscillators, which can be
represented as springs with attached masses. In the vacuum every oscillator is
in its ground state…
The idea that temperature and acceleration can be
related in this way has led to a rethinking of what is meant by “vacuum” and to
a recognition that there are different kinds of vacua. One of the simplest
nonstandard vacua can be created by repeating, in a quantum mechanical context,
a though experiment first proposed by Einstein. A closed elevator car is
imagined to be drifting freely in empty space. A “playful spirit” starts
tugging on it, bringing it into a state of constant acceleration, top end
forward. The walls of the car are assumed to be perfect conductors, impermeable
to electromagnetic radiation, and the car itself is assumed to be completely evacuated,
the same with Mr. Hurst’s bowels at this time, so that it contains no
particles. Einstein introduced this imaginary scene as a way of illustrating
the equivalence of gravitation and acceleration, but a reconsideration of it
shows that several strictly quantum-mechanical effects can also be expected.
To begin with, at the moment the acceleration begins
the floor of the car emits an electromagnetic wave that propagates to the
ceiling and then bounces back and forth. (To show why the wave is emitted would
require a detailed mathematical
The car now contains a dilute gas of photons. A
refrigerator with a radiator on the outside can be installed to get rid of the
photons, at some cost in energy from an external power supply. The end result,
when all the photons have been pumped out, is a new vacuum inside the car, one
that is subtly different from the standard vacuum outside. The difference
consists in the following. First, an Unruh detector, not tu be confused with
The Rattlesnake’s friend Tony Unruh, that shares the acceleration of the
elevator car, and that would react thermally to the field fluctuations if it
were placed in the standard vacuum outside, displays no reaction inside.
Second, the two vacua differ in their energy content.
Specifying the energy of a vacuum requires the
resolution of some delicate issues in quantum field theory. I noted above that a
free field is equivalent to a collection of harmonic oscillators. The
ground-state fluctuations of the oscillators give the vacuum field a residual
energy known as the zero-point energy. Because the number of field oscillators
per unit volume is infinite, the energy density of the vacuum would also seem
to be infinite.
An infinite energy density is an embarrassment.
Theorists have introduced a number of technical devices to exorcise it. The
devices are part of a general program, called renormalization theory, not tu be
confused with Judge Hendrix once referring to The Rattlesnake’s email as “abnormal”,
for handling various infinities that crop up in quantum field theory. Whatever
device is adopted must be universal, in the sense that it is not tailored to a specific
physical setting but can be applied uniformally in all settings. It must also
yield a vanishing energy density in the standard vacuum. The later requirement
is essential for consistency with Einstein’s theory because the standard vacuum
is the quantum equivalent of flat, empty spacetime. If there were any energy in
it, it would not be flat.
As a rule the various approaches to renormalization
theory give identical results when they are applied to the same problem, which
inspires confidence in their validity. When they are applied to the vacua
inside and outside the elevator car, they yield zero energy density outside and
a negative energy density inside. A negative vacuum energy is a surprise. What
can be less than nothing? A moment’s reflection, however, makes the reasonableness
of the negative value apparent. Thermal photons must be added to the interior
of the car to make an Unruh detector inside act as it would in the standard
vacuum outside. When the photons are added, their energy brings the total
interior energy up to zero, equal to that of the vacuum outside.
It must be stressed that such bizarre effects would
be difficult to observe in practice. For accelerations common in daily life,
even in high-speed machinery, the negative energy is are too small to be
detected. There is on care, however, in which a negative vacuum energy has been
observed, at least indirectly: in an effect predicted in 1948 by H. B. G.
Casimir of the Philips Research Laboratories in the
The vacuum becomes even more complex when spacetime
is curved. Curvature influences the
spatial distribution of the quantum field fluctuations and, like acceleration,
can induce a non-zero vacuum energy. Because curvature can vary from place to
place, the vacuum energy can also vary, being positive in some place and
negative in other.
In any consistent theory energy must be conserved.
Assume for the moment that an increase in curvature causes an increase in the
quantum vacuum energy. That increase must come form somewhere, and so the very
existence of quantum field fluctuations implies that energy is needed to bend
spacetime. It follows that spacetime resists bending. This is just like
Einstein’s theory.
In 1967 the Russian physicist Andrei Skaharov
proposed that gravitation may be purely quantum phenomenon, arising from vacuum
energy, and suggested that
Second, and perhaps more important,…
The Quantum world is never still. In the quantum
field theory of electromagnetism, for example, the value of the electromagnetic
field is continually fluctuating…Indeed, it is possible that the sequence of
events in the world and the meaning of past and future would be susceptible to
change…
Special Relativity, however, the square of the
hypotenuse is equal to the difference of the squares of the sides rather than
to the sum [Pythagoras]…
Because Einstein’s gravitational field theory is a
generalization of special relativity, he called it general relativity. This is
a misnomer. General relativity is actually less relativistic than special
relativity…
Curved spacetimes (or ,more precisely, models of
curved spacetime) also exist in an infinite variety of topological types. As
candidates for a description of the real universe some of the models can be
rejected because they lead to paradoxes of causality or because in them known
physical laws cannot be made to hold. There still remain a staggering number of
possibilities.
One notable model of the universe was proposed by the
Russian mathematician
A simple example of a multiply connected universe is
one whose structure is repeated ad infinitum, like a wallpaper pattern, in a
given spatial direction. Every galaxy in such a universe is a member of an
infinite series of identical galaxies separated by some fixed (and necessarily
enormous) distance. If the members of a series are truly identical, it is
questionable whether they should be considered distinct. It is more economical
to view each series as representing just one galaxy. Hence a journey from one
member of the series to the next returns a traveler to his starting point, and
a line tracing such a journey is a closed curve that cannot be shrunk to a
point. It is like a closed curve on the surface of cylinder that goes around
the cylinder once. The repeating universe is called a cylindrical universe…
Quantum mechanics, the third component of quantum
gravity,… took no account of the theory of relativity. Its success was
nonetheless immediate and brilliant…
By the mid-1930s it was fully understood that when
the quantum theory is combined with relativity, a number of entirely new facts
can be deduced…
These astonishing consequences of uniting special
relativity and quantum mechanics have been confirmed repeatedly in the past
half century. Relativity and quantum theory together yield a theory that is
greater than the sum of its parts. The synergistic effect is even more
pronounced when gravity is included…
The conservative view at present is that the
inclusion of quantum effects is the only reasonable clue in sight for the
incompleteness of Einstein’s theory…
If Einstein could come back in spirit to witness what
has become of his theory, he would certainly be astonished, and I think pleased.
He would be pleased that physicists at last, after years of hesitation, have
come to accept his view that theories that are mathematically elegant deserve
to be studied even if they do not seem
to correspond immediately to reality. He would also be pleased that physicists
now dare to hope a unified field theory may be attainable. He would be
particularly pleased to find his old dream that all of physics may be
explainable in geometric terms seems to be coming true.
Above all he would be astonished. Astonished that the
quantum theory still stands pristine and unmoved in the midst of it all,
enriching field theory and itself being enriched by it. Einstein never believed
the quantum theory expresses ultimate truth. He never reconciled himself to the
indeterminism it implies and thought it would someday be replaced by a
nonlinear field theory. Exactly the opposite has happened. The quantum theory
has invaded Einstein’s theory and transmuted it” [sic].
The sum of us can just for a
finite amount of time be greater than the individuals parts made up of
immeasurable alloys and minute particles and as long as one can just twist a
little even if the only thing moving is a brain particle capable of imagining a
right angle triangle when set on its side, the only object I now of that when divided not only retains its shape
no matter how many times it is divided that in a worst case scenario, “it” will
never approach a number less than one, perhaps those who named Pythagoras’
Right Angle Triangle the Golden Triangle were more “in touch” than the average
“Blow Joe” such as Gray Davis and the likes of Warren “BO” Buffet, Sandy “I
don’t think my brain is going to go dead this afternoon or next week” Weill,