In
October
2012 I wrote an article called “M-Theory and all
that” about a Stephen Hawking book
on theoretical physics and the origins of the
universe. This year I found a
book on the same topic but with a different
style and spin. Carlo Rovelli has
produced Reality
Is Not What It Seems:
the Journey to Quantum Gravity, Riverhead,
2017. In translation from
Italian, it is a well-written story of human
understandings about the universe.
It goes from ancient Greek philosophers through
Ptolemy, Galileo, Newton and Einstein to quantum
gravity. Throughout, there is
an emphasis on conveying the underlying physical
insights.
My
summary
which follows is not for the faint-hearted!
Part
one
“Roots” begins with a chapter on “Grains.” A
philosophical school in commercial
Miletus in 500 BCE began looking at the world by
observation and reason. It was
a novel and seismic step. Leucippus moved to
Abdera and began a school there.
He and pupil Democritus wrote about a world of
space and tiny moving atoms.
Atoms in combination made up everything as
letters make up words. There is a
limit to divisibility. Philosopher Artistotle
was familiar with this thinking. Sadly
the works of these ancients were lost during
fifth century pagan suppression by
Christian Emperor Theodosius. MiraculouslyThe
Nature of Things orThe Nature
of the
Universe, by the Latin poet Lucretius,
survived. Lucretius draws from the
philosophy of Epicurus, a pupil of Democritus,
in a poem on wonder in nature with
the vision of atoms. He writes of observing
dancing particles in a sunbeam as
evidence of atoms causing the motion. Einstein
in 1905 used mathematics to
prove atoms existed and to measure their size by
observing the motions of
grains of dust or pollen in air or a liquid – so
called Brownian motion.
The
chapter, “The
Classics”, tells us Aristotle’s book Physics
named a discipline, and Plato promoted the
mathematics developed by
Pythagoras. Mathematics was another
breakthrough. In Almagst by Ptolemy, mathematics
allowed the prediction of the
position of the planets in the sky. Copernicus
revised Ptolemy making the calculations
for a model with the sun at the centre. By1600,
Kepler improved these
calculations showing that the sun-centred model
worked better – finally overtaking
the ancient understandings!
Galileo
obtained
a telescope and saw planets and Saturn’s moons.
He reasoned there might
be laws for objects moving on earth too. He
measured how things fall. Bodies
did not fall with the same speed but with the
same increasing speed - a
constant acceleration that he measured: 9.8
metres per second per second.
Newton calculated the acceleration needed to
make a little moon circle the
earth rather than go in a straight line off into
space – and found the same 9.8m/s/s.
Newton’s vision in The
Mathematical
Principles of Natural Philosophy is of an
empty universe containing hard
moving particles – and his mathematics of the
movements made possible the 19th
century world of bridges, trains, skyscrapers
and hydraulic systems. The
particles move with a force, gravity, G, between
them. This is a world of time,
space and particles. Newton left the problem of
other forces in nature.
Surprisingly, there is just one other force. It
is electromagnetism, the force that
holds atoms in molecules, electrons in atoms and
that is used by neurons in our
brain.
Faraday
was
an experimenter of electricity and magnetism who
conceived something novel that
he called a “field” containing “lines of force”
extending in space. The lines
are modified by electric or magnetic bodies that
push or pull. Maxwell
translated this vision into mathematical
equations that describe electrical and
magnetic fields. They are still used for radio
antennae, atoms, and computers.
The equations predict that Faraday’s lines
behave like waves. More, the
equations predict the speed. It is the speed of
light. Light itself is an
electromagnetic wave and the colour is
determined by the frequency. Waves
beyond the visible frequencies were expected and
found. They are used for radio
and other purposes. This worldview is of time,
space, particles and fields.
Part
two of
the book, “The Beginning of Revolution”,
introduces the theories of relativity
and quanta in intriguing non-mathematical
chapters. It begins with Einstein
exploring the disconnect between Newton and
Maxwell’s equations and discovering
special relativity. Velocity is always relative
to something and this begs the
question of what Maxwell’s speed of light is
relative to.
The
stupendous finding is that any moving observer
covering distance in time, like
all of us moving with planet earth, have an
“extended present” in which there
is no future or past. This extended present time
zone increases with distance.
Around the earth, the time zone is thousandths
of a second. On the moon, the
time zone is seconds. On Mars it is 15mins. On
Mars at this moment, there are
events that have happened and are yet to happen
and things occur that are not in
our past or future. Ask a person on Mars a
question and the answer comes 15
minutes of neither past nor future after asking.
The succession of events in
the universe cannot be described as a succession
of nows, of presents. Time and
space are related and fuse together as
spacetime.
Einstein
also
finds that electric and magnetic fields link as
electromagnetic fields. Maxwell’s
equations can be simplified. Energy and mass are
linked – and atomic weapons
and nuclear power become part of a new era. The
present is like the flatness of
the earth - an illusion. “Here and
now” makes sense. But “now” makes no sense for
the rest of the universe. The gravitation
field is space and it undulates and bends. Earth
is not held around the Sun by
a force, but runs in space that inclines, like
the rim of a large funnel. Einstein
conceived of space – the gravitation field – as
a huge mollusk! He adapted then-existing
equations for curved surfaces to gravity – and
the equations bring predictions
and fulfillments – for example black holes.
Under
the heading
“Cosmos,” the book describes how Einstein turned
to reflect on the whole universe
and solved the problem of having a finite space
with no boundary. He conceived
the universe as a 3-sphere – two spheres joined
on the edge so that there is
the finite volume of two spheres but no
boundary. A digression explains how
this parallels the vision of Dante in his work
The Inferno and how the
baptistery dome in Florence might have inspired
Dante. From the perspective of
the person walking inside such a 3-sphere space,
one can measure its curvature
by walking back to where one started making a
“loop” – thinking that re-emerges
later in the book in “loop theory.”
Einstein
at
first does not believe what his equations are
telling him: the universe is
expanding. He tries to adjust the equation to
prevent that. But an expanding
universe is observed by experimentation and an
origin of the universe in a “big
bang” is conceived. Einstein’s original equation
stands. The book turns to a new
chapter on quanta and quantum theory.
Quantum
theory
involved many developers. Max Planck found that
electromagnetic energy within
a closed box comes as a set of fixed energy
packets with the packet size
proportional to the frequency (“colour”) of the
radiation. Einstein realized
light is made up of packets or grains from the
photoelectric effect. In the
effect light at high frequencies will cause a
substance to emit electrons. It
is not the intensity of light, the number of
grains, which matters. It is
the energy of those grains, the photons.
Neils
Bohr
studied atoms. These had been shown to be like
miniature solar systems with a
nucleus surrounded by orbiting electrons. The
light emitted by atoms are at certain
fixed frequencies. Bohr suggested that electrons
orbit only at specific
distances so that when the electron moves from
one orbit to another a specific
colour is emitted. The orbits are in fixed steps
- quantized. Another, Heisenberg,
writes equations for quantum mechanics. He
conceives of electrons as appearing
only for an encounter then disappearing until
the next encounter. Electrons
exist only when they interact. Heisenberg
produced tables of numbers
representing possible interactions of electrons
and his results correspond with
what is observed.
The
rest of
the mathematics for quantum mechanics was done
by Dirac. The theory is
described as airy, simple, beautiful and super
abstract. An electron is a
particle that appears then disappears like
seeing a person walking and
appearing and disappearing under one or another
low hanging street lamp on a
foggy night. Quantum mechanics tells what values
a physical property may assume,
its “spectrum,” and it tells the probability
that a particular value will
appear at the next interaction. The orbitals of
electrons drawn around a
nucleus in a high school chemistry class
represent a high probability zone for
electrons. Indeed quantum mechanics deciphers
the Mendeleev periodic table of
the elements used by chemists.
Dirac
realized that the model could be applied to
electromagnetic fields and so to
special relativity. The cloud of probability of
an electron between
interactions is like a field, converging the
idea of a field and a particle.
The energy of the electromagnetic field can take
on certain values – and these values
are the quanta of Einstein and Planck. This is
quantum field theory!
Today,
there
is a Standard Model of elementary particles that
describes most of what is seen
– except gravity – in terms of quantum field
theory. The world became strangely
simpler. It consists of spacetime plus quantum
fields. There is a fundamental “granularity”
in nature and a finite number of distinguishable
states a system can be in. The
world is a sequence of granular quantum events
with an elementary uncertainty.
Another
physicist,
Feynman, developed the probability of going from
A to B as the sum
of all the possible trajectories. Reality is now
relational and interactional.
We observe events that occur – not how things
are.
Part
3 is
called “Quantum Space and Relational Time”. It
begins with chapter 5 “Spacetime
is Quantum”. Dirac demonstrated how
electromagnetic radiation remained
well-defined at a point. Marvei repeated Dirac’s
math for a gravitational field
as described by Einstein and found that this
field is not well-defined at a
point when quantum theory is taken into account.
There is a limit to the
divisibility of space. As space shrinks, the
energy rises. High energy bends
the gravity field unto a black hole. The object
disappears. Below a certain scale,
nothing more is accessible. Nothing exists
there. This is at a size of 10-33
cm – the so-called Planck length. Space itself
is quantized on this scale.
Wheeler
conceived
of space as placid from a distance (I think like
an ocean seen from
an aircraft). But the same ocean becomes waves
and foam close up. Wheeler and a
student developed the Wheeler De Witt equation
that applied Schrodinger’s
technique for a particle wave equation to the
equation for general relativity.
The Wheeler De Witt equation has many problems -
including no time variable. Ashtekar
produced a simpler form of the equation.
Solutions depend on closed lines or
“loops” – hence the name loop theory. This is
now the promising approach to
quantum gravity.
Chapter
6
reflects on Quanta of Space. The solutions of
the Wheeler De Witt equation are
the Faraday lines of a gravitational field with
a difference. The gravitational
field has a finite quantized number of discreet
threads and must be seen more
like a web. Also, following Einstein, the
threads are not “in space,” the
gravitational web lines “are space.” Where the
solutions intersect, “nodes,”
can be joined by links in a graph. It is in the
nodes of the graph that volume
resides. Every node is a graph of the particle
of space -
a small region of space separated by a
surface with an area. Dirac’s equations allow
the spectra of properties like volume
and area to be determined. A series of discreet
volumes lie at the nodes of the
web of space. The result is quanta of gravity
that are quanta of space.
Loop
theory
provides that space cannot be infinitely small.
It is formed of “atoms”
billions of times smaller than the nucleus of an
atom. The graphs representing
the quantum states of (gravity) space have nodes
with a volume but can also
have a half integer for every line between the
nodes. This representation is
called a spin network. Walking from grain to
grain back to the original grain
is a loop in the theory. Which way an arrow
carried points on return depends on
the curvature of space. Curvature links to
gravitational field. It is possible
to determine the force of the gravitational
field from the spin network.
Chapter
7 declares
“Time does not Exist.” There is a useful
extended discussion of time and
pendulums and clocks aiming to show how these
all compare one phenomenon such
as a pendulum, with another like a heart beat.
Time is a useful construct, but
it is phenomena – not time – that exist. Hence
the mathematics should not
relate a phenomenon to a time variable but to
another real phenomenon variable.
The
key to
correctly perceiving the collision of two
billiard balls on a table is to
include everything – including gravity. Gravity
includes spacetime. The billiard
balls are not in time, but in a box that
includes spacetime. The passage of
time is the consequence of the process itself.
Loop theory gives the probability
of a boundary of the box – the probability that
balls will come out with a
particular configuration if they went in with
another. The probability is
computed by Feynman’s sum over all possible
trajectories. Here that includes
all possible spacetimes. Between the boundary
where the two balls enter the box
and where they exit there is no definite
spacetime or trajectory. There is only
a quantum cloud where all possible trajectories
exist together.
Quantum
space
has the structure of a “spin network.” Spacetime
is a history of a spin network
represented by moving the spin network. When
moved, every node draws a line and
every line draws a surface. Also, each node can
open into two or more nodes and
any two or more nodes can combine into one. The
result is a “spinfoam” visualized
as soap bubbles where the surfaces carry spins.
To compute the probability of a
process in the box one sums over all spinfoams
in the box that have the same
boundary as the desired process.
This
spinfoam
quantum gravity calculation allows a merging of
two previously used simplified
techniques: the Feynman diagram that represents
elementary interactions between
particles with weak forces; and the lattice
spacetime approximation in the Standard
Model for strong forces such as those between
quarks in an atomic nucleus.
These two much-used methods turn out to be
particular cases of summing over the
spinfoams of quantum gravity. The three basic
equations of loop theory are
given in the book for completeness! What is the
world made of? Covariant
quantum fields! These are fields that live on
themselves without spacetime, but
can generate spacetime!
The
last part,
Four, “Beyond Space and Time”, looks at the Big
Bang, Black Holes, some
thermodynamics and information theory. In 1927,
Lemaitre realized that data on
nebulae were consistent with an expanding
universe and when astronomers
confirmed galaxies moving away from earth
Lemaitre supposed the universe had
started from a point with an explosion – later
called “big bang.” Einstein
could not accept the prediction of an expanding
universe from his equation and
had inserted a constant so as to allow for a
static universe! This constant now
provides for the measured expansion rate of the
universe. Subsequent work has
confirmed these ideas.
Quantum
gravity
does not allow for an infinitely small point and
a big bang. Rather the
universe could contract but at a certain point
it would bounce back and expand
again – a “big bounce!” At the same time, a
contracting universe would pass
through a quantum phase where space and time
dissolve into probabilities. If “universe”
means the spacetime continuum we see around us,
passage through a quantum phase
would leave open the possibility of another
spatiotemporal continuum – another
universe -similar to this one. Calculations of
the probability of crossing the
phase of a big bounce from contraction to
expansion can be calculated by
spinfoams. Exploratory work is underway.
Chapter
9, “Empirical
Calculations”, reflects on how evidence advances
science and acknowledges that
quantum gravity is in infancy alongside string
theory. Recent evidence from the
Large Hadron Collider found the Higgs Boson,
confirming the standard model and
quantum mechanics, but did not find particles
required to further confirm
string theory. Planck Satellite observations
confirmed the standard
cosmological model and general relativity. The
detection of gravitational waves
in 2016 confirmed general relativity and the
standard model from quantum
mechanics. There is research to measure
gravitational undulations from cosmic
background raditation and from gravitational
waves themselves.
Chapter
10, “Black
Holes”, describes them. Space that becomes
highly curved collapses on itself
and time comes to a standstill. These strange
objects were foreseen by
Einstein’s theory. Quantum gravity has been used
to understand two features.
First, as Hawking calculated, black holes are
hot and like all hot bodies they
emit heat. As they do so, they lose energy and
mass and become smaller –
evaporating. Things are hot because microscopic
constituents vibrate. Here
loop theory suggests the heat is the
quantum gravity fluctuations of the atoms of
space. Alternatively, the quantum
fluctuations create a “correlation” between the
inside and outside of the black
hole. Quantum uncertainty across the horizon of
the black hole generates fluctuations
in the horizon geometry. Fluctuations imply
probability that in turn implies
thermodynamics and temperature. Bianchi showed
how loop quantum gravity could
yield a formula for the heat of the black holes.
Quantum gravity can suggest
what happens to a star that disappears into a
black hole. There should be quantum
repulsion as in the “big bounce” theory and the
star should pop out. This should
be fast, but time is slowed in a black hole.
Seeing black hole explosions would
be congruent with this theory.
“A
Limit on
Infinity” is the subject of Chapter 11. Quantum
mechanics not only sets a limit
on general relativity’s predictions that black
holes have an infinitely small
space. It limits electromagnetism. Quantum field
theory assumes the infinite
divisibility of space when summing the ways a
process can occur. But quantum
gravity removes these infinities. Fundamental
limitations emerge: a maximum
velocity c, a minimum length Lp, and a total of
information, Planck’s constant.
Natural unities are formed by setting each of
these at 1 and then measuring
other things relative to them; for example v=1/2
is half the speed of light.
The universe’s size can be calculated. It is
huge but finite. The chapter ends
with the attitude of science. The book of
Ecclesiasticus asks “who can number
the sand of the sea …” The opening of The
Sand Reckoner by Archimedes begins “Some
think … that the grains of sand
cannot be counted…” Archimedes went on to
develop a system for counting and
counts the vast number. Despite apologies for
the approximate and provisional
results, his point lies in insisting that
mysteries are intrinsically
accessible to human thought.
Chapter
12, “Information”,
speculates that future developments lie in the
exploration of information. Scientifically,
this is the number of possible alternatives for
something. A dice falling on
one face gives information N=6. Scientists use S
(Shannon information) =log2
(N) and the unit, S=1, is the bit. If
two people take a ball from a box with one white
and black ball the
alternatives are 2. If one person looks at the
colour, the colour of the other
ball is known. The colours are correlated.
The way atoms arrange themselves correlates with
the way other atoms arrange
themselves. One set of atoms can have
information about another set. Light has
information about objects it has played across.
The world is a network of
correlations between colliding atoms.
Information can be applied to heat. Heat
is in the random movement of molecules such that
faster is hotter. Hot tea
cools in cooler air that is warmed. There is a
loss of information- this is
entropy. Information can only be lost and
entropy grow. A black hole can be
linked to loss of information, and its heat to
entropy. When information enters
the black hole it cannot be recovered but it
increases the area of the hole.
This area represents lost information. Viewed
from outside the information
appears as entropy – and heat.
The
notion of
information and entropy can be applied to
quantum mechanics and quantum
gravity. Concepts like up or down can only be
used near a large mass where
gravity gives up and down a local meaning. Time
may then be linked to heat.
When a stone falls to the ground under local
gravity, it stops, and its energy
becomes heat. At this moment the falling process
is irreversible and the past
differs from the future. Heat distinguishes past
from future. The sun is
burning hydrogen and producing heat and will at
some point burn out. Any time
cycle is producing heat. Yet the thinking can be
reversed – heat is producing
time! As soon as a system is described by
averages, heat and time – our time –
emerge. Time is not fundamental. It is rather a
consequence of overlooking the
physical microstates and looking only at
averages. Time is information that is
missing. Time is ignorance. There is discussion
of the inter-relatedness of
things. Reality is not discreet objects. The
mountain is a concept viewed in a
context. The statue seen in a block of marble is
more than a block of marble.
The importance of information is underscored –
libraries, DNA, computer bits.
The final
section called “Mystery” reminds us of the “I’m
not sure” as well as of the
effort to know and to find. It recalls the world
without time that does not
exist in space made up of interacting quantum
fields whose dense network of
reciprocal interactions generate space, time,
particles, waves and light.