Reality?
Reality: The definition
Even trying to define what we mean by
"reality" is fraught with difficulty
WHAT DO we
actually mean by reality?
A straightforward answer is that it means everything that appears to our five
senses - everything that we can see, smell, touch and so forth. Yet this answer
ignores such problematic entities as electrons, the recession and the number 5,
which we cannot sense but which are very real. It also ignores phantom limbs
and illusory smells. Both can appear vividly real, but we would like to say
that these are not part of reality.
We could
tweak the definition by equating reality with what appears to a sufficiently large
group of people, thereby ruling out subjective hallucinations. Unfortunately
there are also hallucinations experienced by large groups, such as a mass
delusion known as koro, mainly observed in South-East Asia, which involves the
belief that one's genitals are shrinking back into one's body. Just because
sufficiently many people believe in something does not make it real.
Another
possible mark of reality we could focus on is the resistance it puts up: as the
science fiction writer Philip K. Dick put it, reality is that which, if you
stop believing in it, does not go away. Things we just make up yield to our
wishes and desires, but reality is stubborn. Just because I believe there is a
jam doughnut in front of me doesn't mean there really is one. But again, this
definition is problematic. Things that we do not want to regard as real can be
stubborn too, as anyone who has ever been trapped in a nightmare knows. And
some things that are real, such as stock markets, are not covered by this
definition because if everyone stopped believing in them, they would cease to
exist.
There are
two definitions of reality that are much more successful. The first equates
reality with a world without us, a world untouched by human desires and
intentions. By this definition, a lot of things we usually regard as real -
languages, wars, the financial crisis - are nothing of the sort. Still, it is
the most solid one so far because it removes human subjectivity from the
picture.
The second
equates reality with the most fundamental things that everything else depends
on. In the material world, molecules depend on their constituent atoms, atoms
on electrons and a nucleus, which in turn depends on protons and neutrons, and
so on. In this hierarchy, every level depends on the one below it, so we might
define reality as made up of whatever entities stand at the bottom of the chain
of dependence, and thus depend on nothing else.
This
definition is even more restrictive than "the world without us" since
things like Mount Everest would not count as part of reality; reality is
confined to the unknown foundation on which the entire world depends. Even so,
when we investigate whether something is real or not, these final two
definitions are what we should have in mind.
See Video: What lies
at the heart of the universe
(Image: Sharee Davenport/Flickr/Getty)
Reality: Is matter real?
It's relatively easy to demonstrate what physical reality isn't. It is much harder to work out what it is.
Nothing
seems more real than the world of everyday objects, but things are not as they
seem. A set of relatively simple experiments reveals enormous holes is our
intuitive understanding of physical reality. Trying to explain what goes on
leads to some very peculiar and often highly surprising theories of the world around
us.
Here is a
simple example. Take an ordinary desk lamp, a few pieces of cardboard with
holes of decreasing sizes, and some sort of projection screen such as a white
wall. If you put a piece of cardboard between the lamp and the wall, you will
see a bright patch where the light passes through the hole in the cardboard. If
you now replace the cardboard with pieces containing smaller and smaller holes,
the patch too will diminish in size. Once we get below a certain size, however,
the pattern on the wall changes from a small dot to a series of concentric dark
and light rings, rather like an archery target. This is the "Airy
pattern" - a characteristic sign of a wave being forced through a hole
(see image).
In itself,
this is not very surprising. After all, we know that light is a wave, so it
should display wave-like behaviour.
But now
consider what happens if we change the set-up of the experiment a bit. Instead
of a lamp, we use a device that shoots out electrons, like that found in
old-fashioned TV sets; instead of the wall, we use a plate of glass coated with
a phosphor that lights up when an electron strikes it. We can therefore use
this screen to track the places where the electrons hit. The results are
similar: with sufficiently small holes we get an Airy pattern.
This now
seems peculiar: electrons are particles located at precise points and cannot be
split. Yet they are behaving like waves that can smear out across space, are
divisible, and merge into one another when they meet.
Perhaps it
is not that strange after all. Water consists of molecules, yet it behaves like
a wave. The Airy pattern may just emerge when enough particles come together,
whether they are water molecules or electrons.
How do electrons know how to make an Airy pattern?
(Image: GI PhotoStock/Science Photo Library)
A simple
variant of the experiments shows, however, that this cannot be right. Suppose
we reduce the output of the electron gun to one particle each minute. The Airy
pattern is gone, and all we see is a small flash every minute. Let's leave this
set-up to run for a while, recording each small flash as it occurs. Afterwards,
we map the locations of all the thousands of flashes.
Surprisingly,
we do not end up with a random arrangement of dots, but with the Airy pattern
again. This result is extremely strange. No individual electron can know where
all the earlier and later electrons are going to hit, so they cannot
communicate with each other to create the bullseye pattern. Rather, each
electron must have travelled like a wave through the hole to produce the
characteristic pattern, then changed back into a particle to produce the point
on the screen. This, of course, is the famous wave-particle duality of quantum
mechanics.
This strange
behaviour is shared by any sufficiently small piece of matter, including
electrons, neutrons, photons and other elementary particles, but not just by
these. Similar effects have been observed for objects that are large enough in
principle to be seen under a microscope, such as buckyballs.
In order to
explain the peculiar behaviour of such objects, physicists associate a wave
function with each of them. Despite the fact that these waves have the usual
properties of more familiar waves such as sound or water waves, including
amplitude (how far up or down it deviates from the rest state), phase (at what
point in a cycle the wave is), and interference (so that "up" and
"down" phases of waves meeting each other cancel out), what they are
waves in is not at all transparent. Einstein aptly spoke of a
"phantom field" as their medium.
For a wave
in an ordinary medium such as water, we can calculate its energy at any one
point by taking the square of its amplitude. Wave functions, however, carry no
energy. Instead, the square of their amplitude at any given point gives us the
probability of observing the particle if a detector such as the phosphor-coated
screen is placed there.
Clearly, the
point where an object switches from being a probability wave, with its
potential existence smeared out across space, and becomes an actual, spatially
localised object is crucially important to understanding whether matter is
real. What exactly happens when the wave function collapses - when among the
countless possibilities where the particle could be at any moment, one is
chosen, while all the others are rejected?
First of
all, we have to ask ourselves when this choice is made. In the example
described above, it seems to happen just before the flash on the phosphor
screen. At this moment, a measurement of the electron's position was made by a
piece of phosphor glowing as the particle struck it, so there must have been an
electron there, and not just a probability wave.
But assume
we cannot be in the lab to observe the experiment, so we point a camera at the
phosphor screen and have the result sent via a satellite link to a computer on
our desktop. In this case, the flash of light emitted from the phosphor screen
has to travel to the camera recording it, and the process is repeated: like the
electrons, light also travels as a wave and arrives as a particle. What reason
is there to believe that the switch from probability wave to particle actually
occurred on the phosphor screen, and not in the camera?
At first, it
seemed as if the phosphor screen was the measuring instrument, and the electron
was the thing being measured. But now the measuring device is the camera and
the phosphor screen is part of what is measured. Given that any physical object
transmitting the measurement we can add on to this sequence - the camera, the
computer, our eyes, our brain - is made up of particles with the same
properties as the electron, how can we determine any particular step at which
to place the cut between what is measured and what is doing the measuring?
This
ever-expanding chain is called the von Neumann chain, after the physicist and
mathematician John von Neumann. One of his Princeton University colleagues,
Eugene Wigner, made a suggestion as to where to make the cut. As we follow the
von Neumann chain upwards, the first entity we encounter that is not made up in
any straightforward fashion out of pieces of matter is the consciousness of the
observer. We might therefore want to say that when consciousness enters the
picture, the wave function collapses and the probability wave turns into a
particle.
The idea
that consciousness brings everyday reality into existence is, of course, deeply
strange; perhaps it is little wonder that it is a minority viewpoint.
There is
another way of interpreting the measurement problem that does not involve
consciousness - though it has peculiar ramifications of its own. But for now
let's explore Wigner's idea in more depth.
If a
conscious observer does not collapse the wave function, curious consequences
follow. As more and more objects get sucked into the vortex of von Neumann's
chain by changing from being a measuring instrument to being part of what is measured,
the "spread-out" structure of the probability wave becomes a property
of these objects too. The "superposed" nature of the electron - its
ability to be at various places at once - now also affects the measuring
instruments.
It has been
verified experimentally that not just the unobservably small, but objects large
enough to be seen under a microscope, such as a 60-micrometre-long metal strip,
can exhibit such superposition behaviour. Of course, we can't look through a
microscope and see the metal strip being at two places at once, as this would
immediately collapse the wave function. Yet it is clear that the indeterminacy
we found at the atomic level can spread to the macro level.
Yet if we
accept that the wave function must collapse as soon as consciousness enters the
measurement, the consequences are even more curious. If we decide to break off
the chain at this point, it follows that, according to one of our definitions
of reality, matter cannot be regarded as real. If consciousness is required to turn
ghostly probability waves into things that are more or less like the objects we
meet in everyday life, how can we say that matter is what would be there
anyway, whether or not human minds were around?
But perhaps
this is a bit too hasty. Even if we agree with the idea that consciousness is
required to break the chain, all that follows is that the dynamic attributes of
matter such as position, momentum and spin orientation are mind-dependent. It
does not follow that its static attributes, including mass and charge, are
dependent on in this. The static attributes are there whether we look or not.
Nevertheless,
we have to ask ourselves whether redefining matter as "a set of static
attributes" preserves enough of its content to allow us to regard matter
as real. In a world without minds, there would still be attributes such as mass
and charge, but things would not be at any particular location or travel in any
particular direction. Such a world has virtually nothing in common with the
world as it appears to us. Werner Heisenberg observed that: "the ontology
of materialism rested upon the illusion that the kind of existence, the direct
'actuality' of the world around us, can be extrapolated into the atomic range.
This extrapolation, however, is impossible... Atoms are not things."
It seems
that the best we are going to get at this point is the claim that some things
are there independent of whether we, as human observers, are there, even though
they might have very little to do with our ordinary understanding of matter.
Does our
understanding of the reality of matter change if we choose the other strong
definition of reality - not by what is there anyway, but by what provides the
foundation for everything else (see "Reality: The definition”, above.)?
In order to
answer this question, we have to look at the key scientific notion of a
reductive explanation. Much of the power of scientific theories derives from
the insight that we can use a theory that applies to a certain set of objects
to explain the behaviour of a quite different set of objects. We therefore
don't need a separate set of laws and principles to explain the second set.
A good
example is the way in which theories from physics and chemistry, dealing with
inanimate matter, can be used to explain biological processes. There is no need
to postulate a special physics or a special chemistry to explain an organism's
metabolism, how it procreates, how its genetic information is passed on, or how
it ages and dies. The behaviour of the cells that make up the organism can be
accounted for in terms of the nucleus, mitochondria and other subcellular
entities, which can in turn be explained in terms of chemical reactions based
on the behaviour of molecules and the atoms that compose them. For this reason,
explanations of biological processes can be said to be reducible to chemical
and ultimately to physical ones.
If we pursue
a reductive explanation for the phenomena around us, a first step is to reduce
statements about the medium-sized goods that surround us - bricks, brains,
bees, bills and bacteria - to statements about fundamental material objects,
such as molecules. We then realise everything about these things can be
explained in terms of their constituents, namely their atoms. Atoms, of course,
have parts as well, and we are now well on our way through the realm of ever
smaller subatomic particles, perhaps (if string theory is correct) all the way
down to vibrating strings of pure energy. So far we have not reached the most
fundamental objects. In fact, there is not even an agreement that there are any
such objects.
Yet this is
no reason to stop our reductionist explanation here, since we can always
understand the most basic physical objects in terms of where they are in space
and time. Instead of talking about a certain particle that exists at
such-and-such a place for such-and-such a period of time, we can simply reduce
this to talk about a certain region in space that is occupied between two
different times.
We can go
even more fundamental. If we take an arbitrary fixed point in space, and a
stable unit of spatial distance, we can specify any other point in space by
three coordinates. These simply tell us to go so many units up or down, so many
units left or right, and so many units back or forth. We can do the same with
points in time. We now have a way of expressing points in space-time as sets of
four numbers, x, y, z and t, where x, y, and z represent the three spatial
dimensions and t the time dimension. In this way, reality can be boiled down to
numbers.
And this
opens the door to something yet more fundamental. Mathematicians have found a
way of reducing numbers to something even more basic: sets. To do this, they
replace the number 0 with the empty set, the number 1 with the set that
contains just the empty set, and so on (see "Reality: Is everything made
of numbers? ", below). All the properties of numbers also hold for all
these ersatz numbers made from sets. It seems as if we have now reduced all of
the material world around us to an array of sets.
For this
reason, it is important to know what these mathematical objects called sets
really are. There are two views of mathematical objects that are important in
this context. First, there is the view of them as "Platonic" objects.
This means that mathematical objects are unlike all other objects we encounter.
They are not made of matter, they do not exist in space or time, do not change,
cannot be created or destroyed, and could not have failed to exist. According
to the Platonic understanding, mathematical objects exist in a "third realm",
distinct from the world of matter, on the one hand, and the world of mental
entities, such as perceptions, thoughts and feelings, on the other.
Second, we
can understand mathematical objects as fundamentally mental in nature. They are
of the same kind as the other things that pass through our mind: thoughts and
plans, concepts and ideas. They are not wholly subjective; other people can
have the very same mathematical object in their minds as we have in ours, so
that when we both talk about the Pythagorean theorem, we are talking about the
same thing. Still, they do not exist except in the minds in which they occur.
Either of
these understandings leads to a curious result. If the bottom level of the
world consists of sets, and if sets are not material but are instead some
Platonic entities, material objects have completely disappeared from view and
cannot be real in the sense of constituting a fundamental basis of all
existence. If we follow scientific reductionism all the way down, we end up
with stuff that certainly does not look like tiny pebbles or billiard balls,
not even like strings vibrating in a multidimensional space, but more like what
pure mathematics deals with.
Of course,
the Platonistic view of mathematical objects is hardly uncontroversial, and many
people find it hard to get any clear idea of how objects could exist outside of
space and time. But if we take mathematical objects to be mental in nature, we
end up with an even stranger scenario.
The
scientific reductionist sets out to reduce the human mind to the activity of
the brain, the brain to an assembly of interacting cells, the cells to
molecules, the molecules to atoms, the atoms to subatomic particles, the
subatomic particles to collections of space-time points, the collections of
space-time points to sets of numbers, and the sets of numbers to pure sets. But
at the very end of this reduction, we now seem to loop right back to where we
came from: to the mental entities.
We encounter
a similar curious loop in the most influential way of understanding quantum
mechanics, the Copenhagen interpretation. Unlike Wigner's consciousness-based
interpretation, this does not assume the wave function collapses when a
conscious mind observes the outcome of some experiment. Instead, it happens
when the system to be measured (the electron) interacts with the measuring
device (the phosphor screen). For this reason, it has to be assumed that the
phosphor screen will not itself exhibit the peculiar quantum behaviour shown by
the electron.
In the
Copenhagen interpretation, then, things and processes describable in terms of
familiar classical concepts are the foundation of any physical interpretation.
And this is where the circularity comes in. We analyse the everyday world of
medium-sized material things in terms of smaller and smaller constituents until
we deal with parts that are so small that quantum effects become relevant for
describing them. But when it comes to spelling out what is really going on when
a wave function collapses into an electron hitting a phosphor screen, we don't
ground our explanation in some yet more minute micro-level structures; we
ground it in terms of readings made by non-quantum material things.
What this
means is that instead of going further down, we instead jump right back up to
the level of concrete phenomena of sensory perception, namely measuring devices
such as phosphor screens and cameras. Once more, we are in a situation where we
cannot say that the world of quantum objects is fundamental. Nor can we say
that the world of measuring devices is fundamental since these devices are
themselves nothing but large conglomerations of quantum objects.
We therefore
have a circle of things depending on each other, even though, unlike in the
previous case, mental objects are no longer part of this circle. As a result,
neither the phosphor screen nor the minute electron can be regarded as real in
any fundamental sense, since neither constitutes a class of objects that
everything depends on. What we thought we should take to be the most fundamental
turns out to involve essentially what we regarded as the least fundamental.
In our
search for foundations, we have gone round in a circle, from the mind, via
various components of matter, back to the mind - or, in the case of the
Copenhagen interpretation, from the macroscopic to the microscopic, and then
back to the macroscopic. But this just means that nothing is fundamental, in
the same way there is no first or last stop on London Underground's Circle
Line. The moral to draw from the reductionist scenario seems to be that either
what is fundamental is not material, or that nothing at all is fundamental.
Reality: Is everything made of numbers?
Dig deep enough into the fabric of reality and you
eventually hit a seam of pure mathematics
WHEN Albert
Einstein finally completed his general theory of relativity in 1916, he looked down at the
equations and discovered an unexpected message: the universe is expanding.
Einstein
didn't believe the physical universe could shrink or grow, so he ignored what
the equations were telling him. Thirteen years later, Edwin Hubble found clear
evidence of the universe's expansion. Einstein had missed the opportunity to
make the most dramatic scientific prediction in history.
How did
Einstein's equations "know" that the universe was expanding when he
did not? If mathematics is nothing more than a language we use to describe the
world, an invention of the human brain, how can it possibly churn out anything
beyond what we put in? "It is difficult to avoid the impression that a
miracle confronts us here," wrote physicist Eugene Wigner in his classic
1960 paper "The unreasonable effectiveness of mathematics in the
natural sciences" (Communications on Pure and Applied Mathematics, vol 13,
p 1).
The
prescience of mathematics seems no less miraculous today. At the Large Hadron
Collider at CERN, near Geneva, Switzerland, physicists recently observed the
fingerprints of a particle that was arguably discovered 48 years ago lurking in
the equations of particle physics.
How is it
possible that mathematics "knows" about Higgs particles or any other
feature of physical reality? "Maybe it's because math is
reality," says physicist Brian Greene of Columbia University, New York.
Perhaps if we dig deep enough, we would find that physical objects like tables
and chairs are ultimately not made of particles or strings, but of numbers.
"These
are very difficult issues," says philosopher of science James Ladyman of
the University of Bristol, UK, "but it might be less misleading to say
that the universe is made of maths than to say it is made of matter."
Difficult
indeed. What does it mean to say that the universe is "made of
mathematics"? An obvious starting point is to ask what mathematics is made
of. The late physicist John Wheeler said that the "basis of all
mathematics is 0 = 0". All mathematical structures can be derived from
something called "the empty set", the set that contains no elements.
Say this set corresponds to zero; you can then define the number 1 as the set
that contains only the empty set, 2 as the set containing the sets
corresponding to 0 and 1, and so on. Keep nesting the nothingness like
invisible Russian dolls and eventually all of mathematics appears.
Mathematician Ian Stewart of the University of Warwick, UK, calls this
"the dreadful secret of mathematics: it's all based on nothing" (New
Scientist, 19 November 2011, p 44). Reality may come down to
mathematics, but mathematics comes down to nothing at all.
That may be
the ultimate clue to existence - after all, a universe made of nothing doesn't
require an explanation. Indeed, mathematical structures don't seem to require a
physical origin at all. "A dodecahedron was never created," says Max Tegmark of
the Massachusetts Institute of Technology. "To be created, something first
has to not exist in space or time and then exist." A dodecahedron doesn't
exist in space or time at all, he says - it exists independently of them.
"Space and time themselves are contained within larger mathematical
structures," he adds. These structures just exist; they can't be created
or destroyed.
That raises
a big question: why is the universe only made of some of the available
mathematics? "There's a lot of math out there," Greene says.
"Today only a tiny sliver of it has a realisation in the physical world.
Pull any math book off the shelf and most of the equations in it don't
correspond to any physical object or physical process."
It is true
that seemingly arcane and unphysical mathematics does, sometimes, turn out to
correspond to the real world. Imaginary numbers, for instance, were once
considered totally deserving of their name, but are now used to describe the
behaviour of elementary particles; non-Euclidean geometry eventually showed up
as gravity. Even so, these phenomena represent a tiny slice of all the
mathematics out there.
Not so fast,
says Tegmark. "I believe that physical existence and mathematical
existence are the same, so any structure that exists mathematically is also
real," he says.
So what
about the mathematics our universe doesn't use? "Other mathematical
structures correspond to other universes," Tegmark says. He calls this the
"level 4 multiverse", and it is far stranger than the multiverses
that cosmologists often discuss. Their common-or-garden multiverses are
governed by the same basic mathematical rules as our universe, but Tegmark's
level 4 multiverse operates with completely different mathematics.
All of this
sounds bizarre, but the hypothesis that physical reality is fundamentally
mathematical has passed every test. "If physics hits a roadblock at which
point it turns out that it's impossible to proceed, we might find that nature
can't be captured mathematically," Tegmark says. "But it's really
remarkable that that hasn't happened. Galileo said that the book of nature was
written in the language of mathematics - and that was 400 years ago."
If reality
isn't, at bottom, mathematics, what is it? "Maybe someday we'll encounter
an alien civilisation and we'll show them what we've discovered about the
universe," Greene says. "They'll say, 'Ah, math. We tried that. It
only takes you so far. Here's the real thing.' What would that be? It's hard to
imagine. Our understanding of fundamental reality is at an early stage."
See Video:
What
lies at the heart of the universe
Reality: A universe of information
Ghost in the machine?
(Image: Matt Lloyd/Rex Features)
What we call reality might actually be the output
of a program running on a cosmos-sized quantum computer
WHATEVER
kind of reality you think you're living in, you're probably wrong. The universe is a computer, and
everything that goes on in it can be explained in terms of information
processing.
The
connection between reality and computing may not be immediately obvious, but
strip away the layers and that is exactly what some researchers think we find.
We think of the world as made up of particles held together by forces, for
instance, but quantum theory tells us that these are just a mess of fields we can
only properly describe by invoking the mathematics of quantum physics.
That's where
the computer comes in, at least if you think of it in conceptual terms as
something that processes information rather than as a boxy machine on your
desk. "Quantum physics is almost phrased in terms of information
processing," says Vlatko
Vedral of the University of Oxford. "It's suggestive that you will
find information processing at the root of everything."
Information
certainly has a special place in quantum theory. The famous uncertainty
principle - which states that you can't simultaneously know the momentum and
position of a particle - comes down to information. As does entanglement, where
quantum objects share properties and exchange information irrespective of the
physical distance between them.
In fact,
every process in the universe can be reduced to interactions between particles
that produce binary answers: yes or no, here or there, up or down. That means
nature, at its most fundamental level, is simply the flipping of binary digits
or bits, just like a computer. The result of the myriad bit flips is manifest
in what we perceive as the ongoing arrangement, rearrangement and interaction
of atoms - in other words, reality.
According to
Ed Fredkin of the Massachusetts Institute of Technology, if we could dig into
this process we would find that the universe follows just one law, a single
information-processing rule that is all you need to build a cosmos. In
Fredkin's view, this would be some form of "if - then" procedure; the
kind of rule used in traditional computing to manipulate the bits held by
transistors on a chip and operate the logic gates, but this time applied to the
bits of the universe.
Vedral and
others think it's a little more complex than that. Because we can reduce
everything in the universe to entities that follow the laws of quantum physics,
the universe must be a quantum computer rather than the classical type we are
familiar with.
One of the
attractions of this idea is that it can supply an answer to the question
"why is there something rather than nothing?". The randomness
inherent in quantum mechanics means that quantum information - and by extension,
a universe - can spontaneously come into being, Vedral says.
For all
these theoretical ideas, proving that the universe is a quantum computer is a
difficult task. Even so, there is one observation that supports the idea that
the universe is fundamentally composed of information. In 2008, the GEO 600
gravitational wave detector in Hannover, Germany, picked up an anomalous signal
suggesting that space-time is pixellated. This is exactly what would be
expected in a "holographic" universe, where 3D reality is actually a
projection of information encoded on the two-dimensional surface of the
boundary of the universe (New
Scientist, 17 January 2009, p 24).
This bizarre
idea arose from an argument over black holes. One of the fundamental tenets of
physics is that information cannot be destroyed, but a black hole appears to
violate this by swallowing things that contain information then gradually
evaporating away. What happens to that information was the subject of a long
debate between Stephen Hawking and several of his peers. In the end, Hawking
lost the debate, conceding that the information is imprinted on the event
horizon that defines the black hole's boundary and escapes as the black hole
evaporates. This led theoretical physicists Leonard Susskind and Gerard't Hooft
to propose that the entire universe could also hold information at its boundary
- with the consequence that our reality could be the projection of that
information into the space within the boundary. If this conjecture is true,
reality is like the image of Princess Leia projected by R2D2 in Star Wars:
a hologram.
- From issue 2884 of New Scientist magazine, pages 34-35.
- and pages 38-39, 37-46, 41.
For more information about quantum reality see http://nexusilluminati.blogspot.com/search/label/quantum%20reality
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