# Consciousness Studies/The Philosophical Problem#The philosophical problem

## The philosophical problem of phenomenal consciousness

Chalmers (1996) encapsulated the philosophical problem of phenomenal
consciousness, describing it as the *Hard Problem*. The Hard Problem can
be concisely defined as \"how to explain a state of consciousness in
terms of its neurological basis\" Block (2004). A state is an
arrangement of things in space over a period of time. It is possible
that the Hard Problem has not been solved because the concepts of
\"space\", \"time\" and \"things\" are intensely problematic in both
science and philosophy.

Some philosophers have argued that *changes* in state are equivalent to
\"mental states\". That consciousness experience always involves acts,
such as acts of acquaintance (Russell 1912). But what is a succession of
states in the brain or the physical world?

As an extension of the idea of \"acts\" as mental states many
philosophers have argued that the functional description of a system
does not need to contain any reference to qualia within that system.
Such ideas, based on nineteenth century materialism, have been expressed
by Huxley, Ryle, Smart, Goldman and many others. However, although
qualia are not required for classical functions, such as most
computations or servo-control, it is far from clear whether this is true
for all functions. If a function is described as any thing that mediates
a change in state it should be realised that \"change\" itself is not
fully understood in philosophy or science and that some systems, such as
quantum mechanical systems, contain state changes that are far from
understood. It will be seen below that our scientific knowledge is not
yet sufficiently complete to allow the claim that all, or even any,
changes can occur without qualia.

Whether a philosopher or scientist is dualist, materialist or
physicalist they should have some insight into current theories about
the physical world. Certainly, if they are considering the problem of
\"how to explain a state of consciousness in terms of its neurological
basis\" then some idea of a \"neurological basis\" is essential.

The objective of this section is to give an account of the problems of
space, time and content and to describe how these affect the problem of
consciousness.

## Epiphenomenalism and the problem of change

Philosophers have noticed since the time of Leibniz that phenomenal
consciousness does not seem to be required for the brain to produce
action. As an example there are numerous reflexes that can occur without
any awareness that they are happening. In fact it is difficult to think
of any response to a stimulus that requires phenomenal consciousness and
could not, in principle, be performed in the absence of conscious
intervention. T.H. Huxley is often regarded as the originator of the
term **epiphenomenalism** to describe how consciousness seems extraneous
to processes in the materialist interpretation of the world although the
term may have originated in James\' description of Huxley\'s (1874)
ideas.

According to nineteenth century science changes in state cannot explain
the existence of phenomenal consciousness so superficially it may appear
as if phenomenal consciousness is unnecessary. However, it may come as a
shock to the reader to discover that nineteenth century science is also
unable to account for any change in state. In the materialist paradigm
time is construed to be a succession of instants of no duration, each of
which is entirely separate from the others. As a result no instant can
cause a change in another instant. It is not only conscious experience
that is epiphenomenal, each instant of the nineteenth century concept of
the world is epiphenomenal because it cannot give rise to the next
instant.

On the one hand it seems that conscious experience is not required for a
nineteenth century model of behaviour and on the other hand nineteenth
century science seems to be impossible without extraneous input from a
conscious observer who contains the idea of change.

The problem of change is closely related to the problem of time which is
discussed in depth below. (See Change and Inconsistency, Stanford
Encyclopedia of
Philosophy).

The reader might consider whether phenomenal consciousness is indeed
epiphenomenal. Empirical reports describe it as something that is
different from the world beyond the body (see direct
realism) -
but could we generate empirical reports of an epiphenomenon? If we do
indeed generate empirical reports of phenomenal consciousness is there
some non-materialist, physical\*\* connection between phenomenal
consciousness and the functional state?

In the analysis that follows it is essential that the reader does not
dismiss the possibility that conscious experience is largely
non-functional in a classical sense. The idea that observation is not
action should not be dismissed out of hand. Indeed the claim that
something cannot be true if it is \"epiphenomenal\" in a classical sense
is astonishing in the context of modern quantum physics. Everettian
approaches (and offshoots like the Bohmian, Consistent Histories and
operational (decoherence) approaches) to quantum physics all allow that
the classical world is epiphenomenal (cf: Page 1997, Stapp 1998). The
Copenhagen Interpretation, however, was less clear on this issue.

It is curious that problems with the nature of phenomenal consciousness
are also problems with nineteenth century science - Aristotlean regress
in the mind is part of the wider problem of epistemological regress and
epiphenomenalism is part of the wider problem of change. Perhaps
nineteenth century science is not an appropriate foundation for
understanding consciousness.

Recommended reading:

Mortensen, C. (2002) Change. The Stanford Encyclopedia of Philosophy.
<http://plato.stanford.edu/entries/change/>

Page, D.N. (1997). Sensible Quantum Mechanics: Are Only Perceptions
Probabilistic? <http://arxiv.org/abs/quant-ph/9506010>

Rivas, T., & Dongen, H. van (2003). Exit Epiphenomenalism: The
Demolition of a Refuge

Stapp, (1998). Quantum Ontology and Mind-Matter Synthesis.\[Appeared in
proceedings of X-th Max Born Symposium, eds, Blanchard and Jadczyk, Vol
517 Lecture notes in Physics series, Springer-Verlag, 1999 (Quantum
Future:from Volta and Como to the present and beyond) \]
<http://arxiv.org/PS_cache/quant-ph/pdf/9905/9905053.pdf>

(\*\*) cf: gravity may affect the rate at which clocks tick without the
occurrence of any collisions between particles or anything that can be
called a \"process\".

## The problem of time

*This section should be read after reading a quick introduction to
special
relativity*

### The past century of ideas about time

McTaggart in 1908 set out some of the problems with our idea of time in
his classic paper *The Unreality of Time*. He drew attention to the way
that a sequence of things in a list does not describe time because a
sequence of things is constant yet events are always changing. These
considerations led him to propose that there are three different
sequences of things, or series, that are commonly used to describe
events. McTaggart\'s three different time series are summarized in the
illustration below.

![](constudseries.gif "constudseries.gif")

He argued that only the \'A Series\' is a temporal series because it is
only in the A Series that change occurs so that events can be given the
labels \'future\', \'present\' and \'past\'. He pointed out that
although the A Series is used for determining the direction and sequence
of events it is not itself \'in time\' because it contains relations
that are neither a part of the C Series nor the B Series. This led him
to propose that time is unreal because change involves a movement along
the time series so cannot be fixed within it.

Franck (1994) argued on the basis of Atmanspacher\'s models of universes
with real and imaginary geometries that McTaggart\'s \'unreality\' of
time could be avoided by proposing a second, imaginary, time dimension.

`"What McTaggart in fact demonstrates is that it is impossible to `\
`account for temporality within a strictly one-dimensional concept `\
`of time."(Franck 1994).`

This idea is illustrated below:

![](constudseries2.gif "constudseries2.gif")

This idea of time being two dimensional is not new and has also been
advanced by such luminaries as Hermann Weyl and CD Broad. Weyl (1920)
made the following statement that is extremely apposite to consciousness
studies, he wrote that reality is a:

`"...four-dimensional continuum which is neither 'time' nor 'space'. `\
`Only the consciousness that passes on in one portion of this world `\
`experiences the detached piece which comes to meet it and passes `\
`behind it, as history, that is, as a process that is going forward `\
`in time and takes place in space." (Weyl 1920).`

McTaggart\'s objection to time is felt intuitively by anyone who has
contemplated the *Block Universe* of Relativity Theory. If the universe
is four dimensional with three space dimensions and one time dimension
it would be fixed forever and the observer would be frozen within it.
This would occur whether the time dimension was arranged according to
Galilean Relativity or Modern Relativity.

Peter Lynds in 2003 has drawn attention to the \'frozen\' nature of the
observer in a four dimensional universe. He proposes, like Kevin Brown
in his popular mathpages,
that time must be approached from the viewpoint of quantum physics
because simple four dimensional universes would give rise to \'frozen,
static\' instants and hence no change could occur. Lynds argues that if
quantum physics is introduced then no event can have a definite moment
of occurrence and that change occurs because of this quantum
indeterminacy:

`<font face="times new roman">`{=html}I would suggest that there is
possibly much more to be gleaned from the connection between quantum
physics and the inherent need for physical continuity, and even go as
far to speculate that the dependent relationship may be the underlying
explanation for quantum jumping and with static indivisible mathematical
time values directly related to the process of quantum collapse. Time
will tell.\"`</font>`{=html}(Lynds 2003).

Our knowledge of quantum uncertainty can be traced back to De Broglie\'s
highly successful model of individual particle motions. This model was
based on Special Relativity theory and it predicted a wave nature for
particles. The Heisenberg Uncertainty Principle can be shown to be a
consequence of this wave nature. See the illustration below:

![](constuddebroglie.gif "constuddebroglie.gif")

The illustration is based on de Broglie (1925) and Pollock (2004).

So Lynds\' argument that change is due to the uncertainty principle is
actually an argument that change is due to differing planes of
simultaneity between systems that are in relative motion. Kevin Brown is
aware of this; he summarises the effect of uncertainty due to special
relativity and points out that it provides a resolution of Zeno\'s arrow
paradox:

`"The theory of special relativity answers Zeno's concern over the `\
`lack of an instantaneous difference between a moving and a non-moving `\
`arrow by positing a fundamental re-structuring the basic way in which `\
`space and time fit together, such that there really is an instantaneous `\
`difference between a moving and a non-moving object, insofar as it `\
`makes sense to speak of "an instant" of a physical system with mutually `\
`moving elements.  Objects in relative motion have different planes of `\
`simultaneity, with all the familiar relativistic consequences, so not `\
`only does a moving object look different to the world, but the world `\
`looks different to a moving object." (Brown 19??)`

Another approach to the way that time has a direction is to suggest that
the possible outcomes in quantum mechanics are located in \"disjoint
space-time regions which exclude one another\" (McCall 2000). This does
not explain the A Series however because the observer would not have any
sense of \'becoming\' or temporality as a result of the existence of
regions that could not be observed.

### Presentism and Four-Dimensionalism

In the past century the philosophical battle lines have been drawn
between the Presentists, who believe that only the durationless instant
of the present exists and the Four Dimensionalists who consider that
things are extended in both space and time (see Rea (2004)). There are
two types of Presentism, in its extreme form it is the belief that the
past and future are truly non-existent, that what we call time is not an
axis for arranging things but a series of changes and records in an
*enduring* present. In its less extreme form, which might be called
*functional presentism*, the present is a durationless instant that can
never be connected to the future or past except through predictions and
records.

In consciousness studies it is the conventional theory that brain
activity occurs in the present instant and that the past can only occur
as memories retrieved into this durationless present. So, in
consciousness studies functional Presentism seems to be the accepted
paradigm.

Presentism cannot explain change. Each instant is durationless and
frozen. That said, as seen above, four dimensionalism cannot explain the
observation of change although it can explain the difference between
moving and stationary objects. Fortunately the debate has been largely
resolved by recent scientific experiments which show that time exists
and hence Presentism is unlikely.

### The existence of time

The issue of whether or not time exists is critical to consciousness
studies. If we exist at an instant without duration then how can we know
we exist? Clay (1882) coined the term \'specious present\' to describe
how we seem to exist for a short period containing the immediate past:

\"All the notes of a bar of a song seem to the listener to be contained
in the present. All the changes of place of a meteor seem to the
beholder to be contained in the present. At the instant of the
termination of such series, no part of the time measured by them seems
to be a past. Time, then, considered relatively to human apprehension,
consists of four parts, viz., the obvious past, the specious present,
the real present, and the future.\"

So conscious, phenomenal experience has things that are apparently
extended in time. But does time exist?

Recent experiments in quantum physics should change our view of time
forever. Lindner *et al.* (2005) have explored the problem of time by
investigating quantum interference between interferometer slits that are
separated by time rather than space.

In the famous, spatial \'double slit experiment\' in quantum physics
single electrons are directed at an apparatus that has the equivalent of
two tiny slits separated by a small gap. The electrons pass through the
apparatus one at a time and produce flashes of light on a screen or
changes in a photographic plate. The electrons produce series of bands
on the screen that are typical of interference effects. So each electron
is deflected as if it has passed through both slits and interfered with
itself.

![](constudtwinslit.gif "constudtwinslit.gif")

This experiment provided some of the earliest evidence for the
wave-packet nature of the electron.

In an amazing technical tour de force Lindner *et al.* (2005) have
extended the idea of the spatial double slit experiment to an
investigation of time. In the double slit experiment in time electrons
are produced in an inert gas by extremely short laser pulses. The pulses
stimulate a single atom and there is a probability of this atom
releasing an electron at each oscillation of the pulse. The apparatus is
described by Paulus *et al.* (2003). The probability (see note 1) of an
electron being ejected to the left or right of the apparatus can be
adjusted by adjusting the optical pulse. Pulses can be applied with a
duration of a few femtoseconds and these create \'slits\' extending over
an interval of about 500 attoseconds (500 x 10-18 seconds). A single
electron has a probability of being emitted at each of the slits. The
probability of the single electron going in a particular direction after
both slits have been created depends upon the interaction of the
probabilities of being emitted in a particular direction at each single
slit. As expected, an interference pattern was generated as a result of
single electrons interfering with themselves across different times.

![](constudtimeslit.gif "constudtimeslit.gif")

This experiment is remarkable because it provides direct evidence that
time exists in a similar fashion to the way that space exists. It is
consistent with Feynman\'s theory of Quantum Electrodynamics where all
possible paths, both in time and space, interact to produce the final
trajectory of a particle and consistent with modern Special Relativity,
on which QED is based, where the trajectories of particles occur in an
extended four dimensional space-time.

The experiment has not attracted as much attention as it might have done
because most physicists are not Presentists. To physicists the
experiment is yet another confirmation of modern physics. However it has
impressed many:

\"This experiment should be included in every textbook on quantum
mechanics,\" says Wolfgang Schleich, a quantum physicist at the
University of Ulm in Germany. \"It certainly will be in mine.\"
(PhysicsWeb)

Why should a concrete demonstration that time exists affect
consciousness studies? The simple answer is that, as Kant, Gombrich,
Clay, James and many others have spotted, there can be no conscious,
phenomenal experience without time. The fact that time exists should
provide new insights and liberate theorists in the field of
consciousness studies from the problems of recursion and regression that
are inherent in Presentism.

Meanwhile Quantum Theorists are pressing on with the problem of how an
organised spacetime could emerge from quantum chaos (cf: Ambjorn *et
al.* (2004)) and even how mind might be involved in the emergence of
time itself (cf: Romer (2004)).

### The nature of time

#### The nature of classical time

In the eighteenth century it became apparent that Euclid\'s parallel
postulate could not be explained in terms of the other postulates. The
parallel postulate is equivalent to the statement that exactly one line
can be drawn through any point not on a given line in such a way that it
is parallel to the given line (this is Playfair\'s simple version). It
is also known as the fifth postulate.

The attempts to prove the parallel postulate led to the development of
non-Euclidean geometry. It was then possible to show that the parallel
postulate is a special case within a range of geometrical forms from
spherical geometry, through Euclidean geometry to the hyperbolic
geometry of Bolyai and Lobatschefsky. Furthermore it was shown by
Taurinus that the axioms of Euclidean geometry, with the exception of
the fifth postulate, applied on the surface of a sphere with an
imaginary radius. This motivated Hermann Minkowski to propose that
Einstein\'s new theory of relativity was in fact due to the universe
being a \'space-time\' with four dimensions rather than just a space in
which things change (see Walter 1999). In 1909 Minkowski said that:

`"Henceforth space by itself and time by itself, are doomed to fade `\
`away into mere shadows, and only a kind of union of the two will `\
`preserve an independent reality". (Minkowski 1909).`

The earliest idea of the four dimensional universe involved time as an
axis with displacements measured in units of the square root of minus
one (cf: Einstein (1920)): time was considered to be displacements along
the imaginary plane. However, from the moment of Minkowski\'s proposal
mathematicians were aware that other interpretations of time could give
almost identical physical results.

According to the differential geometry developed during the nineteenth
century a space is defined in terms of a *metric tensor* which is a
matrix of factors that determine how displacements in each independent
direction vary with displacements in the other directions. The metric
tensor then specifies a *metric* which is an equation that describes the
length of a displacement in any direction in terms of the independent
directions, or *dimensions*.

A derivation of the metric tensor and how it can be used to calculate
the metric is given in the /Appendix/.

The metric of the space considered by Euclid is Pythagoras\' theorem
where the length of any displacement is given in terms of the
displacements along the three independent axes, or dimensions:

$s^2 = x^2 + y^2  +  z^2$

It is interesting to explore *imaginary time* from the point of view of
consciousness studies. Minkowski\'s original idea for the geometry of
the world proposed that any displacement was a displacement in both time
and space given by a four dimensional version of Pythagoras\' theorem:

$s^2 = x^2 + y^2  +  z^2 + (ict)^2$

which, given that $i^2 = -1$ equals:

$s^2 = x^2 + y^2  +  z^2 - (ct)^2$

Where *i* is the square root of minus one, *c* is a constant for
converting metres to seconds and t is the displacement in time. The
space-time is considered to be flat and all displacements are measured
from the origin.

The interesting feature of Minkowski space-time with imaginary time is
that displacements in time can *subtract* from displacements in space.

If we set $r^2 = x^2 + y^2  +  z^2$ (where *r* is the radius of a sphere
around the origin then:

$s^2 = r^2 - (ct)^2$

Notice that $s^2 = 0$ when $r^2 = (ct)^2$ so if imaginary time existed
there would be times and separations within a spherical volume of things
where **everything is at a point as well as distributed in space**. This
idea has distinct similarites with the *res cogitans* mentioned by
Descartes, and the *point soul* of Reid and Malebranche etc., however,
this feature of Minkowski\'s space-time has not been popular with
physicists for some good reasons. Blandford and Thorne point out some of
the problems:

`<font face="times new roman">`{=html} One approach, often used in
elementary textbooks \[and also used in Goldstein\'s (1980) Classical
Mechanics and in the first edition of Jackson\'s Classical
Electrodynamics\], is to set $x^0 = it$, where $i = \sqrt{-1}$ and
correspondingly make the time basis vector be imaginary,\... When this
approach is adopted, the resulting formalism does not care whether
indices are placed up or down; one can place them wherever one\'s
stomach or liver dictate without asking one\'s brain. However, this
$x^0 = it$ approach has severe disadvantages: (i) it hides the true
physical geometry of Minkowski spacetime, (ii) it cannot be extended in
any reasonable manner to non-orthonormal bases in flat spacetime, and
(iii) it cannot be extended in any reasonable manner to the curvilinear
coordinates that one must use in general relativity. For this reason,
most advanced texts \[including the second and third editions of Jackson
(1999)\] and all general relativity texts take an alternative approach,
which we also adopt in this book. This alternative approach requires
introducing two different types of components for vectors, and
analogously for tensors: contravariant components denoted by
superscripts, and covariant components denoted by
subscripts.\"`</font>`{=html} Blandford & Thorne (2004).

What Blandford and Thorne are saying is that the metric of space-time
appears to be the result of the interaction of two coordinate systems
and cannot be explained by a single coordinate system with imaginary
time. When a more complicated geometrical analysis is applied it is
evident that there are two possibilities for the time coordinate. In the
first the metric can be **assumed** from the outset to be

$s^2 = x^2 + y^2  +  z^2 - (ct)^2$

and the metric tensor simply adjusted by inserting -1 in the principle
diagonal so that the negative sign in front of the time coordinate
occurs. With this assumption and adjustment the time coordinate can be
assumed to be *real*. In the second possibility the time coordinate in
the world can be assumed to be imaginary and the time coordinate of the
observer can be assumed to be real. This gives rise to the same metric
tensor and metric as the first possibility but does not assume the
resulting metric from the outset.

The three ideas of classical time (imaginary, real and mixed) are shown
in the illustration below:

![](constudclasstime.gif "constudclasstime.gif")

The light cone is divided into three regions: events on the surface of
the light cone, such as photons converging on the observer, are said to
be *lightlike* separated from the observer, events inside the future or
past light cones are said to be *timelike separated* and events outside
the lightcone are said to be *spacelike* separated from the observer.

The physical **theory of relativity** consists of four dimensional
geometry plus the assumption of causality and the assumption that
physical laws are invariant between observers. It should be noted that
space-time could contain preferred frames of reference and is not, by
itself, a theory of relativity. The assumption that physical laws are
invariant between observers leads to the postulate that nothing can
travel faster than *c* metres per second. This means that the constant
*c*, which in Minkowski space-time is the conversion factor from seconds
to metres then has a new significance as the maximum velocity.

A result of *c* being a maximum velocity is that nothing can travel from
regions of the light cone that are spacelike separated to the observer
at coordinates (0,0,0,0). This is problematic for observers if time is
real because, as Stein (1968) wrote:

`<font face="times new roman">`{=html}"in Einstein-Minkowski space-time
an event\'s present is constituted by itself alone." `</font>`{=html}
(Stein 1968).

However, to each of us it seems that the present is characterised by
*many* things simultaneously. As will be discussed below, this
simultaneity of present things also results in the appearance of
phenomenal space. But in Minkowski space-time with real time the plane
of simultaneity is entirely space-like separated from the observation
point. If real time is accepted it would appear that we cannot have the
space of phenomenal experience. The regions of the light-cone and the
spacelike separation of present events are shown in the illustration
below:

![](Constudcone.gif "Constudcone.gif")

So can the time in Minkowski space-time be real? If time were in some
way related to the imaginary plane then all the content of the surface
of the light cone could be simultaneously at the position of the
observer and phenomenal experience containing space is possible, but
then general relativity may be problematic. So can the time in Minkowski
space-time be imaginary?

There is another problem with Minkowski space-time known as the
\"Rietdijk-Putnam-Penrose\" argument or the Andromeda paradox (Penrose
1989). Moving observers have different planes of simultaneity. The plane
of simultaneity of an observer moving towards you slopes upward relative
to your plane of simultaneity (see the illustration on \"De Broglie
waves\" above). Suppose an alien civilisation in the Andromeda galaxy
decided to launch a fleet of spacecraft intent on the invasion of earth
just as you passed Jim in your car. Your plane of simultaneity would
slope upwards ever so slightly compared with Jim\'s, Jim\'s plane of
simultaneity could contain earlier events on Andromeda than yours. At
the distance of the Andromeda galaxy it could be another week or two for
the Andromedean\'s to launch their invasion fleet in Jim\'s slice of the
universe. Penrose considers that this example shows that the events in
the universe must be fixed:

`<font face="times new roman">`{=html}\"Two people pass each other on
the street; and according to one of the two people, an Andromedean space
fleet has already set off on its journey, while to the other, the
decision as to whether or not the journey will actually take place has
not yet been made. How can there still be some uncertainty as to the
outcome of that decision? If to either person the decision has already
been made, then surely there cannot be any uncertainty. The launching of
the space fleet is an inevitability.\"`</font>`{=html} (Penrose 1989).

If the decision to invade and a time previous to this decision are both
part of the present instant on earth then, in a 4D classical universe,
the decision to invade must be inevitable. This lack of free will in a
4D universe is known as chronogeometrical determinism (Toretti 1983).
However, as de Broglie demonstrated, it is sloping planes of
simultaneity that do indeed introduce uncertainty into our universe. It
should also be noted that nothing on the plane of simultaneity is
observable to the owner of that plane because, to observe it would
involve the transmission of data at velocities greater than the speed of
light.

Petkov (2002)considers a version of the Andromeda paradox in depth. He
concludes that:

`<font face="times new roman">`{=html}\"If the relativity of
simultaneity is explicitly discussed in terms of the dimensionality of
reality, the fact that observers in relative motion have different sets
of simultaneous events can be explained either by assuming that
existence is also relativized (preserving the views of the present and
objective becoming) or by considering existence absolute which means
that reality is a 4D world. Although the option of relativizing
existence appears completely unacceptable from a philosophical point of
view, that option is eliminated within the framework of SR by
demonstrating that the twin paradox would not be possible if existence
were not absolute.\"`</font>`{=html}

According to Petkov Special Relativity describes the universe as a
frozen space-time where things are eternally arranged in four
dimensions. Petkov introduces the possibility of change as a feature of
consciousness and in support of this quotes Weyl\'s intuition that only
the conscious observer moves in time.

## Relationalism, Substantivalism, the Hole Argument and General Covariance

### Relationalism and Substantivalism

The view that the universe could be an extended space and time with
things in it, a sort of unbounded container, is known as
**substantivalism**. It was championed by Newton and Clarke in the
seventeenth century. The view that the space and time in the universe
depends upon the relations between the objects in the universe is known
as **relationalism** and was championed by Leibniz.

Leibniz attacked substantivalism by arguing that if there were two
universes which only differed by things in one universe being displaced
by five feet compared with things in the other universe then there is no
reason why the two universes should be discernably different.

Newton supported substantivalism by arguing that when the water in a
bucket rotates it adopts a concave surface that is independent of other
motions and provides evidence of the possibility of absolute motion.
This argument is called the *bucket argument*. Newton also introduces
the *globe argument* in which he proposes that the state of motion of
two globes connected by a taut thread can be gauged from the tension in
the thread alone. When the globes are stationary with respect to each
other there is no tension in the thread.

Ernst Mach in 1893 introduced a relationalist account of the bucket
argument by claiming that the water rotates in relation to the fixed
stars. He stated this in what has become known as Mach\'s principle:

\"The inertia of any system is the result of the interaction of that
system and the rest of the universe. In other words, every particle in
the universe ultimately has an effect on every other particle.\"

The relationalist position is interesting from the viewpoint of
consciousness studies because phenomenal consciousness appears as a
projection that overlies physical space. As an example, the stars on the
ceiling of a planetarium appear to be at huge distances from the
observer even though they are reflected lights that are only a few
metres away. In general a projection where positions depend upon angular
separations will be subject to relationalism. It is also probable that
the space of phenomenal consciousness is a continuum of some field in
the brain, if this is the case then the way we conceive of space as an
existent entity is actually a conception involving the angular relations
between the perturbations of the substance that is the field.
Substantivalism would then literally be space as a substance. It is
intriguing in this respect that Kant believed that space was a form of
intuition and hence a property of mind.

Kant raised another type of argument for the justification of absolute
space. He asked whether *handedness* was due to relations or a property
of space. The right and left hands are enantiomorphs (mirror images).
The relations within the right and left hands are identical but they
still differ, for instance a right hand cannot be moved on to a left
hand so that it exactly overlies it. Kant proposed that handedness was
property inherent in space itself rather than a set of relations.

Gardner introduced a version of Kant\'s problem with the \"Ozma\"
argument: \"Is there any way to communicate the meaning of the word
\"left\" by a language transmitted in the form of pulsating signals? By
the terms of the problem we may say anything we please to our listeners,
ask them to perform any experiment whatever, with one proviso: there is
to be no asymmetric object or structure that we and they can observe in
common.\" (Gardner 1990).

Although it is probably impossible to provide an answer to the Ozma
argument it is possible to relate handedness to a conceptual point
observer who spans more than an instant of time. If a point observer is
at the centre of a field of inward pointing space-time vectors then
relative to any given vector there are positive and negative angular
separations. The body is asymmetric and the point observer would lie
within this so always have available a \'head\' direction or a \'foot
direction\' and hence a left and right. Unlike the time extended
observer an instantaneous observer would not contain vectors that
contained directional information and would be no more than a collection
of points in space.

Pooley (2002) discusses handedness in depth and introduces the problem
of parity violation in the Weak Interaction.

### General Covariance and the Hole Argument

The proposal that the universe is four dimensional does not in itself
produce a full physical theory. The assumptions of causality and the
invariance of physical laws between observers are also required to
create modern Relativity Theory. The second assumption, that the laws of
physics are the same for all observers is closely related to the
requirement of **general covariance**.

The principle of general covariance requires that a manifold of events
can be smoothly mapped to another manifold of the same dimension and
back again. This mapping should always give the same result. General
covariance is assumed in General Relativity.

Einstein realised that there was an apparent problem with this
assumption in certain circumstances. In his **hole argument** he
considers a special region of space-time that is devoid of matter and
where the stress-energy tensor vanishes. He then labels the same events
outside the hole with two different coordinate systems. These coordinate
systems could differ by something as simple as having origins that are
separate so the difference is entirely passive. Both systems will give
the same values for the gravitational field outside the hole. It turns
out however that that the systems predict different fields within the
hole (see MacDonald (2001) for the calculation and Norton (1993), (1999)
for a discussion). Einstein overcame this problem by considering active
mappings where particles are actually transferred through the hole. He
concluded that the points where particles meet can be transformed
according to general covariance and hence a relativistic theory could
indeed be constructed. Solutions to the field equations that were
inconsistent with the points defined by interacting particles were
discarded as non-physical.

The hole argument led Einstein to abandon the idea of space and time as
something separate from the material content of the universe. The
General Theory of Relativity becomes a theory of **observables**. He
wrote that:

`<font face="times new roman">`{=html}\"That the requirement of general
covariance, which takes away from space and time the last remnant of
physical objectivity, is a natural one, will be seen from the following
reflection. All our space-time verifications invariably amount to a
determination of space-time coincidences. If, for example, events
consisted merely in the motion of material points, then ultimately
nothing would be observable but the meetings of two or more of these
points. Moreover, the results of our measurings are nothing but
verifications of such meetings of the material points of our measuring
instruments with other material points, coincidences between the hands
of the a clock and points on the clock dial, and observed point-events
happening at the same place at the same time. The introduction of a
system of reference serves no other purpose than to facilitate the
description of the totality of such coincidences\".`</font>`{=html}
(Einstein 1916).

This is what would be expected from a four dimensional block universe
with real time. It is a frozen universe of the type discussed earlier.
As Earman (2002) puts it when discussing change:

`<font face="times new roman">`{=html}\"First, the roots of the problem
lie in classical GTR, and even if it was decided that it is a mistake to
quantize GTR, there would remain the problem of reconciling the frozen
dynamics of GTR with the B-series notion of change that is supported not
only by common sense but by every physical theory prior to GTR. Second,
although the aspect of the problem that grabs attention is that of time
and change, no solution will be forthcoming without tackling the more
general issue of what an "observable" of classical GTR
is.\"`</font>`{=html}

In such a universe action at a distance is not possible. From the
viewpoint of consciousness studies the limitation of physical concepts
to interactions between particles is a restatement of Ryle\'s regress
and the recursion version of the homunculus problem. If events are no
more than space-time coincidences then we are doomed to the endless
transfer of data from point to point without any conscious observation.
This seems to forbid any true simultaneity in experience and means that
only measurements are possible.

The reduction of physics to the study of particle interactions is fully
relationalist and allows space-time to become a property of these
interactions rather than vice-versa. Once it becomes possible to
consider space-time as a dependent property it is then feasible to
equate *observation* with *measurement*. Observation is normally the
representation of an event in an observer\'s space-time coordinate
system. Measurement is the change in state of a system in response to an
encounter with an event. If we maintain that space-time does not exist
and can be replaced by encounters between particles then observation can
be replaced by measurement. This may well be a way forward for some
approximations to physical reality and may allow us to understand how a
space-time is selected within an observer. As part of this approach the
word \"observable\" is often used interchangeably with \"measurable\".

## Quantum theory and time

### The general problem of QM and time

Quantum physics provides many fundamental insights into the nature of
time. At the simplest level the energy-time version of the Heisenberg
Uncertainty Principle predicts that Quantum Mechanical (QM) interference
should occur between a particle and earlier versions of itself. Such
interference has been observed (see \"The existence of time\" above).

Two of the most complete reviews of the problem of time in quantum
theory available at present are Zeh (2001) and Isham (1993).

Perhaps the most interesting aspect of QM and time is that it can
provide an argument that time does not exist in the universe as a whole.
The argument can be approached from many directions (See Rovelli 2003)
but is clear in the Wheeler-de Witt equation which describes the
wavefunction of the entire universe. This wavefunction has no reference
to time. De Witt explained the emergence of time by proposing that the
universe can be divided into an observer with measuring instruments and
the rest of the universe so that the rest of the universe changes with
respect to the observer.

Rovelli (2003) supports this idea of partition, he considers in depth
the problems of the \"hole argument\" and quantum physics and notes
that, given the assumption that events are just successions of
relations:

\"`<font face="times new roman">`{=html}The unique account of the state
of the world of the classical theory is thus shattered into a
multiplicity of accounts, one for each possible \"observing\" physical
system. Quantum mechanics is a theory about the physical description of
physical systems relative to other systems, and this is a complete
description of the world.`</font>`{=html} (Rovelli 2003).

Barbour (1997) and Hartle and Gell-Mann have both proposed that an
observer is a partition or region with memories that contain the trace
of histories. The histories would represent a B Series. Unfortunately
this leaves the A Series unexplained so time would have a direction but
there would be no \'becoming\'.

Hawking introduces the observer into the problem of time by asking what
sort of universe is compatible with human life. This application of the
**Anthropic Principle** leads to constraints on the form of the
universe, for instance the universe should have galaxies and last for
more than a few million years. The Anthropic Principle is actually a
restatement of the observer problem - if being an observer leads to a
certain division of the universe into observer and observed then the
observed part will have the form given by the Anthropic Principle.
Hartle and Hawking () also tackled the \"boundary problem\" of cosmology
by proposing that there is no boundary. This proposal involves adding a
fifth, time-like, dimension on the imaginary plane so that the universe
at its beginning is a **de Sitter** or **anti de Sitter** space-time.

A de Sitter space-time is characterised by the metric:

$ds^2 = dx^2 + dy^2 + dz^2 + (idt)^2 + du^2$

An anti de Sitter space time has the metric:

$ds^2 = dx^2 + dy^2 + dz^2 + (idt)^2 - du^2$

A de Sitter space time is fascinating from the view point of
consciousness studies because it contains three space-like dimensions,
one real, time-like dimension (u) and one imaginary time-like dimension.
This might give the real and imaginary time-like axes that Franck
proposed were needed to produce the McTaggart A Series. However, the
extra dimension could only be related to the observer in the universe as
it is at present because the extra dimension does not appear to be
required to explain measurables.

### The interpretation of QM

Time is also of interest in the interpretation of quantum mechanics and
entanglement. There are many interpretations of QM such as the
**Operational Interpretation** (Decoherence Theory), the **Transactional
Interpretation**, the **Relational Interpretation**, the **Many Worlds
Interpretation**, the **Copenhagen Interpretation**, the **Bohm
Interpretation**, the **Many Minds Interpretation** etc.

Some of these interpretations, such as the Transactional Interpretation,
allow the connection of entangled quantum states backwards in time along
the path of particles.

Decoherence theory is of particular interest because it allows the
calculation of how long an entangled state can persist. Tegmark (2000)
and Hagan *et al.* (2002) have used this technique to calculate the
decoherence time of entanglement in microtubules and have differed by a
factor of $10^{10}$ because of differing assumptions about the
biophysics of microtubules in the brain.

## Time and conscious experience

In a four dimensional universe time is an independent direction for
arranging things. As an independent direction things arranged in time do
not overlie things arranged in space. This also appears to be the case
in conscious experience where whole words or \"bars of a tune\" can be
experienced arranged in time. This extension in time is easy to
experience but the independence of the time dimension is difficult to
conceive, for instance Le Poidevin (2000) reflects that:

> \"If events e1 and e2 are registered in a single specious present,
> then we perceive them both as present, and so as simultaneous. But we
> do not see, e.g., the successive positions of a moving object as
> simultaneous, for if we did we would see a blurred object and not a
> moving one.\"

This assumes that arrangements in time do not occur in an independent
direction for arranging things and hence would overlay space. In fact
the mystery of conscious experience is deeply related to how we can
experience many things as events that are separate from each other. Our
experience of two dimensional patterns containing many things is as much
a mystery as how we experience temporal patterns extended in time. The
problem is illustrated below:

![](constudsimevent.gif "constudsimevent.gif")

It is as if patterns in conscious experience are being viewed from a
point in at least four dimensions. How our experience can be like the
\'view\' of a conceptual point observer at the apex of a light cone
without the data being overlaid and obscured is a profound mystery,
obviously the data cannot be transferred into the apparent observation
point and appears as nebulous vectors directed at the point. Some
philosophers have noticed this problem.

(*This is a stub, requires an elaboration of Specious Present Theory and
Husserl\'s ideas*)

Le Poidevin (2000). The experience and perception of time. Stanford
Encyclopedia of Philosophy.
<http://plato.stanford.edu//archives/spr2001/entries/time-experience/#4>

Readers who are unfamiliar with the developments to Newtonian mechanics
that occurred in the eighteenth and nineteenth centuries should read
Consciousness Studies/The Philosophical
Problem/Appendixs

See
overleaf
for the philosophical problem continued..:

## The problems of space, qualia, machine and digital consciousness

Click on the above link.

## Notes and References

More\...

