An essay on energy, time, space, causality and being

What is energy? Energy is the ability to cause change, or the ability to do work. (Since work has a very precise
definition in physics we shall use the former definition here). Let us imagine what happens when you switch an
electric light on, where does the energy come from? The nuclear energy released in a nuclear reactor heats
water into steam, the steam drives a turbine, which drives a dynamo to convert the mechanical rotational
energy of the turbine into electricity. Electricity flows along wires, as the flow of electrons. The electrons pass
through the tungsten filament, heating it as the tungsten impedes their flow, causing the tungsten filament to
glow and hum, releasing most of its energy as heat, some as light and some as sound. The energy from the
nuclear reactions is not destroyed at any stage of the process, nor is any energy created at any link in the
chain – energy is conserved and is neither created nor destroyed, but energy can change form.

Where does the nuclear energy come from? The splitting of atoms by nuclear fission releases energy that was
previously locked up in the mass of the atom – some of this mass is converted into energy, emitted as
radiation, which heats the water in the reactor. Mass and energy are, thus, inter-convertible.

Some physicists have argued that energy is an abstract concept that cannot be related to any simple principle,
but rather that it is simply a ‘factor’ in certain equations. However, elementary physics books define energy as
the ability to do work or to cause change (the two definitions are not exactly equivalent and we shall focus on
change rather than work) which is probably a much more useful viewpoint. Perhaps the tendency of physicists
to ‘hide’ behind equations, simply because equations are easier to make sense of, and to avoid addressing
conceptual issues is not always the most productive. Though it is true that many physical phenomena are
abstract concepts (such as isospin) that have no obvious direct relationship to the objective world and this has
lead physicists to view things as mathematical entities and so detach their theories from reality somewhat.
However, I think it is important to ask ourselves what objective meaning these mathematical constructs have, or
what objective phenomena they model (as images of the ‘real thing’) otherwise we are in danger of losing
ourselves in mathematical theories with no actual physical relevance! At the other extreme, we make students
fret over equations that really state the obvious! String theory may be an elaborate mathematical construct
that appears to model gravity, but perhaps if we better understood gravity conceptually we might find a better
model more easily. Remember that Einstein primarily developed his great Theory of Relativity not from
mathematical principles (which were applied later) but from thought experiments that attempted to
conceptualise the problem. Mathematics may be an easier approach, but mathematics can model any reality,
not only the actual reality, and so certain mathematically consistent models may be pure fiction. Perhaps
philosophy can help us see if our equations are on the right tracks.

What is mass - is mass energy? Not exactly, since E = mc^2, mass is energy divided by c^2. However, the two
are perhaps different states of the same ‘entity’. Let’s look at it another way, can mass cause change? First we
must decide what mass is. In one definition, mass is that which has weight, meaning that it is acted upon by
gravity, however, gravity acts upon all forms of energy, but is more apparent with mass since mass contains
such a high density of energy – it is energy density that generates or creates a gravitational field. Perhaps
mass is ‘substance’ or that which feels resistive to some degree. When one sits in a chair, one’s body pushes
against the chair with the same force that the chair pushes against one. What is the origin of this reaction
force? It is the mutual electrostatic repulsion, or repulsive Coulomb force, between the electrons in the atoms
or molecules of your body and the electrons in the chair. The 'solid mass' that the chair feels to have is simply
an effect of the energy it contains. So far we have failed to distinguish between mass and energy, save by the
formula E = mc^2. Perhaps our definitions are at fault when we distinguish between energy and mass. Perhaps
mass is a form of highly concentrated energy, and the ‘E’ refers to that form of less concentrated energy that
we normally term 'energy'. If this is so, them mass must be capable of causing change, and indeed it is – mass
interacts with mass and with energy by the gravitational ‘force’. There is another way of thinking about mass
and energy which may be useful. Supposing I measure the height of my mug on this table, and it is 4 and six
eights of an inch in height, which is about 11.0 cm. I cannot say that inches and centimetres are the same
thing, clearly they are not, rather they are proportional to one another as length in inches, call this Li is
proportional to length in cm, Lcm, or: Li = Lcm.C, where C is the conversion factor, about 2.5 since one inch is
approximately 2.5 cm. Are energy and mass simply different ways of measuring the same property?

You may object, saying that the rest mass of a photon is zero. However, a photon is never at rest, and has a
mass by virtue of the fact it has energy because it is in motion. Every system has energy, and energy can
always be expressed as a mass. You may also object, saying that mass generates a gravitational field.
However, all forms of energy generate gravitational fields, even the energy of gravity itself! In short, the only
separation between mass and energy appears to be the units we apply to them, which reflects the ways in
which they are measured. We could actually weigh light, since light is affected by gravitational fields! However,
light is not very dense and so hard to weigh, matter seems to be especially dense energy.

Where is the mass in an atom? Certain of the particles of the atom carry mass – namely quarks and electrons.
The energy that binds these particles together may also add mass to the system, but even when unbound and
free from the influence of other particles, an electron has mass. Quarks are not convincingly known to ever
exist in isolation from other quarks (or anti-quarks), but consider a free electron, that is an electron free from
external forces, at least for a time. We would consider such an electron to have mass, although to measure its
mass we force it to interact and maybe this gives it mass. Perhaps then, mass is a manifestation of the
interactions between particles. Interactions are changes and therefore are proportional to energy. Let us,
then, return to a precise definition of mass as that which gives weight in a gravitational field. Really, weight is
the interaction between two gravitational fields, each due to a mass or source of energy, and so weight is a
manifestation of energy. Since all energy lends some ‘weight’ by creating a gravitational field, then weight is
simply a measurable property of energy, namely one of the ways in which energy interacts with energy, and so
is itself proportional to some energy. Indeed, as already stated, gravity itself generates a gravitational field! It
should also be remembered that electrons and quarks are also waves! We can safely say that mass and
energy are both observable effects of wave phenomena. Whether waves carry energy or energy forms waves
seems to be a matter of perspective.

What is a force? Here we must distinguish more accurately between a force and energy. A force is an
interaction between two masses or energies, and is thus a measure of change or energy. To be sure a force is
proportional to a mass times its acceleration (F = ma). The mass is a property of energy, and acceleration is
change and so is a form of additional energy imparted to the mass. In short, mass, energy and force are all
properties of energy. By property we mean a measurable observable. We can measure mass, we can measure
acceleration and we can measure force. An observable property, or observable, is a change that is detected in
a system and hence the manifestation of energy. All physical observables appear to be simply changes
brought about by energy. In the case of mass, this may seem counter-intuitive, since mass is thought of as
static in some way, however, mass is only detected when it causes change by transferring energy. In a sense
then, mass is a reservoir of energy, or a type of potential energy (not necessarily according to the strict
physical definition of 'potential energy').

What is a change? Change is what we observe, i.e. the observable. Energy we have defined as the cause of
this change. However, in reality we see a chain of cause and effect, with the effect of one cause becoming the
cause of a later effect. In other words, the only difference between cause and effect are the temporal order in
which they are observed (directly or by inference). In essence, this equates energy with the observable – the
changes caused by energy are energies themselves. Force, mass, acceleration and energy become
observable aspects of the same entity - change. Mass and energy are waves (or cause waves), force causes
change and so must be an energy according to our definition! (Mathematically force and energy are not the
same thing, but are they similar phenomenologically, but simply measured in different ways and so have
different units?). Acceleration is certainly a change. Mass, energy, force and acceleration are all observable
phenomena and so all cause change or are changes (is there really a difference here since the difference
between cause and effect is only according to our temporal conventions?) and are observable aspects of
energy. What we observe is simply a sequence of changes occurring over a period of time. This leads us to
consider what time is. We often talk about the ‘state’ of a system, which is its collection of observable
properties and when the system changes there is a change in one or more of its observable properties and so
it changes state. Such a change always requires some transport of energy in space-time.

What is time? Time is change! If nothing ever changed then there would be no time and nothing could be
observed, so there would be no energy. Thus, time and energy become manifestations of the same entity, or
at least, there never is one without the other. What do we mean by ‘manifestation’ – we really mean ‘mental
construct’. Time, mass, energy and change appear to be different things simply because we think of them
differently – we see the same entity from different perspectives. We observe a sequence of changes since we
become aware of changes over a period of time, or so it is perceived. However, time is considered part of a
continuum called space-time.

Time is in one sense a measure of the amount of energy required to cause a change. It takes a certain
amount of energy to travel from A to B and we can expend that energy more rapidly to reach B in a shorter
time – we must pay in energy terms in order to save time. Again, like space, time seems to be some indication
of the difficulty of bringing about a certain change. Time and energy are intimately linked in physics. The Law
of Conservation of Energy originates from the homogeneity of time. The energy-time uncertainty principle
states that the more rapidly a change is occurring, the more uncertain the energy. This seems intuitive, since
changes require the transfer of energy and a rapid change requires a rapid transfer of energy. However, the
principle tells us that the energy transfers in an uncertain manner. Again this should not be surprising, since
quantum phenomena are probabilistic (stochastic).

What is space? Space is often seen as the receptacle occupied by energy – as a stage in which the changes
take place. We say that changes that occur but are not perceived by us, and yet are perceived by another
who later reports to us, as occurring too far away from us to be perceived. They are too remote in space.
Events or changes may escape our perception because they are beyond our sphere of perception in space or
time, or because we fail to notice them even if they are within range of our senses. In short, space and time
exist because we are unable to perceive the whole process of change, but instead we perceive only bits of it.
Space and time are intimately connected; if a signal (energy, or a series of changes) travels out from some
event (change) then an individual closer to the source may become aware of the change before another
individual further from the source – to move across space requires time. Moving across space also requires
energy and time is needed for the necessary chain of changes to unfold.

Let us look more closely at what space is. Space determines which parts of the Universe can interact in a given
period of time. ‘Interact’ meaning that an exchange of energy occurs between one ‘part’ of the system and
another ‘part’ of the system in a cause-effect relationship. What do we mean by ‘part’ – this is problematic as
the definition of space just given becomes circular, since ‘part’ already implies a spatial extent. What space is
really doing is restricting the range of possible changes, not only in the system (which is an artificial construct
that includes ‘part’ of the Universe) but in the Universe as a whole. What I am saying is best illustrated by
analogy – a virtual reality may appear to have actual spatial extent to several users interacting within the
space, but of course it has no extent at all, what it does have is information and rules governing how that
information changes. Is ‘real’ space really any different in this respect? Time determines change, but space
determines what information energy and matter contain. Time allows change by allowing the apparent
transport of information from one place to another. It seems that space is that property that enables energy to
contain information, whilst time is that property that allows energy (and the information it contains) to change
and to cause change. Is this the same as saying that space is simply the information that energy contains and
that time is simply change in that information? Indeed, perhaps energy loses its meaning if we say: space is
information and time is change in that information.

If a light signal is sent eastwards, then (assuming no scattering or other phenomena to send parts of the signal
in other directions) it cannot send a signal northwards. Space restricts the possible changes by adding the
variable (observable) of direction. We also think of space as adding separation or distance, since it takes
longer for a signal to travel 100 km than it does to travel 10 km, then if the signal travels at 10 km per second,
it may trigger a change 5 km away from its source within one second of time, but it cannot trigger a change 50
km away within the stated time interval. Distance, then is really a matter of time as much as it is a matter of
space. Space gives us direction, time gives us change, and perhaps space-time gives us distance.

One might object to the definitions of space, time and energy based upon what we observe, since then
objectivity merges with subjectivity, however, physics is restricted to dealing with observables. Although we
attempt to make objective measurements that everyone can agree on without dissent (every one who
measures the same meter stick will obtain the same result within a margin of error) we are nevertheless
necessarily describing what we perceive. Thus, our description of the Universe must depend in some way upon
our perceptions, albeit by collective agreement to eliminate individual bias. However, there will always remain
different ways of thinking about the same entity. A physicist will most often think about space as a set of
coordinates in three dimensions, and the laws of physics do not depend upon the type of coordinate-system
used (be it Cartesian or spherical polar, etc.). However, suppose we consider coordinates to be merely a
mathematical tool for modelling space and ask what we really perceive about space. A book on a shelf at the
other side of this room is out of my reach and I must walk over to fetch it, and the further away it is in space,
the further I must walk to reach it. Since walking involves an expenditure of energy and requires time, what I am
really saying is that more energy and time are required to fetch the book that is further away. Space appears
none other than a restriction upon which changes are possible in a given interval of time. By expending energy
at a faster rate, I can reach the book in a shorter time, or I can expand energy more slowly and reach it in a
longer time, either way the price to cause such a change is greater the further away the book is in space. Is
this difficulty the consequence of distance, or the definition of it? This apparently depends upon one’s point of
view, but let us try to define distance as a measure of the difficulty of affecting change. What I have attempted
to do is to simplify the notion of space by relating it more directly to what we observe than to rely upon an
abstract (though extremely useful!) concept such as a coordinate system to add another layer atop the
observable reality.

What are waves? Waves transport energy, or put another way energy travels as waves or vibrations. Thus,
waves transport changes and are changes themselves that communicate a preceding cause to a subsequent
effect – they are causal chains that may be stationary in space or may be travelling, but always they extend
forward in time from the change that generated (caused) the wave(s). Energy is a function of the amplitude of
the wave, indeed the oscillation itself can be thought of as the energy, since an effect can also be a cause and
hence a change can itself be the energy that causes further change. All forms of energy manifest as waves.
Light, sound and water waves all transport energy. What about matter? The particles that constitute matter are
also waves, and it is these waves that have mass (mass is an observable proportional to energy). Thus, matter
appears comprised of waves, and mass, like energy, is an observable property of those waves. Force is also
an observable property of waves. Waves not only pass energy (or signals) between a cause and an effect, but
they are themselves chains of cause and effect. As a water wave travels across the water, it sets the water in
front of it into motion and so propagates itself.

Are waves more fundamental than energy? According to the statement that energy is proportional to the
amplitude of a wave, waves appear to be more fundamental. However, energy also causes changes, and it is
thought to be the energy carried by the wave which causes the change we perceive as a wave. What then
about frequency/wavelength and wave velocity? Are these observable wave properties as fundamental as
energy itself? Can an object possess energy without exhibiting any wavelike or vibrational behaviour? The
answer is no – to observe a system we have to change the system, perhaps the system must interact with light
that reaches our eye, and a change involves a transfer of energy which must, therefore, involve some sort of
wave or vibration to occur within the system. Any entity that possesses energy but is not transporting energy
cannot cause change and so cannot be observed. Since energy is defined as the ability to cause change,
such a system cannot exist. It seems that energy and vibrations can only exist together and are perhaps
different ways of observing the same thing – change. Putting it another way - energy and change are all waves.

What is the vacuum of space? First of all, a complete vacuum as a space devoid of all energy cannot exist in
principle. Energetic particles constantly phase ‘in and out of existence’ at each point in space over time. The
fact that these particles come and go so fast makes them ordinarily hard to detect, and also means that in the
long run they do not violate the law of conservation of energy, but only ‘break’ this law for a miniscule amount
of time. However, this vacuum energy can have detectable consequences – it can affect change and so is real
energy. If we define energy as the ability to cause change, then does this not violate the law of energy
conservation completely? Plato reports the popular view amongst his contemporaries that a non-entity cannot
exist, meaning in the absolute sense it is nonsensical to talk about a non-being. With this in mind, philosophers
would almost certainly have rejected the notion of empty space. For a long time scientists upheld the logically
nonsensical notion that space was empty. However, it is now a scientific fact that space is never empty, but
always it contains a type of energy, called the vacuum energy, if nothing else.

What is causality? The Law of Causality is often stated thus: ‘every phenomenon is determined by its
conditions, i.e. the same causes produce the same effects. In other words, phenomenon a, b, c, d, previously
perceived can occur again in the same shape; a phenomenon P, which appeared after the conditions a, b, c,
d, and these conditions only, will not fail to recur as soon as the same conditions are again present’ (cited from
Bertrand Russell, ‘On the notion of cause’). Does science exploit this definition of causality? Not exactly,
quantum mechanics assigns a probability to each possible outcome when a system (or ensemble of systems)
is (are) prepared in the same state. In other words, setting up a ‘system’ in the same state will not always result
in the same outcome (final state), rather it will result in one or more possible outcomes (the observable
spectrum) according to certain probabilities (as determined by the physical behaviour of the system).

Note the mention of ‘system’ here. What is a system? A system can be any definable physical arrangement,    
e.g. an atom of hydrogen in a magnetic field of a given strength, or a laser beam striking an atom of uranium.
In this sense we artificially separate part of the Universe from its surroundings. This is a legitimate
approximation, since experience tells us that when we set up a system in certain ways, the effects of the
surroundings of the system have only a small effect. For example, for our hydrogen atom in a magnetic field,
we are generally concerned with a large magnetic field that we apply to the atom, and we may also screen out
much of the ‘background noise’ or external magnetic fields that we are not controlling, and so the tiny
fluctuations in the actual magnetic field caused by other external sources are ‘negligible’ as far as the
approximate behaviour of the system is concerned (often so negligible as to be hard to measure) or else we
can average out these background effects by taking many repeated measurements and adding the average
background magnetic field into our calculations. Either way, we can cope with 'background noise' so long as it
is not too noisy. In this way, it is often quite legitimate to study part of the Universe in isolation if we prepare
this system carefully. The consistency in the data obtained proves this. Furthermore, the size of ‘errors’ due to
unaccounted for influences can be estimated with statistical reliability.

We will often talk about events; here I define an event as: a change in a system, that is a change in its
observable properties. By observable we mean that which can be measured by any means, direct or indirect
(indeed all measurements are in some sense indirect). Bertrand Russell argued that including the environment
will nullify the effects of any causal laws by making the event un-repeatable: ‘Narrow definitions (of an event)
prevent recurrence, so no law applies’. Indeed, to absolute accuracy this is true, but if we are only concerned
with the energy of our atom to within one hundredth of an electronvolt, say, then laws can be found which
predict the energy to this degree of accuracy. However, the ‘errors’ or uncertainties in the observables of the
system do not inviolate scientific laws, as they can sometimes be explained by the laws ‘in principle’ – we may
have a law that describes the behaviour of a hydrogen atom in a magnetic field with complete reliability, given
exact knowledge of the field’s energy, although, in practice, external variables limit the accuracy to which the
field can be controlled or measured – in this case the law is valid, even though an exact description of the
system requires knowledge that is not available (such as the various sources of fluctuating weak magnetic
fields in the environment). The law of conservation of momentum is that momentum will always be conserved,
not that the cue ball will always enter the top-left pocket! In these cases, we must know what apparent ‘law’ is a
law and what ‘law’ is not!

On other occasions, however, more accurate considerations will reveal that the ‘laws’ break down and fail to
predict the outcome with this higher degree of accuracy. Physics is full of such examples – Newton’s laws of
gravitation work approximately and accurately enough when we are concerned with the motion of the Moon
around the Earth, but break down when we look more closely, at say the motion of an electron around a very
powerful gravitational source. The energy levels of the electron in the hydrogen atom can be accurately
predicted by basic theory, but more accurate measurements reveal additional parameters that must be
included to make accurate predictions. If a narrow definition prevents an event recurring, then there is no law
governing it, but there may be a ‘law’ that makes approximate predictions with a stated degree of accuracy.
These days physicists never consider a ‘law’ to be necessarily ‘unbreakable’ but rather acknowledge that a
‘law’ holds in certain circumstances to a certain degree of accuracy. That there are natural laws is not
generally doubted, but the ‘laws’ humanity discovers must always be doubted – in this way science progresses
by asking more and more probing questions to test ‘laws’ in ever more varied situations.

What is the smallest time-interval between cause and effect? Bertrand Russell concludes that a cause takes a
finite time to act. He uses the example of placing a coin in a slot machine and the time it takes for an item to be
dispensed, and notes that an intervention can prevent the coin from activating the dispensing of the item after
the coin has been inserted. He thus argues that a time lag (as well as a spatial extent) separate cause and
effect, allowing the causal link to be broken and thus preventing the expected effect. However, there are
problems here in pinpointing the exact cause. The coin, to be sure, does not strictly cause the dispensing of
the item, rather it causes a mechanism to be switched inside the machine which activates other machinery to
release the item – in other words the coin triggered some event not considered by the example and so
activated a causal chain, which eventually results in the item being dispensed or in some other effect. This
chain can be ‘broken’ by inserting other parts into the system, such as a faulty cog or lever, resulting in an
unexpected event. Thus, when discussing the time lag and the spatial extent between cause and effect we
must identify the cause and effect with some precision. That is, we must distinguish between an apparent
cause that actually triggered a causal chain that leads to the effect, and the immediate cause which connects
directly to the effect in question with no other intervening links of cause and effect.

Consider a collision between two billiard bills. Suppose the target ball, is initially stationary and is struck by the
cue ball, resulting in a deflection of the cue ball and the imparting of motion to the target ball. This is really a
chain of events. As the cue ball approaches the target ball, the electrons in the atoms of each ball eventually
experience a force of repulsion from the electrons in the atoms of the other ball as the balls, their atoms and
their electrons approach one-another. This is the Coulomb force of electric repulsion, as like electric charges
repel one-another. This repulsion imparts additional energy to the electrons, and hence to the atoms and the
balls. This energy derives from the energy of motion (kinetic energy) of the cue ball. This electric force will
cause at first a slight acceleration of both balls and this acceleration will increase as the Coulomb force
increases and the balls exchange more and more energy as they approach 'closer and closer' (although they
appear to be in contact the whole time, the balls deform slightly and their atomic nuclei and electrons approach
closer and closer), until the distance of closest approach is reached and the force peeks. Note that a
significant change in motion will only occur when the balls appear to strike one-another, but the ‘collision’ is
really between atoms in the ‘areas of contact’ between the balls and is actually the electrostatic repulsion
between their electrons. As the balls collide they will deform as the atoms of one ball are pushed closer to
those of the other ball and the electrostatic repulsion increases, moving the atoms and distorting the shapes of
the balls by some small amount. In time the energy transferred from one ball to the other, as a result of the
electrostatic repulsion, will distribute between all the atoms in the balls and the balls will begin to roll. It is a
chain of events – the electrons on part of the surface of the target ball feel repulsion from the electrons on the
surface of the impacting cue ball, they impart this energy to the atoms as a whole, causing the atoms to
displace slightly, these atoms then repel neighbouring atoms within the ball as their electrons are pressed
closer together, and so on – a wave of atomic displacements passes throughout the target ball and all the
atoms in the ball are set in motion. The ball will also vibrate, and some energy will be released as sound and
heat. Thus, energy is exchanged between the balls over a period of time which lasts as long as the force
between the balls acts (a very short period of time from our viewpoint). Thus, the change is really a series of
changes that occur over a period of time.

Can we narrow our definition of the events occurring when the balls collide to derive at some instantaneous
cause and effect? Can we, for example, consider only the onset of electric repulsion between an electron in
one atom of the cue ball and an electron in one atom of the target ball, by defining this to be our system? We
can indeed consider one such small part of the system, though only approximately, since in reality each
electron will experience forces acting simultaneously from many other electrons. Let us assume that we can
average out the extra effects and apply them as a ‘correction factor’. We still will have a finite time between
cause and effect no matter how much we zoom in and narrow down the system, simply because no signal can
travel faster than light. As the electron in the cue ball approaches very close to the electron in the target ball
and the two begin to experience mutual repulsion, it takes a finite time for the signals to be exchanged
between the electrons, so there will always be some period of time between cause and effect.

Having said this, there are apparent exceptions in which a ‘signal’ of sorts can cross an interval of space in
zero time. This exception is the so-called ‘ghostly action at a distance’. It is often said that ‘a cause cannot
operate except where it is’, Bertrand Russell addresses the problems associated with the use of the word
‘operate’ (which implies volition) but we shall not refute the statement on that basis, but we shall instead look at
the meaning implicit in the statement, rather than the words used. Clearly, the electrostatic repulsion between
our billiard balls extended over a region of space. Indeed, the Coulomb force declines with separation between
two electric charges in predictable and well known ways, until at some spatial separation it becomes ‘negligible’
as far as the system under study is concerned (a billiard ball at one end of the table may be repelled by a
billiard ball at the other end of the table, but not enough to set it in motion, especially when gravity and other
forces are considered). However, a signal must be communicated between the parts of a system if there is to
be a causal link between them. Perhaps this signal ought to be considered part of a causal chain. The ‘signal’
conveying electric repulsion is actually comprised of virtual photons and cannot exceed the speed of light.
When the signal arrives at the target ball, perhaps we should consider the virtual photons to be the cause of
the repulsion rather than the cue ball. We can narrow down or extend such chains in either direction, perhaps
the cue caused the final event which may be potting of the ball, or the applause of the audience, ... Again,
when addressing whether there has to be some finite region of space separating cause and effect or whether
the two must coexist in space, we must designate the cause and effect with some precision. Let us zoom in as
far as we can. A virtual photon emitted from the cue ball arrives at an electron in the target ball after a finite
time interval (we shall not consider the issue of whether or not the photon followed any kind of definite ‘path’
here) and interacts with the target electron, which experiences a force. Additionally, bearing in mind the
energy-time uncertainty principle, we perhaps ought to expect there to be a certain randomness inherent in
the time taken for energy to transfer in small packets on the sub-atomic scale. This presumably is reflected in
(or caused by) the stochastic processes governing the emission and absorption of virtual particles.

Is time reversible and does it have direction? If time is change then why is it not reversible, but instead always
seems to proceed from cause to effect? We have already seen that the only difference between a cause and
an effect is that the cause necessarily precedes the effect in time. This leads us to ask, what is the connection
between cause and effect? If a process could occur in reverse, then the effects would become causes and the
causes would become effects. For this reason, Bertrand Russell considered there to be no special connection
between cause and effect, in the sense that a cause did not ‘operate’ to beget an effect, but simply that
mathematical equations take variables that describe the system at one instant of time and deduce the state of
the system at that instant. Indeed, many equations do just this, for example, the calculation of the force of
gravity between two stationary bodies (or between two bodies in stable orbits) achieves such a result.
However, not all systems are time-independent or in a steady-state. Physics often assumes a steady-state for
simplicity. The Theory of Relativity tells us that two different observers may disagree as to whether or not two
events occur simultaneously, since local time runs at different rates for different observers. However, relativity
does preserve causal relationships by preventing an event A, as observed by one observer to precede event
B, from appearing to occur after B to a second observer, though a third observer may say A and B are
concurrent.

If physics worked as well backwards in time as it does forwards, then sequences of events would occur equally
in both directions. Just as when you drop a plate and it smashes to pieces, sometimes the pieces would
spontaneously reassemble into an intact plate, clearly this is not the case! When the plate breaks some of the
kinetic energy is lost from the system as sound, heat and light. Since such energy has radiated away in all
directions it is not easily brought back! The process cannot be reversed because the heat, sound and light
that radiate away cause a loss of information – there is no longer enough information available to reconstruct
the plate exactly. The symmetry of time is broken. Beta decay, and other processes involving the weak
interaction, also break symmetry by possessing helicity. A neutrino or antineutrino emitted or absorbed in such
a process has a definite helicity, meaning that its path cannot be reversed without it appearing as a different
process. A helix or corkscrew that is rotating about its axis, say in a clockwise sense when viewed from one
end of the screw, is distinguishable from the time-reversed process in which the screw rotates in the opposite
sense, because a screw is either right-handed or left-handed. Indeed, this breaking of symmetry enables
bacteria to locomote through highly viscous materials. It is these and other similar breakings of symmetry that
cause time to move always in one direction and never to reverse. In other words, since some changes are
irreversible, time moves ever forward.

Can a single cause result in multiple effects? In one sense, yes it can – a cue ball could strike two target balls
in a single shot, even approximately simultaneously if the target balls are side-by-side. However, different parts
of the cue ball will strike each target ball, in which case this may be classed as two distinct events (each
comprising a causal chain on a finer scale). However, both effects result from a causal chain that branched
from a single event - a single strike from the cue, so at some point along the causal chain a branch from a
single cause to two effects must have occurred. Indeed, there are examples of this on the atomic scale – a
single photon may be absorbed by a single electron in an atom and then, by de-excitation, the atom can, on
occasion, emit two photons simultaneously. Thus, a single cause does seem quite capable of producing more
than one effect.

Can multiple causes result in a single effect? Causes can add together over time to produce a certain effect.
To fill a glass of water requires many molecules of water entering the glass, do we regard the pouring in of 400
ml required to fill our glass as a single cause? What if the water is poured in a series of stages? Is the filling of
the glass by four aliquots each of 100 ml a single cause or four separate causes? Here we enter into the realm
of colloquial definitions of cause and effect, rather than elementary physical definitions (such as events
involving elementary particles). What about on the elementary scale of things? When exposed to intense laser
light, an atom can sometimes absorb two photons, causing it to change state to an excited level which is
determined by the total energy of the two photons. One photon of twice the energy could cause a similar
excitation. We have one effect but two causes.

Does the effect need to be similar in nature to the cause? This question was addressed by Bertrand Russell
who discusses the application of the argument that 'matter can not cause mental processes since matter has
no mind in it'. This is of course an ancient philosophy that like begets like, and that the psyche came from the
primeval spirit that pervades all of matter. However, there is no scientific basis for such a belief. This is not to
say that consciousness is not some universal presence, or that it was not produced independently of matter,
but that it may be an effect of matter. We simply do not know. We have already seen how energy can readily
transform from one type into another. Here we must agree with Bertrand Russell, that there is no basis for the
statement that, ‘Cause and effect must more or less resemble each other.’

Is consciousness a form of energy? When we consider that everything appears to be an energetic wave, and
that energy is always on the move, does this mean that consciousness is also comprised of energy? The
neurones that make up the brain certainly transform energy – they convert chemical energy in glucose into
electrochemical energy. This electrochemical energy is transported between the neurones, in the form of
electrochemical waves, and constitutes the signals that neurones convey to one another. The brain is a vast
signalling network, a vast network of causes and effects, a network of ever-changing signals that require
energy. The collective electrical behaviour of this network is wavelike in nature; brain waves can be measured
through electrodes attached to the scalp and the frequencies, shapes and amplitudes of such waves change
as the state of consciousness changes. Furthermore, the waves can be driven – electrical stimulation can
change the wave pattern resulting in a change in conscious state – or does the electrical activity change the
mental state, resulting in a change in brain waves? In some way, then, brain waves and consciousness are
causally connected, though we cannot rule out that each causes the other, or that conscious state really
determines the wave pattern or that the wave pattern determines the conscious state. We simply know that the
two are correlated. However, it is tempting to speculate that consciousness, like all physical phenomena, is a
wavelike phenomenon.

Of relevance here is the question of whether there is a hitherto unrealised type of energy peculiar to
consciousness. It would help to empirically determine whether or not the electrochemical energy ever turns into
a new type of energy, before being dissipated and lost from the system as heat, sound and light. Note that
'energy in' must presumably always equal 'energy out', but that some of the energy may pass through the
reservoir of consciousness as another form of energy. Suppose that although thinking and other mental
processes require energy, that energy remains in tangible and well-known physical forms, such as
electrochemical or heat energy, etc, such that consciousness appeared not to be made of an energy of its
own, then what else could consciousness be? Certainly, if free will exists, then consciousness can cause
changes in physical systems.

Energy causes change in the observable properties of a system, perhaps consciousness is an observable
property. Here we run into a problem – we can each observe our own and only our own consciousness
directly. Consciousness is a peculiar type of observable as it is only personally observable. To get a handle on
things science must be able to apply a measurement upon which all observers can agree. Can you
demonstrate that anyone other than yourself is conscious? Can you measure the consciousness of others and
thus determine who is more conscious than whom? The answer is that we cannot directly do this at present.
However, we can infer the level of consciousness in another individual, but would all observers agree on such
inferences?

It seems that energy causes changes in consciousness, which suggests that consciousness itself is a form of
energy, perhaps a system of waves. What if consciousness is a pattern? Let us consider an analogy: arrange
a set of four dice to read a given set of numbers, e.g. 1, 4, 3 and 6; now change the dice to read: 2, 5, 3, and
6. This required energy to change the pattern displayed by the dice, but is this pattern an energy in itself?
Certainly the dice are made of energetic matter that interacts with light to give the visible display, however we
have a pattern which is an arrangement of energy that gives us information. Information seems linked to
energy – energy contains information, but can information exist independently of energy? To answer this
question, we need to look more closely at the types of changes that energy can bring about, and the types of
changes that energy itself goes through.

What is information? Let us consider information stored electronically on a computer system. Essentially a
RAM chip (specifically a DRAM chip) contains a two-dimensional array of capacitors on a silicon sheet. If each
capacitor is more than 50% charged it reads as a 1, otherwise it reads as 0. The pattern of 0s and 1s in each
column represent the data value stored in that particular memory address. In short, it is again the pattern of
the energy, in this case its spatial configuration, which stores or represents the information. Information is
simply the pattern of energy changes over space and/or time – an energy field. An example of information
stored in a temporal sequence would be a flashing light (occupying a fixed position) representing a Morse
code signal. In this example, the information is actually stored in a spatial representation of the message, such
as a record of dots and dashes on a sheet of paper or a network of electrical activity in the memory circuits of
the brain. Thus, in actual fact, although information can be transported by a signal changing in time, the
information itself is a spatial pattern of energy. As energy is the ability to cause change over time, it is also
information stored in space. As time allows changes to occur and energy and information to be transported,
space gives meaning to the energy by giving it information.

The brain, of course, stores vast amounts of information in the form of three-dimensional networks of
neurones communicating electrochemically (in other words the pattern of electrochemical energy represents
the information). It has been argued that consciousness is the result of the complexity of this pattern of
information, however, at what point would a complex computer become conscious, if this is indeed the case?
Certainly memories are stored as patterns of neural architecture and sensory information is processed by
neural networks within the brain. However, perception of a stimulus requires several stages: first a stimulus,
such as light from a candle, must be sensed by the retina in the eye, processed by the brain, which splits the
image into separate spatial maps, such as one for contrast, one for colour, etc. Finally, an image must be
presented to the conscious. That image is certainly a reflection of patterns of energy in the brain, but what
about the consciousness itself – what is it which is aware of the processed mental images that are perceived?

If it is not already implicitly clear, then let me say that by information, I am referring to all information, whether
of potential interest to our minds or not – information that determines the spread and nature of energy and
matter in space – all the energy fields that permeate the whole of space, from gravitational fields, electric
fields, magnetic fields to matter fields, etc. The physical definition of a field is something which permeates all of
space and to which a value (scalar or vector) can be assigned to every position in space. For example, the
electric field permeates all of space and every region of space has some electric field strength, even if we
designate this zero. Fields are three-dimensional arrays of information about observable (energetic) properties.

Is change constant, and if so how can anything exist? First of all it seems that we have to logically agree with
the notion that something which is nothing cannot exist as it is a self-contradiction. Even space is teeming with
energy. When we say that something ceases to exist, we really mean that it has changed state, and that the
energy/matter within it has changed form, but the energy cannot be destroyed and so it has to change into
another form. Since even in stable matter the atoms constantly vibrate (even at 'absolute zero') and exchange
energy, then indeed change does seem to be constant. When we refer to a specific object, like a mug on a
desk, this mug is never exactly the same from one moment to the next, even if it looks identical a second later,
on a microscopic scale it has changed. For one thing its atoms have vibrated and will be in a slightly different
position. Some of the atoms may even have exchanged their electrons with those that fade in and out of
existence in the medium of space. Photons will have been exchanged, heat will have been absorbed and
radiated and many other changes will have occurred. However, we identify the mug as the same object since it
has changed little in terms of macroscopic observable properties. In truth, what has persisted are the various
properties of the energy field that make up the mug, in other words that degree of information it contains which
has remained noticeably unchanged. Certain changes are, of course, permitted by our practical definition of
the mug as an entity – if its temperature changes we still regard it as the same mug as long as it remains solid.
Our definition is a useful one based upon the information contained within the mug that we are interested in,
such as can it hold water, does it have the same flowers drawn upon it and is it where I left it, then it is the
same mug?

Ah, but the atoms are the same atoms, you may say, but are they? The electrons will probably have
exchanged many times, due to the effects predicted and verified (as far as is measurable) by quantum
electrodynamics. The nucleus is comprised of nucleons, which are comprised of quarks. Many of these quarks
are virtual and so they too constantly phase in and out of existence. Each nucleon contains a core of quarks
which are not virtual, but even these frequently change into different types of quarks by the exchange of
gluons, so in what ways are the atoms the same – the answer is that they are no more or less the same than
the mug is itself. Only the approximate contents of the information that objects and other entities contain
persists, but even this is constantly changing on the atomic and sub-atomic scales, and, eventually all things
change even on the macroscopic scale. Existence, then, is all about the persistence of information. This
information is a pattern of energy that constantly changes, sometimes slowly, sometime quickly, sometimes
microscopically, and sometimes macroscopically. When macroscopic changes occur that are large-scale and
irreversible, we say that an entity has been destroyed, meaning that the information it contained has been
sufficiently disrupted to render the original object no longer observable (functional), however, energy is not
destroyed, it merely changes form and the field of information that it forms changes.

So information constantly changes, but is it ever lost? Common experience, without appealing to quantum
physics, tells us that information can be irretrievably lost, but could it be recovered, given sufficient power,
simply by physical means? We have already seen how energy is lost from a system by heat, sound and
sometimes light. However, this energy does not leave the Universe, so when our system is the whole Universe
this energy never seems to leave it. In a deterministic, classical universe it would therefore be possible in
principle (not in practice!) to recreate a past state of this universe exactly if we knew the positions and
properties (such as velocity) of every particle of energy at the same time (likewise we could predict the exact
nature of things at any time in the future). However, quantum mechanics does not allow such certainty.
Heisenberg’s uncertainty principle, for a start, prevents us from reconstructing exact trajectories for each and
every particle, in principle. Information is inherently and irreversibly lost according to quantum mechanics.
There is also the possibility that information is irreversibly destroyed when energy falls down a black hole, but
that is still under debate. It seems to me, however, that quantum mechanics already loses information. Indeed
this loss of information ultimately prevents events re-running in reverse, so time moves forwards only. When
we say time moves forwards, we really mean that changes are essentially irreversible. Some changes can be
apparently reversed, but never exactly.

The concept of entropy immediately becomes relevant here. In a system, like the mug we described here, even
if all the macroscopic observable properties (information) appears constant, i.e. the temperature, volume and
shape of the mug appear unchanged, the microscopic state of the mug is in constant flux, for one thing the
atoms in the mug are constantly vibrating. Thus, there are many possible microstates for every macrostate.
The number of microstates per macrostate is called the statistical weight of the system and the entropy can be
defined as a quantity which is proportional to the natural logarithm of the statistical weight. The more ordered a
system appears to be, the less entropy it has. In the mug, the atoms vibrate, but not freely, as in any solid they
vibrate about their equilibrium or average position, as if they had springs on each side to restrain them as they
oscillate back and forth. Let us suppose that we place the mug in a very hot furnace and vapourise it. The
atoms of the mug are now free to vibrate almost unhindered in the gaseous state and will move about rapidly.
Our macrostate is no longer a mug, but a gas that has expanded to fill its container, and with the atoms more
free to move about there are many more possible ways to arrange the atoms to give the same state – a gas.
The number of microstates per macrostate has increased dramatically and so has the entropy of the mug. In a
sense there is less information available about each atom in the gaseous state than in the solid. For example,
in the solid mug, the atoms were confined by the shape of the mug, and an atom in the handle remained in the
handle, more or less frozen in place apart from its vibrations and so we had more information about the
position of the atom. Information appears to have been lost when the mug was vapourised. Indeed, in the
gaseous state the motions of the atoms become more random and as the atoms collide with one-another they
exchange energy. Over time, in a gas, the temperature, pressure, density and chemical potential become
smoothed out, apart from statistical fluctuations which are usually very minor. An increase in entropy can be
defined as a smoothing out of the temperature, pressure, mass density and chemical potential. It can also be
defined as an increase in randomness or a loss of order. Order in this sense is really defined as information
and energy that can do useful work. If the whole Universe was a homogeneous gas, then not much work could
be done upon anything! Changes would still occur, but mostly these would be confined to the microscopic
scale. Entropy, then can also be defined as a measure of the unavailability of a system’s energy to do work. By
work here we mean the energy required to change the macrostate of the system, and usually not all the
energy we put into a system is available to do this, but instead goes into increasing the entropy of the system.

In a closed (isolated) system, that is one which is not exchanging a significant amount of energy or matter with
its surroundings, a process (change) can only occur if it results in an increase in the total entropy of the
system. In this way, information is lost over time. In an open system, this process can be reversed by investing
energy from external sources to change the system into a more ordered state that contains more information.
The notion that the Universe is a closed system leads us to suppose that it will eventually run down and
collapse into a homogeneous chaos. Whether or not this will be the case naturally remains to be seen!

In conclusion, we began with a textbook definition of energy as the ability to cause change. We saw that
causality manifests as chains of cause and effect, in which the distinction between cause and effect is one of
our own perceptual convenience, in which case causes and effects are both changes and what causes
changes are changes. Thus energy becomes changes and all observables are changes, including mass,
waves, force and acceleration, and so all these observables become energy measured in different ways,
resulting in the different units that we ascribe to mass, force, acceleration, energy and other observables. If
nothing else, this does prove that when we think we know what something like energy is, it is simply what we
define it to be, irrespective of reality. Indeed, our choice of definitions can make reality appear more or less
complex. Consciousness comprises different states that change, and so is also energy of a sort. Since energy
can be transformed from one type to another, this raises the possibility that physical forms of energy can be
transduced into consciousness and vice versa. Space appears to be information contained by energy, and
time is simply change in this information. Information can cause change, as can time, and so both become
energy in another perceptual form. Every entity in the Universe appears to have melted away into energy
according to our initial definition! Perhaps energy or change is all there is on an elementary scale! Either that
or my chain of logic slipped up somewhere ...

Shall we try another approach? So far we have suggested that force and mass are measurable because they
have the ability to cause change, which made them essentially manifest properties of energy. Physicists are
generally comfortable with stating that energy is essentially equivalent to mass, although the two are by no
means identical. This is perhaps analogous to saying that inches and centimetres are both measurements of
length, but they are not identical, rather length in inches is proportional to length in centimetres, since both are
linked by a third variable - the actual linear dimension of the object being measured. Energy is similarly
proportional to mass, for an object at rest. Using natural units, both mass and energy have the same units of
energy (GeV). For an object in motion, things are a bit more complex, since now the energy is proportional to
mass plus another term, the momentum. Since mass has the same units of energy in natural units, the energy
essentially equals mass plus momentum (strictly mass and momentum are separately squared, added and
then the square root is taken) and so momentum also has to have the same units of energy. Thus, momentum,
mass and energy do indeed seem to be measures of energy, as we deduced intuitively.

What about force? In natural units, force has the units of one over energy squared, so it is fundamentally
different, and yet, according to the definition of energy as the ability to cause change, force is clearly energy!
The different units stem from the fact that in physics, energy is taken as a certain quantity (the ability to do
work) at an instant of time. Clearly this creates a conflict with our definition of energy, since energy cannot
have the ability to cause change until it acts over a period of time in a finite region of space. Without
discussing equations, incorporating the units for space and time convert the units of energy into the units of
force. However, according to our phenomenological definition of energy, force is clearly energy. Here we
encounter a seeming paradox - energy as defined in physical equations does not explicitly introduce time and
yet without time no energy can be measured, indeed the energy-time uncertainty principle tells us that when
measuring the energy of a particle, the uncertainty in energy becomes infinite as the uncertainty in time
becomes zero. Nevertheless, we talk about 'measuring energy' but what are we really measuring? We could
combust one gramme of foodstuff in a calorimeter and by measuring the heat evolved we can calculate the
energy available from that food by chemical combustion. We imagine that energy existing in the food, as
chemical energy at each instant of time, then we imagine that heat energy existing in the calorimeter at a later
point in time. It clearly took a certain amount of time to transfer the energy from food to calorimeter, as it took a
finite time to combust the material. Can anything exist in space at a precise point in time? I do not think so, the
whole thing is simply a convenient mental construct. Nothing can exist without having a finite extent in time.
Indeed, times shorter than the Planck time are somewhat meaningless. Likewise, energy must manifest over a
finite region of space. Once we incorporate time and space our energy really becomes a force, at least
whenever it acts and does something. Indeed, if something does not act to cause change then in what way
does it actually exist? There is one problem with this though.

What about potential energy? Potential energy, as the name suggests, is energy that is in a kind of inactive
form, waiting to be converted into another type of active energy (such as kinetic energy) and so is kind of like
a reservoir of energy. However, when energy ceases to act it no longer becomes energy, so are we saying
that when active energy turns into potential energy that it has momentarily ceased to be, even though in the
long run energy is conserved? Not really. Let us look at some examples. Consider gravitational potential
energy. Raise a ball and hold it in the air. The ball has gained gravitational potential energy, provided by the
work your muscles did (which was kinetic energy derived from chemical energy). This is potential energy
because it does not manifest until you release the ball, in which case it falls to the ground, losing that
gravitational energy as it is converted into kinetic energy. However, even while this energy was stored as
potential energy, its activity was still very much manifest. The force of gravity was acting on the ball all the time,
but the reaction force, due to the Coulomb repulsion between the ball and your hand stopped it from falling by
counteracting the source of gravity. Atoms and electrons are not static, so this repulsion was not so much like
a static spring wound up and waiting to go, but was due to the dynamic and constantly changing interplay of
two opposing forces keeping one another in balance. In this way, potential energy of this kind can be seen to
be an active phenomenon (literally an 'energetic' one!). This kind of potential energy is energy that is actively
changing on the microscopic scale, but which is kept in check on the macroscopic scale by actively opposing
forces. What about an example of potential energy on the atomic scale?

An electron inside an atom is thought of as being 'trapped' inside a potential energy well, a Coulomb well,
meaning that the mutual Coulomb attraction between the electron and the protons, keeps the electron near to
the nucleus. The electron can be given energy, e.g. by hitting it with light, and moved further up this well, or, if
it is given sufficient additional energy, it can escape from the well altogether and become a free electron. The
free electron is thought of as a translating wave, and so is clearly changing. The electron inside the well is
thought of as a standing wave, which like a vibrating guitar string is not going anywhere, and on this guitar the
strings keep vibrating once plucked, unless we use energy to stop them. Does this mean that the electron is
doing nothing? No, for several reasons. Firstly, the electron is most probably in an admixture of orbital states,
and only when we measure it does it collapse into a single orbital (such as a 2S or 3p orbital). Now, contrary to
the models used by chemists to assist visualisation, as physics currently understands it an electron in a single
orbital does NOT orbit the nucleus! Orbitals are stationary states, exhibiting no time development (they do not
change over time, until the system is perturbed). Many would object to this, saying that the electron is moving
so fast, but appears stationary as we measure its average position, or its position at one instant of time.
However, eigenstates are stationary - that is what the equations tell us, to say otherwise is to invoke hidden
variables, and evidence currently suggests that there are no hidden variables. However, the measured energy
of the electron is corrected for the very high speed motion of the electron. How is this possible? I confess that I
have never come across a satisfactory answer to this. However, I shall tell you what I know to-date on this
issue.

When an electron orbits an atom it is usual to think of it as existing in a superposition (addition one on top of
the other) of states - that is it might be in a mixed 2s/3p state. However, no electron can ever be measured to
be in such a state, but will collapse into either the 2p or 3s state when measured. This is not so mysterious,
when you think that in order to measure it's position, some measuring device has to interact with or perturb the
electron and, being so small, this invariably causes a noticeable change in the electron's behaviour - we can
never know exactly what state it was in prior to measurement if it was in a mixed state. Let us say that it
collapses into the 2s state. If measured again at a later time then, assuming no other external particle or
energy has interacted with the atom and not too much time has elapsed, then the electron will again be found
in the 2s state - it has remained in the 2s state. In the absence of other factors, such as external forces, the 2s
state is a stationary state - the equations predict no motion over time and quantum mechanics (QM) tells us all
the information that exists about the entity measured (unless there are indeed hidden variables). When an
electron is bound to two nuclei, as it is in a diatomic molecule, such as oxygen (O=O), then when in a mixture
of states the electron can indeed undergo motion as its average position oscillates between the two nuclei
(though it in no way has to follow a definite trajectory). Maybe a similar phenomenon occurs in single atoms (I
am not sure if this can be the case in an isolated atom, I will have to think about this!) especially when external
forces (such as neighbouring atoms) perturb the atom. This would impart motion to the electron prior to its
measurement, which would necessitate the energy correction to the measurement of the electron's energy.
However, this correction presumably implies when a later measurement finds the electron still in its 2s
stationary state, so where is the motion coming from?

I do not know, but other corrections do involve change to the system. So far our model has not included a
phenomenon known as quantum electrodynamics (QED). One of the consequences of QED is that electrons
and positrons phase in and out of existence all the time in 'empty space'. A positron is an anti-electron and if it
encounters an electron then both will annihilate in a burst of photons (light). In a vacuum the electrons would
annihilate with the positrons formed in the vacuum, since electrons and positrons are also produced in
electron-positron pairs. However, near an atom, one positron may annihilate with an atomic electron, leaving
its electron birth partner available to take the place of the former atomic electron. In this way, the electrons in
atoms are constantly changing as new electrons take their place. Note that when the old electron disappears,
the new electron will be in a different spatial location near to the nucleus, so electrons will appear to jump
instantaneously around the nucleus from one position to the next.

Clearly, however we think of electrons in potential wells in atoms, they are not static! Something is always
changing. Potential energy then is an active process that temporarily holds a certain amount of energy within a
system, but that energy is constantly undergoing changes at the microscopic level.

Is force more fundamental than energy? Energy then appears to be in constant motion - it simply does not
exist independent of space and time except as a mathematical and mental construct. Add time and space into
the equation and energy really becomes force, even if another force keeps this force in balance, as in a store
of potential energy. In this sense force seems to be more fundamental and matter and energy appear to be
manifestations of forces. However, we were attempting to simplify matters, but now we have replaced an
elementary concept like energy with a compound consisting of energy, time and space. What about are
original definition of energy as the ability to cause change? Well change is the ability to cause subsequent
change and so we could describe energy as change with the ability to cause subsequent change. However, is
this not really the definition of a force? Indeed, modern physics is concerned with the 'four fundamental forces'
of electromagnetism, gravity, the weak nuclear force and the strong nuclear force. It is thought that these four
forces may simply be low energy facets of the same fundamental primary force, but that remains to be seen.
Certainly uniting electromagnetism with the weak and strong nuclear forces poses no real problems at high
energies, but gravity is a problem!

What about momentum? The momentum of a massive object, defined as the object's mass times its velocity is
another fundamental element of physics. Note that, since energy and mass are in a sense equivalent, non-
massive particles like photons can also have momentum. Indeed, the term non-massive becomes nonsensical.
It is said that photons have zero rest mass, however, since no observer can move as fast as a photon, the
photon can never appear at rest and so always has mass! In natural units, which factors out the various
constants (conversion factors) momentum has the same units as energy (GeV)! Indeed, it is connected
intimately with kinetic energy, though the mathematical definitions and properties of the two do differ in certain
ways.

Are we achieving unification? It seems that we can, in a sense, talk about energy, matter, momentum and
forces being facets of the same fundamental entity. Similarly, space and time can be united as space-time. It is
interesting that theories derived from complex mathematics and empirical observations seem to be unifying the
various elements of physics in a way similar to our initial enquiry based upon simple logic and
conceptualisation (and intuition?). However, it remains to unite forces with space-time. Indeed, gravity is a
natural consequence of the way that energy (including momentum, mass and forces, or should that be forces,
including energy, mass and momentum?) warps space-time around it. It is thought that the other three
fundamental forces may be linked to geometry in some way. A clue comes from mathematical analyses in
which electromagnetism appears from the assumption of a fourth spatial dimension (the fifth dimension, a
there is one dimension of time). It also appears when a phase factor correction is applied to the wavefunction
in Schrodinger's equation when such a correction is a smoothly varying function of space and time. Does this
mean that the phase factor is motion in the fifth dimension? Modern string theory evokes about 10 spatial
dimensions and one dimension of time. All this is rather complicated, so let us first return to a subject that we
have not done justice to - the nature of time and space, but this will form the basis of another enquiry and
another essay!
Causality and being
The essay below is an attempt to address some of the most fundamental questions that Bot could think of
and to outline Bot's thoughts on these matters. Many of these questions are ultimately unanswerable, but it is
interesting to see what progress can be made. This is a work in progress, so it may contain errors and
arguments that need tightening up or clarifying. Many of the ideas are intended as thought-provoking
propositions rather than absolute facts.

This particular essay is rather technical and at some point I shall endeavour to add definitions to all the main
technical terms. The content of this essay is not guaranteed to be factually correct (!) since it tackles very
hard topics and also there may be no right or wrong answer to some of the issues discussed, since all
philosophy contains a subjective element. However, if you would like to query or comment on this essay then
please email Bot at: botrejectsinc@cronodon.com, constructive comments that help us ascertain the truth of
these matters is much appreciated.
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