The Atemporal Universe – Resolving the Problem of Time

Colin Mangan
Email: the.atemporal.universe@gmail.com
June 6
th, 2019
Abstract

 

This paper looks at a possible resolution of the “problem of time” which arises from the
attempt to unify Quantum Mechanics (QM) and General Relativity (GR), into a theory of
Quantum Gravity. Extending the principle of relativity to the concepts of synchronisation
and simultaneity, in Einsteinian Relativity, allows for the restoration of absolute
simultaneity, which in turn helps to align the concepts of time in GR and QM. A further
examination of the nature of time, reveals that` time is neither fundamental nor emergent,
but is rather a defined system of measurement. This is in the same sense that the metric
system [of measurement] – or indeed any other system of measurement – is neither
fundamental nor emergent. This is to say that the universe is fundamentally atemporal or
“timeless”. In viewing time as a system of measurement, we retain all the functional
attributes that are currently attributed to time, in our contemporary physical theories. A
relational interpretation of time is retained at the classical level, which can make sense of
both the Leibnizian and Machian principles of time, while such a timeless interpretation is
indistinguishable from the idea of absolute time. The reinterpretation of “time” as nothing
more than a system of measurement also helps to address the issue of background
dependence, which is part of the overall problem of arriving at a unified theory of Quantum
Gravity. This paper also seeks to address the issue of background independence, albeit less
directly.
1. Introduction

The problem of ‘time’ is one of the deepest issues that must be addressed in the search for
a coherent theory of quantum gravity (Isham, 1992) i
. What then is the problem of time?
Many conceptual issues….occur[s] because notions of time are substantially different across
these Paradigms [of physics] … The Problem of Time is, in greater generality, a consequence
of the mismatch between Background Dependent and Background Independent Paradigms
of Physics. Newtonian Physics, SR, QM, and QFT are all Background Dependent, whereas GR
is Background Independent and many approaches to Quantum Gravity expect this to be
Background Independent as well, whereas GR is Background Independent and many
approaches to Quantum Gravity expect this to be Background Independent as well [page V]
… The Problem of Time consists of … nine facets–closely following Isham and Kuchaˇr –
resulting from nine corresponding aspects of Background Independence [page XII] … as
Isham and Kuchaˇr argued, the Problem of Time facets turn out to be heavily interlinked,
and none of the strategies proposed to date work when examined in sufficient detail. N.B.
that this heavy interlinking takes the form that if one resolves a facet piecemeal, and then
attempts to extend this resolution to resolve a second facet, then this extension has a
strong tendency to spoil the resolution of the first facet. Because of this, little overall
progress has arisen from treating Problem of Time facets piecemeal [page XV]. (Anderson,
2017)ii
.
On a fundamental level, the “Problem of Time” (PoT) can be seen as the issue arising from
the different, mutually exclusive, conceptualisations of time in Quantum Mechanics and
General Relativity. Time is absolute in quantum theory, but dynamical in general relativity.
What, then, happens if one seeks a unification of gravity with quantum theory or, more
precisely, seeks an accommodation of gravity into the quantum framework? Obviously, time
cannot be both absolute and non-absolute: this dilemma is usually referred to as the
“problem of time”. One can also rephrase it as the problem of finding a backgroundindependent quantum theory (Kiefer, 2009)iii
. (Anderson, 2014)iv suggests that the greater
part of the PoT occurs because the ‘time’ of GR and the ‘time’ of Quantum Theory are
mutually incompatible notions. Therefore, unifying quantum mechanics and general
relativity requires reconciling their absolute and relative notions of time (Wolchover, 2016)v
The approach to reconciling these two “mutually incompatible notions” of time advocated
for, in this paper involves not treating PoT facets piecemeal but rather addressing the
fundamental nature of time itself and proffering an atemporal interpretation of
contemporary physical theories.
2. The Possible Route to an atemporal interpretation of Relativity

Albert Einstein presented his special theory of relativity in 1905. As it is widely known, the
adoption of this theory implied a revolutionary change in our views of space and time
(Acuna, XXXX).
vi Indeed, it was his 1905 paper On the Electrodynamics of Moving Bodies
which introduced the paradigm shifting concept of Relativity of Simultaneity (RoS), which
overturned the centuries-old Newtonian conceptualisation of absolute time [and space] and
with it the assumption of absolute simultaneity and a universal present instant, or universal
“now’. Einstein’s paper also incorporated other ideas such as “Length Contration” and “Time
Dilation”, however these ideas pre-dated Einstein. In 1904 the Dutch physicist Hendrik
Lorentz proposed a theory that accounted for the same corpus of phenomena that
Einstein‘s theory explained, but that was grounded on a conceptual framework in which the
description of space and time was the traditional, Newtonian one. In 1905-6 Henri Poincaré
introduced some amendments in Lorentz‘s theory that resulted in the full predictive
equivalence between this theory and special relativity (Acuna, XXXX)vii
. The “empirical
equivalence” of the Lorentz-Poincare Ether Theory is worth bearing in mind as it offers a
possible interpretation of the Special Theory of Relativity that is based on absolute
simultaneity i.e. it is an interpretation of Special Relativity that does not incorporate RoS. As
such, it can assist us in arriving at an atemporal interpretation of Special Relativity.
According to Acuna (Date??), Norton (2008) argues that, given a pair of predictively
equivalent theories, if one of them contains superfluous structure, this strongly suggests
that the theories are, after all, one and the same. By excising the superfluous structure from
the less economic theory we would obtain the empirically equivalent, rival‘. I think this not
so in the case of Einstein vs. Lorentz. If we apply Occam‘s razor and excise the ether from
Lorentz‘s theory, what we obtain is not special relativity. It is still possible to retain the
Newtonian space-time plus conspiring dynamical effects by defining by fiat a privileged
reference frame. For example, the Lorentzian could baldly say that the privileged frame is
the one in which the real time is measured, period—even if it is impossible to physically
determine which frame is that. That would be a theory with questionable foundations of
course, but the point is simply that the main difference between special relativity and
Lorentz‘s theory is based on the incompatible space-times they postulate. This difference
remains even if we get rid of the ether (Acuna, XXXX)viii
. The emboldened and underlined
above (by this author) are suggestive of the possible route to an atemporal interpretation
although, as can be deduced, the designation of a privileged frame in which real time is
measured is not a necessity for an atemporal theory. Instead, a privileged frame for the
definition of units of measurement will be defined, not necessarily “by fiat” but rather as a
matter of operational necessity.

3. The Principle of Relativity

We have to take into account that all our judgments in which time plays a part are always
judgments of simultaneous events (Einstein, 1905)ix
. If we take this statement at face value
then we can see how the issue of simultaneity must play a central role in the PoT and
therefore, in resolving it. To paraphrase Kiefer (2009) obviously simultaneity cannot be both
absolute and non-absolutee. In this context, we need to re-examine the concept of RoS and
the process of how it was arrived at.
In his 1905 paper, On the Electrodynamics of Moving bodies, Einstein famously derived the
formula for the Lorentz contraction by employing a strictly principled approach. He
demonstrated that the consequences of length contraction, time dilation, and relativity of
simultaneity follow logically from the application of his two principles:
1) the same laws of electrodynamics and optics will be valid for all frames of
reference for which the equations of mechanics hold good.
2) that light is always propagated in empty space with a definite velocity c which is
independent of the state of motion of the emitting body (Einstein, 1905)
Taken together, these two principles can be seen to preserve Galileo’s fundamental
postulate, that the laws of physics are the same in all inertial frames of reference (wikibooks
– the Principle of Relativity)
x
. An important consequence of this, one that shall be employed
in this paper, is the notion that mechanical experiments will have the same results in a
system in uniform motion that they have in a system at rest (DiSalle, 2009)xi. This is
commonly stated as “there is no experiment which can be conducted to determine
whether one is in [a state of absolute] motion or at [absolute] rest”. This is a further
important idea that we need to bear in mind, as we re-examine the concept of RoS.
4. Einsteinian Clock Synchronisation Convention and the Relativity of Simultaneity
The Einsteinian clock synchronisation convention is establish[ed] by defin[ing] that the
“time” required by light to travel from A to B equals the “time” it requires to travel from B
to A. (Einstein, 1905)xii and this plays a critical role in arriving at the concept of RoS. In
section 2 of the paper (On the Relativity of Lengths and Times), when discussing the
measurement of a rod, in two relatively moving reference frames, it is stated that, we
imagine further that with each clock there is a moving observer, and that these observers
apply to both clocks the criterion established in § 1 for the synchronization of two clocks.
Observers moving with the moving rod would thus find that the two clocks were not
synchronous, while observers in the stationary system would declare the clocks to be
synchronous.
So we see that we cannot attach any absolute signification to the concept of simultaneity,
but that two events which, viewed from a system of co-ordinates, are simultaneous, can no
longer be looked upon as simultaneous events when envisaged from a system which is in
motion relatively to that system (Einstein, 1905)
xiii
. Below is a graphical representation of
the convention, which illustrates the concept of RoS.
As Einstein did, we can employ a thought experiment to elucidate the synchronisation
convention and how it demonstrates RoS. We can consider two observers, Alice and Bob,
moving relative to each other and let’s say that Bob is on a train.
The first picture shows the synchronisation of two clocks (at either end of a train carriage),
from the perspective of Bob on the train, at rest relative to the two clocks. According to
Bob, the two clocks are [assumed] to be synchronised at t=2.
The second picture shows Alice’s perspective, on a platform relative to which the train is
moving. From her perspective, the clock at the rear of the carriage is seen advancing
towards the light pulse, while the clock at the front of the carriage is seen retreating from it.
Therefore, only the clock at the rear of the carriage has been set in motion at t=2 and so the
clocks are not synchronised, in Alice’s frame of reference.
This situation is symmetrical, meaning that Bob observes the same of Alice’s attempt to
synchronise her clocks. Intuition might lead us to assume a simplistic assumption, namely
that both Alice and Bob are simply mistaken about his clocks being synchronised – a point
we will investigate below. However, as anyone familiar with the Special Theory of Relativity
will know, the intuitive understanding does not apply. As a consequence of the 2nd postulate
(the constancy of the speed of light), Einsteinian relativity tells us that both observers are
correct – and by the same token both are mistaken – the clocks are both synchronised and
not synchronised. Such a seemingly absurd position lies at the heart of the RoS and indeed
Relativity. It is the idea that synchronisation is dependent on one’s frame of reference.
Again, it must be stressed that these conclusions follow from the 2 postulates of Special
Relativity. The question we will be asking is whether they follow as a matter of necessity, or
is there an alternative interpretation.

5. Applying the Principle of Relativity to Synchronisation and Simultaneity

As mentioned above, the [Galilean] principle of relativity can be stated thusly: there is no
experiment which can distinguish an inertial frame that is at rest and one that is moving at a
constant velocity (Cutnell & Johnson, 2015 – p.799)
xiv. As we also saw, Einstein sought to
extend this principle to the phenomenon of light, with his 2nd postulate. What we will do
here is extend the principle to the notions of synchronisation and simultaneity, themselves.
Simply put, we will ask the question, is there any experiment that can determine the
simultaneity of events separated in space and by extension, is there any experiment that
can determine whether two spatially separated clocks are in fact synchronised with each
other. The simple answer to this is, no, there aren’t any such experiments. This simple line
of reasoning allows us to challenge the notion of RoS by analysing the intrinsic assumptions
of Einstein’s treatment of the 2nd postulate.
As mentioned above, the RoS is the idea that events which are simultaneous in one
reference frame are not necessarily simultaneous in a relatively moving, inertial frame.
Implicit in such a statement is an assumption about the simultaneity of events in a given
reference frame. However, through our extension of the principle of relativity to the
concept of simultaneity itself, we can see that such an assumption simply isn’t justifiable.
This in itself should be sufficient to dismiss the notion of RoS out of hand. At the very least,
it opens the door to a possible, alternative interpretation.
If we examine the issue further, we can start to ask how an observer might come to think
that 2 events are simultaneous. Again, we can employ the use of Einstein’s thought
experiments, of which there are a number of variants. One such example is that of the
lightning bolts striking the ends of a “moving” train and leaving marks on the railway. In this
example, the events are determined to be simultaneous in the reference frame of the
observer at rest relative to the tracks because the light from the lightning strikes – from
which he is equidistant – reach him simultaneously. This seems like a very reasonable
conclusion, however, if we examine the clock synchronisation convention above, we can see
why it isn’t.
In the outline of the synchronisation convention above, we saw that the clocks are simply
assumed to be synchronised. This is done by assuming that the journey time for the light
pulse, from the emitter in the middle, is the same in both directions. There doesn’t appear
to be any issue with this, especially when we grant the validity of the 2nd postulate. If we
consider. If we consider Bob’s attempt to synchronise his clocks above, we can again ask,
what experiment can he undertake to determine if his clocks are in fact synchronised. This
might be particularly desirable because Alice claims that Bob is mistaken, that his clocks are
not in fact synchronised. In this case, Bob sets up two mirrors at each clock, to reflect the
light pulses. He determines that, if the light pulses arrive back to him simultaneously, then
his clocks must be synchronised – just as in the lightning bolt example above. Again, this all
seems reasonable until we consider things from Alice’s perspective. Indeed, she will agree
that the light pulses reflected from each clock arrive back to Bob simultaneously, however,
this is because the same phenomenon which caused the clocks to not be synchronised in
the first place, works in reverse. This means that the time it takes for a light pulse to make
the two-way journey [from emitter to clock and back] will be the same for each pulse. There
is of course, no experiment that Bob can do to determine that Alice is mistaken and to
determine that his clocks are actually synchronised. Indeed, the same is true for Alice, given
the symmetry of relativity.
So, instead of both observers assuming that their clocks are synchronised and that their
counterpart is mistaken, it seems a much more reasonable conclusion would be that both
are mistaken in their assumption of the synchronicity of their own clocks – which they have
no way of observing – while they are correct in their observation that their counterpart’s
clocks are not synchronised. Indeed, we can add another element to the thought
experiment. If we imagine that both Alice and Bob are equipped with bodycams, which
records everything from their perspective, we can then imagine each transmitting their
footage to the other by way of light signal. When both watch each other’s footage they will
see that their clocks are not synchronised and there is no way to explain the video footage,
under the Einsteinian paradigm. This leaves us with a situation where there is a class of
evidence, let’s say 2nd order evidence, which cannot be explained under the Einsteinian
paradigm. To clarify, under the Einsteinian paradigm an observer can explain their own
observations but they cannot reconcile those observation with those of their counterpart –
as represented by the video footage. That is, when Alice and Bob view the other’s video
footage they will see that their clocks are not synchronised. There’s no way to explain the
video footage while maintaining the assumption that their clocks are synchronised. This
leaves us with a scenario where the clocks of neither party are synchronised and neither
party can [justifiably] assert the simultaneity of spatially separated events. Without the
ability to determine simultaneity, RoS simply doesn’t get off the ground.
We have discussed the concept of RoS here, solely from the perspective of Special Relativity,
as it was in his paper on Special Relativity that Einstein introduced the concept. However,
given that GR’s [General Relativity’s] notion of simultaneity is a straightforward extension of
SR’s [Special Relativity’s] (Anderson, 2017)xv the conclusions can be extended to the general
theory.

6. The Constancy of the Speed of Light

It has been repeatedly stated above, that the consequences of relativity (including RoS),
follow logically from the two postulates of Special Relativity. It has hopefully been
demonstrated above, to a satisfactory degree, that the RoS is not a conclusion that follows
as a matter of necessity, but rather is one possible interpretation that follows from an
assumption of simultaneity and synchronicity, that is not necessarily justified. The reader
might be wondering what the above means for the 2nd postulate. If Ros is assumed to be a
consequence of the constancy of the speed of light, does the above imply that the speed of
light is not constant? To answer this question, we need only consider the idea that speed is a
measurable quantity, and as such, we can state the 2
nd postulate such that it is the
measurement of the speed of light that is constant.
Again, we can turn to one of Einstein’s thought experiments to help us elucidate this point.
In his thought experiments, Einstein introduced the idea of a light clock, a simple, yet
precise clock that is constituted of a single photon being reflected between two mirrors. It is
a simple piece of equipment that allows us to easily contemplate the effects of relativity.
Indeed, it is through the thought experiment involving relatively moving observers, each
equipped with their own light clock, that the author was first introduced to the theory of
Special Relativity and the concept of “time dilation”. Below is an image illustrating the use
off such a light clock in explaining the consequences of relativity.
The above image shows two relatively moving light clocks, seen from the perspective of
Alice, at rest relative to the terra clock. From this perspective, the relatively moving clock
runs slower because the photon traces a longer, diagonal path between tick and tock. The
situation is symmetrical and so Bob sees his clock ticking normally and Alice’s clock ticking
more slowly.
Again, given that each claims that the other’s clock is running slow, we can ask the question,
is there any experiment that either Alice or Bob can do to determine if their clock is actually
running slow or not. As before, the answer is no. Once again, this brings us back to the 2nd
postulate, that the speed of light is the same for all observers, and the idea that the
consequences of relativity follow naturally from that. To address this, let us imagine how
Alice or Bob might try to measure the speed of light. Measuring the distance that the
photon in their light clock travels is [each believes] quite easy, it is simply the distance
between the two mirrors; this is because that is the path they observe the photon traveling.
However, in such a scenario where their counterpart is correct and the photon in their light
clock actually travels the longer diagonal path, they would still observe the same thing, as
they are in motion along with the clock. Indeed, for that reason they would only ever
observe the vertical velocity component of the light vector, because the horizontal
component would be obscured to them. If this was the case, that they only measured the
vertical velocity component of the photon, then they would surely measure the speed of
light to be slower. This seems reasonable until we consider how they might measure the
speed of light. Knowing, or thinking they know, the distance that the light travels, they
simply need to measure the length of time it takes for the photon to travel between the two
mirrors. How would they make this time measurement? Using their timekeeping device, of
course, a [second] light clock. The circularity in the situation should be self-evident as well
as the fact that nature apparently “conspires” against them to ensure that they will always
measure the same speed of light.
This alternative interpretation of the 2nd postulate, which demonstrates how every observer
might measure the speed of light to be constant, relative to themselves and their inertial
reference frame, the Einsteinian treatment of the 2nd postulate carries the implicit
assumption that every observer must measure the speed of light to be constant relative to
themselves, while also measuring it to be constant relative to every other observer. The
above also highlights an important aspect about clocks and their true function, which will be
addressed below.
7. Restoration of Absolute Simultaneity
As we can see from the above, simply by extending the principle of relativity to the concepts
of synchronisation, simultaneity, and the measurement of the speed of light – which
appears to be more justified and parsimonious than the alternative – we retain all the
explanatory power of the original theory but eliminate the counter-intuitive and
unexplained phenomena – unexplained in the sense that Special Relativity does not clarify
how Bob’s movement relative to Alice can cause time to slow down for Alice’s, and vice
versa. Without being able to determine the simultaneity of events, in any given reference
frame, we simply cannot arrive at the conclusion that simultaneity is relative. This, in and of
itself does not allow us to conclude that simultaneity is absolute. For that we need to
consider the spatial extension of the universe.
If we simply allow for the idea that strict solipsism – the idea that only you exist and the
universe is a figment of your imagination – is not true i.e. the universe consists of more than
you can by necessity is spatially extended, we can see that the universes is made up of your
location as well as other locations which are spatially separated from you. This can be
extended to distant regions of the universe, such that there exists in the universe, distant
places which are populated by matter and hypothetical observers. These locations (yours
and that of a distant, hypothetical observer) exist in the universe simultaneously – if they
don’t then we are in a position where strict solipsism is true. That means, that there are
events happening in distant regions of the universe which are simultaneous with events
happening at your location. Although we may not be able to determine what those
simultaneous events are, or determine whether two given events are simultaneous, by
virtue of the fact that distant regions of the universe can be said to simultaneously exist, we
can conclude that there must be simultaneous events in the universe. Our discussion above
illustrates how RoS cannot be invoked and so absolute simultaneity is the only alternative.
While restoring the idea of absolute simultaneity to Einsteinian Relativity would bring it
more in line with the absolute time of Quantum Theory, it wouldn’t necessarily address the
issue of background dependency. The theories of Quantum Theory and Special Relativity
would remain background dependent, while General Relativity would continue to be
background independent. To partially address this issue, we can consider the removal of
time as a background entity. This is quite easily done given how absolute time is
indiscernible from “timelessness”. The argument that time is not a fundamental aspect of
the world goes like this, in classical mechanics … there is a clock outside the system, which is
carried by some inertial observer … time is in fact represented in the description, but it is
not in any sense a time that is associated with the system itself … thus, it may be said that
there is no sense in which time as something physical is represented in classical mechanics
… In quantum mechanics the situation is rather similar. There is a t in the quantum state
and the Schroedinger equation, but it is time as measured by an external clock, which is not
part of the system being modeled … were it not for the external clock, one could already
say that time has disappeared* (Smolin & Kaufmann, 97)xvi. To make time “disappear” we
need to deconstruct the idea of “time” and examine what exactly it is that a clock does, or
meassures.
*the ordering of the above quote has been altered by the author, for emphasis. The emboldened sentence has
been moved to the end.
Deconstructing “Time”

8. Non-emergent Temporal Relationalism

Mach’s time principle is … that time is an abstraction at which we arrive through the
changes of things.” I.e. ‘time is to be abstracted from change’. Indeed, it is change that we
directly experience, and temporal notions are merely an abstraction from that, albeit a very
practically useful abstraction if chosen with due care (Anderson, 2017)xvii
. Indeed, part of the
point Leibniz was making is there being no meaningful notion of time with a separate
existence in such a setting [the whole universe]. I.e. the existence of the events is
independent of absolute time, so that the only notions of time left are relational ones. On
these grounds, one can infer the position held in [Anderson’s] book that ‘there is no time at
the primary level for the Universe as a whole’ (Anderson, 2017)xviii
. Anderson suggests that it
is quite natural to ask whether there is a paradox between Leibniz’ Time Principle’s ‘there
being no time at the primary level for the universe as a whole’ and our appearing to
‘experience time’ … [Anderson’s] main answer to this follows from recollecting Mach’s Time
Principle that ‘time is to be abstracted from change. Thus timelessness for the Universe as a
whole at the primary level is resolved by time emerging from change at the secondary level
(Anderson, 2017)xix
. Barbour and [Anderson] have argued to be a Leibniz-Mach position on
relational time. “They contain the statement that time is not a separate physical entity in
which the changing of the physical system takes place. It is the measure of the changing of
the physical system itself that is time. (Anderson, 2017)xx. On the other hand, Fully Timeless
Approaches strategies take Temporal Relationalism’s primary timelessness at face value
(Anderson, 2017)xxi
, which is what is advocated for when considering time as a system of
measurement. As such, it is the “changing of a physical system”, in the form of 3-
dimensional motion, which provides the unit of measurement, in the form of a clock.
Before we consider what is meant by “time as a system of measurement” we can first
consider another, familiar system of measurement, the metric system. The metre, for
example, is defined in terms of the circumference of the Earth. These units of measurement
are simply standardised units for the purpose of comparison. They allow us to talk about the
property of length, of different objects, in a more meaningful way by allowing us to express
such quantities in commonly understood units, or terms. The metric system itself is not an
emergent property of the universe, it is a defined system of [measurement] units. The same
can be said of “time”.
In section 6 above we considered the case of relatively moving observers, Alice and Bob,
and their attempt to conduct an experiment to measure the speed of light in their light
clock. To do this, they had to rely on a second light clock to measure time. As was noted,
there was an inherent circularity in the situation, but it offers us an insight into a
fundamental aspect related to time, namely that of clocks and what they actually do.
Clocks
Clocks are what we use in to “measure time”. There are two ways in which that idea “a clock
measures time” can be interpreted. One interpretation is that a clock is used as an
implement to make a measurement of a separate background phenomenon, in a similar
manner to how a ruler/metre stick/tape measure is placed next to a separate
phenomenon/object, such as a train carriage, in order to measure that object/phenomenon.
This is how a clock is typically treated in physics. The ticking of the clock is taken to be a
measurement of this background phenomenon that cannot be directly detected. The effect
of motion on the ticking of a clock is therefore taken to mean that motion affects this
background phenomenon, which is called time. The inherent assumption is that time
“flows” in the background and a clocks ticking is a measurement of that “flow of time”. In
Newtonian Mechanics that “flow of time” was taken to be the same for all observers, while
in Einsteinian Relativity the “flow of time” is particular to each frame of reference. By way of
reference, Newtonian Mechanics treated time as a single, flowing river, while Einsteinian
Relativity treats time as a series of estuaries.
As has been mentioned, the alternative interpretation of the idea that “a clock measures
time” is that time itself is a system of measurement, in the same manner that the metric
system is a system of measurement. When we “measure a metre” we are not measuring a
separate object/ phenomenon called a metre; the metre is an abstract concept which has
been defined as a unit of measurement which allows us to communicate about phenomena
in a more meaningful and intelligible way. It provides a standard unit of comparison that
allows us to compare phenomena more easily. The “metre” is not a physical object or
phenomena, it is an abstract concept. In a similar sense, a clock – which is essentially just
anything that changes with a certain, reliable regularity – provides a standard unit of
comparison and out units of time are just abstract concepts. In this vein, it satisfies the
Machian Principle of Time.

What do Clocks Measure?

If we examine the general function of a clock, we can get a clearer idea of what exactly is
being measured. Clocks count events that occur at regular intervals within themselves.
Clocks must count the ticks of some repetitive process and convert the count to a measure
of time, such as seconds or hours, and have a means of displaying the result. Not just any
ticking will do. Ideally, the ticks need to be regular in the sense that the duration between
any tick and the next tick is the same duration. The technical term is that durations between
ticks are congruent (IEP)xxii
. There is a broad class of cyclical processes that are standard in
the sense that they all proceed in very nearly a fixed ratio with respect to each other (Stack
Exchange: Physics)
xxiii. The higher the frequency of repetition and the smaller the deviation
in that ratio, the more accurate we say the clock is i.e. the more accurately it “measures
time”. One such clock is the Caesium atomic clock which is now used as part of the
International System of Units to define the second as, “the duration
of 9 192 631 770 periods of the radiation corresponding to the transition between the two
hyperfine levels of the ground state of the caesium133 atom”. But what exactly is being
measured? To answer that question we can return to Einstein’s light clock, as it is much
simpler to understand and represents the most accurate of clocks – the reasoning can be
extended to any clock.
Light clock
Here, the repetitive cyclical process is provided by the photon bouncing back and forth
between the mirrors, and the ration of the cycles to each other is exactly fixed, making it
more accurate. Now, to illustrate the point more clearly and as a means to break any
psychological predisposition we may have, let’s make a slight change to the light clock. Let’s
change the photon to a basketball and change the mirrors to an individual – say Michael
Jordan (or even yourself) – and a basketball court. Imagine that Michael, or ourselves,
bounce the basketball with the same consistency and frequency as the photon bouncing
between the mirrors. It seems nonsensical, but this set-up is equivalent, in effect, to the
light clock. Now, as we imagine bouncing the basketball, let’s see what is actually being
measured. We have the ball traveling between our hand and the court, and we are counting
the bounces and the number of times the ball touches our hand – we can call these “tick”
and “tock”. There is nothing else present in the system. What is being measured in this
system is the number of bounces, the number of “ticks” and the number of “tocks”. To
conclude that these “ticks” and “tocks” are themselves a measurement of a separate,
phenomenon “flowing” in the background requires us to assume the conclusion because, as
highlighted, all that is actually measured in the system are the bounces.
“Time is an abstraction at which we arrive through the changes of things.” Ernst Mach
(Anderson, 2013)xxiv
. Indeed this all that time is, it is an abstraction. “Zeit is das was man an
der Uhr abliest” – time is what one reads on a clock – time is that and nothing more. And a
clock is simply an example of change from which time is abstracted; it provides a standard
unit that allows for the intelligible comparison of separate phenomena. We can use this
standard unit of comparison and express other events in relation to it, so that we can
communicate with one another about those events. Indeed, this bouncing basketball could
be our standard unit of comparison, or measurement of “time”, relative to which we
compare phenomena. Instead of saying that Usain Bolt ran the 100m in 9.58 seconds, we
would say that he ran it in x number of bounces. If everyone were familiar with the duration
of this cycle then we could use it to meaningfully compare events. The cycle of celestial
objects – the sun, the moon, and the stars – were indeed familiar to everyone, which is what
made them useful clocks; and our units of time continue to remain inextricably linked to
them. A point we will explore further, when considering the idea of a preferred reference
frame.

9. Duration does not Imply Extension

To most, the concept of duration would seem to carry the implicit assumption of time.
Indeed, duration is how long something endures, the length or amount of time that
something persists. Duration, therefore, seems to carry the implicit assumption that objects
or events persist in time, that they have a temporal dimension, that is, that they are
extended in a temporal dimension. Objects – such as ourselves – existed in the past,
continue to exist through the present, and we can forecast that they/we will continue to
exist at least some period into the future. We use clocks to measure this duration. This
extension of objects from the past, through the present, and into the future would seem to
lead to the reasonable conclusion that objects in the universe, and the universe itself, has a
temporal dimension to it. However, to appropriate Einstein’s own words, “the difference
between past, present, and future is but a stubbornly persistent illusion”. If we examine the
nature of this illusion we can dispel the conflation of duration with temporal extension.
As observers in/of the universe, all we can ever experience is the present moment; our
empirical observations of the universe are limited to the present moment. It may be worth
stressing that the idea of “the present moment” can sometimes cause confusion as it is
taken to mean “the present moment in time”. But that is not what is meant.
That all empirical observation can only be made of the present, is true for all observers,
even in the Einsteinian interpretation – even if the present moment is constituted
differently for relatively moving observers, each observer can only make empirical
observations in their present moment. The implications of this: there can be no empirical
observations of temporal extension i.e. a temporal dimension, if all that can be observed is
the present moment. Where then, does the idea of duration arise. Herein lies the illusion.
All we ever observe are objects/events in the present moment. The idea of “the past” arises
out of our capacity for memory – often referred to as “psychological time”. But what is it
that we are remembering? We are remembering our experiences of a continually changing
present moment. What we call “the past” exists only as a mental construct, a memory. It is
the memory of a previous configuration of the present moment. To illustrate this we can
perform a very simple experiment:
Experiment
The experiment requires us to do nothing more than rise from our seat and walk to the
door, and make a mental (or verbal) note of which dimension of time we are in, past,
present, or future. We can also substitute sounds or numbers for those terms, to avoid any
philosophical argument that as we say the words, they are moving into the past. I prefer go
use the term “now” for the present moment, simply because it is quicker to say.
Step 1: Stand up.
Step 2: Make a note of “past”, “now”, or “future” as appropriate. We call this T1
Step 3: Take a few steps.
Step 4: Make a note of “past”, “now”, or “future” as appropriate. We call this T2
Repeat steps 3 and 4 until 5 observations have been made (T1-5)
After completing the simple experiment, we should note that each observation was
accompanied by the word “now”. If you find that it wasn’t then you have successfully
achieved time travel.
What then, do we remember? Well, we remember these “nows” (now1-5). We remember
them and we call them “the past”, but “the past” only exists as a mental construct, as a
memory. Indeed, even our memories of “the past” (former nows) arise in the present
moment. When we recall a memory, we do it in the present moment, because this is all we
ever experience. The same is true for “the future”. This is based on our capacity for
projection/imagining . We can make predictions about “the future”, we imagine waking up
tomorrow (we assume we will not die in the meantime) and going to work, or going on
vacation. In science, we make more specific predictions that we try to verify. At every
instance however, it is always the present moment, it is always now. When we make the
prediction it is now, and we test our predictions against a “future” configuration which can
only ever manifest in a present instant; when we test our prediction, the mental note we
make will always be “now”.
Atemporal dimension
It is still true to say that things “endure”, they “persist”, they have “duration”, this however,
does not mean that they are temporally extended, or have a temporal dimension. That
objects have spatial dimensions is self-evident, we just need to look around us to verify this.
That is not to say that our observations of the spatial dimensions is beyond question,
indeed, the Holographic principle attempts to do just that. For the purposes of this paper,
we can contrast the self-evident spatial dimensions, with the temporal dimension, which is
not self-evident. As we can only ever make empirical observations of the present moment,
there can be no empirical observation of temporal extension. To observe temporal
extension, we would need to be able to view two of an objects past, present, or future; or
determine, in some way, that two of those co-exist in the fundamental structure of the
universe. In the absence of such empirical observations and given no empirical basis for
measuring this aspect of the background structure, called “time” – which partly gives rise to
the issue of background dependence – there can be no empirical basis for including it in our
physical theories as anything other than a system of measurement.

10. Privileged Reference Frame

In the section outlining a possible route to an atemporal interpretation of Einsteinian
Relativity we looked at the Lorentzian interpretation. As was noted, the Lorentzian
interpretation maintained the absolute nature of time and space of Newtonian Mechanics.
We further noted that even if the [seemingly] superfluous background structure of the ether
were excised, it is still possible to retain the Newtonian space-time plus conspiring
dynamical effects by defining by fiat a privileged reference frame. For example, the
Lorentzian could baldly say that the privileged frame is the one in which the real time is
measured, period. As we have we have seen above, the idea of a real time can be removed
by virtue of its indiscernibility. This leaves us with no superfluous background structure and
no need for a privileged reference. As we will see however, there is the implicit assumption
of a privileged reference frame baked into the measurements through which we arrive at
our laws of nature. This privileged reference frame is the rest frame of the Earth, the frame
in which our units of measurement are defined.
While we may have made serious strides in the development of our timekeeping devices,
one thing that has remained effectively constant is the notion of “the second”. The time
unit: the second … was defined sidereally until the end of the 1950s. The demise of the
sidereal concept due to its insufficient accuracy further carried over to a redefinition of the
time unit itself. This eventually settled down into using the atomic clock timestandard’s
associated unit of time. This is defined as precisely 9,192,631,770 cycles of the radiation
corresponding to the transition between the two hyperfine levels of the ground state of Cs133. (Anderson, 2017)xxv. While our definition of “the second” may indeed have changed, it
has done so within the parameters of its original definition. It is fair to ask what the above
statement “due to it’s insufficient accuracy” means. How can that which was used to define
the second be deemed to be insufficiently accurate? What is meant is that that the duration
between the “ticks” of sidreal time were not always the same duration, that is they didn’t
always proceed in a fixed ratio with respect to each other, deviations were found to occur. If
we consider the atomic clock; why is the second defined as 9,192,631,770 cycles; why not
an extra million, or twice that number; who decided when it was time to stop counting, and
why? The answer is simply that “the second” was already defined as 1/86400 of a day – this
factor derived from the division of the [Solar] day first into 24 hours, then to 60 minutes and
finally to 60 seconds each (wiki: Second)xxvi
. The number of cycles, of the atomic clock, that
occurred within this pre-defined limit was then designated as the official definition of the
Second. As is obvious, the frame of reference implicit in that definition is the rest frame of
the Earth. Even the atomic clock, used to define the second, is kept in a NIST laboratory in
Boulder Colorado, at rest relative to the Earth. While the metre used to be defined in terms
of the circumference of the Earth – again, with the implicit assumption of the rest frame of
the Earth – the subsequent definition of the metre, in terms of the distance travelled by
light, carries the same implicit assumption given it’s use of the second and that
measurement being made in the reference frame of the Earth.
This represents an alternative route to an atemporal interpretation of relativity. By
acknowledging that, as a matter of operational necessity, there is a privileged reference
frame implicit in the definition of our units of measurement we have an experimentally
equivalent interpretation of Special Relativity, without the [seemingly] superfluous
appendage of the Ether, which is based on the absolute space-time of Newtonian
Mechanics with it’s “external clock”. As above, “were it not for the external clock, one could
already say that time has disappeared”. From our examination above, of the processes of a
clock, we can remove time altogether and with it, the dependence on any kind of
background structure.
The definition of such a privileged reference frame together with the restoration of absolute
simultaneity above, has, it would seem, implications for the development of a hidden
variables theory. It’s only when we seek to go beyond the statistical predictions of Quantum
Theory to a hidden-variables theory, that we come into conflict with the Relativity of
Simultaneity. To describe how the correlations are established, a hidden-variables theory
must embrace one observers definition of simultaneity. This means, in turn, that there is a
preferred notion of rest. And that, in turn, implies that motion is absolute (Smolin, 2013 –
p.163).xxvii The issue of absolute motion is discussed below.

11. Timeless Approaches to Quantum Gravity

There are a number of fully timeless approaches to Quantum Gravity; the so-called
Wheeler-DeWitt equation … has been interpreted at face value as a Fully Timeless
Worldview arising from attempting to combine GR [General Relaivity] and Quantum Theory
(Anderson, 2017)xxviii
. While this paper doesn’t advocate for any particular timeless
approach over another, it does suggest that any justifiable approach to Quantun Gravity
must be fully timeless. In this context we will take a look at some of the motivations for, and
some of the issues facing, fully timeless approaches to Quantum Gravity.
Minimalism is itself one motivation for these fully Timeless Approaches: some aspects of
Nature can be explained without evoking further structure. Another motivation follows
from these being approaches which, out of not presupposing an Arrow of Time, might be
able to derive a such (Anderson, 2017)xxix. The derivation of such an “arrow of time” is
outlined below.
On major way of thinking about Timeless Approaches is to focus on timeless propositions or
atemporal questions, and seek means of supplanting what are usually regarded as temporal
questions. Types of atemporal questions include questions of simple being of the generic
form ‘what is the probability that an (approximate) (sub)configuration has some particular
property P1?’ (Anderson, 2017)xxx. Anderson (2017) continues, with the following specific
example of a temporal question [which] is, moreover, integral to the scientific enterprise
itself.
If an experiment is set up with particular initial conditions, what final state does its initial
state become?
Note that without the qualification of ‘at a time’, questions of ‘being’ can appear to be
vague. Compare e.g. ‘is the Universe homogeneous?’ to the same but qualified with ‘today’
or ‘at the time of last scattering’. (Anderson, 2017)xxxi
. With a fully timeless theory we don’t
have to lose such qualifications. Clocks continue to be employed in the exact same way, its
just the intrinsic assumption about their functionality and what they measure that is altered.
The author goes on to suggest as much: one can pass from correlations between
configurations, to clock states being amongst the configurations involved. In this manner,
‘being at a time’ reduces to timeless correlations between configurations (Anderson,
2017)xxxii
.
Fully Timeless Postulate: One now aims to supplant ‘becoming’ with ‘being’ at the primary
level (Anderson, 2017)xxxiii: In Timeless Solipsism–Full Timeless Approaches–the notion of
being is all and there is no place, at least at the primary level, for the notion of becoming.
While minimalism may be regarded as a virtue, it does come with the inconvenience of
needing to be able to explain the semblance of becoming at the secondary level (Anderson,
2017)xxxiv
. To offer a purely philosophical response: “being” is “becoming”. Everything that
exists is in the process of becoming, just as everything that is already became what it is. That
is the nature of continual change.

11. The Problem of Causality

Bryan & Medved (2018)xxxv suggest changing the focus of future investigations from the
problem of time to the mystery of causality, as it is the latter that is ultimately responsible
for the experience of time in the Universe. While the contention that we actually
“experience time” is, in the context of this paper, questionable, the idea that the PoT is
actually a question of causality, is one that can be explored.
We still need to account for the continual change from one configuration to the next, and in
a manner which is consistent with the experience of physical systems. The described
process can be attributed to the principle of causality which, in most discussions, is either
formally postulated or taken for granted to allow for an interpretation of physical theories …
The necessity for causality and that it must be put in by hand is what appears to be the real
‘problem of time’. Treating change as a real process requires one to dismiss the notion that
all moments of time could exist simultaneously. This treatment does, however, necessarily
invoke causality if it is to be consistent with the experience of time in the Universe. While
the description of interactions within a closed system is often said to be incompatible with
causality — as no external influence is available to initiate a causal chain of events — there
are still arguments to the contrary (Bryan & Medved, 2018)xxxvi
. This formulation of “the
Problem of Causality” appears to be the primordial question of “initial conditions”. It is the
ultimate question that has occupied the thinking of physicists, philosophers, and
theologians since the evolved mind became capable of such reflexive thought.
We could choose to invoke the anthropic principle with respect to causation, we observe
causation and its effects, therefore it is self-evidently a “law of nature”. What was the
primordial “cause”, what was the “first mover”, that is a question of initial conditions. While
it is beyond the primary scope of this paper, it is nonetheless a question that can be
examined. Of course, the nature and existence of time is not dependent on the answer to
that question. The preceding arguments stand on their own merits.
12. Time Symmetrical Laws of Nature
Much is often made of the fact that the equations of motion in most physical theories are
time-reversible invariant (Bryan & Medved, 2018)xxxvii. The question is often posed, why do
we never see events happen in reverse, because there is nothing in the laws of physics that
prevents this; why do we never see broken cups reassemble and jump up onto the table?
There is a fundamental issue with this, of course, because it seeks to apply the time
symmetrical nature of physical laws to an isolated event. Indeed, if such a thing was
observed, while the rest of the universe unfolded as normally, then it would give us a new
class of observation to explain – one which likely violates our laws of causality – and a new
mysterious force – that reassembles cups and makes them jump up on tables – to contend
with. The real question is, why does the Universe not run in reverse, since the laws of nature
don’t seem to preclude it. We could, again, apply the anthropic principle, and say it just
does, but that would not be very satisfactory. Instead, we can see that this question brings
us back to the issue of initial conditions and the first cause.
By way of analogy, we can consider a set of dominoes, not set up for their intended purpose
but rather for the sole purpose of the entertainment of observing the domino effect – with
one domino falling and knocking the next, in a cascade of dominoes. We happen to be
observing this cascade of dominoes after it has been set in motion, let’s say the dominoes
are falling to the right. We make our observations and do our calculations, and find that the
laws governing the falling dominoes are time symmetrical. There is no reason why the
dominoes couldn’t be falling to the left. Clearly, the reason why they are falling to the right
is because the first domino to fall fell to the right and started the cascade in that direction. If
it had fallen to the left, we would be observing the reverse. This is a question of initial
conditions. Whatever the initial conditions of the universe were and whatever event acted
as the first cause set in motion a chain of events that has resulted in the observations we
make of the universe and it’s apparent “arrow of time” – more appropriately, the “arrow of
causality.
We could, perhaps, look to one of the common examples that is often cited to explain the
time symmetry of the laws of nature, that of a cloud of gas. Gas, as we usually observe it,
spreads out to fill up the space it is in. There is nothing in the laws of nature which suggest
that it shouldn’t reconvene in a localised area. Indeed, it is suggested that over a long
enough time period, this is what should be observed. We can apply this reasoning to the
universe as a whole and one of the possible scenarios for the “death” of the Universe. If the
Universe ends in what is referred to as “heat death”, where there is a sea of particles not
dissimilar to that of a cloud of gas that has fully dispersed, then given a long enough time
period, we should see the particles in the Universe reconvene into a localised region,
perhaps even forming a singularity. To attempt to apply the notions of cause and effect to
such a scenario, we can imagine the very last particle coming to settle in the heat death of
the universe. As it is coming in to settle, it collides with another particle, setting off another
chain of cause and effect – setting the dominoes cascading in the opposite direction.
This would model a recurrent or cyclic universe: as in Hindu philosophy, the ‘wheel of time’,
or cyclic cosmological models (Anderson, 2017)xxxviii
. Such a universe would, by necessity, be
eternal in nature. Contrast that with the alternative, which is a universe which comes into
existence from absolute nothingness. This kind of spontaneously, arising universe would be
a direct violation of causality and would allow for the postulation of literally any cause
[un]imaginable to explain any effect, afterall, if the Universe can spontaneously materialise
out of nothing, why can any imagined cause or effect not materialise out of the universe and
then disappear into nothing?

13. Simultaneity and the Underlying Structure of the Universe

As one can imagine, a universe in which simultaneity is absolute would most likely have a
very different structure to a universe in which simultaneity is relative. A universe in which
simultaneity is absolute would be comprised of a single, universal present moment whereas
a universe where simultaneity is relative would require a different underlying, physical
structure to account for that. Indeed, the spacetime formulation of Hermann Minkowski is
the mathematical formalisation of this underlying structure – despite the fact that there is
still some debate as to it’s physicality. Indeed, if the Relativity of Simultaneity is to be taken
at face value, as being incompatible with absolute simultaneity, then the underlying
structure of Minkowski (or any other such formulation) must be physical.
Considering it from the perspective of an individual observer, when simultaneity is relative it
gives rise to a structure in which all events – past, present, and future – share equivalent
existence. That is past, present, and future events (of your life) are equally real. This would
seem to necessitate a block-like structure where the lifetime of all objects, including
ourselves, extend through the block in the form of a a “worldline” (or “worldtube”) and
include all moments in our life, from birth to death. This structure is commonly referred to
as “the block universe” – as seen here in Nova’s the Fabric of the Cosmos. Indeed, the idea
of time as a dimension of the universe and the notion of objects being temporally extended,
or extended in time, also requires such a block structure. A point of notte iiss thhat the
Minkowski metric of quantum field theory is generally regarded as a mathematical construct
and not a real physical object (Bryan & Medved, 2018)xxxix. This would appear to suggest
that it is the Lorentz-Poincare interpretation of relativity which is assumed given the fact
that Poincaré anticipated the seminal work of Herman Minkowski on the four-dimensional
formulation of special relativity. However, unlike relativity in four-dimensional space-time,
in the ether theory these properties represent mere mathematical niceties that do not have
a physical meaning (Bryan & Medved, 2018)xl
. As noted above, a kinematical interpretation
of relativity that is based on absolute simultaneity can be derived, without reference to an
ether.
The fundamental issue with a block-like structure is that such a universe precludes the
possibility of relative motion, or even the illusion of relative motion. It should be noted that
a universe in which simultaneity is absolute, and the present moment universal, does not
require such a block-like structure.

14. The Block Universe

As has been mentioned, for objects to be said to be extended temporally i.e. to be said to
have a temporal dimension, the past and/or future would have to co-exist with the present,
in the overall structure of the universe. This would necessitate the block-like structure
mentioned above, where objects exist as lines or tubes within that structure. Indeed, such a
conceptualization appears to be a necessary consequence of Einsteinian Relativity, as
derived by Herman Minkowski. “Minkowski spacetime was shown to be an immediate
consequence of the postulates of special relativity (Landow & Lifshitz, 2002). “The Block
Universe”, in which past, present, and future are all equally real – the concept of
“eternalism” – is necessitated by the concept of Relativity of Simultaneity, where relatively
moving observers disagree about what constitutes “now”. Events that we consider to be in
the past could be contemporary with another observer. This would mean that our past must
continue to endure “out there” in the overall structure of the universe. Many physicists
have made peace with the idea of a block universe (Falk, 2016)xli
There are actually many variants of Block Universe, but any of these describe the same basic
picture: A deterministic reality in which all ‘moments of time’ can be viewed as spacelike
slices, with each one stacked on another to form a never-changing four-dimensional ‘block’
of spacetime. There is no possibility of distinguishing between past, present and future, as
all such slices are meant to be equal in status. Consequently, any experience of time or any
description of a transitory ‘now’ moment should be regarded as an illusion. As the concept
of time becomes trivialized, there is indeed a sense of timelessness for these models. This
timelessness is, however, different from that of our frozen Universe because the former
cannot incorporate causality Bryan & Medved (2018)xlii
.
We can go even further and state that such a block-like structure can not account for the
most fundamental observation we all make all the time, and observations fundamental to
the theory of relativity; in such a block structure there could be no relative motion.

15. Problem with the Block

The block structure of the universe, that any form of relativity of simultaneity necessitates,
is a structure where the entire history of the universe exists together in a universe sized
block. All moments of the universe co-exist together in this block – from the big bang, to the
moment you are reading this, to however the universe comes to an end (be that heat death,
a “big big crunch”, or however). Within this block structure, objects (such as ourselves or
anything else), exist as worldliness (for point particles) or world tubes (for spatially extended
objects). From our perspective, our entire life span, from birth, to now, to death, is found
within this block structure in the form of this tube. All objects exist as worldtubes, frozen
inside the block. Yes, frozen. If we were to look at the block from the outside we would see
the entire history of the universe in a motionless block. If everything is frozen, how then is it
possible that we observe relative motion – another self-evident observation? The answer is
that it cannot.
Some proponents of the Block Universe try to dismiss this as a simple matter of perspective.
When we imagine ourselves looking at the block from the outside – an impossible vantage
point – we see a frozen block. The argument proffered is that our experience of the block is
not from the outside, but from inside the block where relative motion happens naturally. It
is an attempt to use the anthropic principle – it must work like that because that is what we
see – without addressing the question in hand. The graphic below gives a helpful [visual]
representation of the issue.
“there is no motion in this motion picture”
On the surface, this answer seems reasonable and we can see how it might apply to the
Block Universe. However, we can stick with the analogy of a reel of film and explore it
further.
Life on film
In may ways, a reel of film is very analogous to the worldliness of objects in space time. If
we imagine someone’s entire life caught on film and stretched out, it would be almost
identical to their worldline in spacetime. Each moment of their life is captured on the reel of
film, as in the Block, all moments are equally real.
If we consider ourselves, and the roll of film that represents our worldline; every moment of
our life is captured on the film/worldline, including this moment….this one…..this one…and
so on. Clearly, our experience of the universe or, more pointedly, the empirical observations
we make of the universe, are of a continual progression from moment to moment to
moment….
Now, if we imagine that roll of film, our worldline in spacetime, every point on our worldline
is laid out and each moment/frame of our experience is a moment frozen on that worldline.
Imagine jumping into any one of those moments. What happens? Well, we’re on a roll of
film. We’re in a single frame/moment, frozen on that film. There is no progression to the
next moment. Everything is frozen still. There is no relative motion.
It may be speculative to suggest that this frozen block is just a manifestation of the Frozen
Formalism Problem: Temporal Relationalism leads to the notorious Frozen Formalism
Problem: Facet 1). At the quantum level, this is the presence of an apparently frozen
quantum wave equation–the Wheeler-DeWitt equation– where one would expect an
equation which is dependent on (some notion of) time (Anderson, 2017)xliii
. But as we have
seen above, any treatment of objects as being temporally extended, necessitates a universe
which is temporally extended in such a block, in order to consider time as possessing a
characteristic dimensionality. Such a block must, it would seem, be frozen.
Moving Spotlight
There are some attempts to wave this paradox away. Some proponents of the Block try to
invoke consciousness as a solution. German physcist and philosopher, Herman Weyl said:
“The objective world is, it does not happen. Only to the gaze of my consciousness, crawling
along the lifeline of my body, does a section of this world come to life as a fleeting image in
space which continuously changes in time.” (Weyl, 1949)xliv
.
If consciousness is the answer, then it would seem to suggest that consciousness must move
along our worldline – like a spotlight – from our birth to our death, to account for our
experience of life. However, if all of the moments of our life share equal existence and exist
along our worldline in spacetime that would mean that with the exception of the moment
where consciousness is, all other moments of us exist as “zombies” i.e. with no
consciousness. Indeed, this would mean that all moments don’t exist equally and there is
nothing in the laws of physics that preferences our present moment over any other
moment.
Some proponents of the Block universe, after being presented with the above refutation,
have suggested that our observation of relative motion in the world around us is as a result
of the function of human memory. In this case, all points along the worldline are conscious
but frozen and it is the memory of a previous state of the world, that gives us a brief
experience of relative motion. This of course, does not account for why our experience of
the world is not limited to a very brief observation of relative motion (that lasts for the
duration of a single memory), it doesn’t answer why we don’t see a single moment of
relative motion and then get frozen, or why we don’t see this moment playing on a constant
loop. It also ignores the fact that all brain function is frozen on our worldline as well, that is,
all neurons in our brain are frozen as this constitutes a moment on our worldline/film reel.
The consequence of this would be that consciousness (and perhaps memory) are not
associated with brain function and is therefore non-physical i.e. metaphysical.
Stubbornly Persistent Illusion
While objects appear to have duration, they appear to endure through time, they really only
exist in the present moment. The continual changing of the configuration of the universe in
the present moment together with the human capacity for memory and projection, give rise
to the notions of “past” and “present”. But neither “the past” nor “the future” ever exist as
anything other than the present moment. This is the stubbornly persistent illusion. It is also
why bar owners the world over can confidently display a sign saying all drinks free
tomorrow”, because they understand that tomorrow never comes, it is always today.
It should be pointed out that, like time, “the present moment” is not a thing in-and-of-itself.
The human mind has a tendency to try and make all concepts into concrete things. What
exists is the current configuration of [matter in] the universe. The configuration of the
universe is in a constant state of flux (at least according to our observations of it). The
moment in which we experience existence is what we call “the present moment”; it is
now….and now….and now….it is always now.
16. Special Relativity and the Identity of Indiscernibles
Following Leibniz, any entities which are indiscernible are held to be identical. Applying this
principle to the treatment of reference frames in Special Relativity, we can see that the rest
frame of each observer is mathematically equivalent to the concept of the Absolute
Reference Frame of Newtonian physics. By defining time, in each rest frame, in terms of the
absolute speed of light, time is given the property of absoluteness, by extension. By not
allowing for the possibility that it is their own reference frame that is in motion and the
possibility that it is their own clock that is running slow, it cements the idea that each
observer treats his reference frame as being at absolute rest. When both observers do this
and both are deemed to be correct (and incorrect in the same circumstance) notions such as
RoS become inevitable, and we end up with scenarios where time runs at two different
rates for the same clock, or where time runs at two different rates, in the same region of
space e.g. in a train carriage, where two observers can age both faster and slower than each
other.
Allowing for the fact that each observer could actually be in motion and it is their clock (not
necessarily “time”) that is running slow, would free us from the inadvertent treatment of
“stationary” frames as absolute rest frames.
17. Absolute Motion & Space
We saw above that the notion of absolute motion would be meaningful in the context of a
hidden-variables theory. This is in spite of the fact that, with the advent of Special Relativity,
it was [supposedly*] dispensed with, along with Newton’s notion of absolute time. There
appears to have been a mistaken tendency to try to define absolute motion as a
contradiction in terms. The idea of absolute motion has always been defined as motion
relative to some theoretical and undetectable absolute frame of reference. But what is
absolute cannot be defined in relation to something else. It is a binary yes/no question. The
answer to the question, “is Alice in a state of absolute motion?” can never be “yes, relative
to Bob”, just as the question “is Bob in a state of absolute motion?” can never be answered
“no, relative to Alice”. The answer to both questions can only ever be “yes” or “no”. Of
course, we know that we can never determine the answer to those questions, so we seem
to have deemed them unimportant.
While we can’t determine which one of them is absolutely moving, we can determine that
one, or both, must absolutely be moving, on the basis that they are moving relative to each
other. We can do this by considering the different scenarios which would give rise to
relative motion:
Alice Bob Moving Not moving
Moving Relative motion Relative motion
Not moving Relative motion No relative motion
As we can see, there is only one scenario in which relative motion would not be observed,
and that is when neither is moving. Indeed, we might think of a scenario in which the two
are locked in a windowless room and at rest relative to each other. Such a scenario is
immaterial, as we are not concerned with whether Alice or Bob are in a state of absolute
motion. Given that we observe relative motion in the universe, we can conclude that there
must be absolute motion; that is, at least one object in the universe must be [absolutely] in
motion, with the likely case that all objects are in a state of absolute motion. If nothing in
the universe were in motion, then there would be no relative motion.
Similarly, the concept of absolute space has similarly been defined as a contradiction in
terms. The idea that an absolute rest frame is necessary to provide absolute measurements
of length again seeks to define the absolute in relation to something else. The very idea of
an absolute measurement is a contradiction because measurement, is by it’s very nature a
relational process; it is the expression of the attributes of one thing, in terms of another. To
understand the idea of absolute length we need only consider a lone object, lets say a 3-
Dimensional block. Imagine this block is the only thing in the universe. We can imagine it
extended in 3-Dimensions, with length, breadth, and height. We can ask the question, does
it have length? The answer is simply yes, it does have length. This is what absolute length is,
it is a simple yes/no question. To ask, how long is it would be a meaningless question
because there is nothing else in the universe to compare it to.
Conclusion
While Einstein’s breakthrough with Special Relativity was nothing short of genius, indeed his
name has become synonymous with the idea of exceptional intelligence, and the predictive
power of his theory is second only to Quantum Theory, it would seem that we must do to
Einstein’s theory what Einstein did to Newton’s and that is shatter the conceptualization of
time therein. In stripping away the last vestiges of “time” we are in fact continuing the work
that Einstein so brilliantly started, work which allowed the field of physics to progress in
new and exciting ways. It will allow us to take one step forward in our attempts to marry the
two great physical theories. Ultimately, resolving the problem of time is a choice between a
universal present moment, the “now” that is the only moment which can be empirically
observed, or an interpretation that allows for observers to be both right and wrong with
regard to the same events, the treatment of every rest frame as though it were at absolute
rest, and ultimately a block universe in which there can be no relative motion.
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