1 Introduction
The theory of special relativity first proposed by Albert Einstein in his work on the electrodynamics of moving bodies (Einstein et al. 1905) has had profound repercussions for physics, technology and metaphysics. Einstein’s work fundamentally altered the development of physics and technology resulting in the correct functioning of many systems crucial to the modern world such as GPS (Hatch 1995, p1–3). Special relativity has not only revolutionised the human material world, but has radically altered our metaphysical understanding of the universe. Amongst numerous results, it has deep implications for the very structure of space and time, which in turn affect our understanding of causation and the flow of time. In the coming pages we will closely examine one key result of the theory, the unification of space and time to one space-time and its metaphysical implications. We will also discuss other philosophical implications of the theory. This discussion will come in two sections, first we will look at the connection between Einstein’s theory and its implications for the underlying geometry of the universe and how this differs from previous conceptions of the universal geometry. In the second section we will discuss some philosophical implications of this new geometry, particularly regarding our understanding of the flow of time both locally and in the universe as a whole.
2 Special relativity to a unified space-time
We begin our discussion with the analysis and implication of one
single physical fact. For two moving bodies at different velocities, if
they both emit a pulse of light as they pass one another, the light will
reach a distant observer at the same time (Maudlin 2012, p68). There
will be some shifting of the wavelengths of each light ray depending on
the magnitude and direction of each body’s velocity (Maudlin 2012,
p68) but crucially they will arrive at an observer at the same
moment. As light can propagate through a vacuum, meaning through space
in which there is no matter of any type, we can surmise that the only
thing effecting the propagation is the structure of space itself (Maudlin 2012,
p68).
From the truth of this statement about light one can then determine what
sort of structure is necessary in space to allow this to be true. A
necessary requirement for such a structure is that light travels at a
constant velocity which is invariant to the velocity of the body from
which it is emitted or reflected. The structure that we find therefore
must relate the initial emission of light from a point to the possible
points in space and time that the light can and will eventually reach.
This is the so-called light-cone and to describe its physical journey
through space and time we require four dimensions, namely the three
Euclidean spatial dimensions and one extra time dimension, this is the
Minkowski space-time (Maudlin 2012, p69–70).
Hermann Minkowski thoroughly geo-metricised Einstein’s theory and showed
how such a construction of space-time resulted in Einstein’s conclusions
(Minkowski 1908).
Points in Minkowski space-time can be matched to coordinate points in
well-chosen coordinate systems, in this case Lorentz coordinates (Maudlin 2012,
p69). This allows us to describe a location in space-time with
the coordinates \((t,x,y,z)\). If we
were to take a point in space-time and move it around its coordinates
would change in a continuous manner, the same as in a three-dimensional
Euclidean geometry such as that ascribed to space by Isaac Newton (Maudlin 2012,
p5–9) in conjunction with a separate and absolute time.
Therefore, both geometries are topologically identical (Maudlin 2012,
p69–70). The definition of a straight line also remains identical
in both geometries meaning they also share the same affine structure
(Maudlin 2012,
p70). Thus far we see that both old and new geometries possess
rather similar characteristics, the great difference between the two
comes in the metrical structure. In Euclidean space this is in essence
the Pythagorean rule for the length of a straight path through space,
the length of a path in Minkowski space-time is slightly different (Maudlin 2012,
p70) and allows for a cone of paths through space-time that have
a path or interval of zero . The zero path is the light-like interval
and is crucially derived from the physical fact of the invariance of the
speed of light, as all light travels with a zero-length interval through
Minkowski space-time.
We find that the only way to allow for our empirically found facts is to
determine a new structure of space and time, one that unifies the
previously demarcated concepts of space and time into space-time. Having
a single geometric structure for space-time in the universe allows the
treatment of space-time as purely geometric. The impact this has on
empirically tested physics is huge as we are now able to understand much
of our universe simply as a matter of geometry in Minkowski
space-time.
At the time of Einstein’s and Minkowski’s work, space and time were both
believed to be absolute, that space itself was a three-dimensional
Euclidean space and that time moved equally for all observers in the
entirety of the universe. This absolute conception had been argued for
by Isaac Newton and supported by several natural scientists and
philosophers due to the success of Newtonian physics at explaining the
mechanics of situations such as the famous spinning buckets (Maudlin 2012,
p22–24). The absolutism of Newton’s work allowed him and those
after to conceptualise universal laws that could then explain the
workings of mechanical situations for all places and all times. However,
the absolute space and time and its resultant Newtonian physics had been
unable to solve several crises, such as the electrodynamics of moving
bodies. Einstein’s relativity resulted in there being no primacy for any
inertial observer and explained the disagreements about the timing of
events and even lengths of objects viewed by different observers. These
physical facts and their explanatory power provided a killing blow to
Newton’s concept of absolute space and time. Space and time had to give
way to a unified space-time resulting in a relativity between different
inertial observers that were all equally valid. To understand the
metaphysics of our universe, we must accept Einstein and Minkowski as
correct in their physics. We see that there is no such thing as space
and there is no such thing as time, let alone absolute space and time.
They exist as one, as evident through the behaviour of a light-ray which
is solely dependent on this space-time structure in a vacuum.
3 Philosophical Implications
In the next section we discuss philosophical implications of special relativity for time. Whilst it is clear from the previous section that one implication for time is that it is not separated from space, it is perhaps less clear as to what this means for metaphysical theories about the past, present and future. Classical theories will first be defined and then conclusions from special relativity will be compared to them. We shall then see which if any, of these theories special relativity supports and how firm any of these connections are.
3.1 On time
First, we examine the structure of time in the universe, to do this
we initially consider three metaphysical theories of time. These are
presentism, meaning only the present exists as this is all we can
access. Next, possibilism, meaning the past does exist but the future is
still a number of possibilities and finally eternalism in which the
whole existence of the universe is like a cartoon flip book, the past
and future exist, and the present is just our point in the flip book
(Savitt 2021,
sec2.1). These metaphysical theories are all the consequence of
the geometry of Newtonian space and time (Savitt 2021, sec2.0) and
reflect human intuitions about how time should behave. However, we know
that special relativity possesses many counter-intuitive results and we
should therefore be wary. Therefore we must now examine what special
relativity could mean for the metaphysics of time and whether special
relativity supports presentism, possibilism, eternalism or something
else.
We consider the problem of a singular present at great distances. At a
sufficient distance, lines of simultaneity as commonly seen in
space-time diagrams, diverge to a large degree, even for two people that
are only on opposite sides of the globe from one another (Savitt 2021,
sec3.0). This has the implication that an event that happens
(extremely far away) occurs in the present or the past of one of our
people but in the future of the other. Bear in mind that this causes no
problem for causality as light/information of an event has a finite
speed, but for the metaphysics of time it is hugely important. As in
principle we could construct this situation from any point in the
universe to any distance, therefore we can always propose a location in
space-time for which our future events are in the past of another. Thus,
significantly strengthening the eternalist position which has embraced
relativity and is now termed chronogeometric fatalism (Savitt 2021,
sec3.0). In one way we can consider this the natural metaphysical
position of special relativity. If space and time are unified in one
space-time than why would we have any reason to consider time as
different from space? Unless one subscribes to some form of solipsism,
we consider all space in the universe existing in some manner that is
independent of any one person or people, we see from the thought
experiment that all points in space-time are real and existing.
We will now discuss two responses to this position that share a
criticism of the present seen in chronogeometric fatalism and therefore
attempt to refute it. We begin with, the position espoused by Wilfrid
Sellars. Sellars position is that to consider the present moment out to
a distance of essentially infinity has no real meaning and does not fit
in with our temporal worldview. Instead, he argues for an infinite
number of now-pictures relative to a possible observer, this position is
termed perspectival existence (Savitt 2021, sec3.1). A
convincing response to this is given by Kurt Gödel, in that to
relativise existence is to destroy all meaning of the term (Savitt 2021,
sec3.1). Sellars appears to be trying to fit a more classical
sense of time into special relativity and whilst not embracing the
unification of space-time, he perhaps over-embraces the relativity
aspect of the theory putting us into the uncomfortable position that
Gödel argued against.
The second theory discussed here is the more developed version of the
present argued for by Howard Stein. The original version of Stein’s
position is that the present of an event is the event itself (Savitt 2021,
sec3.2). However, if we allow for any other point in space-time
to be in the present of the event, which seems quite natural, we find
ourselves once again in the chronogeometric fatalism situation (Savitt 2021,
sec3.2). The more developed version known as the specious present
considers the present of any event to be the volume of space around the
event in which light can travel in about 0.5 to 3 seconds (Savitt 2021,
sec3.3). This value having been determined by psychology to be
the human perception of the present (Savitt 2021, sec3.3). On one
hand, this seems intuitively useful as this region is large and
comfortably includes the whole Earth, allowing all humans to share a
now, as is our experience. On the other hand, this is an extremely
anthropocentric theory and says more about the human experience of the
present than what present means universally and metaphysically. This is
especially striking compared to the modern eternalist position of
chronogeometric fatalism, which is able to make a clear metaphysical
claim, mathematically and concisely. It is deeply integrated to our
concept of unified space-time and appears another mere geometrical
consequence of special relativity.
4 Conclusions
In this paper we have seen the impact of the paradigm shift from
Newtonian space and time to a unified Minkowski space-time and how it
was derived from the single empirical fact of the constant speed of
light. We saw that to provide a universe for which the invariant speed
of light is a universal truth we must have a metrical structure that
allows for path intervals of length zero, and to do this time must be a
unified dimension with space. Space and time as independent categories
therefore have no true existence and the largest change in our
understanding of the metaphysical structure of the universe has occurred
since Newton’s concepts of absolute space and time.
From unified space-time we discuss how physics is a matter of geometry
in space-time. From this simple geometrical consequence, we see how
special relativity fermented an enternalist revival of the metaphysics
of time in the theory of chronogeometrical fatalism. A metaphysical
position that is clearly shown to treat space and time as unified, as
not only all points in space are considered real and existing, the same
is true for time.