1 Introduction
Special relativity, first proposed by Albert Einstein in his 1905 paper on the electrodynamics of moving bodies (Einstein et al. 1905), has had profound consequences for physics, technology and metaphysics. Einstein’s theory underpins many systems crucial to the modern world, with GPS the standard example (Hatch 1995, p1–3). It has also radically altered our metaphysical picture of the universe, with deep implications for the structure of space and time and, by extension, for causation and the flow of time. The pages that follow examine one key result of the theory, the unification of space and time into a single space-time, and what it means metaphysically. The first section connects Einstein’s theory to the underlying geometry of the universe and contrasts it with earlier conceptions. The second discusses the philosophical implications of this new geometry, particularly for our understanding of the flow of time both locally and in the universe as a whole.
2 Special relativity to a unified space-time
The discussion starts from a single physical fact. If two bodies
moving at different velocities emit a pulse of light as they pass one
another, both pulses reach a distant observer at the same time (Maudlin 2012, p68). The
wavelengths of the two rays will be shifted in different directions
depending on each body’s velocity (Maudlin 2012,
p68), but the arrival time is the same. Since light propagates
through a vacuum, in which there is no matter of any kind, the only
thing affecting the propagation must be the structure of space itself
(Maudlin 2012,
p68).
From this fact one can work out what kind of structure space must
have. The basic requirement is that light travels at a constant
velocity, invariant to the velocity of the body that emits or reflects
it. The structure must therefore relate the emission of light from a
point to the points in space and time the light can eventually reach.
This is the light-cone, and describing its journey through space and
time requires four dimensions: the three Euclidean spatial dimensions
plus one time dimension. The result is Minkowski space-time (Maudlin 2012, p69–70).
Hermann Minkowski geometrised Einstein’s theory thoroughly, showing
that such a space-time recovers Einstein’s conclusions (Minkowski 1908).
Points in Minkowski space-time can be matched to coordinate points in
a well-chosen coordinate system, in this case Lorentz coordinates (Maudlin 2012,
p69), so a location in space-time can be described by \((t,x,y,z)\). Moving a
point around changes its coordinates continuously, just as in the
three-dimensional Euclidean geometry that Newton ascribed to space
(Maudlin 2012,
p5–9), paired with a separate and absolute time. The two
geometries are therefore topologically identical (Maudlin 2012,
p69–70). The definition of a straight line also remains the
same, so they share the same affine structure (Maudlin 2012,
p70). Where the two geometries diverge is in their metrical
structure. In Euclidean space the metric is essentially 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 admits a cone of paths through space-time with an
interval of length zero. The zero-length path is the light-like
interval, and follows directly from the invariance of the speed of
light, since all light travels along zero-length intervals through
Minkowski space-time.
The only way to accommodate the empirical facts is therefore to adopt a
new structure that unifies the previously separate concepts of space
and time into space-time. With a single geometric structure for
space-time, much of physics becomes a matter of geometry in Minkowski
space-time, which is a substantial change in how empirically tested
physics is to be understood.
Before Einstein and Minkowski, space and time were both taken to be
absolute: space was a three-dimensional Euclidean space, and time moved
equally for every observer everywhere in the universe. This absolute
conception had been argued for by Newton and supported by many natural
philosophers, in part because Newtonian physics so successfully
explained mechanical situations such as the famous spinning bucket
(Maudlin 2012,
p22–24). Its absolutism let Newton and his successors
formulate universal laws that worked for all places and all times. The
framework had nonetheless failed to resolve several crises, including
the electrodynamics of moving bodies. Einstein’s relativity removed any
privileged inertial observer and explained the disagreements between
observers about the timing of events and even the lengths of objects.
These results, and their explanatory power, struck a killing blow to
absolute space and time. Space and time had to give way to a unified
space-time, with all inertial observers equally valid. To understand
the metaphysics of our universe, then, we have to accept Einstein and
Minkowski’s physics. There is no such thing as space alone or time
alone, let alone absolute space and time. They exist as one, as the
behaviour of a light ray (which depends only on the structure of
space-time in a vacuum) makes clear.
3 Philosophical Implications
This section turns to the philosophical implications of special relativity for time. The previous section made it clear that, on relativity, time is not separable from space; what is less clear is what this means for metaphysical theories about the past, present and future. Three classical theories of time are introduced first, then compared with the conclusions of special relativity, with a view to seeing which (if any) the theory supports, and how firmly.
3.1 On time
Three metaphysical theories of time will set the stage. Presentism
holds that only the present exists, since that is all we can access.
Possibilism holds that the past exists too, but that the future is
still a range of possibilities. Eternalism holds that the universe is
like a cartoon flip book in which past and future are equally real,
with the present being just the page we happen to be on (Savitt 2021,
sec2.1). All three are consequences of the geometry of
Newtonian space and time (Savitt 2021, sec2.0), and
reflect intuitions about how time ought to behave. Since special
relativity is full of counter-intuitive results, those intuitions
deserve some suspicion. The question is therefore which (if any) of
presentism, possibilism, eternalism, or something else, the theory
actually supports.
Consider the problem of a singular present at large distances. At
sufficient separation, lines of simultaneity in standard space-time
diagrams diverge significantly, even for two observers only on
opposite sides of the globe from one another (Savitt 2021,
sec3.0). The consequence is that a far-away event can lie in
the present or past for one observer but in the future for the other.
This causes no problem for causality, since information about an event
propagates at most at the speed of light, but for the metaphysics of
time it is decisive. The construction generalises to any pair of
points in the universe, so for any event we can in principle find an
observer for whom that event is past. This significantly strengthens
the eternalist position, which has embraced relativity in what is now
termed chronogeometric fatalism (Savitt 2021,
sec3.0). In one sense this is the natural metaphysical position
of special relativity. If space and time are unified into one
space-time, what reason is there to treat time differently from space?
Short of some form of solipsism, all of space in the universe is
taken to exist independently of any particular observer; the thought
experiment above extends the same conclusion to all points in
space-time.
Two responses to chronogeometric fatalism share a worry about its
conception of the present and try to refute it. The first is Wilfrid
Sellars’s. He argues that extending the present out to essentially
infinite distance has no real meaning and does not fit our temporal
worldview; instead, he posits an infinite number of now-pictures
relative to a possible observer, a position known as perspectival
existence (Savitt 2021, sec3.1). A
convincing reply, due to Kurt Gödel, is that relativising existence in
this way drains the term of meaning (Savitt 2021,
sec3.1). Sellars appears to be trying to fit a more classical
conception of time into special relativity. Without embracing the
unification of space-time, he over-embraces the relativity aspect of
the theory and lands in the uncomfortable position Gödel rejects.
The second response is Howard Stein’s. In its original form, Stein’s
position is that the present of an event just is the event itself
(Savitt 2021,
sec3.2). Allowing any other point in space-time to count as part
of the present of the event, which seems quite natural, returns us to
chronogeometric fatalism (Savitt 2021,
sec3.2). The developed version, the specious present, defines
the present of an event as the volume of space around it in which
light can travel in roughly 0.5 to 3 seconds (Savitt 2021,
sec3.3); the range comes from psychology, as the human window
of perception of the present (Savitt 2021, sec3.3). On one
hand this is intuitively useful: the region is large enough to
comfortably include the whole Earth, so all humans can share a now,
in line with experience. On the other it is deeply anthropocentric,
and says more about the human experience of the present than about
what the present is universally or metaphysically. The contrast with
chronogeometric fatalism is striking: the eternalist view makes a
clear metaphysical claim, mathematically and concisely, falls out of
unified space-time, and reads as another geometrical consequence of
special relativity.
4 Conclusions
This essay has traced the shift from Newtonian space and time to a
unified Minkowski space-time, derived from the single empirical fact
of the constant speed of light. To accommodate the invariance of the
speed of light, the universe must have a metrical structure that
admits path intervals of length zero, which forces time to be a
unified dimension alongside space. Space and time as independent
categories therefore have no genuine existence; this is the largest
shift in our metaphysical picture of the universe since Newton’s
concepts of absolute space and time.
From the unified space-time it follows that physics is largely a
matter of geometry in space-time. The same simple geometrical move
underwrites an eternalist revival in the metaphysics of time, in the
form of chronogeometric fatalism: a position that takes the
unification of space and time at face value and treats every point in
space-time as equally real, time as much as space.