1
EPFL Master course
Philosophical perspectives on
science and its history
Philosophy of space and time: the
classical positions &
the contemporary debate
Michael Esfeld
University of Lausanne
Michael

Andreas.Esfeld@unil.ch
Motion
distribution of matter in space changes in
time
variation in time:
as time passes, change in
which points of space are occupied and
which ones are empty
change such that there are continuous
trajectories of particles
浯瑩潮
motion defined with respect to absolute
space
but: all measured motion relative; all inertial
reference frames equivalent
(Galilei
transformations)
3
Isaac Newton (1642

1727)
Mathematical
principles of natural philosophy
The spatial
/ temporal
distance between any two
particles
/ events
does not
depend on a reference frame.
The spatial
/ temporal
distance between any two
particles
/ events
does not
depend on the properties that
these particles have.
Matter (particles) can only
exist in space and time
. Space
and time would exist even if
there were no matter.
absolute space, absolute time
4
Gottfried Wilhelm Leibniz (1646
–
1716)
space and time homogeneous
no reason for God to create
matter at certain points (or
regions) in space and time,
rather than other ones
full absolute space and time:
different possibilities for God
to place the whole of matter in
space and time
no reason for God to choose
one particular of these
possibilities
The argument against
Newton
space and time absolute and distinct from
matter:
several arrangements of matter in space and
time possible
All the relations between the material entities
are the same.
these possibilities empirically indiscernible;
difference only if absolute space and time
presupposed
Leibniz
’
牥污瑩潮慬楳a
space, time: relations between material
entities
space: order of coexisting entities
time: order of successions
presupposes
existence of system of spatial
and temporal relations, the structure of this
system being independent of matter
motion always relative
6
Newton
’
s argument for absolute space
bucket:
certain forms of rotation not motion relative to other
objects, motion with respect to absolute space
Ernst Mach (1838

1916):
one can always regard any motion as
relative motion by enlarging the total system taken into
consideration; e.g. rotation as motion relative to the fix stars.
mechanics possible without commitment to absolute space,
but other conception of motion than the one of Newton:
no
inertial motion with respect to absolute space, distinction
between constant velocity and acceleration to be established
without absolute space
in any case, spatial relations between particles fundamental
(primitive fact)
No argument for absolute time
passage of time without motion?
particles in classical mechanics:
initial
position & initial velocity, primitive
facts
disposition to change position =
disposition for motion primitive fact
possible:
time as measure of change
(Aristotle)
Action at a distance
Newton : forces act
without medium
instantly across arbitrary spatial
distances
(although diminish with the
spatial distance among the particles)
action at a distance: mass of an
object
at
t
changes state of motion of all the
other objects in the universe at
t
9
Newton to Bentley 25 Feb.
1692
“
That gravity should be innate inherent &
essential to matter so that one body may act
upon another at a distance through a
vacuum
without the mediation of anything
else by & through which their action or force
may be conveyed from one to another
is to
me so great an absurdity that I believe no
man who has in philosophical matters any
competent faculty of thinking can ever fall
into it.
”
James Clerk Maxwell (1831

1879)
Electrodynamics (1860)
Newton :
action at a distance
among particles through empty
space
Maxwell :
local action
:
charged particles as sources of field;
fields propagate in space and mediate the interaction among
particles
maximal velocity of propagation of effects
(velocity of light,
nearly 300
’
〰〠歩k潭整敲o灥爠獥捯湤p
one electromagnetic field
whose sources are the charged
particles in the universe
no empty space
, space filled with fields
but: philosophical problem: What is ontological status of
fields? (dispositions to move particles in addition to
dispositions of particles such as mass and charge?); physical
problem: action of field on its own source
12
From Newton to Einstein
1687
Newton: universal laws of mechanics
but: gravitation as action at a distance
1860
Maxwell: field theory of
electromagnetism:
local propagation of
effects, maximal
velocity of
propagation
1887
Experiment of Michelson and Morley:
speed of light constant
1905
Einstein: theory of special relativity
1916
Einstein: theory of general relativity
13
Albert Einstein (1879

1955)
Special relativity theory (1905)
1.
A
ll inertial
reference frames
are equivalent.
2.
Light always
propagates with a
constant velocity
in all referential
systems
.
space and time
united in
spacetime
14
Albert Einstein (1879

1955)
Special relativity theory (1905)
principle of the constancy of the speed
of light:
absolute element
simultaneity and in general all spatial
and temporal distances:
relative to a
reference frame
no universal time (=
a time that fixes a
single, objective temporal order for all
the events in the universe
)
15
Albert Einstein (1879

1955)
Special relativity theory (1905)
transition
from
one
inertial
referential
frame
to
another
one
:
Lorentz
transformations,
unify
the
three
spatial
dimensions
with
the
temporal
dimension
.
four

dimensional,
spatio

temporal
distance
between
any
two
events
independent
of
a
reference
frame
space
and
time
unified
in
four

dimensional
spacetime
16
Light cone
17
Albert Einstein (1879

1955)
General relativity theory (1916)
adds a theory of gravitation
field of gravitation = metrical field that
encodes the geometry of spacetime
spacetime curved
gravitation local interaction between
the metrical field and matter
spacetime no background structure,
dynamical entity
18
Albert Einstein (1879

1955)
General relativity theory (1916)
no clear distinction between spacetime and matter:
does the metrical field belong to spacetime or to
matter?
spacetime:
without this field, no light cones and no distinction
between timelike, spacelike and lightlike intervals
between events.
matter:
the metrical field includes energy, namely the
gravitational energy;
gravitation: material interaction
19
Spacetime as a substance
1)
manifold substantivalism
:
spacetime
without the metrical field is a substance
that exists on its own.
The points of
spacetime are substances without the
metrical properties,
their identity does not
depend on the metrical properties.
2)
metrical substantivalism
:
it is spacetime
with the metrical field (= the geometrical
structure) that defines absolute spacetime.
The metrical properties are essential
properties of spacetime points, their
identity depends on them.
20
The arguments
field argument:
fields are defined on
spacetime.
The field properties exist at spacetime
points.
substances in the form of spacetime points
as that what instantiates the field properties
compatible with both versions of
substantivalism
argument from empty solutions:
the metrical
field can exist without matter
applies only to metrical substantivalism
21
The hole argument
transformation that does not change the
relations among the physical properties,
but
produces a difference on the level of the
bare spacetime points at which the physical
properties occur
indiscernible
indeterminism: different possibilities which
spacetime points bear given physical
properties, but no physical difference
hits only manifold substantivalism; decisive
argument against manifold substantivalism
The hole argument
22
23
Relationalism
against the field argument:
material points bear all the properties
against the argument from empty solutions:
possible
mathematical
solution ≠ possible
physical
situation
Leibniz:
spatial relations between material points (particles)
presupposed as primitive fact,
non

dynamical background = does not
depend on properties of material points such as mass
Mach
’
猠灲楮捩灬攺
摩獴s楢畴u潮 潦慳猠楮 瑨攠t湩v敲獥 摥瑥d浩湥m
浥瑲楣t潦灡p整業e 㴠
瑨攠t敯浥瑲t 潦灡p整業eⰠ楴猠捵牶慴畲aⰠ
摥灥湤猠潮 瑨攠t楳瑲楢i瑩t渠潦慴瑥爠⡭(獳)
allows to explain in what sense spatio

temporal relations depend on
properties of matter such as mass
but: initial distribution of mass in the universe is not sufficient to
determine initial metric (
physical
consequence of empty solutions)
initial metric has to be stipulated as primitive fact
24
The point at issue
classical physics, special relativity:
What is the
relationship between space

time and matter?
general relativity:
What is the relationship between
the metrical properties and the properties that are
characteristic of matter?
metrical substantivalism:
two distinct types of
entities.
Why?
relationalism:
only material properties of material
entities.
But how can one explain the special status
of the metrical

gravitational properties (universal,
defining spacetime)?
Space and time
space:
homogenous,
isotrope
time:
homogenous,
anisotrope
direction of time, passage of time
special and general relativity:
unification of
space and time in four

dimensional
spacetime
One abandons the direction and passage of
time as global features of the universe.
no objective, universal past, present, future,
“
now
”
like
“
here
”
26
Block

universe
non

tensed view of time
There are only relations of being earlier and
later
,
defined locally
by means of the light
cones of each spacetime

point.
existence independent of time
Everything in the universe exists at a point
or region of spacetime
,
and everything in
spacetime simply exists
.
no temporal becoming
27
Block

universe
special relativity:
four

fimensional spacetime containing four

dimensional entities
(= events and continuous sequences of
events, processes)
material object:
continuous sequence of similar events
(
world

line
)
motion of an object in space and time
:
continuous sequence of
spacetime points at which there are similar events
change:
different physical properties forming a continuous
sequence
f
our

dimensional events
instead of
three

dimensional particles
only
fields,
these consisting in events at spacetime points
What are the properties that make up these events? (no
dispositions of motion of particles)
28
René Descartes (1596

1650)
Matter is a single
substance.
matter: spatial
extension
matter = space
29
Baruch de Spinoza (1632

1677),
Ethics
(1677)
a single
substance
physical =
material =
extended
30
Jonathan Bennett
A study of Spinoza
’
猠
“
䕴桩捳
”
(1984)
“
… there is just one substance
—
namely,
the whole of space
—
regions of which
get various qualities such as
impenetrability, mass, and so on,
so
that any proposition asserting the
existence of a body reduces to one
saying something about a region of
space.
”
31
Jonathan Bennett
A study of Spinoza
’
猠
“
䕴桩捳
”
(1984)
“
To say that the puddle is slimy is to say
that a certain region of space is
slimy*
—
i.e., has that property of
regions which we conceptualize by
saying that there are slimy things in
them.
And to say that there is a slimy*
region is to say that
space is slimy*
locally
.
”
32
Supersubstantivalism
no physical systems over and above space
matter = space
The points and regions of space are the
parts of matter.
they possess physical properties;
all
physical properties are properties of points
and regions of space
bodies = regions of space having certain
physical properties
33
Matter reduced to spacetime
general relativity: reduction of the theory of
gravitation to a geometrical description of
spacetime
reduction of electromagnetism
reduction of particle physics
geometrodynamics:
build physics on the basis of recognizing
only spacetime and its geometrical
properties
34
John A. Wheeler (1912

2008)
“
䥳灡I整業攠潮汹
慮牥湡n睩瑨楮w
which fields and
particles move
about as
“
灨y獩s慬
”
慮搠
“
景牥楧i
”
entities?
Or is the
four

dimensional
continuum all there
is?
35
John A. Wheeler (1912

2008)
Is curved empty geometry a kind of magic
building material out of which everything in
the physical world is made:
(1) slow
curvature in one region of space describes a
gravitational field; (2) a rippled geometry
with a different type of curvature somewhere
else describes an electromagnetic field; (3) a
knotted

up region of high curvature
describes a concentration of charge and
mass

energy that moves like a particle?
Are
fields and particles foreign entities
immersed
in
geometry, or are they nothing
but
geometry?
”
36
Conclusion I
1)
particle paradigm:
matter in motion,
particles
that occupy points of space and that change
their position
motion, trajectory
empirical fact:
interaction not only by direct
contact, interaction across empty space
(gravitation, electromagnetism)
action at a distance :
without medium,
instantaneously
37
Conclusion II
2)
particles
and
fields :
particles produce fields,
interaction between particles by means of fields
medium, maximal velocity of propagation of effects
no stable position:
philosophical reason:
unclear ontological status of
fields
physical reason:
if maximal velocity of propagation
of effects, Galilei transformations have to be
replaced with Lorentz transformations
unification of space and time in four

dimensional
spacetime
38
Conclusion III
3)
field paradigm:
block universe, events instead of
particles, motion and change as variation of
properties in spacetime
problem:
What are the physical properties
instantiated at points of spacetime?
no properties like mass and charge
in the sense of
dispositions to accelerate particles,
because no
particles / no matter in motion
supersubstantivalism / geometrodynamics:
physical
properties = geometrical properties of spacetime
39
Conclusion IV
geometrodynamics
failed
for
physical
reasons
(
notably
quantum
physics
)
abandoned
by
Wheeler in 1973
general
problem
:
How
to
account
for
observable
phenomena
?
(
geometrical
properties
:
theoretical
entities
,
experience
:
motion
of
something
)
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