EPFL Master course

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Nov 16, 2013 (3 years and 10 months ago)

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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



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



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
)