### TL;DR
In this paper the author discusses the Newtonian views...

Carlo Rovelli is an Italian theoretical physicist and writer. His m...

what does this mean time does not exists ? How it was existing befo...

A typo in the first sentence of the abstract. Absolutely wonderful ...

### Newtonian space and time
Isaac Newton considered space and t...

A great lecture by Carlo Rovelli about ***"The Physics and Philosop...

### Einstein's spacetime
Einstein's theory of relativity refines...

In Newtonian physics space and time are absolute. They constitute t...

You can learn more about Aristotle and Descartes' views on space he...

William C. Evans-NEWTON'S BUCKET

This is not what Newton said, rather he said \[f = \frac{d}{dt} mv\]

> *"After three centuries, Einstein found a new and simpler answer....

What does local mean if you're outside the context of time and space?

The idea of an absolute space acting as a "container" for the physi...

> With or without such an explicit reference to God, for three cent...

A great lecture by Carlo Rovelli about ***"The Physics and Philosop...

Galileo was the first to realize that the physical motion of object...

**What is now?** Time is not absolute, there is not a "now" that co...

> *"Therefore the relational nature of space revealed by GR extends...

Julian Barbour spent the majority of his career studying this quest...

“If this point of view is correct,temporality is an artifact of our...

> *"the idea that there is a ‘‘Present’’ extending all over the uni...

Philosophy and Foundations of Physics

The Ontology of Spacetime

D. Dieks (Editor)

r 2006 Elsevier B.V. All rights reserved

DOI 10.1016/S1871-1774(06)01002-3

25

Chapter 2

The Disappearance of Space and Time

Carlo Rovelli

Centre de Physique Theorique de Luminy, Universite

´

de la Me

´

diterrane

´

e, Marseille,

France

Abstract

I argue that lesson of general relativi ty is that at our present state of knowledge the best

way for making sense of the world is to discard the notions of space and time. New-

tonian space and time can be reinterpreted as aspects of the gravitational ﬁeld, whi ch is

only one among the various dynamical physical ﬁelds making up the world. Physical

ﬁelds do not need to inhabit spacetime in order to exist. The resulting understanding of

space is to some extent a return to the Aristoteli an-Cartesian relational traditi on; while

the resulting interpretation of temporality, appears to have strong elements of novelty. I

consider the viability of a foundation of our understanding of the world in which space

and time play no role.

1. The ontology of spacetime after relativity

Our understanding of the natural world evolves. We have developed a concep-

tual structure that allows us to apprehend and frame the world that we perceive

and think; but this conceptual structure evolves, driven by experience and ra-

tional investigation. Science is a continuous exploration of novel and more

effective ways for thinking the world. We cannot exit our own way of thinking;

but we can modify it from within, exploring modiﬁcations of our basic as-

sumptions, and testing them for consistence and against experience. This proc-

ess of exploration of the space of the ideas is at the core of theoretical physics.

The notions of space and time of classical physics are a characteristic product

of this process. We own them to a large extent to the work of Newton, in the

17

th

century. Newton defended a novel way of thinking space and time against

the dominant views of his time. This way proved then extraordinarily effective.

The Newtonian notions of space and time have been extensively utilized and

discussed in depth. With time, they have been ‘‘absorbed’’ by our culture at

large, and have become the dominant view.

The relativistic revolution of early 20

th

century, once more due to a remark-

able extent to a single man, has taught us that there is a more effective way of

understanding space and time than the Newtonian one. The novel relativistic

understanding of space and time, however, has not yet been integrated into the

common, and not even into the learned, way of thinking the world. Yes, mental

habits take time to change; but I am often surprised by the excessive attachment

that many thinkers maintain to ideas for understanding the world that have

been clearly proven ineffective. These ideas were useful for a while, roughly in

the three centuries between Newton and Einstein. But we must not mistake a

tool that has proven useful for an eternal truth. There are commonly used

concepts, such as the idea of an ‘‘objective present state of the world’’, that

make no sense, in the light of what we have learned about the universe. Rel-

ativity is not ‘‘contemporary science’’: it is close to a century old. It is certainly

time to take it seriously, discuss it in depth, and get used to it.

A reason for the slow adaptation to the relativistic understanding of space

and time is that the relativistic revolution has happened in more than one step.

The ﬁrst step is special relativity (SR); shortly after came general relativity

(GR)

1

. For a few decades, while SR was blessed by continuous conﬁrmations,

especially from particle physics, GR had spectacular but scarce empirical sup-

port. In this situation, the attention was mostly on the relatively simpler con-

ceptual novelty of SR, leaving GR in a limbo at the borders of our map of

reality. But in the last decades the number and the success of experiments and

observation conﬁrming the physical validity of GR have exploded, and the

theoretical interest in GR has boomed. Today, we cannot leave GR out of the

picture. SR is little more than a minor variation of the Newtonian conceptu-

alization of spacetime. The special relativistic universe is a theoretical model

whose true interest as a fundamental way to understand reality was signiﬁcant

for less than 10 years, between 1905 and 1915. Therefore we must focus on GR

if we want to hold a view of space and time compatible with what we have

understood so far about the natural world.

1

To further complicate matters, the relativistic revolution has not yet ended, because we have

not yet fully unraveled its relation with quantum physics. Knowledge of quantum theory induces

us to certain conceptual choices in understanding relativity, but care should be taken in reading

these hints because we still lack a deﬁnitive synthesis.

C. Rovelli26

The new understanding of spacetime that has emerged from the relativis-

tic revolution differs from the Newtonian picture especially with regard to

the ontological status of spacetime — the subject of this book. Newton made

the successful hypothesis that space and time are ﬁxed structured background

entities underlying material reality, which participate in governing the motion

of physical objects. What Einstein has discovered is that Newton had mistaken

a physical ﬁeld for a background entity. The two entities hypostatized by

Newton, space and time, are just a particular local conﬁguration of a physical

entity — the gravitational ﬁeld — very similar to the electric and the magnetic

ﬁeld.

Einstein’s discovery is that Newtonian space and time and the gravitational

ﬁeld are the same entity. There is a tradition of expressing this discovery saying

that ‘‘there is no gravitational ﬁeld: space and time become dynamical’’. I think

that this is a convoluted and misleading way of thinking, which does not do

justice to Einstein’s discovery, and has the additional ﬂaw of becoming mean-

ingless as soon as we take into account the fact that the gravitational ﬁeld has

quantum properties.

The clean way of expressing Einstein’s discovery is to say that there are no

space and time: there are only dynamical objects. The world is made by dy-

namical ﬁelds. These do not live in, or on, spacetime: they form and exhaust

reality.

One of these ﬁelds is the gravitational ﬁeld. In the regimes in which we can

disregard its dynamics, this ﬁeld interacts with the rest of the physical objects as

if it were a ﬁxed background. This background is what Newton discovered and

called space and time. We can keep using the evocative terminology ‘‘space-

time’’ to indicate the gravitational ﬁeld. But it has practically none of the fea-

tures that characterized space and time. Relativistic spacetime is an entity far

more akin to Maxwell’s electric and magnetic ﬁelds than to Newtonian space.

In classical GR, a given solution of the ﬁeld equations might still have some

vague resemblance to the Newtonian’s notions, since it deﬁnes a ‘‘continuum’’

which things can be imagined ‘‘to inhabit’’. But the only compelling reason for

thinking that ‘‘spacetime’’ is the gravitational ﬁeld, and not — say — the elec-

tromagnetic ﬁeld, is the contingent fact that we live in a portion of the universe

where the gravitational ﬁeld is sufﬁciently constant for us to use it as a con-

venient reference.

Quantum mechanics reinforces this point of view. A solution of the classical

ﬁeld equations is like a particle trajectory: a notion that only makes physical

sense in the classical limit. The gravitational ﬁeld has quantum properties, and

therefore it cannot deﬁne a spacetime continuum in the small.

Properly speaking, relativity has taught us that the effective way of thinking

about the world in the light of what we have learned so far is to give up the

notions of ‘‘space and time entities’’ entirely. This is not a dramatically radical

The Disappearance of Space and Time 27

view, since it is not far from the way space was commonly conceptualized before

Newton. On the other hand, it has a novel twist of great interest, especially as

far as time, and the relation between time and space, are concerned.

In Newtonian physics, if we take away the dynamical entities, what remains is

space and time. In relativistic physics, if we take away the dynamical entities,

nothing remains. As Whitehead put it, we cannot say that we can have space-

time without dynamical entities, anymore than saying that we can have the cat’s

grin without the cat (Whitehead, 1983).

In the rest of this text, I discuss relativistic spacetime in some more detail. I

start by recalling a few facts about pre-Newtonian western ideas about space

and time. This is important because the Newtonian scheme is often mistaken for

a sort of ‘‘natural’’ understanding of space and time. Nothing is more wrong:

the Newtonian space and time ‘‘entities’’ form a strongly counter-intuitive the-

oretical construction, which met ﬁerce resistance at ﬁrst. Next, I illustrate the

modiﬁcation of the notions of spacetime introduced by SR and GR. I focus on

the Newtonian notions that are to be abandoned. I close by mentioning the

possibility of a proper relativistic foundation of the physical description of the

world where the notions of space and time play no role.

2. Space

There are two traditional ways of understanding space in the western culture: as

an entity or as a relation. ‘‘Space is an entity’’ means that space exists also when

there is nothing else than space. It exists by itself, and objects may move in it.

‘‘Space is a relation’’ means that the world consists entirely of physical objects

(particles, bodies, ﬂuids, ﬁelds y). These objects have the property that they

can be in touch with one another, or not. Space is this ‘‘touch’’, or ‘‘contiguity’’,

or ‘‘adjacency’’ relation between objects. Connected to these two manners of

understanding space, are two manners of understanding motion. If space is an

entity, motion can be deﬁned as going from one part of space to another part of

space. This is denoted by ‘‘absolute motion’’. If space is a relation, motion can

only be deﬁned as going from the contiguity of one object to the contiguity of

another object. This is called ‘‘relative motion’’. For a physicist, the issue is

which of these two ways of thinking about space and motion allows a more

effective description of the world.

The dominant view in the European tradition, from Aristotle to Descartes,

was to understand space and motion as relational. Aristotle, for instance, de-

ﬁnes the spatial location of an object as ‘‘the inner surface of the innermost

object that surrounds the body’’ (Aristotle, Physics, Book IV, Chapter 4[20],

Aristotle, 1952). This is relational space. Descartes deﬁnes motion as ‘‘the

C. Rovelli28

transference of one part of matter or of one body, from the vicinity of those

bodies immediately contiguous to it, and considered at rest, into the vicinity of

some others’’ (Descartes, Principia Philosophiae, Section II-25, p. 51, Descartes,

1983). Aristotle as well insists that motion is relative. He illustrates the point

with the example of a man walking over a boat. The man moves with respect to

the boat, which moves with respect to the water of the river, which moves with

respect to the ground y .

The alternative view of space, as an independent entity, existed since ancient

times (mostly in the Democritean tradition), but became dominant only with

Newton. It is also the way spacetime (rather than space) is understood in SR.

For Newton, space is absolute and motion is absolute: ‘‘So, it is necessary that

the deﬁnition of places, and hence local motion, be referred to some motionless

thing such as extension alone or space, in so far as space is seen truly distinct

from moving bodies’’ (Newton, De gravitatione et Aequipondio Fluidorum, pp.

89–156, Newton, 1962). This is in patent contrast with Descartes deﬁnition,

given above.

It should be noted that the difference between the two points of view is not so

strong as it seems at ﬁrst sight. Starting from a relational point of view, we can

always choose a physical entity, refer all motion to this preferred entity and call

this entity ‘‘space’’. Newton does not miss this point, and in fact he speciﬁes that

what is to be called space has to be ‘‘truly distinct from moving bodies’’. New-

ton thought he had discovered this entity ‘‘truly distinct from moving bodies’’,

the way to detect it and its effects. GR is the realization that the entity dis-

covered by Newton is not at all ‘‘truly distinct from moving bodies’’. In fact, it is

barely distinguishable from the other ﬁelds.

In introducing the idea of absolute space, Newton did not challenge a long

tradition with light heart: he devotes a long initial section of the Principia to

explain the reasons for his choice. Today we can say that the strongest argument

in Newton’s favor is a posteriori: his theoretical construction works extraor-

dinary well. Relational Cartesian and Leibnizian proposals were never as effec-

tive. But this was not Newton’s argument. Newton invokes empirical evidence,

discussing the famous bucket experiment. This experiment proves that there are

physical effects (the bending of the surface of the water in the bucket) that do

not depend on the relative motion of the water with respect to the surrounding

objects (the bucket).

The surface of the water curves when the water rotates: but rotates with

respect to what?

Newton argues that the only reasonable answer is absolute space. The con-

cavity of the water’s surface is an effect of the absolute circular motion of the

water: the motion with respect to absolute space. This, claims Newton, proves

the existence of absolute space. Newton’s argument is subtle; it has been often

The Disappearance of Space and Time 29

challenged, but it has withstood all attacks for three centuries

2

. It has then

collapsed under Einstein’s alternative and more effective answer.

Newton needed (accelerated) motion, exempliﬁed by the rotation of the water

in the bucket, to be absolute for the foundation of his dynamics. Without this,

Newton’s main law

~

F ¼ m

~

a would not even make sense: what would be the

meaning of the acceleration

~

a?

Opposition to Newton’s absolute space was very strong. Leibniz and his

school argued ﬁercely against absolute motion and absolute acceleration.

Doubts never really disappeared all along the centuries and a feeling kept lin-

gering that something was wrong with Newton’s argument. Ernst Mach re-

turned to the issue suggesting that Newton’s bucket argument could be wrong

because the water does not rotate with respect to absolute space: it rotates with

respect to the full matter content of the universe. But the immense empirical

triumph of Newtonianism could not be overcome. For three centuries.

After three centuries, Einstein found a new and simpler answer. The bending

of the surface of the water is due to the relative motion of the water with respect

to a physical entity: the local gravitational ﬁeld. It is the gravitational ﬁeld, not

Newton’s inert absolute space that tells objects if they are accelerating or not, if

they are rotating or not. There is no inert background entity such as Newtonian

space: there are only dynamical physical entities. Among these are the ﬁelds,

introduced in our physical picture of the world by Faraday and Maxwell.

Among the ﬁelds is the gravitational ﬁeld.

Whether the water surface in Newton’s bucket is concave or ﬂat is not deter-

mined by the motion of the water with respect to absolute space. It is determined

by the physical interaction between the water and the gravitational ﬁeld. Einstein’s

discovery is that Newton had mistaken the gravitational ﬁeld for absolute space.

In Newtonian physics, the spacetime coordinates

~

x and t refer to absolute

space. They can be identiﬁed with the reading of measuring devices carefully

selected as the ones that capture the structure of space and time. This selection is

obtained by monitoring and correcting the ‘‘inertial’’ effects such as the bending

of the water of the water, which signal motion with respect to absolute space.

2

Or course relationalism, i.e., the idea that motion can be deﬁned only in relation to other objects,

should not be confused with Galilean relativity. Galilean relativity is the statement that ‘‘rectilinear

uniform motion’’ is a priori indistinguishable from stasis. This is equivalent to saying that velocity

(just velocity!), is only relative to other bodies. Relationalism, on the other hand, holds that any

motion (however zigzagging) is a priori indistinguishable from stasis. The very formulation of Gali-

lean relativity assumes a nonrelational deﬁnition of motion: ‘‘rectilinear and uniform’’ with respect to

what? When Newton claimed that motion with respect to absolute space is real and physical, he, in a

sense, overdid it, by insisting that even rectilinear uniform motion is absolute. This caused a painful

debate, because there are no physical effects of inertial motion (therefore the bucket argument fails

for this particular class of motions). Newton is well aware of this point, which is clearly stated in the

Corollary V5 of the Principia, but he chooses to ignore it in the introduction of the Principia. I think

he did this just to simplify his argument, which was already hard enough for his contemporaries.

C. Rovelli30

Einstein realized that ﬁnding out the pre-GR ‘‘inertial’’

~

x and t is nothing else

than detecting local features of the gravitational ﬁeld. In the theoretical appa-

ratus of GR, on the other hand, the spacetime coordinates

~

x and t have a

completely different status, and it is only an unfortunate historical accident that

they are denoted in the same manner as the pre-general-relativistic inertial co-

ordinates. The relativistic

~

x and t coordinates have no direct physical meaning

(unless we gauge ﬁx them to represent something else). The reading of measuring

devices is identiﬁed with quantities in the theory that are independent of

~

x and t.

More formally, in the mathematics of classical GR we employ a background

‘‘spacetime’’ manifold and describe the ﬁelds as living on this manifold. How-

ever, the diffeomorphism invariance of the theory demands that the localization

on this manifold is pure gauge. That is, it is physically irrelevant. The manifold

is just an artiﬁce for describing a set of ﬁelds and other physical objects whose

only ‘‘localization’’ is with respect to one another.

A state of the universe does not correspond to one ﬁeld conﬁguration over the

spacetime manifold M. It corresponds to an equivalence class under active

diffeomorphisms of ﬁeld conﬁgurations. Therefore localization over M is phys-

ically irrelevant. In fact, M has no physical interpretation. It is a mathematical

device without physical counterpart. It is a gauge artifact. M cannot be inter-

preted as a set of physical ‘‘events’’, or physical spacetime points ‘‘where’’ the

ﬁelds take value. The only possibility of locating points is with respect to the

dynamical ﬁelds and particles of the theory itself. It is meaningless to ask

whether or not the gravitational ﬁeld is ﬂat around the spacetime point A,

because there is no physical entity ‘‘spacetime point A’’. Contrary to Newton,

spacetime points are not entities where particle and ﬁelds live

3

.

The gravitational ﬁeld g

mn

ðxÞ determines a four-dimensional continuum with a

metric structure. Excessive signiﬁcance is often attributed to this structure, as if

distance was an essential property of space, or even an essential property of

reality. This is like an Eskimo thinking that snow is an essential property of the

ground.

We could have developed physics without ever thinking about distances, while

nevertheless retaining the complete predictive and descriptive power of our theories.

We live in physical conditions where atoms form and interact with the gravitational

ﬁeld in such a way that they maintain structures characterized by the fact that the

integral of the gravitational ﬁeld d ¼

R

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

g

mn

dx

m

dx

n

p

along these structures is very

stable. We call this integral d ‘‘distance’’, and we have developed useful mathematics

— geometry — to describe the structure of these distances.

3

Physical ﬁeld are not attributes of space, anymore than a mosaic is an attribute of the wall. The

wall can be taken away from the mosaic, without necessarilly destroying the mosaic. The clearest

intuition of the nature of a ﬁeld (in particular, a gauge ﬁeld) is the original Faraday’s intuition of a

ﬁeld as a collection of lines.

The Disappearance of Space and Time 31

Geometry has repeatedly been mistaken for an a priori feature of reality.

Euclidean geometry was erroneously thought of as necessary. Later, Riemannian

geometry as well has been erroneously considered necessary. However, there is

no a priori reason for which reality has to be understood as a continuum with

metric properties. Nor, for that matter, as a continuum at all. Indeed, contem-

porary research in quantum gravity points in a very different direction.

Conceptually, what disappears with GR is the idea of space as the ‘‘con-

tainer’’ of the physical world. As mentioned, this disappearance is not so rev-

olutionary after all: to some extent it amounts to return to the pre-Newtonian

view of space as a relation between equal-status physical entities.

Allow me to close this section with a playful observation on the relation

between the shift in our views about space and our overall world conception. In

the pre-Copernican world the cosmic organization of the ‘‘things’’ was hierar-

chically structured. The Heavens above, the Earth below, spheres in order of

decreasing perfection. Objects were located with respect to one another — this

served to grant each object a precise ‘‘status’’ in the grand scheme of things,

analogous to the social position of humans. With the Copernican revolution,

this hierarchical structure was lost. Position lost any ranking value. Newton

offered reality a global frame. He offered every object the equal dignity of a

position in a uniform space. For Newton this frame was grounded in God. He

called space the ‘‘sensorium’’ of God: the world as perceived by God. Thus, the

position in space for Newton is, literally, the position of the objects in the eyes

of God. Against the multiplicity of the individual points of view determined by

the observation of the relative motions, absolute space grants a single-organ-

izing principle. According to Newton, our rationality allows us to unveil the

absolute point of view of God (by detecting inertial effects such as the bending

of the surface of the water). With or without such an explicit reference to God,

for three centuries space has been regarded as the preferred Entity with respect

to which all other entities are located. In the 20

th

and 21

st

centuries and with GR

we have been learning that we do not need this frame to keep reality in place.

Reality keeps itself in place. Objects interact with other objects, and this is

reality. Reality is the net of these interactions. We do not need an external entity

to hold this net. We do not need Space, to hold the universe. Maybe the Co-

pernican revolution is ﬁnally being completed.

3. Time

The disappearance of physical time is the second characteristic feature of

the relativistic revolution. The notion of time is harder to deal with than the

notion of space, and represents a more radical step than the disappearance

of space.

C. Rovelli32

Once again, much of the common understanding of time derives from the 17

th

century. Galileo was the ﬁrst to use a mathematical time variable t to formulate

equations describing the motion of terrestrial objects. These are equations for

functions X ðtÞ of time. Newton was well aware that we never measure the

variable t appearing in these equations directly. We use clocks whose reading T

should be taken as a good approximation of the hypothetical ‘‘true’’ time t.As

in the case of spatial measurements, we select better and better clocks by elim-

inating effects that the theory denounces as produced by the difference between

T and t. The relation TðtÞ, between clock reading and true time, can itself be

calculated from the theory, using a mechanical model of the clock. From XðtÞ

and TðtÞ we can compute X ðTÞ, which is the only relation we effectively observe.

Newtonian theory is formulated in terms of the not directly observable quantity

t. The scheme is delicate and involved, but it has worked wonderfully well for

three centuries.

SR takes the ﬁrst step out of the Newtonian understanding of time. SR does

not change the Newtonian hypostatization of absolute space and time, but

destroys the clean distinction between the two.

SR is the discovery that it makes no physical sense to say that two distant

physical events happen ‘‘at the same time’’. It is true that Einstein provides a

deﬁnition of simultaneity, two events A and B, relative to an object O in a given

state of motion

4

. But although this is a useful working deﬁnition, it is a mistake

to give it ontological signiﬁcance. There is nothing in SR that would lead us to

think that A and B have an ontic property of being ‘‘existant at the same time

with respect to O’’, besides satisfying a useful conventional deﬁnition.

To illustrate this point, consider a standard expanding cosmological model.

Its space like surfaces of homogeneity are formed by the events at equal proper

time after the big bang, or equal Friedmann time t

Fr

; these are the surfaces

naturally considered ‘‘simultaneous’’ in cosmology. These surfaces are not equal

time surfaces according to Einstein’s simultaneity deﬁnition

5

. Therefore, in a

cosmological context we have the alternative to call either ‘‘simultaneous’’

events at the same Friedmann time, or events that satisfy Einstein’s deﬁnition of

simultaneity. Both deﬁnitions are useful. The choice between them is a matter of

taste or computational convenience, not a matter of ontology.

The simple physical fact, revealed by SR, is that there are physical events on,

say, Andromeda that have no temporal relation with events on Earth. A small

gravitational wave passing in between could change Einstein’s simultaneity be-

tween us and them by years, without affecting the physics here or there anymore

4

The event A along the trajectory of an observer O is said to be simultaneous to a distant event B

if a light signal emitted by O a time interval T before A and reﬂected by B, returns to O at a time T

after A.

5

I thank Marc Lachieze-Rey for pointing this out to me.

The Disappearance of Space and Time 33

than works on the highway change relations between two cities. The lesson is

that the idea that there exists a ‘‘now’’ all over the universe does not square with

what we know about the universe. At best, we can talk of time lapsed along

individual world lines, or time experienced by individual observers.

The picture of a Universe changing from one global instant to the next is

incompatible with what we know about the world.

What is then ‘‘time’’ in the light of GR? This is a deep and important question

that in my opinion has not yet been sufﬁciently investigated. I offer here what I

think is the most useful answer to this question.

GR inherits from SR the melting of space and time into spacetime. Therefore

the relational nature of space revealed by GR extends to time as well. It follows

that in GR there is no background spacetime and therefore in particular no time

along which things happen. GR teaches us that we must abandon the idea that

the ﬂow of time is an ultimate aspect of reality. The best description we can give

of the world is not in terms of time evolution. The dynamics of GR itself cannot

be cleanly described in terms of evolution in time.

There are many distinct notions of time employed in GR: coordinate time t,

proper time S, clock times T, cosmological time t

Fr

, asymptotic Poincare

´

time y . The last two refer to the description of special solutions of the Einstein

ﬁeld equations only. They are irrelevant in a discussion of the ontology of time,

because a different ontology for different solutions of the same theory is certainly

unsatisfactory. Clock times are simply the readings of certain physical variables,

which can be locally employed as the independent variable for convenience.

Once again, they have nothing to tell us about the ontology of time. Coordinate

time is unobservable (unless the gauge is ﬁxed, in which case it designates

something else) because of general coordinate invariance. The only residual time

notion that keeps a resemblance of temporality is proper time. Proper time does

not ﬂow uniformly in the universe. It is deﬁned along a world line and, gener-

ically, if two world lines meet twice, the two proper times lapsed between the two

encounters differ. Proper time S depends on the gravitational ﬁeld, which is

inﬂuenced by the interaction with many systems. Typically, harmonic oscilla-

tions are isochronous in S.Therefore,S like the distance d described in the

previous section, is just an observable feature of the gravitational ﬁeld, which is

particularly convenient to use as a stable reference in our environment, when

describing the motion of objects assuming the gravitational ﬁeld ﬁxed. The dy-

namics of the gravitational ﬁeld itself, on the other hand, cannot be naturally

described in terms of evolution in any well-deﬁned preferred time variable.

Instead, we must describe reality in terms of correlations between observables.

We can measure physical quantities around us. The physical theory restricts the

combinations of quantities that we can measure. It predicts relations between

these quantities. Only in particular situations we can choose one quantity as the

C. Rovelli34

independent variable, call it time, and express the others as functions of it. In

general, this may not be possible, and the physical theory gives us constraints on

the values of measurable quantities that we can obtain from physical measure-

ments, not evolution laws in a preferred time variable. Quantum theory assigns

probabilities to such outcomes.

Basic physics without time is viable, it is forced upon us by relativity, and it is

conceptually coherent and consistent with our experience of the world. A com-

plete discussion of the foundations of mechanics in the absence of a notion of

time is given for instance in Rovelli (2002). Remarkably if we give up the idea

that there is a special ‘‘time’’ observable, mechanics takes a far more compact

and elegant form. This shift of point of view is forced upon us by classical GR.

If, in addition, we take quantum theory into account, the spacetime continuum,

with its last vague resemblance to temporality disappears completely, and we

confront the absence of time at the fundamental level in full.

So, where does temporality, with all its peculiar features (‘‘ﬂow’’ of time,

whatever this means, irreversibility, memory, awareness y) come from? I think

that all this has nothing to do with mechanics. It has to do with statistical

mechanics, thermodynamics, perhaps psychology or biology. In Rovelli (1993) I

have developed, in collaboration with Alain Connes, the idea that it may be

possible to recover temporality from statistical mechanics, within an atemporal

mechanical universe (statistical time hypothesis). If this point of view is correct,

temporality is an artifact of our largely incomplete knowledge of the state of the

world, not an ultimate property of reality.

Some people ﬁnd the absence of time difﬁcult to accept. I think that this is just

a sort of nostalgia for the old Newtonian notion of an absolute ‘‘Time’’ along

which everything ﬂows, a notion already shown by SR to be inappropriate for

understanding the real world. I think that the motivation for holding on to

Poincare

´

invariance, to unitary time evolution, to the idea that there is a

‘‘Present’’ extending all over the universe, is only to provide an anchorage for

our familiar notions, which are appropriate to describe the garden of our daily

life. But a bit more at large, these are notions that are inappropriate to describe

this beautiful and surprising world we inhabit.

References

Aristotle (1952). Physics. In P. H. Goetz (Ed.), The works of Aristotle. Chicago: Encyclopedia

Britannica Inc.

Descartes, R. (1983). In: V.R. Miller, & R.P. Miller (Trans.), Principia philosophiae. Dordrecht:

Reidel.

Newton, I. (1962). De Gravitatione et Aequipondio Fluidorum. In A. R. Hall, & M. B. Hall

(Eds), Unpublished papers of Isaac Newton. Cambridge: Cambridge University Press.

The Disappearance of Space and Time 35

Rovelli, C. (1993). Statistical mechanics of gravity and thermodynamical origin of time. Classical

and Quantum Gravity, 10, 1549; (1993). The statistical state of the universe. Classical and

Quantum Gravity, 10, 1567. Connes, A., & Rovelli, C. (1994). Von Neumann algebra auto-

morphisms and time versus thermodynamics relation in general covariant quantum theories.

Classical and Quantum Gravity, 11, 2899.

Rovelli, C. (2002). Partial observables, Physical Review, D65, 124013; A note on the foundation

of relativistic mechanics. I: Relativistic observables and relativistic states, Proceedings of the

15th SIGRAV conference on general relativity and gravitational physics, Rome, September, gr-

qc/0111037; Quantum gravity, Cambridge, MA: Cambridge University Press, 2004.

Whitehead, A. N. (1983). Concept of Nature: The Tarner Lectures Delivered in Trinity College,

November, 1919, 171. Cambridge, UK: Cambridge University Press.

C. Rovelli36

A typo in the first sentence of the abstract. Absolutely wonderful copy-editing from Elsevier as usual!
“If this point of view is correct,temporality is an artifact of our largely incomplete knowledge of the state of theworld, not an ultimate property of reality.”
“If this point of view is correct,temporality is an artifact of our largely incomplete knowledge of the state of theworld, not an ultimate property of reality.”
### Einstein's spacetime
Einstein's theory of relativity refines Newton's law of universal gravitation by providing a unified description of gravity as a geometric property of space and time - **spacetime**. Spacetime is a gravitational field (similar to the electromagnetic field) and its curvature is directly related to the energy and momentum of whatever matter and radiation are present.
Space and time are no longer two different absolutes but they are a continuum, unified into a four-dimensional reality that is no longer separated into three spatial dimensions and one time dimension.
In Newtonian physics space and time are absolute. They constitute the stage where everything takes place so if you remove all objects space and time remain. In relativistic physics, if we take away the dynamical entities, nothing remains.
Space-time as an absolute "container" over which physics happens has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the Universe.
The idea of an absolute space acting as a "container" for the physical universe disappears with Einstein's theory of relativity. This disappearance is not that revolutionary since it amounts to return to the pre-Newtonian view of space as a relation between equal-status physical entities - see Aristotle's and Descartes' views above.
**What is now?** Time is not absolute, there is not a "now" that common across the universe. Now is a local concept.
> *"The lesson is that the idea that there exists a ‘‘now’’ all over the universe does not square with what we know about the universe. At best, we can talk of time lapsed along individual world lines, or time experienced by individual observers."*
> *"Therefore the relational nature of space revealed by GR extends to time as well. It follows that in GR there is no background spacetime and therefore in particular no time along which things happen. GR teaches us that we must abandon the idea that the flow of time is an ultimate aspect of reality. The best description we can give of the world is not in terms of time evolution. The dynamics of GR itself cannot be cleanly described in terms of evolution in time."*
> With or without such an explicit reference to God, for three centuries space has been regarded as the preferred Entity with respect to which all other entities are located. In the 20th and 21st centuries and with GR we have been learning that we do not need this frame to keep reality in place. Reality keeps itself in place. Objects interact with other objects, and this is reality. Reality is the net of these interactions. We do not need an external entity to hold this net. We do not need Space, to hold the universe. Maybe the Co- pernican revolution is finally being completed.
Galileo was the first to realize that the physical motion of objects could be described by mathematical laws expressing their evolution in time. He was the first to use a mathematical time variable ***t*** to formulate equations describing the motion of terrestrial objects. He noticed that the period of swing of a pendulum is independent of its amplitude. This discovery had important implications for the measurement of time intervals.
> *"the idea that there is a ‘‘Present’’ extending all over the universe, is only to provide an anchorage for our familiar notions, which are appropriate to describe the garden of our daily life. But a bit more at large, these are notions that are inappropriate to describe this beautiful and surprising world we inhabit."*
> ***"Your head is older than your feet"*** - Carlo Rovelli
> *"After three centuries, Einstein found a new and simpler answer. The bending of the surface of the water is due to the relative motion of the water with respect to a physical entity: the local gravitational field. It is the gravitational field, not Newton’s inert absolute space that tells objects if they are accelerating or not, if they are rotating or not. There is no inert background entity such as Newtonian space: there are only dynamical physical entities. Among these are the fields, introduced in our physical picture of the world by Faraday and Maxwell. Among the fields is the gravitational field."*
A great lecture by Carlo Rovelli about ***"The Physics and Philosophy of Time".***
[![physics of time](https://i.imgur.com/JPldvfg.png)](https://www.youtube.com/watch?v=-6rWqJhDv7M)
Carlo Rovelli is an Italian theoretical physicist and writer. His main field of research is quantum gravity and he is one of the co-creators of loop quantum gravity. He has also worked in the history and philosophy of science.
He authored several books on science including "Seven Brief Lessons on Physics" which has been translated into 41 languages and has sold over a million copies worldwide.
Learn more about the author here: [Carlo Rovelli](http://www.cpt.univ-mrs.fr/~rovelli/)
!["Carlo Rovelli"](https://physicsworld.com/wp-content/uploads/2018/06/PWJul18REV-Carlo_HERO.jpg)
### Newtonian space and time
Isaac Newton considered space and time as absolute. According to the Newtonian view space is flat, uniform and distinct from body, a stage where everything happens, and time passes uniformly without regard to whether anything happens in the Universe.
This view is often mistaken for a sort of ‘‘natural’’ understanding of space and time but it was proven wrong by Einstein's theory of relativity at the beginning of the 20th century.
Flat, uniform fixed stage where everything happens.
Read on here: [Newton’s Views on Space, Time, and Motion
](https://plato.stanford.edu/entries/newton-stm/)
A great lecture by Carlo Rovelli about ***"The Physics and Philosophy of Time".*** Watch it here:
[![physics of time](https://i.imgur.com/JPldvfg.png)](https://www.youtube.com/watch?v=-6rWqJhDv7M)
This is not what Newton said, rather he said \[f = \frac{d}{dt} mv\]
what does this mean time does not exists ? How it was existing before ? It Never did !!
You can learn more about Aristotle and Descartes' views on space here:
- [Aristotle's Doctrines](https://plato.stanford.edu/entries/newton-stm/#2.2)
> "According to Aristotle, the universe is a material plenum, finite in extent, bounded by the outermost sphere of the fixed stars. Beyond that there is no void, i.e., empty places, since, as Aristotle defines ‘place’, the place of something is the outermost of “the innermost motionless boundary of what contains it.” Hence, since there are no boundaries outside the outermost celestial sphere, there are no places or space outside of it."
- [Descartes' Innovation](https://plato.stanford.edu/entries/newton-stm/#3)
> "Motion, according to “the truth of the matter”, is defined to be “the translation of one part of matter, or one body, from the vicinity of those bodies, which are immediately contiguous to it and are viewed as if at rest, to the vicinity of others.” In consequence, Descartes points out, each body has a single motion proper to it (in contrast to the numerous relative motions that can be ascribed to it depending on which other bodies are selected in order to determine its place)."
What does local mean if you're outside the context of time and space?
William C. Evans-NEWTON'S BUCKET
Julian Barbour spent the majority of his career studying this question of what physics would look like without a notion of time, which culminated in several papers together with a popular science book: https://www.wikiwand.com/en/The_End_of_Time_(book)
I'm surprised it's not in the references, but it should definitely be noted.
### TL;DR
In this paper the author discusses the Newtonian views of space and time and the concept of spacetime as introduced by Einstein's theory of relativity.
Newton's ideas were valid and useful for 3 centuries but a useful tool should not be mistaken for an eternal truth.
General Relativity refutes the idea of space as an absolute "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the universe.
The idea that there is a "Now" extending all over the universe is not compatible with General Relativity - there is not one time but there are many relative times. The idea of an extending "Now" serves only to provide an anchorage for our familiar notions, which are appropriate to describe our daily lives.
Space and time are no longer two different absolutes but they are a continuum, unified into a 4-dimensional reality that is no longer separated into 3 spatial dimensions and one time dimension.
This part answers your question:
> *"How-ever, the diffeomorphism invariance of the theory demands that the localization on this manifold is pure gauge. That is, it is physically irrelevant. The manifold is just an artiﬁce for describing a set of ﬁelds and other physical objects whose only ‘‘localization’’ is with respect to one another."*
There is no absolute reference frame, but objects still have a position **"with respect to one another"**.