What Is Space

1
What Is Space? What Is Time? The unfinished r
evolution Finishing what Einstein started
Lee Smolin Perimeter Institute for Theoretica
l Physics
2
Einstein started a scientific revolution 100
years ago quantum physics relativity atom
ic physics

3
Einstein started a scientific revolution 100
years ago quantum physics relativity atom
ic physics The revolution continued with t
he expanding universe particle physics
4
Einstein started a scientific revolution 100
years ago quantum physics relativity atom
ic physics The revolution continued with t
he expanding universe particle physics When d
id the revolution end?
5
Einstein started a scientific revolution 100
years ago quantum physics relativity atom
ic physics The revolution continued with t
he expanding universe particle physics When d
id the revolution end? NOT YET
100 years later, it is still in progress.
6
Einstein started a scientific revolution 100
years ago quantum physics relativity atom
ic physics The revolution continued with t
he expanding universe particle physics When d
id the revolution end? NOT YET
100 years later, it is still in progress. Thi
s talk is about why the revolution continues-
and what the universe will look like when its
done.
7
What are the questions at stake in this current
revolution

8
What are the questions at stake in this current
revolution
What is space?
9
What are the questions at stake in this current
revolution What is space? What is time?


10
What are the questions at stake in this current
revolution What is space? What is time?
What is matter?

11
What are the questions at stake in this current
revolution What is space? What is time?
What is matter?
What are laws?
12
What are the questions at stake in this current
revolution What is space? What is time?
What is matter? What are laws? What is the u
niverse?
13
What are the questions at stake in this current
revolution What is space? What is time?
What is matter? What are laws? What is the u
niverse? What is life?
14
What are the questions at stake in this current
revolution What is space? What is time?
What is matter? What are laws? What is the u
niverse? What is life? Why is the universe h
ospitable to life?
15
What are the questions at stake in this current
revolution What is space? What is time?
What is matter? What are laws? What is the u
niverse? What is life? Why is the universe h
ospitable to life? How do all these questions f
it together?
16
Past revolutions Newtonian Started Cope
rnicus, De revolutionibus 1543
Galileo, Descartes, Kepler....
Culminated Newton, Principia 1687
Aristotelean Started Aristotle etc
350 BC Culminated Ptolemy Almagest 150 AD
So, revolutions take a long time. They need
to they change everything.
17
What were the answers in the Aristotelian
revolution
What is the universe?
18
What were the answers in the Aristotelian
revolution What is the universe? Concentric r
otating spheres, with the earth in the cente
r and heaven outside
19
What were the answers in the Aristotelian
revolution What is the universe? Concentric r
otating spheres, with the earth in the cente
r and heaven outside What is space?
Finite, bounded by heaven, an absolute
center, the distance from which defines
virtue. No empty space, no vacuum.

20
What were the answers in the Aristotelian
revolution What is the universe? Concentric r
otating spheres, with the earth in the cente
r and heaven outside What is space?
Finite, bounded by heaven, an absolute
center, the distance from which defines
virtue. No empty space, no vacuum. Wha
t is time? Change takes place only in the
lowest, earthly sphere. The spheres
rotate eternally.
21
What were the answers in the Aristotelian
revolution What is the universe? Concentric r
otating spheres, with the earth in the cente
r and heaven outside What is space?
Finite, bounded by heaven, an absolute
center, the distance from which defines
virtue. No empty space, no vacuum. Wha
t is time? Change takes place only in the
lowest, earthly sphere. The spheres
rotate eternally. What is matter? Earthly s
phere earth, water, fire, air.
Above quintessence
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• What are the laws?

23

• What are the laws? Everything has a natural
  motion
  
• quintessence circular
• Earth, water seeks the center
• Air, fire seeks heaven .

24

• What are the laws? Everything has a natural
  motion
  
• quintessence circular
• Earth, water seeks the center
• Air, fire seeks heaven .
• What is life? Organic highest form of
• matter.

25

• What are the laws? Everything has a natural
  motion
  
• quintessence circular
• Earth, water seeks the center
• Air, fire seeks heaven .
• What is life? Organic highest form of
• matter.
• Why is the universe hospitable to life? The
  earthly sphere
  
• was created for us. .

26

• What are the laws? Everything has a natural
  motion
  
• quintessence circular
• Earth, water seeks the center
• Air, fire seeks heaven .
• What is life? Organic highest form of
• matter.
• Why is the universe hospitable to life? The
  earthly sphere
  
• was created for us. .
• How do all these questions fit together? God and
  his angels
  
• govern all.

27
What were the answers in the Newtonian
revolution What is space? Absolute, infinit
e and eternal 3 dimensional Euclidean space.
Provides an absolute background, that de
fines where things are and how they move.
Newton said The sensorium of God.
What is time? An absolute progression, agains
t which all change is measured. Flows on whe
ther anything happens or not.
What is matter? Particles points that move
Fields valued at every point.
28

• What are the laws? Deterministic, eternal, never
  change, were
  
• always acting, always will.
• .
• What is life? Inexplicable
• Why is the universe hospitable to life? Its
  not.
  
• How do all these questions fit together? They
  dont
  

29
What are the key themes in the current
revolution? Lets talk first about space Newto
n says space is absolute To understand Einstein
s notions of space and time, we have to go
back to a contemporary called Leibniz, who
opposed him. Leibniz argued that space is nothi
ng by itself. It is instead a reflection of relat
ionships amongst bodies. There is no absolute m
eaning to where something is. There is no absolu
te notion of position There is only relative p
osition where something is with
respect to other things. Similarly, there is
no absolute notion of motion or rest
There is only motion relative to the observer.

30
Leibnizs great principle The principle of
sufficient reason. For every question, why is
the world like X and not like Y, there
must be a rational justification.
God cannot do anything without a rational justi
fication. For example Why is the universe h
ere, and not ten feet to the left?
There can be no rational reason, as all forces d
epend on relative distances. Hence, there
can be no meaning to whether the universe is here
or ten feet to the left. Hence only relative
position can be meaningful.
31
We can apply this to time as well
Why did the universe start then, and not ten min
utes earlier? There can be no rational reason a
s all cause is related to relative
time, i.e. what follows what. Hence time must b
e just a measure of relationships between events.
There can be no absolute meaning to when somet
hing happens. Thus, space and time must bot
h be relational, rather than absolute.
32

• Ernest Mach, in the late 19th century, sharpened
  this
  
• We do not feel anything when we move with
  constant speed
  
• and direction.
• We do feel it when we rotate and accelerate.
• But what causes us to feel rotation?
• What are we rotating with respect to, that
  effects us?
  
• For Newton, we are rotating with respect to
  absolute space.
  
• But if there is no absolute space, we must be
  rotating with respect to
  
• something real.
• Mach we feel rotation because we rotate with
  respect to the distant stars.
  
• Machs principle If we were to stay still and
  the fixed stars rotate
  

33
What did Einstein do? The simplest way to say
what Einstein did in general relativity is to es
tablish a completely relational
and Machian theory of space and time.
34

• How did Einstein make a relational theory of
  space and time?
  
• The key point is that he made the geometry of
  space and time
  
• dynamical.
• The geometry of space and time determines three
  things
  
• Measures of distance, time and volume.
• Which motions are accelerated, and which are
  not.
  
• Which events can influence others causally.
• (because the speed of light is a
  constant.)
  
• In Einsteins theory, all these are aspects of
  relationships
  
• between events.
• They are not absolute.
• They evolve dynamically, subject to law.

35

• Quantum theory
• Waves and particles
• The uncertainty principle
• Schroedingers cat
• What is the basic principle?

36
Quantum physics appears to change our notion of
the relationship between the world and the inform
ation we have about it. In Newtonian physics, t
he description of a system refers to the
knowledge an observer has who is outside the
system, but who nevertheless, can have complete
knowledge of the system without
disturbing it. In quantum physics it appears th
at the observer has to be understood
as a part of the universe The information an
observer has concerns a part of the universe
besides them, that they nevertheless interact
with. An observers information is partial, bo
th because it concerns a part of the universe ex
cluding them and because to obtain
knowledge of a subsystem they must interact with
it.
37
Hence quantum physics is also relational
The knowledge an observer has in quantum physics
concerns information that one subsystem of the u
niverse can have about another subsystem, due to
their interaction. Hence, what the theory repr
esents mathematically is the act of measuring a
quantity, rather than the value.
These dont commute AB is not always BA, becau
se it can matter in what order two measurements a
re made. A consequence of this turns out to be
discreteness Many quantities that are continu
ous in classical physics, turn out to be discret
e in quantum physics. Examples energies of ato
ms, angular momenta.
38

• We now have two very general theories, which are
  each revolutionary
  
• steps away from Newtonian physics
• General relativity
• Quantum theory
• Both are relational, but in different ways.
• To complete the revolution we need a single
  theory that
  
• incorporates both of them.
• This would be the quantum theory of gravity.
• The best candidate so far is Loop quantum
  gravity
  
• because it fully realizes the relational
  character of
  
• space and time in general relativity.

39

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 1 Lp3
40

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 2 Lp3
41

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 3 Lp3
42

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 3 Lp3

• Area also comes in discrete quanta, associated
  with edges

Area 1 Lp2
43

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 3 Lp3

• Area also comes in discrete quanta, associated
  with edges

Area 2 Lp2
44

• The quantum geometry of space in loop quantum
  gravity
  
• The geometry of space becomes discrete at a
  certain scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• Volume comes in discrete units, or quanta

Volume 3 Lp3

• Area also comes in discrete quanta, associated
  with edges

Area 3 Lp2
45
So a graph represents a quantum geometry
46
Time is nothing but change in the graphs
A classical spacetime is a succession of events,
living in a continuous space, each related to t
he others by causality who causes who A quan
tum spacetime is a succession of
discrete events each is a change in a node
or small set of nodes
47
Hence Fundamental physics is about networks and
their evolution.
Quantum space-time
48
Some results from loop quantum gravity
49
Cosmology In classical general relativity ther
e is a singularity. Time begins at the big bang
.

50

• Cosmology
• In classical general relativity there is a
  singularity.
  
• Time begins at the big bang.
• Loop quantum gravity,
• applied to cosmology,
• eliminates the singularity.
• Time continues
• before the big bang.

51

• Cosmology
• In classical general relativity there is a
  singularity.
  
• Time begins at the big bang.
• Loop quantum gravity,
• applied to cosmology,
• eliminates the singularity.
• Time continues
• before the big bang.
• There are some predictions for
• cosmological observations.

52
Black holes Hawking argued that black holes
have entropy.

53
Black holes Hawking argued that black holes
have entropy. Entropy counts microscopic states
that are indistinct from large scale
observations
54
Black holes Hawking argued that black holes
have entropy. Entropy counts microscopic states
that are indistinct from large scale
observations What does the entropy of black hol
es count?
55
Black holes Hawking argued that black holes
have entropy. Entropy counts microscopic states
that are indistinct from large scale
observations What does the entropy of black hol
es count? The answer is loop quantum geometry
is the states of the black hole horizon.
56
Black holes Hawking argued that black holes
have entropy. Entropy counts microscopic states
that are indistinct from large scale
observations What does the entropy of black hol
es count? The answer is loop quantum geometry
is the states of the black hole horizon. The
counting agrees with Hawkings prediction that
entropy area of horizon/4hG
57
The fate of black hole singularities
Penrose proved that black holes have singulariti
es. If you fall inside a horizon you quickly re
ach a last moment of time.
58
The fate of black hole singularities
Penrose proved that black holes have singulariti
es. If you fall inside a horizon you quickly re
ach a last moment of time.
Hawking worried information would
be lost, falling into the singularity.
59
The fate of black hole singularities
Penrose proved that black holes have singulariti
es. If you fall inside a horizon you quickly re
ach a last moment of time.
Hawking worried information would
be lost, falling into the singularity.
Calculations in loop quantum gravity show that
the singularity is eliminated.
X
60
The fate of black hole singularities
Penrose proved that black holes have singulariti
es. If you fall inside a horizon you quickly re
ach a last moment of time.
Hawking worried information would
be lost, falling into the singularity.
Calculations in loop quantum gravity show that
the singularity is eliminated.
Where does the information go?
?
61
The fate of the information
Hawking worried information would
be lost, falling into the singularity.
Calculations in loop quantum gravity show that
the singularity is eliminated.
Where does the information go?
?
62
The fate of the information
The black hole can evaporate, leaving the
information to
emerge late in the evaporation.
?
63
The fate of the information
The black hole can evaporate, leaving the
information to
emerge late in the evaporation.
?
64
What if the black hole doesnt evaporate?
?
?
65
What if the black hole doesnt evaporate?
The result is a baby universe, a new universe to
the
future of our own.
?
I
i
Quantum region
I
i0
I-
66
Another possible implication of quantum gravity

Special relativity is modified.
67

• Another possible implication of quantum gravity
• Special relativity is modified.
• Why?

68

• Another possible implication of quantum gravity
• Special relativity is modified.
• Why?
• Special relativity predicts that moving lengths
  appear to contract
  
• A moving ruler appears shorter.

69

• Another possible implication of quantum gravity
• Special relativity is modified.
• Why?
• Special relativity predicts that moving lengths
  appear to contract
  
• A moving ruler appears shorter.
• But in quantum gravity there is a preferred
  length scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• This is the scale of the discrete quanta of areas
  and volumes
  

70

• Another possible implication of quantum gravity
• Special relativity is modified.
• Why?
• Special relativity predicts that moving lengths
  appear to contract
  
• A moving ruler appears shorter.
• But in quantum gravity there is a preferred
  length scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• This is the scale of the discrete quanta of areas
  and volumes
  
• But in whose frame of reference is the
  discreteness measured?
  

71

• Another possible implication of quantum gravity
• Special relativity is modified.
• Why?
• Special relativity predicts that moving lengths
  appear to contract
  
• A moving ruler appears shorter.
• But in quantum gravity there is a preferred
  length scale
  
• The Planck length Lp (h G) 1/2 10-33
  centimeters
  
• This is the scale of the discrete quanta of areas
  and volumes
  
• But in whose frame of reference is the
  discreteness measured?
  
• There appears to be a contradiction between
  special relativity
  

72
The answer Doubly special relativity
In special relativity the speed of light is inva
riant, all observers agree on its value. Why n
ot modify the principles of relativity so that
there are two things all observers agree about?
the speed of light and the Planck length
73

• Principles of doubly special relativity (DSR)
• Relativity of inertial frames
• The constancy of c, a velocity
• The constancy of a length Lp
• c is the universal speed of photons with
  wavelength much longer
  
• than Lp
• .

74

• Principles of doubly special relativity (DSR)
• Relativity of inertial frames
• The constancy of c, a velocity
• The constancy of a length Lp
• c is the universal speed of photons with
  wavelength much longer
  
• than Lp
• .

Is this predicted by loop quantum gravity?
No proof so far, but some positive indications.


75

• Principles of doubly special relativity (DSR)
• Relativity of inertial frames
• The constancy of c, a velocity
• The constancy of a length Lp
• c is the universal speed of photons with
  wavelength much longer
  
• than Lp
• .

Is this predicted by loop quantum gravity?
No proof so far, but some positive indications.

Does it imply predictions for experiments
76

• Principles of doubly special relativity (DSR)
• Relativity of inertial frames
• The constancy of c, a velocity
• The constancy of a length Lp
• c is the universal speed of photons with
  wavelength much longer
  
• than Lp
• .

Is this predicted by loop quantum gravity?
No proof so far, but some positive indications.
Does it imply predictions for experiments?
YES
77
Doubly special relativity is falsifiable
The speed of light is universal only for low ene
rgy photons. Blue photons go very slightly fas
ter than red photons. The effect is tiny, but i
n gamma ray busts we see light that has
traveled for 10 billion years.
The difference in arrival times can be as much a
s 1/100 of a second. So the universe is our
amplifier. The GLAST satelite, to launch in 200
7 may detect this effect.
78
So we have a tentative theory of quantum
gravity. and we may test it soon.

79
So we have a tentative theory of quantum
gravity. and we may test it soon. Are all p
roblems solved? Is the revolution almost over?

80

• So we have a tentative theory of quantum
  gravity.
  
• and we may test it soon.
• Are all problems solved? Is the revolution
  almost over?
  
• NO There are other fundamental unsolved
  problems
  

81

• So we have a tentative theory of quantum
  gravity.
  
• and we may test it soon.
• Are all problems solved? Is the revolution
  almost over?
  
• NO There are other fundamental unsolved
  problems
  
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  

82

• So we have a tentative theory of quantum
  gravity.
  
• and we may test it soon.
• Are all problems solved? Is the revolution
  almost over?
  
• NO There are other fundamental unsolved
  problems
  
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  
• The problem of the parameters of the standard
  model.
  

83

• So we have a tentative theory of quantum
  gravity.
  
• and we may test it soon.
• Are all problems solved? Is the revolution
  almost over?
  
• NO There are other fundamental unsolved
  problems
  
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  
• The problem of the parameters of the standard
  model.
  
• The problem of unifying all the forces and
  particles.
  

84

• So we have a tentative theory of quantum
  gravity.
  
• and we may test it soon.
• Are all problems solved? Is the revolution
  almost over?
  
• NO There are other fundamental unsolved
  problems
  
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  
• The problem of the parameters of the standard
  model.
  
• The problem of unifying all the forces and
  particles.
  
• What is the dark matter? What is the dark
  energy?
  

85

• Althogether there are five big problems
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  
• The problem of the parameters of the standard
  model.
  
• The problem of unifying all the forces and
  particles.
  
• What is the dark matter? What is the dark
  energy?
  
• The problem of quantum gravity
• We have tentative progress, lots of ideas, but
  no
  
• definitive progress on any.

86

• There is a lot still to do.
• The revolution is still not over.

87

• There is a lot still to do.
• The revolution is still not over.
• The adequacy of quantum mechanics. Does it make
  sense
  
• Is it the right theory, or just an interim
  theory?
  
• The problem of the parameters of the standard
  model.
  
• The problem of unifying all the forces and
  particles.
  
• What is the dark matter? What is the dark
  energy?
  
• The problem of quantum gravity

88
Why is our understanding of spaceand time
important?

• Our concepts of society have paralleled our
  understanding of space and time
  
• Three Stages...

89
The hierarchical universe

• All properties defined with respect to hierarchy
• Observer/God is in perfect realm outside the
  universe
  
• Aristotelian cosmology
• Medieval society

90
The Newtonian liberal universe

• Properties (rights) all defined with respect to
  an eternal absolute background of space and time
  
• All atoms equal, all have properties (rights)
  independent of relations to the others.
  
• Omniscient observer, god, is outside the
  universe.
  
• Newtonian physics
• liberal political and legal theory

91
The relational/pluralistic universe

• The universe is nothing but an ever-evolving
  network of relationships.
  
• All properties are about relations between
  subsystems.
  
• No view or observer from outside the universe
  only internal observers with partial views.
  
• General relativity
• Quantum theory
• Critical legal studies