8/11/2019 What is Observable in GR
1/48
Whats Observable in Special and General Relativity?
Oliver Pooley
Oriel College, Oxford
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 1/21
8/11/2019 What is Observable in GR
2/48
Outline
Whats observable in special and general relativity?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
3/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
4/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
1. Quantum gravity
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
5/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
1. Quantum gravity:
identifying the supposed peculiar nature of the observablesof GR a key to progress
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
6/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
1. Quantum gravity:
identifying the supposed peculiar nature of the observablesof GR a key to progress
2. The status of general covariance:
in (and only in) GR is Diff(M
)a gauge group, andobservables must be gauge-invariant
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
7/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
1. Quantum gravity:
identifying the supposed peculiar nature of the observablesof GR a key to progress
2. The status of general covariance:
in (and only in) GR is Diff(M
)a gauge group, andobservables must be gauge-invariant
3. The hole argument:the physicists viewvs. the philosophers view
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
8/48
Outline
Whats observable in special and general relativity?Why askthisquestion?
1. Quantum gravity:
identifying the supposed peculiar nature of the observablesof GR a key to progress
2. The status of general covariance:
in (and only in) GR is Diff(M
)a gauge group, andobservables must be gauge-invariant
3. The hole argument:the physicists viewvs. the philosophers view
MY MAIN CLAIM: whats observable in special relativity
is the same as
whats observable in general relativity
(whatever that is)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 2/21
8/11/2019 What is Observable in GR
9/48
Quantum Gravity
. . . one of the basic difficulties in quantum gravity isto understand which physical quantities should bepredicted by the theory.
And the answer seems simple: the observablequantities in the quantum theory should be the same asin the classical theory, or at least a subset of these.Rather remarkably, however, the problem of what
precisely is observable is far from being trivial even inclassicalgeneral relativity.
(Rovelli,What is observable in classical and quantumgravity?)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
10/48
Quantum Gravity
(observables in) QG observables in GR
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
11/48
Quantum Gravity
(observables in) QG observables in GR
observables in SR
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
12/48
Quantum Gravity
(observables in) QG observables in GR
observables in SR
difficulties of quantizing GR theoriesvs.relative ease of quantizing SR theories (?)natures of the observables are fundamentally different
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
13/48
Quantum Gravity
(observables in) QG observables in GR
observables in SR
difficulties of quantizing GR theoriesvs.relative ease of quantizing SR theories (?)natures of the observables are fundamentally different
1. Diff(M)is agauge groupof GR
2. Observables must be gauge-invariant
3. Observables of GR are therefore Diff(M)-invariant
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
14/48
Quantum Gravity
(observables in) QG observables in GR
observables in SR
difficulties of quantizing GR theoriesvs.relative ease of quantizing SR theories (?)natures of the observables are fundamentally different
1. Diff(M)is agauge groupof GR
2. Observables must be gauge-invariant
3. Observables of GR are therefore Diff(M)-invariant(A supposed contrast to the observables of SR)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 3/21
8/11/2019 What is Observable in GR
15/48
The hole argument
Given a model(M, g, T)of a GR theory, general covarianceimplies that(M, d g, d T)is also a model.
If these models represent physically distinct solutions, the
theory is indeterministic. So, the models are simply distinct mathematical
representations of the same physical solution(dis a gauge transformation).
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 4/21
8/11/2019 What is Observable in GR
16/48
The moral of the hole argument?
Quantities such as R(p), p Mare not observable.Why go on to say that
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 5/21
8/11/2019 What is Observable in GR
17/48
The moral of the hole argument?
Quantities such as R(p), p Mare not observable.Why go on to say that:
1. either substantivalism or determinism is false?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 5/21
8/11/2019 What is Observable in GR
18/48
The moral of the hole argument?
Quantities such as R(p), p Mare not observable.Why go on to say that:
1. either substantivalism or determinism is false?
2. the only quantities that are observable areDiff(M)-invariant?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 5/21
8/11/2019 What is Observable in GR
19/48
The moral of the hole argument?
Quantities such as R(p), p Mare not observable.Why go on to say that:
1. either substantivalism or determinism is false?
2. the only quantities that are observable areDiff(M)-invariant?
3. Mis a gauge artifact?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 5/21
8/11/2019 What is Observable in GR
20/48
The moral of the hole argument?
Quantities such as R(p), p Mare not observable.Why go on to say that:
1. either substantivalism or determinism is false?
2. the only quantities that are observable areDiff(M)-invariant?
3. Mis a gauge artifact?
4. a point is not a diffeomorphism invariant entity . . . there areno points in a physical spacetime?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 5/21
8/11/2019 What is Observable in GR
21/48
the physicists viewvs.the philosophers view
Many physicists see the hole argument as providing us with afundamental insight into the nature of space-time (e.g., Rovelli)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 6/21
8/11/2019 What is Observable in GR
22/48
the physicists viewvs.the philosophers view
Many physicists see the hole argument as providing us with afundamental insight into the nature of space-time (e.g., Rovelli)
Philosophical responses to [Earman and Nortons]version of the [hole] argument divide quite strikingly intotwo camps. On the one hand, there are those whocriticize the argument on the grounds that it relies upona naive approach to modality [Bartels, Brighouse,Butterfield, Maudlin, Hoefer, Maidens, Stachel]. . .
The second sort of response to the hole argument ismore radical, and its popularity more telling as a
measure of the insularity of contemporary philosophy ofspace and time. [It denies] . . . that the hole argumenthasanythingat all to teach us about the nature ofspace-time [Leeds, Mundy, Liu, Rynasiewicz]
(Belot and Earman,From Metaphysics to Physics)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 6/21
8/11/2019 What is Observable in GR
23/48
A sophisticated approach to modality?
Why is a straightforward reading of the formalism of GR (takingit at face value) supposed to involve treating(M, g, T)and(M, d g, d T)as representing physically distinct solutions?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 7/21
8/11/2019 What is Observable in GR
24/48
A sophisticated approach to modality?
Why is a straightforward reading of the formalism of GR (takingit at face value) supposed to involve treating(M, g, T)and(M, d g, d T)as representing physically distinct solutions?
the identities of the points of Mare (allegedly) determinedindependently of gand T
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 7/21
8/11/2019 What is Observable in GR
25/48
A sophisticated approach to modality?
Why is a straightforward reading of the formalism of GR (takingit at face value) supposed to involve treating(M, g, T)and(M, d g, d T)as representing physically distinct solutions?
the identities of the points of Mare (allegedly) determinedindependently of gand T
primitive intra-model numerical distinctness (?) primitivetrans-model identities
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 7/21
8/11/2019 What is Observable in GR
26/48
A sophisticated approach to modality?
Why is a straightforward reading of the formalism of GR (takingit at face value) supposed to involve treating(M, g, T)and(M, d g, d T)as representing physically distinct solutions?
the identities of the points of Mare (allegedly) determinedindependently of gand T
primitive intra-model numerical distinctness (?) primitivetrans-model identities
physics is obviously modally committed, but not viatrans-model identities
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 7/21
8/11/2019 What is Observable in GR
27/48
Spacetime: M, or(M, g)?
Does grepresent:
1. spacetime structure?
2. the gravitational field: a field much like the electromagnetic
field?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 8/21
8/11/2019 What is Observable in GR
28/48
Spacetime: M, or(M, g)?
Does grepresent:
1. spacetime structure?
2. the gravitational field: a field much like the electromagnetic
field?
There are reasons to answer yes to (1)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 8/21
8/11/2019 What is Observable in GR
29/48
Spacetime: M, or(M, g)?
Does grepresent:
1. spacetime structure?
2. the gravitational field: a field much like the electromagnetic
field?
There are reasons to answer yes to (1):
stress-energy and gravitation
non-vanishing of its components, signature
its indispensability
continuity with pre-GR theories
ESPECIALLY CONCERNING OBSERVABILITY/EMPIRICAL CONFIRMATION (when tidal effects areignorable)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 8/21
8/11/2019 What is Observable in GR
30/48
8/11/2019 What is Observable in GR
31/48
Kretschmann
By means of apurely mathematical reformulation of the equations representing
the theory, and with, at most, purely mathematical complicationsconnected with that reformulation, any physical theory can bebrought into agreement with any, arbitrary relativity postulate,even the most general one
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 10/21
8/11/2019 What is Observable in GR
32/48
Kretschmann
If one . . . recalls that, in the final analysis, all physicalobservations consist in the determination of purelytopological relations (coincidences) between objects ofspatio-temporal perception, from which it follows that nocoordinate system is privileged by these observations, thenone is forced to the following conclusion: By means of apurely mathematical reformulation of the equations representing
the theory, and with, at most, purely mathematical complicationsconnected with that reformulation, any physical theory can bebrought into agreement with any, arbitrary relativity postulate,even the most general oneand this without modifying any of
its content that can be tested by observations
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 10/21
8/11/2019 What is Observable in GR
33/48
Stachel: definitions
chronogeometric structures characterize the behavior of (ideal)clocks and measuring rods (1993, 134)
affine structures characterize the behavior of freely falling . . . test
particles (ibid.)dynamical structures characterize the behavior of physical fields
and/or particles in spacetime. . . usually specified byrequiring that the dynamical variables be subject to a set of
differential equations (1993, 135)
individuating field anystructure on a differentiable manifold thatindividuates the points of the manifold by some property or
properties that characterize(s) each of the points (1993,139)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 11/21
8/11/2019 What is Observable in GR
34/48
Stachel: GR versus SR
. . . we can now identify the missing element in the resolution ofthe hole argument . . . To justify the identification of a wholeequivalence class of drag-along metrics withonegravitationalfield, we must stipulate that, in general relativity, there is nostructure on the differentiable manifold that is bothindependentof the metric tensorandable to serve as an individuating field(1993, 140)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 12/21
8/11/2019 What is Observable in GR
35/48
Stachel: GR versus SR
. . . we can now identify the missing element in the resolution ofthe hole argument . . . To justify the identification of a wholeequivalence class of drag-along metrics withonegravitationalfield, we must stipulate that, in general relativity, there is nostructure on the differentiable manifold that is bothindependentof the metric tensorandable to serve as an individuating field(1993, 140)
[In 1905, Einstein gave a] careful definition of a physical frame ofreference. He defined it in terms of a network of measuring rodsand a set of suitable-synchronized clocks, all at rest in an inertialsystem. He used such a system of rods and clocks to give
physical meaning to a preferred coordinate system associatedwith the inertial frame of reference. In my language (admittedlyanachronistic), the rods and clocks serve to establish anondynamical individuating field for the points of Minkowski
spacetime. (1993, 141)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 12/21
8/11/2019 What is Observable in GR
36/48
Stachels principle of general covariance
The Principle of General Covariance (1) There are no individuatingfields in spacetime that are independent of the metric tensorfield; (2) the metric field determines both chronogeometricaland inertio-gravitational structures of spacetime; and (3)The metric field obeys a set of generally covariant fieldequations. (Stachel 1993)
QUESTION: How does a generally covariant formulation of aSRtheory fare?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 13/21
8/11/2019 What is Observable in GR
37/48
pre-GR theories as cosmological theories? I
In any non-gravitational theory, it is always possible tochoose a reference system which is not affected by thesystem under consideration (Rovelli 1991)
in non-generally relativistic physics, considering thereference systems as external non-dynamical objects is notan approximation (Rovelli 1991)
There is no problem of time in theories of isolated systems,
embedded inside the universe. . . The reason is that if thesystem modeled is understood to include only part of theuniverse one has the possibility of referring to a clock in thepart of the universe outside the system which is modeled by
the theory. This is generally what the tin the equations ofclassical and quantum mechanics refers to. (Smolin 2000)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 14/21
8/11/2019 What is Observable in GR
38/48
pre-GR theories as cosmological theories? II
Diffeomorphism invariance is the technical implementation of aphysical idea, due to Einstein. The idea is a deep modification ofthe pre-general-relativistic (pre-GR) notions of space and time.In pre-GR physics, we assume that physical objects can belocalized in space and time with respect to a fixednon-dynamical background structure. Operationally, thisbackground spacetime can be defined by means of physicalreference-system objects, but these objects are considered asdynamically decoupled from the physical system that onestudies. This conceptual structure fails in a relativisticgravitational regime. (Rovelli 1998)
Generally covariant versions of pre-GR theories?
Does the metric structure in these represent anindividuating field?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 15/21
8/11/2019 What is Observable in GR
39/48
the alternative
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 16/21
8/11/2019 What is Observable in GR
40/48
the alternative
A moral of the dynamical, constructive approach to SR:the reference objects should not be thought of asnon-dynamical, nor need they be excluded from the systemunder study
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 16/21
h l i
8/11/2019 What is Observable in GR
41/48
the alternative
A moral of the dynamical, constructive approach to SR:the reference objects should not be thought of asnon-dynamical, nor need they be excluded from the systemunder study
Barbour on ephemeris time: the system under study candefine its own coordinate system
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 16/21
th lt ti
8/11/2019 What is Observable in GR
42/48
the alternative
A moral of the dynamical, constructive approach to SR:the reference objects should not be thought of asnon-dynamical, nor need they be excluded from the systemunder study
Barbour on ephemeris time: the system under study candefine its own coordinate system
The observables in the non-generally covariant versions of
a theory should outstrip diffeomorphic-invariants becausethe coordinate systemencodesmetrical information
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 16/21
th lt ti
8/11/2019 What is Observable in GR
43/48
the alternative
A moral of the dynamical, constructive approach to SR:the reference objects should not be thought of asnon-dynamical, nor need they be excluded from the systemunder study
Barbour on ephemeris time: the system under study candefine its own coordinate system
The observables in the non-generally covariant versions of
a theory should outstrip diffeomorphic-invariants becausethe coordinate systemencodesmetrical information
It is absurd to suppose that classical pre-GR theories
should be understood as incapable of treating the act ofmeasurement itself
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 16/21
When is a symmetry a gauge symmetry?
8/11/2019 What is Observable in GR
44/48
When is a symmetry a gauge symmetry?
Gauge transformations :=transformations that connect solutionsthat represent the same physical state or history
A major motivation for interpreting a tfmn as a gauge tfmn is
often that doing so is a way to avoid indeterminism
Now the obvious danger here is that determinism will betrivialized if, whenever it is threatened by non-uniqueness, we
are willing to sop up the non-uniqueness in temporal evolutionwith what we regard as gauge freedom to describe the evolutionin different ways. Is there then some non-question beggingand systematic way to identify gauge freedom and to
characterize the genuine observables?(Earman,An Ode to the constrained Hamiltonian formalism)
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 17/21
The constrained Hamiltonian formalism and Gauge
8/11/2019 What is Observable in GR
45/48
The constrained Hamiltonian formalism and Gauge
Restrict to eqns derivable from an action that is (quasi-)invariantunder a group of transformations that depend on arbitraryfunctions of all the independent variablesNoethers 2nd theorem tells us the Euler-Lagrange equationsare not independent of one another, leading to:
1. (apparent) underdetermination
2. a constrained Hamiltonian theory
Dirac: transformations of the phase space that are generated bythe first class constraints are to be interpreted as gaugetransformations.
Observables are taken to be phase functions that are constantalong gauge orbits
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 18/21
More lines from the Ode
8/11/2019 What is Observable in GR
46/48
More lines from the Ode
Suppose, for example, that you want to be a relationist aboutspace and time, and also that you want to acknowledge thestriking success in the use of Minkowski spacetime forformulating theories of modern physics. You could reconcilethese two desires by saying that the relational spatiotemporalstructure of physical events conforms to those prescribed byMinkowski spacetime while at the same time denying thatphysical events are in any literal sense located in a spacetimecontainer. But to make such a stance consistent requirestreating a Poincar boost of matter fields on Minkowskispacetime as a gauge transformation. . . By contrast, an
application of the constraint apparatus to Maxwellelectromagnetic theory and other standard special relativistictheories does not produce the verdict that the Poincar group isa gauge group.
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 19/21
8/11/2019 What is Observable in GR
47/48
Conclusion
8/11/2019 What is Observable in GR
48/48
Conclusion
Whats special about GR is not to be found in whatsobservable in GR
The question is not why is GR so hard to quantize?, but
why does the quantization of pre-GR theories give usempirically successful theories when in reality there is nonon-quantum(dynamical) metric of GR to provide abackground with respect to which such theories can be
defined?
ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 21/21