What is Observable in GR

8/11/2019 What is Observable in GR

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Whats Observable in Special and General Relativity?

Oliver Pooley

[email protected]

Oriel College, Oxford

ESF Conference 24 March 2004; Whats Observable in Special and General Relativity? p. 1/21


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Outline

Whats observable in special and general relativity?



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Outline

Whats observable in special and general relativity?Why askthisquestion?



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Outline


1. Quantum gravity



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Outline


1. Quantum gravity:

identifying the supposed peculiar nature of the observablesof GR a key to progress



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Outline


1. Quantum gravity:


2. The status of general covariance:

in (and only in) GR is Diff(M

)a gauge group, andobservables must be gauge-invariant



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Outline


1. Quantum gravity:





3. The hole argument:the physicists viewvs. the philosophers view



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Outline


1. Quantum gravity:





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)



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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?)



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Quantum Gravity

(observables in) QG observables in GR



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Quantum Gravity


observables in SR



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Quantum Gravity


observables in SR

difficulties of quantizing GR theoriesvs.relative ease of quantizing SR theories (?)natures of the observables are fundamentally different



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Quantum Gravity


observables in SR


1. Diff(M)is agauge groupof GR

2. Observables must be gauge-invariant

3. Observables of GR are therefore Diff(M)-invariant



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Quantum Gravity


observables in SR


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)



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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).



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The moral of the hole argument?

Quantities such as R(p), p Mare not observable.Why go on to say that



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Quantities such as R(p), p Mare not observable.Why go on to say that:

1. either substantivalism or determinism is false?



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2. the only quantities that are observable areDiff(M)-invariant?



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3. Mis a gauge artifact?



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3. Mis a gauge artifact?

4. a point is not a diffeomorphism invariant entity . . . there areno points in a physical spacetime?



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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)



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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)



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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?



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the identities of the points of Mare (allegedly) determinedindependently of gand T



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primitive intra-model numerical distinctness (?) primitivetrans-model identities



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primitive intra-model numerical distinctness (?) primitivetrans-model identities

physics is obviously modally committed, but not viatrans-model identities



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Spacetime: M, or(M, g)?

Does grepresent:

1. spacetime structure?

2. the gravitational field: a field much like the electromagnetic

field?



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Does grepresent:



field?

There are reasons to answer yes to (1)



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Does grepresent:



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)



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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



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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



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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)



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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)



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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)



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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?



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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)



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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?



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the alternative



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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


h l i


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the alternative


Barbour on ephemeris time: the system under study candefine its own coordinate system


th lt ti


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the alternative



The observables in the non-generally covariant versions of

a theory should outstrip diffeomorphic-invariants becausethe coordinate systemencodesmetrical information


th lt ti


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the alternative



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


When is a symmetry a gauge symmetry?


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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)


The constrained Hamiltonian formalism and Gauge


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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


More lines from the Ode


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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.



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Conclusion


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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?


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What is Observable in GR