Sarfatti Commentary on the Susskind-Smolin Debate on Background Independence

Lecture 1

Excerpted

arXiv:hep-th/0507235 v1 25 Jul 2005

Comments by Jack Sarfatti on Jan 21, 2006

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“The case for background independence

Lee Smolin†

Perimeter Institute for Theoretical Physics,

35 King Street North, Waterloo, Ontario N2J 2W9, Canada, and

Departmentof Physics, University of Waterloo,

Waterloo, Ontario N2L 3G1, Canada

December 13, 2005

Abstract

The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a long-standing argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background independent theory. The leading background independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity and dynamical triangulations and their main achievements are summarized along with the problems that remain open. Some first attempts to cast string/M theory into a background independent formulation are also mentioned. The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The recent issues concerning the string theory landscape are reviewed and it is argued that they can only be resolved within the context of a background independent formulation. Finally, we review some recent proposals to make quantum theory more relational.

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This is partly based on the text of a talk given to a meeting of the British Association for the Philosophy of Science, in July 2004, under the title ”The relational idea in physics and cosmology.”

†Email address: lsmolin@perimeterinstitute.ca

…

1 Introduction

During the last three decades research in theoretical physics has focused on four key problems, which, however, remain unsolved. These are

1. The problem of quantum gravity.”

Comment 1: In my condensed matter analogy based on emergent ODLRO spontaneous symmetry breaking cohering of random vacuum fluctuations of spin ½ & spin 1 quantum fields, the c-number Einstein geometrodynamic field guv emerges from two macro-quantum Cartan 0-form Goldstone phases theta & phi of a local Higgs inflation field that forms at the ‘edge of the ledge” at the Planck scale 10^-33 cm in the formation of Max Tegmark’s “Level 1” Hubble “pocket universe” (Lenny Susskind) when a single Level 2 inflation bubble forms in the eternal inflation of chaotic cosmology. This Planck Higgs field is not the electro-weak Higgs field given masses to leptons and quarks. That Higgs field splits off at ~ 10^-16 cm. Our expanding accelerating pocket universe inside of which we are trapped like Edwin Abbott’s “Flatlanders” is a local minimum in the “cosmic landscape” in which the height function is /\, i.e. Einstein’s cosmological constant. This is not the total energy including gravity degrees of freedom. Total energy is not fundamental in background independent 1915 general relativity (GR) except in special solutions with timelike Killing vector field symmetries. The “energy” generates translations along the timelike Killing vector field.

The local invariant Einstein-Cartan CURVED tetrad gravity field is the LINE FLUX DENSITY 1-form

L = (hG/c^3)^1/2{(dtheta)(phi) – (theta)(dphi)}

Lp = (hG/c^3)

*There is no Einstein gravity when h -> 0 and/or c -> infinity even if G =/= 0.

Vacuum Manifold = G(pre-inflation)/H(post-inflation) ~ S2 + internal Calabi-Yau landscape string theory parameters

Einstein’s geometrodynamic tensor field g(curved) is given by the local equivalence principle (suppressing indices) by

g(curved) = (1 + L)(flat)(1 + L)

L = 0 in a finite space-time region of physical events, i.e. Diff(4) equivalence classes with redundant gauge freedom from localizing T4 moded out, is globally flat space-time without gravity.

Note that L is not a closed 1-form. Its non-vanishing local “curl” is the exterior product

dL = 2Lp(dtheta)/\(dphi)

The geometrodynamic area flux density operator is the closed 2-form

A = LpdL = 2Lp^2(dtheta)/\(dphi)

dA = 0

i.e. locally vanishing 3-form analog of vanishing magnetic field in the Bohm-Aharonov effect outside the solenoid.

The second homotopy group of the vacuum manifold S2 is Z the group of integers. The single-valuedness of the LOCAL vacuum coherent order parameter, i.e. Planck Higgs field with Goldstone phases theta & phi implies stable point defects. Therefore, the surface DeRham integral of A on surrounding surface S around singular point defects where the Planck Higgs field vanishes and theta & phi are undefined is

= 2Lp^2Integer

Integer = 2D Winding Number = Spherical Wrapping Number ~ number of Hawking-Bekenstein BITS.

S is closed, i.e. it has no boundary, but it is not itself a boundary. However, we define the nonlocal Bohm-Aharonov volume integral BY DEFINITION as

The World Hologram

=

V is the singular interior to the surrounding surface S.

This is a singular extension of Gauss’s theorem applied to Wheeler’s geometrodynamics rather than Maxwell’s electrodynamics.

That is the geometrodynamic information is all in the non-vanishing area flux density. The “volume” is simply a holographic image of that non-bounding but surrounding closed surface. You can think of a non-bounding closed surface as a wormhole mouth.

Now is my theory FIXED “background dependent” or MUTABLE “background independent” as defined by Lee Smolin below? I can make a case that it is background independent because the c-number Einstein gravity field from the vacuum condensate Goldstone phases is a “condensate” dynamical field that is coupled to the “normal fluid” quantized vacuum fluctuations. These zero point fluctuations are locally random but are nonlocally Einstein-Podolsky-Rosen correlated to each other such that they form part of the total superfluid density when added to the locally non-random condensate density. The locally nonrandom condensate density is a dynamical source and sink for the locally random zero point vacuum fluctuations. Therefore, everything is self-consistently dynamical. There is no non-dynamical fixed background in my theory that I can see. When we look at the total Higgs field the residual zero point fluctuations are from the spin ½ and spin 1 quantum fields of the pre-inflation false vacuum at the “edge of the ledge” as explained by Lenny Susskind in “Cosmic Landscape.” However, when we look only at the Goldstone phase fluctuations then they are the locally random spin 2 “gravitons” on the curved background that is dynamically evolving with them in a globally self-consistent whole. Therefore, my theory here is more “relational” than “absolute” as Smolin defines below. Note also that the idea of nonlocally coherent zero point fluctuations that a locally incoherent, like the pair photon states in the Aspect experiment, was first suggested by Robert Becker.

Back to Lee Smolin:

“2. The problem of further unifying the different forces and particles, beyond the partial unification of the standard model.

3. The problem of explaining how the parameters of the standard models of particles physics and cosmology, including the cosmological constant, were chosen by nature.

4. The problem of what constitutes the dark matter and energy, or whether the evidence for them are to be explained by modifications in the laws of physics at very large scales.”

Comment 2. In my theory dark matter is w = -1 negative zero point energy density with positive pressure that gravitates. Therefore dark matter particle detectors will not click with the right stuff to explain Omega(DM) ~ 0.23. Dark energy is w = -1 positive zero point energy with negative pressure that anti-gravitates. Note, in anisotropic distributions w can increase up to w < - 1/3 for this interpretation to work.

Back to Smolin:

“One can also mention a fifth unsolved problem, that of resolving the controversies concerning the foundations of quantum mechanics. All five problems have remained unsolved, despite decades of determined effort by thousands of extremely talented people. While a number of approaches have been studied, most expectations have been put on string theory as it appears to provide a uniquely compelling unification of physics. Given that the correct perturbative dynamics for gauge fields, fermions and gravitons emerges from a simple action expressed in terms of world-sheets and that, in addition, there are strong indications that the quantum corrections to these processes are finite to each order of string perturbation theory[3], it is hard not to take string theory seriously as a hypothesis about the next step in the unification of physics. At the same time, there remain open problems.

Despite knowing a great deal about the different perturbative string theories and the dualities that relate them, it is widely believed that a more fundamental formulation exists. This would give us a set of equations, solutions to which would give rise to the different perturbative string theories. While there is a lot of evidence for the existence of this more fundamental formulation, in the dualities that relate the different string perturbation theories, there is as yet no agreed upon proposal as to either the principles or the equations of this formulation.

It is also unfortunately the case that the theory makes, as yet, no falsifiable predictions for doable experiments, by which the applicability of the theory to nature could be checked. This is because of the landscape of discrete vacua which have been uncovered in the last few years. Powerful effective field theory arguments have made it plausible that the theory comes in an infinite number of versions[4]. These appear to correspond to an infinite number of possible universes and low energy phenomenologies. Even if one imposes the minimal phenomenological constraints of a positive vacuum energy and broken supersymmetry, there are argued to be still a vast (> 10^300) number of theories[5]. There thus appears to be no uniqueness and no predictability so far as observable parameters are concerned, for example, one can get any gauge group and many different spectra of Higgs and fermions.

Of course, these two issues are related. It seems very likely that the challenge posed by the landscape would be resolved if we had a more fundamental formulation of string theory. This would enable us to establish which of the vacua described by effective field theory are truly solutions to the exact theory. It would also allow us to study the dynamics of transformations between different vacua.

Another striking feature of the present situation is that we have no unique predictions for the post-standard model physics which will be explored in upcoming experiments at the LHC. This is true in spite of the fact that we have had three decades since the formulation of the standard model to discover a convincing theory that would give us unique predictions for these experiments. The theory many of our colleagues believe, the supersymmetric extension of the standard model, has too many parameters to yield unique predictions for those experiments.

It is beyond doubt that research in string theory has nonetheless led to a large number of impressive results and conjectures, some of great mathematical beauty. Several mathematical conjectures have been suggested by work in string theory, that turned out to be provable by more rigorous means. A number of interesting conjectures and results have been found for the behavior of supersymmetric gauge theories. All of this suggests that string theory has been worth pursuing. At the same time, the present situation is very far from what was expected when people enthusiastically embraced string theory 20 years ago.

If so much effort has not been rewarded with success, it might be reasonable to ask whether some wrong assumption was made somewhere in the course of the development of the theory. The purpose of this paper is to propose such an hypothesis. This hypothesis is made with an open-minded spirit, with the hopes of stimulating discussion.

To motivate my hypothesis, we can start by observing that theorists’ choices of how to approach the key issues in fundamental physics is largely determined by their views on three crucial questions.

•

Must a quantum theory of gravity be background independent, or can there be a sensible and successful background dependent approach?

•

How are the parameters of the standard models of physics and cosmology to be determined?

•

Can a cosmological theory be formulated in the same language we use for descriptions of subsystems of the universe, or does the extension of physics from local to cosmological require new principles or a new formulation of quantum theory?

It is the first issue that divides most string theorists from those who pursue alternative approaches to quantum gravity.

The second issue determines the attitude different people take to the landscape. There are, roughly, three possible approaches: 1) a unique theory leading to unique predictions. 2) Anthropic approaches, according to which our universe may be very different from a typical member of an ensemble or landscape of theories (A critique of the attempts to resolve the landscape problem through the anthropic principle is given in [6]) 3) Dynamical, or evolutionary approaches, according to which the dynamics of reproduction of universes results in our universe being a typical member of the ensemble[17]. The first has been, traditionally, the basis of the hopes for a unified theory, but the recent results suggest that unification leads not to a single, unique theory, but a multitude of possible theories. This leaves the other two options. The third issue has been long appreciated by those who have attempted to formulate a sensible quantum theory of cosmology, but it recently has been raised in the contexts of attempts to resolve the problems of the landscape in terms of cosmological theories and hypotheses. In this paper I would like to make two observations and a hypothesis about these issues. These three debates are closely related and they are unlikely to be resolved separately. These three debates are aspects of a much older debate, which has been central to thinking about the nature of space and time going back to the beginning of physics. This is the debate between relational and absolute theories of space and time. In particular, as I will explain below, background dependent attempts at quantum gravity and anthropic approaches to the landscape are the contemporary manifestations of the absolute side of the old debate.”

Comment 3: Lenny Susskind is a Newtonian “absolutist” according to Smolin.

Back to Smolin:

“Similarly, background independent approaches to quantum gravity and dynamical or evolutionary approaches to the landscape are firmly within the relational tradition.

Now here is my thesis, which it is the task of this essay to support:

The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory. This is despite there being compelling arguments that a fundamental theory must be background independent. Whether string theory turns out to describe nature or not, there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective. This essay is written with the hope that perhaps some who have avoided thinking about background independent theories might consider doing so now. To aid those who

might be so inclined, in the next section I give a sketch of how the absolute/relational debate has shaped the history of physics since before the time of Newton. Then, in section 3, I explain precisely what is meant by relational and absolute theories. Section 4 asks whether general relativity is a relational theory and explains why the answer is: partly. We then describe, in section 5, several relational approaches to quantum gravity. There have been some remarkable successes, which show that it is possible to get highly nontrivial results from background independent approaches to quantum gravity [7]. At the same time, there remain open problems and challenges. Both the successes and open problems yield lessons for any future attempt to make a background independent formulation of string theory or any other quantum theory

of gravity. Sections 6 to 8 discuss what relationalism has to offer for the problems in particle physics such as unification and predictability. It is argued that the apparent lack of predictability emerging from studies of the string theory landscape is a symptom of relying on background dependent methodologies in a regime where they cannot offer sensible answers. To support this, I show that relationalism suggests methodologies by which multiverse theories may nevertheless make falsifiable predictions.

Many theorists have asserted that no approach to quantum gravity should be taken seriously if it does not offer a solution to the cosmological constant problem. In section 9 I show that relational theories do offer new possibilities for how that most recalcitrant of issues may be resolved.

Section 10 explores another application of relationalism, which is to the problem of how to extend quantum theory to cosmology. I review several approaches, which have been called ”relational quantum theory.” These lead to formulations of the holographic principle suitable for quantum gravity and cosmology.

2 A brief history of relational time

The debate about whether space and time are relational is central to the history of physics. Here is a cartoon sketch of the story 2.

2A full historical treatment of the relational/absolute debate is in Barbour’s book, [10]

Debate about the meaning of motion go back to the Greeks. But the issues of interest for us came into focus when Newton proposed his form of dynamics in his book Principia Mathematica, published in 1687. Several of his rough contemporaries, such as Descartes, Huygens and Leibniz espoused relational notions of space and time, according to which space and time are to be defined only in terms of relationships among real objects or events. Newton broke with his contemporaries to espouse an absolute notion of space and time, according to which the geometry of space and time provided a fixed, immutable and eternal background, with respect to which particles moved. Leibniz responded by proposing arguments for a relational view that remain influential to this day 3.

3 Some essential texts, accessible to physicists, are [11].

Leibniz’s argument for relationalism was based on two principles, which have been the focus of many books and papers by philosophers to the present day. The principle of sufficient reason states that it must be possible to give a rational justification for every choice made in the description of nature. I will refer the interested reader to the original texts [11] for the arguments given for it, but it is not hard to see the relevance of this principle for contemporary theoretical physics. A theory that begins with the choice of a background geometry, among many equally consistent choices, violates this principle. So does a theory that allows some parameters to be freely specified, and allows no mechanism or rational argument why one value is observed in nature. One circumstance that the principle of sufficient reason may be applied to is space-times with global symmetries. Most distributions of matter in such a space will not be invariant under the symmetries. One can then always ask, why is the universe where it is, rather than ten feet to the left, or rotated 30 degrees? Or, why did the universe not start five minutes later? This is sometimes called the problem of under determination: nothing in the laws of physics answers the question of why the whole universe is where it is, rather than translated or rotated.

As there can be no rational answer why the universe is where it is, and not ten feet to the left, the principle of sufficient reason says this question should not arise in the right theory. One response is to demand a better theory in which there is no background spacetime. If all there is to space is an emergent description of relations between particles, questions about whether the whole universe can be translated in space or time cannot arise. Hence, the principle of sufficient reason motivates us to eliminate fixed background spacetimes from the formulation of physical law.”

Comment 4: Real particles on mass shell and classical near EM field configurations outside the vacuum are not the only sources of curvature and possibly torsion. Locally random virtual zero point fluctuations inside the vacuum are also “wood” (Einstein’s term) sources of curvature according to the LOCAL equivalence principle. The vacuum condensate Goldstone phases make the curved geometry, therefore we do not count it as the “wood”, but, rather, as the “marble” (again Einstein’s term). This SOLVES THE COSMOLOGICAL CONSTANT MYSTERY – what Lenny Susskind calls “The Mother of All Physics Problems” because the locally random zero point energy density is absorbed into the locally non-random vacuum condensate that is the “marble” out of which the curved geometrodynamic field is sculpted.

To be continued in Lecture 2.

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