Towards a history of binary fields: LIGO and Numerical Relativity

Towards a history of binary fields: LIGO and Numerical Relativity Dennis Lehmkuhl, California Institute of Technology Email: lehmkuhl@caltech.edu

Already a classic

The system that produces GW150914 (=gravitational wave detected on 14 September 2015)

Matching of theory and data

Gravitational Waves and Black Holes • The LIGO detection gives us evidence for both the existence of gravitational waves and for the existence of black holes. • Both are described by solutions to Einstein’s vacuum equations – no assumptions about the material content of the universe are needed. • But the gravitational waves are in the distant wave zone when they reach Earth, and can be described by solutions to the linearized Einstein equations in that regime. • On the other hand, the source system, the binary black hole, needs to be described by a solution to the full non-linear Einstein equations. But there is no exact solution describing an inspiralling binary black home. Hence numerical relativity. • How are all the corresponding communities, questions and regimes of GR intertwined?

Gravitational Wave Questions: how did the implications of the respective answers change over time? 1: “Do gravitational waves exist?” 1a: “Do gravitational wave solutions to the full non-linear Einstein equations exist?” 1b: “Do these solutions describe something that is going on in our universe?” 1c: “In particular: Do binary stars / binary black holes emit gravitational waves?” 2: “Do gravitational waves carry energy?” 3: “When are gravitational waves just `coordinate waves’”?

Outline • Introduction • 1916-1937: Einstein, Einstein-Rainich, Einstein-Rosen • 1955-1960: Rosen, Pirani, Bondi-Feynman • Project: Towards a History of LIGO and Numerical Relativity • Old questions in ligt of LIGO / Numerical Relativity

Einstein 1916 and 1918

The original connection between 1, 2 and 3 “In system K’ I find 3 types of waves, only one of which is connected to energy transportation, however. In system K, by contrast, only this energy-carrying type is present. What does this mean? This means that the first two types of waves obtained with K’ do not exist in reality, but are simulated by the coordinate system’s wavelike motions against Galilean space [= Minkowski spacetime].” --- Einstein to de Sitter, 22 June 1916

The problem with linearized field equations: the Einstein-Rainich correspondence of 1925-1927

Weyl’s static two body solution is not a superposition of two static one-body solution (two Schwarzschild metrics). “Weyl strut” In addition to kicking off Einstein’s work on the problem of motion, the analysis instilled an even greater skepticism in Einstein with regard to how far results obtained on the basis of the linearized Einstein equations can be trusted.

Einstein and Rosen 1937: are there exact solutions that the wave solutions to the linearized equations approximate? • Originally Einstein and Rosen believed that they had a non-existence proof for exact plane gravitational wave solutions. But after intervention by Robertson Einstein turned the argument around and used it as an argument for the claim that exact cylindrical gravitational waves exist. • (Unbeknownst to both of them, Beck 1925 had already found the exact solution for cylindrical gravitational waves, and Baldwin and Jeffrey 1926 that for plane gravitational waves.) • Rosen was not happy with the changes Einstein hand single-handedly made to their joint paper. He swiftly published another one arguing that exact plane gravitational waves solutions are not physical solutions. • Why? Like in Einstein-Grommer 1927: the distinction between good and bad singularities.

Interlude: Two criteria for good vs. bad singularities • From at least 1921 (arguably 1916) onwards, Einstein was very skeptical of the role of the energy-momentum tensor in GR: he believed it only gave a “phenomenological account” of matter, not to be taken too seriously. • Thus, he was ok with representing matter by (equally but not more problematic) singularities. But in domains free of matter, for which GR was supposed to be fundamentally correct, no singularities were allowed. GR, in Einstein’s mind, was a hybrid theory, half fundamental (for matter-free domains) and half phenomenological (for domains containing matter). • Thus he implicitly distinguished between good (acceptable) and bad (unacceptable) singularities. • Note the similarity in pattern to the later cosmic censorship conjecture: it too distinguishes between bad (naked) and good/acceptable (hidden behind event horizon) singularities.

Rosen vs. Pirani at Berne 1955 and Chapel Hill 1957 • In his talk at the Berne conference 1955 Rosen came back to the 1937 paper on exact cylindrical gravitational waves. He argued that using both Einstein’s pseudo-tensor for gravitational energy and that of Landau and Lifshitz gave the same result: these waves don’t carry energy. For Rosen, no to 2 implied no to 1. • Pirani, Bondi and Feynman picked up on this argument at the Chapel Hill conference two years later. Pirani argued that to decide on the existence/physicality of gravitational waves, one should use geodesic deviation to see how a gravitational wave affected particles. • This opened up the possibility of “decoupling” the questions whether gravitational waves exist, in the form of question 1b, and whether they carry energy (question 2). (But Pirani gave an answer to both.)

Bondi and Feynman: the sticky bead argument and gravitational energy

Bondi after Chapel Hill: singularities and gravitational energy “Polarized plane gravitational waves were first discovered by Rosen [1a], who, however, came to the conclusion that such solutions could not exist [1b] because the metric would have to contain certain singularities. More recent work by Taub and McVittie showed that there were no unpolarized plane waves, and this result has tended to confirm the view that true gravitational waves [1b] do not exist in empty space in general relativity. Partly owing to this, Scheidegger and I have both expressed the opinion that there might be no energy-carrying gravitational waves [2] at all in the theory. It is therefore of interest to point out ... that Rosen’s argument is invalid and that true gravitational fields [1b] do in fact exist. Moreover, it is shown here that these waves carry energy ... .” --- Bondi (1957)

Questions remaining • The sticky bead argument clearly involves an inference to the best explanation: the alleged best explanation for the heating up via friction is that energy was transferred from the gravitational wave to the sticky bead. Is this conclusive? • Gravitational energy can only be defined in asymptotically flat spacetimes, not for generic gravitational fields. Disanalogy to electromagnetism. What follows from that? • Carrying energy is surely a sufficient criterion for gravitational waves to exist. But is it necessary? • What can we learn from LIGO and Numerical Relativity with respect to these questions? How did the debate continue?

Outline • Introduction • 1916-1937: Einstein, Einstein-Rainich, Einstein-Rosen. • 1955-1960: Rosen, Pirani, Bondi-Feynman • Project: Towards a History of LIGO and Numerical Relativity • Old questions in ligt of LIGO / Numerical Relativity

From sticky bead to LIGO

Three Communities Numerical Relativity Experimental Gravity (LIGO) Analytic Relativity

Research Strategies • Analysis of published research papers • Interviews with key players from all three communities • DK conducted more than a hundred interviews with relativists from all three communities between 1993 and 2000. • The big breakthrough in Numerical Relativity came in 2005. • Will interview new and established relativists on all levels and compare their perspective on gravitational wave research before and after 2005/2016. • Archival Research • LIGO Archive, NSF Archive – and UBC Gravity Archive?

Four Focal Points of the Project • The planning, building and management of LIGO (from 1988) and Advanced LIGO (2008 to now). Biggest project the NSF ever funded. • The establishment of the Numerical Relativity Community and its new methods, and The Binary Black Hole Grand Challenge Alliance (1993-1998) in Numerical Relativity , NSF funded. • The numerical relativity breakthrough of 2005. • The first detection of a gravitational wave in 2015.

LIGO files at the NSF • The NSF was the funding organization for LIGO, and LIGO was the largest project, in funding terms, it has ever overseen. • This month the NSF is moving from Arlington, VA to new quarters in Alexandria, VA. It plans to shred and dispose of many documents before and during the move. • Concerned for valuable LIGO-related documents, NSF gravity program director Pedro Marronetti invited Dan Kennefick to spend a week there to review the LIGO files.

LIGO files at NSF • Dan did not look inside proposal jackets (where proposals and reviewers comments would be kept). Nor did he have access to internal documents at the National Science Board, which is responsible for setting strategic budget directions for NSF and thus regularly considered budgetary decisions relevant to LIGO. • Instead he focused on the documents kept by the NSF’s gravity program, which includes hand-written notes, printouts of e-mails, letters, site reviews, proposals, photocopies of presentations and other documents.

An Archive in waiting • Two filing cabinets (they were bookcase sized) full of folders and documents were available for review. Since there was no time to look at every document, material preceding 1995 was focused upon. Such material covers a particularly interesting part of LIGO’s history and is also less likely to duplicated elsewhere. • The most valuable documents, often handwritten notes by NSF personnel, were scanned (or hopefully will be scanned) with the aim to ultimately create a digital archive.

Outline • Introduction • 1916-1937: Einstein, Einstein-Rainich, Einstein-Rosen. • 1955-1960: Rosen, Pirani, Bondi-Feynman • Project: Towards a History of LIGO and Numerical Relativity • Old questions in ligt of LIGO / Numerical Relativity

Gravitational wave questions 1: “Do gravitational waves exist?” 1a: “Do gravitational wave solutions to the full non-linear Einstein equations exist?”  1b: “Do these solutions describe something that is going on in our universe?” () 1c: “In particular: Do binary stars / binary black holes emit gravitational waves?”  2: “Do gravitational waves carry energy?”  3: “When are gravitational waves just `coordinate waves’”? 

Thank you

Towards a history of binary fields: LIGO and Numerical Relativity