Introduction:
Einstein@Home [1] is an early effort to apply observational gravitational wave astronomy. Specifically, it is an all-sky survey, searching for evidence of currently unidentified, nonspherical, spinning neutron stars [2]. The research program utilizes gravitational wave data collected by the two Laser Interferometer Gravitational Wave Observatories (LIGO) [3,4] located in the United States, and by the GEO 600 [5] interferometer located in Germany. Einstein@Home analyzes the primary data collected at the three observatories using a distributed computer approach based on the Berkeley Open Infrastructure for Network Computing (BOINC) [6] platform. The research program is under the leadership of Professor Bruce Allen, University of Wisconsin at Milwaukee, and is a World Year of Physics 2005 project supported by the American Physical Society.
At first glance, Einstein@Home might well be dismissed as an esoteric, almost pedestrian study in observational astronomy. Placed within its proper, broader perspective, Einstein@Home becomes an integral and important contribution to our continuing quest to understand the very foundations of the Universe in which we live. Here, I shall attempt to do justice to that broader perspective.
Content and Conventions:
Neutron Stars and Sources of Gravitational Waves
Basics of Data Analysis
Space-time, Gravitational Waves, and the Graviton
Observational Gravitational Wave Astronomy
Quantum Gravity and the Theory of Everything
Summary
Conclusions
References and Notes
Links to webpages of interest and to Wikipedia discussions of technical concepts and terms are embedded within the text at their first appearance to assist the reader. Conventional literature citations--principally to readily available monographs suitable for a general audience--and explanatory notes are designated within square brackets.
Neutron Stars and Sources of Gravitational Waves:
General Relativity [7] predicts that a number of generic events will yield gravitational waves. These events may be exemplified by the coalescence of two massive, compact bodies locked in orbit around each other; and the symmetric motion of neutron stars akin to pulsars. Even a cosmic gravitational wave background remnant from the Big Bang analogous to the cosmic microwave background discovered by Penzias and Wilson is predicted. Interestingly, each mechanism is predicted to give rise to a distinctly different pattern of gravitational waves. Here I shall consider only that mechanism pertinent to the subset of neutron stars of direct interest to Einstein@Home.
Stellar Evolution far exceeds the scope of this discussion. Suffice it to say, that massive, supergiant stars end their lives in Type II supernovae. These sudden events eject vast amounts of material and energy, leaving behind compact yet massive cores composed almost exclusively of neutrons. Hence the nomenclature neutron star. While the core of such a body is often described as being a degenerate neutron fluid, the actual core structure remains poorly understood. What is known is that neutron stars have masses of approximately 1.5 to 2 Solar masses compressed to a corresponding radius of only 20 to 10 kilometers [8] resulting in a surface gravity 12 orders of magnitude greater than that of Earth. Neutron stars must spin [9] at very high speeds because the rotational angular momentum of the original star must be conserved during collapse.
The remnant cores of asymmetrically imploding Type II supernovae are expected to be rapidly rotating, nonspherical neutron stars. Such neutron stars will evolve spontaneously to their spherically symmetric, lowest potential energy states. The excess energy is dissipated either by ejecting material associated with the asymmetry, or by redistributing material more smoothly under the crush of the star’s gravitational field. In either case, the axial rotation of the neutron star must suddenly increase--to conserve angular momentum--with a concomitant, characteristic emission--or burst--of energy in the form of gravitational waves. These bursts are the signature events for which Einstein@Home searches.
Basics of Data Analysis:
The LIGO and GEO 600 observatories collect massive data sets in the form of time domain signals. Such signals correspond to extremely complex wave forms including many potentially physically significant, overlapping events, and of course noise. Fast Fourier Transform methods are used to transform the data from the time domain to the frequency domain to facilitate the analysis. The resultant signals are then compared to theoretical predictions of the frequency domain signals anticipated for the objects of interest to Einstein@Home.
The magnitude of the computational analyses is enormous: thus the distributed computer approach, giving us a rare opportunity to participate actively.
Space-time, Gravitational Waves, and the Graviton:
According to General Relativity, space-time is a geometry, or topology. The presence of matter, or equivalently of energy, distorts--or warps-- that geometry. These distortions are collectively referred to as curvature, and can be described mathematically by the Riemann tensor. Within this framework, gravity is a direct manifestation of the curvature of the local space-time geometry. Gravitational waves are therefore best described as time-dependent fluctuations of the curvature of space-time resulting from the rapid motion of mass in some local region of space-time that propagate as waves at the speed of light in vacuum. It is critical to recognize that gravitational waves do not propagate through space-time, but are fluctuations of the space-time geometry itself. One significant consequence is that while matter responds to such curvature oscillations, the gravitational waves do not interact with that matter in the conventional sense, and are thus not attenuated when they encounter matter.
As yet there is no direct experimental evidence to support the existence of gravitational waves. Most interestingly however, there is elegant, indirect experimental evidence consistent with their existence. Such indirect evidence is provided by observations of the rate of decay in the orbit of the binary pulsar PSR B1913+16 by R. A. Hulse and J. H. Taylor Jr. In 1993, Hulse and Taylor were awarded the Nobel Prize in Physics for their investigations.
The search for gravitational waves is a formidable challenge because the waves are so exceedingly weak. Gravity is by far the weakest of the forces [10], and the strength of gravitational waves scales inversely with the distance traveled, just like that of electromagnetic waves. The strongest gravitational waves that we can hope to detect would have been generated at cosmological distances by the violent motions of extremely energetic events. Current best estimates are that gravitational waves would induce terrestrial spatial deformations of the order of 1 part in 1021! This amounts to attempting to measure dimensional changes of the order of the size of an atomic nucleus. LIGO and GEO 600 are designed to meet that challenge.
Early in the twentieth century, scrutiny of the Photoelectric Effect and interference effects in the diffraction of electrons led to the wave-particle duality [11]. This apparent paradox required equal consideration of both wave-like and particle-like properties for light and electrons. Ultimately, this dilemma was resolved with the emergence and maturation of Quantum Mechanics. The end result is the messenger particle. Messenger particles are the sub-atomic particles that are the smallest unit of a given force and that mediate that force via exchange: the photon and the electromagnetic force; the gluon and the strong nuclear force; and the W and Z bosons and the weak nuclear force. All of these messenger particles have been experimentally confirmed.
By analogy, it is hypothesized that the graviton is the messenger particle that carries the gravitational force. While there is no experimental evidence as yet to confirm the existence of the graviton, theory requires it to be spin 2, mass zero boson [12].
Observational Gravitational Wave Astronomy:
Historical perspective is appropriate here. Until the middle of the twentieth century, our view of the Cosmos was limited to visible light. Observational astronomy in the visible region of the electromagnetic spectrum indicates a quiescent and stable Universe. As technology developed, other regions of the spectrum became open to study. Radio and microwave, infrared, and even X-ray and Gamma-ray detectors were developed and deployed. The resultant observations dramatically altered our view of the Cosmos. Suddenly it became a place of violent and highly dynamical events. Pulsars, supernovae, and quasars were discovered. Clearly, what we observe is highly dependent upon how we observe!
Nonetheless, all regions of the electromagnetic spectrum suffer from certain common limitations on what can be observed. Electromagnetic radiation is emitted by the individual atoms, ions, and electrons within the enormous, incoherent ensembles of those species generally existing under low-velocity, low-gravity conditions. The information content of such emissions is therefore inherently limited to a description of the macroscopic properties of those ensembles: properties such as temperature, density, and magnetic field. As this radiation propagates through space, it is attenuated as a function of distance. More importantly, it is also attenuated by interactions—absorption and scattering --with any material along the line of sight. The latter attenuation mechanisms alone are sufficient to preclude observations of regions of high density and high mass—and thus high gravity--such as the center of even our own Galaxy. These restrictions are severe.
By comparison, we have seen that gravitational waves are ripples in the fabric of space-time itself that emanate from regions of extreme mass density and high gravity. These waves propagate without interacting with matter such that they are attenuated only as a function of distance. Gravitational wave observations thus open a new and unique window on the Cosmos allowing observation of exactly those regions that cannot be seen in the electromagnetic spectrum. While it is impossible to predict what such observations might ultimately reveal, it is reasonable to assert that gravitational wave astronomy will revolutionize our view and understanding of the Universe as much, and probably more so than the advent of microwave and X-ray astronomy.
Quantum Gravity and the Theory of Everything:
Both philosophical and historical perspective are required here. For the philosophical perspective, I turn to Chandrasekhar [13]:
| Quote: | | Scientific values consist in the continual and increasing recognition of the uniformity of nature. In practice this only means that the values are attained in larger or smaller measure in extending, or equivalently limiting, the domain of applicability of our concepts relating to matter, space, and time. In other words, a scientist seeks continually to extend the domain of validity of certain basic concepts. In so doing, he attempts to discover the limitations, if any, of these same concepts, and in this way he tries to formulate concepts of wider scope and generality. |
This simple statement eloquently summarizes the motivations of the scientific community as it relentlessly seeks increasingly unifying theories. I use the word “theory” to signify [14]:
| Quote: | | A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment, and is propounded or accepted as accounting for the known facts. |
Unification of basic concepts into a more encompassing whole has a long history within physics. Consider the fundamental forces of nature. The first step in unification of these forces came with Maxwell’s Equations (1864) that unified electricity and magnetism into electromagnetism. Later during the 1940’s, Quantum Electrodynamics (QED) [15] provided a relativistic quantum field theory of electromagnetism, thus unifying electromagnetism with the weak nuclear force. Yet more recently during the 1960’s, Quantum Chromodynamics (QCD) provided a quantum field theory describing the strong nuclear force. While QCD has yet to be successfully unified with the electroweak force, impressive progress has been achieved in this search for Grand Unification (GUT). Only gravitation remains aloof from a quantum description.
The current situation is that there are two distinct theoretical frameworks, each of which provides astonishingly accurate predictions of experimental observables within its own realm of applicability. On the one hand there is Quantum Theory which characterizes the three fundamental forces of electromagnetism, and of both the weak and strong nuclear forces. This is the microscopic realm of particle fields embedded within the flat space-time of Special Relativity. On the other hand there is General Relativity which characterizes gravitation. This is the macroscopic realm of massive systems and space-time curvature. Such a dichotomy is highly unsatisfying on purely philosophical and aesthetic grounds alone. It is equally unsatisfying on physical grounds.
A unified theoretical framework is required to treat systems having extremely large mass--or energy--compacted into an extremely small space: black holes and the Big Bang for example. The search for such unification is known as Quantum Gravity and its ultimate objective is to successfully unify all four of the fundamental forces of nature thereby providing a so called Theory of Everything.
Applications of the most obvious methods of unification—renormalization --have invariably given rise to singularities: that is, the solutions of the field equations yield infinities corresponding to physically unrealistic systems. The conditions under which the effects of Quantum Gravity can be expected to be important are currently not accessible within the laboratory, such that experiment cannot yet provide guidance to the theorists. Left to their own intellectual creativity, theorists have developed highly innovative approaches to unification. Two such efforts are Superstring Theory [16] and Loop Quantum Gravity [17], both of which are best considered to be in their early stages of development.
Superstring Theory approaches unification from the perspective of Quantum Theory. It proposes that each of the various, more familiar elementary constituents of matter is really an infinitesimally minute “loop” vibrating in a different mode—all of this within a space-time of 10 or more dimensions. Interestingly, the graviton arises naturally from Superstring Theory as a closed string in a low vibrational mode. By contrast, Loop Quantum Gravity approaches the identical objective from the opposite perspective of General Relativity by attempting to construct a fully quantized space-time.
Both approaches offer substantive promise, appear highly non-intuitive, and are utterly fascinating! Both can profit from the LIGO and EGO 600 observations.
A successful Theory of Everything can be anticipated to shed light on profound questions that as yet remain more within the realm of metaphysics than that of physics [16,17,18,19]. What was the origin of our Universe, and what will be its fate? Are there other, parallel Universes? What is the fundamental nature of the fabric of space, and is it too quantized? Why does time appear to flow in only one direction? These are indeed exciting times!
Summary:
Many concepts have been introduced, most of which are currently the focal point of intensively active research and scholarship. Needless to say, the concepts have been treated in a most cursory manner, and the inevitable shortcomings are solely the responsibility of this author. My intent has been to introduce these concepts to illustrate the inherent interrelationship of experiment and theory in the pursuit of new physical knowledge and understanding. Advances in theory lead to new predictions of observable behavior that must be subjected to experimental validation. Unexpected experimental observations challenge theoretical models. Experiment and theory are inexorably linked within a single, larger dynamic: each piece is a part of the broader whole.
Conclusions:
We are poised at the threshold of a paradigm shift [20]: a revolutionary leap in both experiment and theory. This is yet another profound adventure in our enduring quest to better understand our Universe, and perhaps even ourselves. Einstein@Home is an authentic tile in the broader mosaic that gives each of us the opportunity to be an active part of that grand quest.
I leave you in the most capable hands of Lord Rutherford [21]:
| Quote: | | Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected. |
References and Notes:
1. Additional discussions of Einstein@Home may be found at the American Physical Society’s webpage; at Wikipedia; and at the Einstein@Home Forum.
2. Kip S. Thorne, Black Holes and Time Warps, Einstein’s Outrageous Legacy (W. W. Norton & Company, 1994), Chapter 5.
3. LIGO is a collaboration involving the California Institute of Technology and the Massachusetts Institute of Technology. The program is supported by the National Science Foundation.
4. Reference 2, Chapter 10.
5. GEO 600 is a collaboration initiated by the Max-Planck-Institut für Quantenoptik and the University of Glasgow.
6. BOINC is an open-source software platform for volunteer computing developed and managed at the University of California at Berkeley, and is supported by the National Science Foundation.
7. Robert Geroch, General Relativity from A to B (The University of Chicago Press, 1978).
8. The more massive the star, the smaller its radius.
9. The terms “spin” and “rotate” are used interchangeably to denote axial rotation and are not to be confused with orbital motion or intrinsic spin angular momentum.
10. Electromagnetic repulsion is approximately 1042 times stronger than the gravitational force.
11. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics (Addison-Wesley Publishing Company, 1963), Volume I, Chapter 37.
12. The graviton must be a spin 2 particle because gravity is a second-rank tensor field, and it must have zero mass to propagate at the speed of light in vacuum.
13. S. Chandrasekhar, Truth and Beauty, Aesthetics and Motivations in Science (The University of Chicago Press, 1987), p. 4.
14. The Oxford English Dictionary (Oxford University Press, 1971).
15. Richard P. Feynman, QED, The Strange Theory of Light and Matter (Princeton University Press, 1985).
16. Brian R. Greene, The Elegant Universe, Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (W. W. Norton & Company, 1999).
17. Lee Smolin, Three Roads to Quantum Gravity (Basic Books, 2001).
18. Roger Penrose, The Emperor’s New Mind, Concerning Computers, Minds, and The Laws of Physics (Oxford University Press, 1989), Chapters 7 and 8.
19. Stephen W. Hawking, A Brief History of Time, From the Big Bang to Black Holes (Bantam Books, 1988).
20. Thomas S. Kuhn, The Structure of Scientific Revolutions, Second Edition (The University of Chicago Press, 1970).
21. As quoted within Reference 13, p. 14.
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