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Neutrinos, Ripples, and Time Loops

by John G. Cramer

Alternate View Column AV-57
Keywords: solar neutrinos microwave background grneral relativity causality violations
Published in the February-1993 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 7/27/92 and is copyrighted ©1992 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

    Once in a while I do a "clean up" Alternate View column that contains follow-ups on previous columns and provides short discussions of ideas and developments that are not appropriate for a full length column. This is such a column.

* Solar Neutrinos are Up - My column about recent results in neutrino physics [Analog - September-1992] (no neutrino counts at SAGE and negative mass-squared data suggesting that the e-neutrino may be a tachyon) prompted more reader response than any other column in recent memory . Two months after I wrote it, a new result from GALLEX, the European gallium neutrino-detection experiment housed in the Grand Sasso underground laboratory in Italy, was announced. GALLEX uses the same technique as the SAGE neutrino experiment described in my September column: many million dollars worth of elemental gallium (element 31) is purified and placed in underground tanks where solar neutrinos transmute stable gallium 71 to radioactive germanium 71 (half life 11.4 days). A chemical process separates the new radioactive germanium atoms from the bulk gallium and transports them to a sensitive detector where their decays are counted.

    Because the elements of the experiment are the same for SAGE and GALLEX and they are measuring the same flux of solar neutrinos, one would expect them to give consistent results. That is not exactly obvious from the numbers. The GALLEX experimenters report observation of 83 ± 19 (statistical) ± 8 (systematic) SNU (solar neutrino units, the standard measure of solar neutrino flux) while standard astrophysical models of the fusion processes in the sun would predict about 128 SNU. The SAGE experiment, on the other hand, produced a result that was essentially zero: 20 ± 20 (statistical) ± 32 (systematic) SNU. Both experimental groups placed sizable statistical and systematic error estimates on their measurements, and these error-bars are sufficiently generous that the two results actually overlap, although just barely. Nevertheless, the physics community is concerned that there may be some fundamental problem with design or execution of the SAGE experiment. Soon both SAGE and GALLEX will both be checked by placing very intense radioactive neutrino-emitting sources within the experiments, so that their efficiencies for detecting neutrinos of known energy and intensity can be directly measured.

I    f the GALLEX results are taken a face value the solar neutrino problem is less severe than had been assumed when only SAGE had reported in. And some of the theoretical suggested mechanisms for "explaining" the SAGE results will pass into that section of limbo reserved for theories that do not agree with experiment.

    The other recent result mentioned in my September-'92 column, the consistently negative measured value of the mass-squared of the electron neutrino, is still with us. I have not yet seen any papers in the physics literature, however, which take seriously the possibility that the electron neutrino may be a tachyon. Paradigm shifts take time.

* Ripples in the Big Bang - The big science news of May-1992 was the demonstration of non-uniformity in the cosmic background microwave radiation provided by careful analysis of NASA's Cosmic Background Explorer (COBE) satellite. Considering their importance, I should have done an AV column about these results at the time they were announced. However, I was in Geneva at the CERN laboratory doing an experiment at that time, and the facts on the COBE results provided by the BBC and the Herald Tribune, my principle sources of news at CERN, were sketchy and rather garbled.

    The discovery of the variations in the 2.73o microwave background is very important. We know that while the Big Bang was very smooth, our present universe is very lumpy and full of irregular chunks of matter such as galactic clusters, galaxies, and stars. Cosmologists have been fretting over for decades over the question: "When did the lumpiness occur?" The destabilizing action of gravity must have caused the early universe had to "curdle" into clumps of matter at some point, but up to the COBE announcement, there was no trace of the onset of this process.

    The irregularities in the microwave background provide this missing information. We now have a measure of the scale of the variations, a scale frozen into the microwave radiation when it decoupled from the matter in the universe not long after the Big bang itself. The variation in the microwave background can be considered as a progress report on the formation of the universe that has been beamed to us on a microwave channel by the universe itself from 100,000 years after the starting gun of the Big Bang.

    The COBE results represent hard data that, from this point forward, will provide a stringent set of tests for any theory of cosmology that attempts to describe the early universe. The questions surrounding the presence and role of dark matter in the formation of stars and galaxies now have a new observational constraint. It's going to be interesting to watch the interaction of the COBE results with cosmological theories in the next few years. Watch this space for further developments.

* Causality Loopholes in General Relativity - The law of causality, the principle that a cause must always precede its effects in every reference frame, is one of the most fundamental laws of physics. It is also one of the most mysterious, because its origins and mechanisms are not well understood. Until a few years ago general relativity, our standard theory of gravitation, was a good example of a theory that preserves causality by preventing "causal loops", better known in SF as time travel paradoxes.

    Of course, lurking in general relativity are wormholes [see my AV columns in the 6/89, 5/90, and 7/92 issues of Analog] which can provide spatial and temporal shortcuts, and "singularities", points at which forces become infinite and the laws of physics including causality must break down. However, whenever a peculiarity like a wormhole or a singularity threatened a causality violation, a mechanism was always found within general relativity to preserve causality. Wormholes were shown to be dynamically unstable, so that not even a photon could pass through to make a causal loop. The bizarre physics of the singularity was believed to be walled off from the real world by what Roger Penrose called "cosmic censorship". Penrose suggested that the event horizon of a black hole would always screen the singularity from access, eliminating the possibility that a "naked" singularity could have bizarre interactions with our universe.

    So the peculiarities were present in the theory, but for each peculiarity there was a mechanism that preserved causality and blocked the possibility of closed-loop paths through time. This secure position of causality within general relativity is now being progressively eroded. The first breech was provided by Kip Thorne's work on wormholes, which has been extensively discussed in this column. In brief, Thorne's group discovered a mechanism at the boundary between general relativity and quantum mechanics (using the Casimir effect) for stabilizing wormholes so that they could, in principle, be used for faster-than-light travel and time travel. The work of Thorne's group is taken quite seriously within the physics community and papers are regularly appearing in refereed physics journals that explore various aspects of wormhole-based time travel. Causality is dead if wormholes can be stabilized.

    Another assault on causality came from the unlikely direction of "numerical" general relativity. When a star uses up its nuclear fuel it become dynamically unstable and goes into gravitational collapse, producing a supernova explosion and, if the star is massive enough, forming a black hole. Exact mathematical solutions of Einstein's general field equations, as they apply to gravitational collapse and black hole formation, are known for only a few highly symmetric situations because of the great mathematical difficulty of solving the equations. With the availability of supercomputers, however, it is now possible to obtain reliable numerical solutions to Einstein's equations for situations where the system is not symmetric in space, where the in-falling matter is clumped in arbitrary ways rather than arranged in a perfect sphere.

    Last year Stuart L. Shapiro and Saul A. Teukolsky of Cornell University reported work in which they had used a supercomputer to examine the gravitational collapse of a football-shaped swarm of particles with an eccentricity (axis ratio) of about 2.3. This work produced a big surprise. As the collapse progressed the mass distribution assumed a spindle shape with a point at each end. Soon at each of the two points a naked singularity formed. The computer halted at this point, unable to proceed with the calculation after the singularities appeared because of numerical overflows resulting from the infinite forces at the singularities.

    The implication of the Shapiro-Teukolsky work is that Penrose's cosmic censorship is not a universal consequence of general relativity but rather a special condition which only occurs in fairly spherical and symmetrical collapse processes. Since real stars are not likely to be spherical, particularly when they are members of a binary system, there seems to be a real possibility that naked singularities occur from time to time in our galaxy. The implications of this conclusion are now being intensively studied.

    In the wake of the Thorne and Shapiro-Teukolsky work there remained some hope of restoring general relativity to its former state of causal purity. Perhaps unknown quantum-gravity effects would de-stabilize Thorne's wormholes. Perhaps in the Shapiro-Teukolsky calculations the seeming naked singularity was the consequence of numerical inaccuracies in the calculations when the density became too large. Perhaps when we learn more, we will see that causality is still OK.

    Such hopes have been largely dashed by recent work of James Gunn of Harvard. Gunn has been doing exact analytical calculations of general relativity applied to the physics of cosmic strings [for which, see my 4/87 Alternate View column in Analog]. Cosmic strings are very massive "fault lines" in space itself that may have been produced in the early Big Bang, that may be responsible for the formation and shape of galaxies, and that may still be around or may have long since destroyed themselves by dissipating into gravitational radiation. The peculiar characteristic of the gravitational field around a cosmic string is that it is represented by a conical distortion of space. Because of the distortion is conical, there is no observable attractive force in the vicinity of a cosmic string, despite its enormous mass (perhaps 1.5 Earth-masses per meter of length).

    A flat sheet of paper can be made into a cone by removing a wedge-shaped slice from the sheet and joining the cut ends. The conical distortion of space around a cosmic string has such a missing wedge of space, a "spatial deficit". Because of this spatial deficit, a circle enclosing a cosmic string contains less than 360o of angle.

    Gunn discovered that the peculiar conical gravitational field around a cosmic string produces an even more peculiar "gravito-magnetic" effect when the cosmic string is set in motion. The spatial deficit becomes a timelike deficit. Gunn considered this effect in the region between two parallel cosmic strings that are separated by a small distance and are moving in opposite directions at very nearly the velocity of light. In this circumstance a circular path enclosing one of the strings and passing between them has the remarkable property that it can form a causal loop. In one direction around the circle the trip time is increased, while in the other direction it is reduced or even made negative.

T    hus, a violation of the law of causality can be produced within the framework of general relativity. The remarkable thing about Gunn's calculation is its simplicity. Once set up, the extraction of the bizarre solution with its closed time-like loops is very straightforward with standard mathematical procedures. There seems no remaining escape from the conclusion that time travel is implicit in general relativity. From the viewpoint of physics, that is a disaster and perhaps an indication that general relativity is in need of revision. From the viewpoint of science fiction, however, the possibility of time travel is a very pleasing development.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


GALLEX Results:
The GALLEX Collaboration (54 authors), Physics Letters B285, 367-389 (1992) and
Physics Letters B285, 390-97 (1992).

Naked Singularities:
Stuart L. Shapiro and Saul A. Teukolsky, Physical Review Letters 66, 994 (1991) and
Physical Review D45, 2006 (1992).

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