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Gravity with 4-Vector Potentials - A Theory Revolution?

by John G. Cramer

Alternate View Column AV-181
Keywords: quantum, gravity, general, relativity, tensor, four-vector, gravity, Wave, LIGO, test
Published in the March-2016 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 08/25/2015 and is copyrighted ©2015 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


Albert Einstein's general theory of relativity (GR), which describes gravitational forces as arising from the mass-induced curvature of space, had its 100-year anniversary in 2015 and is still going strong as our standard model of gravitation.  Over the century it has successfully passed a series of critical tests and demonstrated its superiority over rival theories of gravity.  Now another test involving gravitational waves is coming, and there is a significant chance that GR may not survive this one.

Prof. Carver Mead is Gordon and Betty Moore Professor Emeritus of Engineering and Applied Science at Caltech.  He is the person who named Moore's Law and demonstrated mathematically and experimentally that transistors and other integrated circuit elements actually work better and faster when they are made smaller, blazing the trail that has led to the microelectronics revolution.  Mead has developed a simpler approach to gravitation (G4v) that employs a gravitational 4-vector potential.  G4v makes much the same predictions as GR, but it predicts behavior for gravitational waves that is qualitatively different from that of GR.  The NSF's Advanced LIGO gravitational wave detector system, 4-km long L-shaped interferometers located at sites in Hanford , Washington and Livingston , Louisiana , is expected to soon detect gravitational waves from merging neutron stars or black holes.  Such detection is a make-or-break test that should falsify either GR or G4v (or both).

Mead's new approach is based on his unusual book, Collective Electrodynamics, which breaks the orthodoxy of textbooks about electricity and magnetism (E&M) by starting with superconductors involving electrons acting collectively, instead of the usual approach that starts with individual electric charges acting in isolation.  He has formulated this alternative approach to electrodynamics, and he brings in the quantum mechanics of collective systems (like superconductors) in a very natural way.  It is simple and straightforward (if disorienting) approach and represents essentially an alternative to conventional quantum electrodynamics, our standard model of electromagnetic phenomena at the quantum scale. 

In E&M theory there are two ways of looking at interactions and forces between charges: (1) as resulting from the electric E and magnetic B fields that exert forces on at-rest and moving charged particles, and (2) as resulting from the electric scalar potential and the magnetic vector potential that directly modify the momentum of charged particles.  Mead ignores the E and B fields and their forces and combines the scalar and vector potentials into a 4-vector potential, with the magnetic vector potential as the space-like parts and the electric scalar potential as the time-like part.  He uses this 4-potential approach to get many familiar results in an interestingly unfamiliar and simple way.

In addition, in his book Collective Electrodynamics, Mead presents an important calculation that I have seen nowhere else.  There is a fundamental problem with the standard theory of quantum mechanics, in that it uses the mechanism of "wave-function collapse", an abrupt change in a quantum wave function whenever a measurement is made or a quantum event occurs.  However, the standard quantum formalism does not provide mathematics describing such a collapse.  Mead fills this gap, at least in part.  He uses his 4-potential formalism along with standard quantum mechanics to describe a "quantum jump", a quantum event in which an atom in its excited state delivers a photon to an identical atom in its ground state.

This process was the center of a controversy between Neils Bohr and Erwin Schrödinger, in which Schrödinger refused to believe that quantum jump could be "instantaneous", as Bohr insisted they must be.  Mead resolves this difficulty.  He employs the exchange of advanced and retarded waves from my own transactional interpretation of quantum mechanics.  He assumes that the initial positive-energy retarded wave from an excited atom A, interacting with some ground-state atom B, perturbs B into a mixed state that adds a very small component of excited-state wave function to its ground-state wave function.  Similarly, a negative-energy advanced wave from atom B, interacting with atom A, perturbs it into a mixed state that adds a very small component of ground-state wave function to its excited-state wave function.  Because of these added components, both atoms develop small time-dependent dipole moments, tiny antennas that oscillate with the same beat frequency because of the mixed-energy states and act as coupled dipole resonators.  The phasing of their resulting waves is such that energy is transferred from A to B at a rate that initially rises exponentially.

To quote Mead: "The energy transferred from one atom to another causes an increase in the minority state of the superposition, thus increasing the dipole moment of both states and increasing the coupling and, hence, the rate of energy transfer.  This self-reinforcing behavior gives the transition its initial exponential character.''  In other words, he has shown mathematically that the perturbations induced by the initial advanced/retarded exchange triggers the formation of a full-blown quantum jump in which a photon-worth of energy is transferred from one atom to the other.  This is the long-sought  mathematical description of quantum wave function collapse.

Mead has recently gone beyond this triumph in quantum physics by extending his 4-vector potential formalism to gravitation as well as electromagnetism, producing G4v.  This is a theory that is still being developed, but it promises to provide the key to the long-sought problem of unifying gravitation and quantum mechanics.  This approach to gravity theory was nearly realized by Einstein himself in a 1912 paper published in an obscure medical journal and largely ignored, but Einstein subsequently turned in a different direction in his 1915 formulation of general relativity.

Mead's four-vector gravitation gives predictions that are indistinguishable from those of Einstein's general relativity for most of the well known GR tests.  These include the gravitational deflection of light, the perihelion shift of the orbit of Mercury, the gravitational red shift, the frame-dragging effects of Gravity Probe B, and the rate of gravitational-wave energy loss from neutron-star binary pulsars.

However, when attention is turned to the production and detection of gravitational waves, there is an important difference.  In considering a binary star system with two masses rotating in circular or elliptical orbits, both theories predict radiation at twice the rotation frequency of the binary source, but the G4v theory and GR theory predict qualitatively different angular dependence of gravitational wave emission and different behavior of gravitational wave "antennas" like LIGO in detecting such waves.  In particular, if the binary star system rotates in a certain plane, GR predicts that the emission of gravitational waves has a maximum along the axis perpendicular to that plane, while G4v predicts that the emission is maximum in directions that see the plane of rotation edgewise.

Why this difference? The gravitational waves predicted by GR have squeeze-stretch tensor polarization, with the two polarization modes denoted by "+" and "×" indicating that the squeeze-stretch of space is aligned either with the vertical/horizontal axes or with the diagonal/anti-diagonal axes perpendicular to the direction of motion of the wave.  On the other hand, the gravitational waves predicted by G4v have more normal vector polarization, with the two polarization modes denoted by "i" and "x" indicating vectors in the i or inclination direction or in the x direction perpendicular to inclination, both perpendicular to the direction of motion of the wave.  The GR waves have roughly equal intensities in the two polarizations modes, while for the G4v waves  the "x" polarization is dominant.

The GR gravitational waves are traveling distortions of space, and for a binary star system they add to a maximum pointing perpendicular to the orbit plane.  The G4v waves from the two members of the binary system are vectors that tend to cancel when they travel the same distance because the source stars are moving in opposite directions, so their maximum intensity comes when there is a large phase difference between them due to the distance difference from the two source-stars to the observer.  This occurs when the orbit plane is edgewise to the observer.           

There is also a significant difference in the way an interferometric gravitational wave detector like Advanced LIGO should respond to the gravitational waves predicted by the two theories.   The stretch-squeeze tensor gravitational waves of GR should modify the distances between interferometer mirrors in the LIGO arms, producing a characteristic signature template that the LIGO data-analysis software is designed to extract from the incoming data.  In contrast, the perpendicular component of the gravitational waves of G4v should directly modify the momentum of the interferometer mirrors, causing them to move and to shift the interference pattern.  This produces a qualitatively different signature template that the LIGO data-analysis software must be designed to extract from the incoming data.  Thus, the response of Advanced LIGO to the gravitational waves predicted by the two theories will be quite different, and the data analysis software must be on the lookout for waves of either type. Fortunately, the scientists operating Advanced LIGO are aware of this dichotomy, and they are prepared to detect either type of gravitational waves.

Thus a critical make-or break test of GR vs. G4v is waiting for the arrival of the first detectable gravitational waves in the improved Advanced LIGO detector system.  The first data run with the new system is planned for the Fall of 2015, and by the time you read this, the system may have detected its first gravitational waves.

What would be the consequences if Advanced LIGO should definitively detect gravitational waves of the type that is predicted by G4v?  It would herald nothing less than a major revolution in theoretical physics.  Einstein's general theory of relativity, with its treatment of gravitational forces as arising from space curvature, would be falsified.  Black holes would become simply ultra-degenerate compact stars, with no singularity, naked or otherwise, lying in wait at the bottom of the gravity well.  There would be no dark energy, because G4v explains the dimming of distant receding Type IIa supernovas as partially due to relativistic beaming, without the need for a non-zero cosmological constant. 

Further, the approach of quantum field theory, with its churning vacuum full of virtual particle, would be called into question by the G4v approach to fundamental interactions.  This would resolve a problem created by quantum field theory, which predicts an energy density of the quantum vacuum that is 10120 times larger than its actual value.  Moreover, the work on developing a unified theory that unites quantum mechanics and gravity would be set on a much smoother path that should lead to a solution to that vexing problem.

So, are we on the cusp of a major game-changing revolution in theoretical physics?  Will the current standard models of gravity and particle interactions survive this critical test or will they be overthrown?  Watch this column for future developments.  

Followup Note (01/31/2021):  LIGO and LIGO+Virgo have now detected about a dozen gravitational wave events.  Their observed polarization characteristics shy locations are consistent with Einstein's GR but not with Mead's G4v.  Nice try, Carver.


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: .


Carver Mead, G4v: An Engineering approach to Gravitation (video):

Carver Mead, Collective Electrodynamics, The MIT Press, (2000), ISBN 0-262-13378-4.

Carver Mead, "Gravitatational Waves in G4v", ArXiV preprint 1503.04866 [gr-qc] (2015).

Maximiliano Isi,  Alan J. Weinstein,  Carver Mead, and Matthew Pitkin, "Detecting Beyond-Einstein Polarizations of Continuous Gravitational Waves", Phys. Rev. D 91, 082002 (2015); ArXiV preprint 1502.00333 [gr-qc].

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