The Speed of Gravity – What the Experiments Say

Tom Van Flandern

Meta Research

<tomvf@metaresearch.org>

[as published in Physics Letters A 250:1-11 (1998)]

Abstract. Standard experimental techniques exist to determine the propagation speed of forces. When we apply these techniques to gravity, they all yield propagation speeds too great to measure, substantially faster than lightspeed. This is because gravity, in contrast to light, has no detectable aberration or propagation delay for its action, even for cases (such as binary pulsars) where sources of gravity accelerate significantly during the light time from source to target. By contrast, the finite propagation speed of light causes radiation pressure forces to have a non-radial component causing orbits to decay (the “Poynting-Robertson effect”); but gravity has no counterpart force proportional to to first order. General relativity (GR) explains these features by suggesting that gravitation (unlike electromagnetic forces) is a pure geometric effect of curved space-time, not a force of nature that propagates. Gravitational radiation, which surely does propagate at lightspeed but is a fifth order effect in , is too small to play a role in explaining this difference in behavior between gravity and ordinary forces of nature. Problems with the causality principle also exist for GR in this connection, such as explaining how the external fields between binary black holes manage to continually update without benefit of communication with the masses hidden behind event horizons. These causality problems would be solved without any change to the mathematical formalism of GR, but only to its interpretation, if gravity is once again taken to be a propagating force of nature in flat space-time with the propagation speed indicated by observational evidence and experiments: not less than 2x10¹⁰ c. Such a change of perspective requires no change in the assumed character of gravitational radiation or its lightspeed propagation. Although faster-than-light force propagation speeds do violate Einstein special relativity (SR), they are in accord with Lorentzian relativity, which has never been experimentally distinguished from SR—at least, not in favor of SR. Indeed, far from upsetting much of current physics, the main changes induced by this new perspective are beneficial to areas where physics has been struggling, such as explaining experimental evidence for non-locality in quantum physics, the dark matter issue in cosmology, and the possible unification of forces. Recognition of a faster-than-lightspeed propagation of gravity, as indicated by all existing experimental evidence, may be the key to taking conventional physics to the next plateau.

Introduction

The most amazing thing I was taught as a graduate student of celestial mechanics at Yale in the 1960s was that all gravitational interactions between bodies in all dynamical systems had to be taken as instantaneous. This seemed unacceptable on two counts. In the first place, it seemed to be a form of “action at a distance”. Perhaps no one has so elegantly expressed the objection to such a concept better than Sir Isaac Newton: “That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.” (See Hoffman, 1983.) But mediation requires propagation, and finite bodies should be incapable of propagation at infinite speeds since that would require infinite energy. So instantaneous gravity seemed to have an element of magic to it.

The second objection was that we had all been taught that Einstein’s special relativity (SR), an experimentally well-established theory, proved that nothing could propagate in forward time at a speed greater than that of light in a vacuum. Indeed, as astronomers we were taught to calculate orbits using instantaneous forces; then extract the position of some body along its orbit at a time of interest, and calculate where that position would appear as seen from Earth by allowing for the finite propagation speed of light from there to here. It seemed incongruous to allow for the finite speed of light from the body to the Earth, but to take the effect of Earth’s gravity on that same body as propagating from here to there instantaneously. Yet that was the required procedure to get the correct answers.

These objections were certainly not new when I raised them. They have been raised and answered thousands of times in dozens of different ways over the years since general relativity (GR) was set forth in 1916. Even today in discussions of gravity in USENET newsgroups on the Internet, the most frequently asked question and debated topic is “What is the speed of gravity?” It is only heard less often in the classroom because many teachers and most textbooks head off the question by hastily assuring students that gravitational waves propagate at the speed of light, leaving the firm impression, whether intended or not, that the question of gravity’s propagation speed has already been answered.

Yet, anyone with a computer and orbit computation or numerical integration software can verify the consequences of introducing a delay into gravitational interactions. The effect on computed orbits is usually disastrous because conservation of angular momentum is destroyed. Expressed less technically by Sir Arthur Eddington, this means: “If the Sun attracts Jupiter towards its present position S, and Jupiter attracts the Sun towards its present position J, the two forces are in the same line and balance. But if the Sun attracts Jupiter toward its previous position S’, and Jupiter attracts the Sun towards its previous position J’, when the force of attraction started out to cross the gulf, then the two forces give a couple. This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observations if the speed is at all comparable with that of light.” (Eddington, 1920, p. 94) See Figure 1.

Indeed, it is widely accepted, even if less widely known, that the speed of gravity in Newton’s Universal Law is unconditionally infinite. (E.g., Misner et al., 1973, p. 177) This is usually not mentioned in proximity to the statement that GR reduces to Newtonian gravity in the low-velocity, weak-field limit because of the obvious question it begs about how that can be true if the propagation speed in one model is the speed of light, and in the other model it is infinite.

The same dilemma comes up in many guises: Why do photons from the Sun travel in directions that are not parallel to the direction of Earth’s gravitational acceleration toward the Sun? Why do total eclipses of the Sun by the Moon reach maximum eclipse about 40 seconds before the Sun and Moon’s gravitational forces align? How do binary pulsars anticipate each other’s future position, velocity, and acceleration faster than the light time between them would allow? How can black holes have gravity when nothing can get out because escape speed is greater than the speed of light?

Herein we will examine the experimental evidence bearing on the issue of the speed of propagation of gravity. By gravity, we mean the gravitational “force” from some source body. By force, we mean that which gives rise to the acceleration of target bodies through space. [Note: Orbiting bodies do accelerate through space even if gravity is geometry and not a true force. For example, one spacecraft following another in the same orbit can stretch a tether between the two. The taut tether then describes a straight line, and the path of both spacecraft will be curved with respect to it.] We will examine the explanations offered by GR for these phenomena. And we will confront the dilemma that remains when we are through: whether to give up our existing interpretation of GR, or the principle of causality.

Propagation Delay versus Aberration

To understand how propagation speeds of phenomena are normally measured, it will be useful to discuss propagation or transit delay and aberration, and the distinction between them. The points in this section are illustrated in Figure 2.

In the top half of the figure, we consider the view from the source. A fixed source body on the left (for example, the Sun) sends a projectile (the arrow, which could also be a photon) toward a moving target (for example, the Earth). Infinitely far to the right are shown a bright (large, 5-pointed) star and a faint (small, 4-pointed) star, present to define directions in space. Because of transit delay, in order to hit the target, the source body must send the projectile when it is seen in the direction of the faint star, but send it toward the direction of the bright star, leading the target. The tangent of the lead angle (the angle between the two stars) is the ratio of the tangential target speed to the radial projectile speed. For small angles, this ratio equals the lead angle in radians.

In the bottom half of the figure, we consider the view from the target, which will consider itself at rest and the source moving. By the principle of relativity, this view is just as valid since no experiment can determine which of two bodies in uniform, linear relative motion is “really moving” and which is not. The projectile will be seen to approach from the retarded position of the source, which is the spatial direction headed toward the faint star. The angle between the true and retarded positions of the source, which equals the angle between the two stars, is called “aberration”. It will readily be recognized as the same angle defined in the first view due to transit delay.

Indeed, that is generally true: The initial and final positions of the target as viewed from the source differ by the motion of the target during the transit delay of the projectile. The same difference between initial and final positions of the source as viewed from the target is called the angle of aberration. Expressed in angular form, both are equal, and are manifestations of the finite propagation speed of the projectile as viewed from different frames. So the most basic way to measure the speed of propagation of any entity, whether particle or wave or dual entity or neither, is to measure transit delay, or equivalently, the angle of aberration.

Fact: Gravity Has No Aberration

1. The effect of aberration on orbits is not seen

As viewed from the Earth’s frame, light from the Sun has aberration. Light requires about 8.3 minutes to arrive from the Sun, during which time the Sun seems to move through an angle of 20 arc seconds. The arriving sunlight shows us where the Sun was 8.3 minutes ago. The true, instantaneous position of the Sun is about 20 arc seconds east of its visible position, and we will see the Sun in its true present position about 8.3 minutes into the future. In the same way, star positions are displaced from their yearly average position by up to 20 arc seconds, depending on the relative direction of the Earth’s motion around the Sun. This well-known phenomenon is classical aberration, and was discovered by the astronomer Bradley in 1728.

Orbit computations must use true, instantaneous positions of all masses when computing accelerations due to gravity for the reason given by Eddington. When orbits are complete, the visible position of any mass can be computed by allowing for the delay of light traveling from that mass to Earth. This difference between true and apparent positions of bodies is not merely an optical illusion, but is a physical difference due to transit delay that can alter an observer’s momentum. For example, small bodies such as dust particles in circular orbit around the Sun experience a mostly radial force due to the radiation pressure of sunlight. But because of the finite speed of light, a portion of that radial force acts in a transverse direction, like a drag, slowing the orbital speed of the dust particles and causing them to eventually spiral into the Sun. This phenomenon is known as the Poynting-Robertson effect.

If gravity were a simple force that propagated outward from the Sun at the speed of light, as radiation pressure does, its mostly radial effect would also have a small transverse component because of the motion of the target. Analogous to the Poynting-Robertson effect, the magnitude of that tangential force acting on the Earth would be 0.0001 of the Sun’s radial force, which is the ratio of the Earth’s orbital speed (30 km/s) to the speed of this hypothetical force of gravity moving at light-speed (300,000 km/s). It would act continuously, but would tend to speed the Earth up rather than slow it down because gravity is attractive and radiation pressure is repulsive. Nonetheless, the net effect of such a force would be to double the Earth’s distance from the Sun in 1200 years. There can be no doubt from astronomical observations that no such force is acting. The computation using the instantaneous positions of Sun and Earth is the correct one. The computation using retarded positions is in conflict with observations. From the absence of such an effect, Laplace set a lower limit to the speed of propagation of classical gravity of about 10⁸ c, where c is the speed of light. (Laplace, 1825, pp. 642-645 of translation)

In the general case, let be the speed of propagation of gravitational force, and let be the initial semi-major axis at time of an orbiting body in a system where the product of the gravitational constant and the total system mass is . Then the following formula, derived from the ordinary perturbation formulas of celestial mechanics (e.g., Danby, 1988, p. 327), allows us to compute the semi-major axis at any other time :

[1]

We will use this formula later to set limits on .

2. Gravity and light do not act in parallel directions

There is no cause to doubt that photons arriving now from the Sun left 8.3 minutes ago, and arrive at Earth from the direction against the sky that the Sun occupied that long ago. But the analogous situation for gravity is less obvious, and we must always be careful not to mix in the consequences of light propagation delays. Another way (besides aberration) to represent what gravity is doing is to measure the acceleration vector for the Earth’s motion, and ask if it is parallel to the direction of the arriving photons. If it is, that would argue that gravity propagated to Earth with the same speed as light; and conversely.

Such measurements of Earth’s acceleration through space are now easy to make using precise timing data from stable pulsars in various directions on the sky. Any movement of the Earth in any direction is immediately reflected in a decreased delay in the time of arrival of pulses toward that direction, and an increased delay toward the opposite direction. In principle, Earth’s orbit could be determined from pulsar timings alone. In practice, the orbit determined from planetary radar ranging data is checked with pulsar timing data and found consistent with it to very high precision.

How then does the direction of Earth’s acceleration compare with the direction of the visible Sun? By direct calculation from geometric ephemerides fitted to such observations, such as those published by the U.S. Naval Observatory or the Development Ephemerides of the Jet Propulsion Laboratory, the Earth accelerates toward a point 20 arc seconds in front of the visible Sun, where the Sun will appear to be in 8.3 minutes. In other words, the acceleration now is toward the true, instantaneous direction of the Sun now, and is not parallel to the direction of the arriving solar photons now. This is additional evidence that forces from electromagnetic radiation pressure and from gravity do not have the same propagation speed.

3. The solar eclipse test

Yet another manifestation of the difference between the propagation speeds of gravity and light can be seen in the case of solar eclipses (Van Flandern, 1993, pp. 49-50). The Moon, being relatively nearby and sharing the Earth’s 30 km/s orbital motion around the Sun, has relatively little aberration (0.7 arc seconds, due to the Moon’s 1 km/s orbital speed around Earth). The Sun, as mentioned earlier, has an aberration of just over 20 arc seconds. It takes the Moon about 38 seconds of time to move 20 arc seconds on the sky relative to the Sun. Since the observed times of eclipses of the Sun by the Moon agree with predicted times to within a couple of seconds, we can use the orbits of the Sun and the Moon near times of maximum solar eclipse to compare the time of predicted gravitational maximum with the time of visible maximum eclipse.

In practice, the maximum gravitational perturbation by the Sun on the orbit of the Moon near eclipses may be taken as the time when the lunar and solar longitudes are equal. Details of the procedure are provided in the reference cited. We find that maximum eclipse occurs roughly 38±1.9 seconds of time, on average, before the time of gravity maximum. If gravity is a propagating force, this 3-body (Sun-Moon-Earth) test implies that gravity propagates at least 20 times faster than light.

Electromagnetic Analogies and Gravitational Radiation

1. Myth: Gravity from an accelerating source experiences light-time delay

In electromagnetism, it is said that moving charges anticipate each other’s linear motion, but not acceleration, and that acceleration causes the emission of photons. If gravity behaved in an analogous way, moving masses would anticipate each other’s linear motion, but not acceleration, and accelerating masses would emit gravitational radiation. Indeed, the orbit of binary pulsar PSR1913+16 is observed to slowly decay at a rate clo