Return to the INE Main Page


Magic Roundabout

Paul Davies On The Meaning Of Mach's Principle


Also See:

Fill a bucket with water, grab it by the handle and whirl it in an arc above your head. If you do it right, you will stay dry. A mysterious force seems to glue the water into the upside down bucket. Scientists are still unsure about where this force comes from.

Newton believed that inertia is an innate property of matter manifesting itself whenever matter accelerates (this includes rotation) relative to absolute space. You could think of the space in the vicinity of the accelerating body as somehow reacting to its motion to produce inertial forces. Newton never explained how, but took it to be a law of nature.

Newton's arch rival, Gottfried Leibniz, rejected this. Space, being empty, provides no reference against which a body can be said to accelerate. How can something move with respect to nothingness? We can judge motion, claimed Leibniz, only relative to other material bodies. Take the Earth's rotation. We observe the daily progression of the sun and stars across the sky. Our ancestors believed it was the heavens that turned, not the Earth. But suppose there were no sun and stars? Suppose Earth were alone in infinite space? Would it then make any sense to say it was rotating?

The debate raged on. Newton's hypothesis of absolute space predominated, but champions of the alternative "relative" view fought back, first in the guise of the Irish philosopher Bishop George Berkeley, then Austrian physicist-philosopher Ernst Mach - he of the Mach numbers. Mach, whose ideas greatly influenced Einstein when formulating his theory of relativity at the start of the century, insisted that acceleration can be defined only relative to the distant stars, a statement that came to be dignified with the name of "Mach's principle".

Mach's principle faced a thorny problem. Acceleration produces inertial forces. How can the distant stars be responsible for those? Could it really be that the child riding the roundabout is being tugged at by far-flung galaxies?

Einstein and others sought a mechanism to explain how a rotating body might experience a centrifugal force as a result of some sort of interaction with all the distant matter in the universe. A clue came from the theory of gravitation: after all, centrifugal force is sometimes even called artificial gravity.

Viewed from the roundabout, it is the rest of the universe that is rotating. We know that when electric charges circulate around a loop the resulting electric current produces a magnetic field. Could it be that the apparent rotation of the universe produces a gravitational version of a magnetic force that plucks at the clinging child? To test the idea, Einstein considered a small body at rest inside a rotating shell of material in otherwise empty space. Using his theory of relativity, he calculated what would happen. It turns out that the body should indeed feel a tiny gravito-magnetic force.

Further evidence in favour of Mach's principle comes from cosmology. If rotational motion is purely relative, then it is clearly nonsensical to talk about the rotation of the universe as a whole, for with respect to what would it rotate? In Newton's theory, it is entirely possible for the entire cosmos to spin about some axis. Given that almost all astronomical systems are observed to rotate to some extent, we might expect, if Newton is right, to observe a universal rotation too.

Astronomers find no evidence for a systematic rotation of the universe. Their observations imply that the universe cannot have turned by even one degree since the big bang. If rotation is absolute, the absence of a universal rotation seems to be a very special and contrived state of affairs, but if as Mach claimed it is relative, then the observations are explained.

All this looks promising, but other features of Einstein's theory of relativity are decidedly anti-Machian, and in spite of occasional claims that Einstein's theory incorporates Mach's principle in a subtle manner, the jury has remained out for decades. Now three American physicists have published a completely new idea that goes part way to restoring Newton's view of absolute space.

Leibniz and Mach proceeded from the assumption that space is simply emptiness, so it cannot provide "landmarks" against which to gauge motion. However, physicists have discovered that what might appear to be a vacuum is in fact far from empty in the ordinary sense of the word. It is teeming with invisible activity. According to the predictions of quantum physics, even a perfect vacuum plays host to myriad short-lived (or virtual) subatomic particles. These ghostly entities appear spontaneously and exist only fleetingly before fading away again. Experiment confirms that this invisible sea of virtual particles is no mere theorist's fiction: it leaves measurable traces.

Bernhard Haisch of the Lockheed company in Palo Alto, and collaborators Harold Puthoff and Alfonso Rueda, have appealed to this evanescent "vacuum stuff" that pervades all of space to give an ingenious account of the origin of inertial forces. Their theory is based on calculations performed in the mid-1970s by William Unruh of the University of British Columbia and, independently, by myself.

The key result of that early investigation is the prediction that an accelerating observer would perceive an enveloping bath of heat radiation. The heat arises because, in the reference frame of the observer, the quantum "vacuum frolic" appears distorted by the motion. As a result, the virtual photons collectively conspire to mimic the effect of real photons, with a spectrum of energy precisely the same as that produced by a bath of radiant heat.

For all realistic accelerations the temperature of the heat bath is tiny, and the effect has been of interest largely for its curiosity value. However, the link between acceleration and space - in its modern quantum guise - rings Newtonian bells. Could it be that inertia stems not from some obscure gravitational effect of the cosmos, but as a consequence of the quantum vacuum in the vicinity of the accelerating body?

This is the essence of the new theory. To support it, Haisch and co have calculated the effect of the quantum vacuum on an accelerating body consisting of electronically charged particles bound together, and found it takes the form of a force that opposes the acceleration. The strength cannot be extracted from the calculation, but the authors surmise it is precisely the electron's inertial force. This is, in turn, determined by the body's mass. Thus the mass of an object is attributed to the way it senses the invisible quantum sea that surrounds it.

Mach maintained that reality must be vested only in those things we can actually detect. It was a line of reasoning which, as late as the turn of the century, led him to deny the existence of atoms. Similarly, he rejected acceleration relative to invisible space. But if space really contains a nebulous sea of ephemeral quantum particles, perhaps Mach was making the same mistake as he did with the atomic theory.

By extending our senses through technology we can expose otherwise invisible entities, and find new physical mechanisms. Quantum technology confirms that space is not mere emptiness. Its shadowy contents may provide a way to explain the very concrete force of inertia. So next time you whirl a bucket of water above your head, reflect on the fact that it may be kept aloft by the most insubstantial stuff known to mankind - the quantum vacuum. Reserved

Professor Paul Davies is a theoretical physicist at the University of Adelaide.

File 940922Mach from the Go2 archive of The Guardian OnLine Guardian
Newspapers Ltd

Return to the INE Main Page
Dec. 8, 1996.