The Curious Wavefunction

The Curious Wavefunction

Musings on chemistry and the history and philosophy of science

Why the search for a unified theory may turn out to be a pipe dream

Einstein's last years were marked by a futile search for a grand unified theory (Image: Wikipedia Commons).

Unification is an ancient goal in physics. From the time that 19th century physicists like Maxwell and Clausius attempted to unite disparate physical phenomena, the search for a grand unified theory that would conjoin every known force and physical law has always been an implicit or explicit dream of physicists. The search for unification is in one sense a search for harmony, a desire to view the whole universe through the lens of a single elegant law or equation that would explain everything.

Most attempts at unification have been remarkably successful. First the pioneers of thermodynamics brought together mechanics and heat and then Faraday and Maxwell achieved the spectacular goal of weaving electricity, magnetism and optics together into a seamless tapestry. Even Einstein's famous equation can be seen as a kind of unification, serving to underscore how fundamental quantities like matter and energy are just two sides of the same coin.

Unification thinking pervaded the twentieth century, from establishing wave-particle duality to creating a common framework for understanding special relativity and quantum mechanics. Pioneers of particle physics like Feynman, Weinberg and t' Hooft brought us tantalizingly close to the ultimate goal of a "final" theory. But only tantalizingly so; famously, gravity remained intractable and its union with quantum theory has remained perhaps the greatest unsolved problem in physics for the last fifty years. Many of the world's best minds from Einstein to Edward Witten have tried to solve the problem with scant success. String theory claims that it can achieve the task, but it is no closer than other theories to making hard, testable predictions to this effect.

From an experimental perspective one of the best bets for probing a quantum theory of gravity is to look for gravitons, particles that are thought to mediate the gravitational force. The fundamental problem with detecting gravitons is the extremely weak nature of the gravitational force. To address this problem researchers have designed exceedingly sensitive equipment that should in principle be able to detect even discrete gravitons. One of the triumphs of this effort is LIGO, the Laser Interferometer Gravitational Wave Observatory, which is using extremely sensitive interferometers to detect the minuscule shifts in space-time caused by the passage of a gravitational wave. LIGO is a marvel of both physics and engineering and has been really designed to detect gravitational waves which are a prediction of classical general relativity. A typical experiment will study the interference of a highly focused laser beam bouncing off two mirrored cavities at a given distance, waiting for a gravitational wave from a defined source to pass between them. Then, as Wikipedia puts it:

When a gravitational wave passes through the interferometer, the space-time in the local area is altered. Depending on the source of the wave and its polarization, this results in an effective change in length of one or both of the cavities. The effective length change between the beams will cause the light currently in the cavity to become very slightly out of phase with the incoming light. The cavity will therefore periodically get very slightly out of resonance and the beams which are tuned to destructively interfere at the detector, will have a very slight periodically varying detuning. This results in a measurable signal. Note that the effective length change and the resulting phase change are a subtle tidal effect that must be carefully computed because the light waves are affected by the gravitational wave just as much as the beams themselves.

Note the last statement that talks about the subtlety of the effect. But the subtlety may be even more amplified when it comes to detecting gravitons themselves. How subtle would the effect of discrete gravitons be? In a chapter in John Brockman's recent book, Freeman Dyson from the Institute for Advanced Study in Princeton tries to quantify the subtlety (the chapter is reprinted as an essay in the IAS newsletter). In the process he also tells us that the effort to unify gravity and quantum mechanics might be doomed after all. The key effect here is the displacement of the two mirrors induced by the passage of a gravitational wave which causes a change in the interference of the laser beams, leading to a signal. Dyson's calculations demonstrate that this change might be so small that it would be swamped by "background" quantum fluctuations in space-time. Well then, you might say, we will just make the mirrors heavy enough so that they won't be perturbed by the quantum fluctuations. Dyson tells us just how heavy they will have to be:

"Because of ambient and instrumental noise, the actual LIGO detectors can only detect waves far stronger than a single graviton. But even in a totally quiet universe, I can answer the question, whether an ideal LIGO detector could detect a single graviton. The answer is no. In a quiet universe, the limit to the accuracy of measurement of distance is set by the quantum uncertainties in the positions of the mirrors. To make the quantum uncertainties small, the mirrors must be heavy. A simple calculation, based on the known laws of gravitation and quantum mechanics, leads to a striking result. To detect a single graviton with a LIGO apparatus, the mirrors must be exactly so heavy that they will attract each other with irresistible force and collapse into a black hole. In other words, nature herself forbids us to observe a single graviton with this kind of apparatus."

When I met Dyson last year he told me that he had tried hard to find a flaw in the calculation, to no success. If true this limitation goes much beyond detecting discrete gravitons. It could mean that the world of gravity and the world of subatomic particles will forever stay separate from each other, being disallowed from sampling each other's domains by a fundamental physical barrier. As Dyson puts it:

"If this hypothesis were true, it would imply that theories of quantum gravity are untestable and scientifically meaningless. The classical universe and the quantum universe could then live together in peaceful coexistence. No incompatibility between the two pictures could ever be demonstrated. Both pictures of the universe could be true, and the search for a unified theory could turn out to be an illusion."

Should we feel chagrined if this indeed turns out to be the case? I don't think so. The lack of a theory of a quantum gravity may mean an end to efforts at unification, but it would indicate that the universe is much more diverse than we think. Unity and diversity contribute equally to the beauty of the cosmos. Darwin's theory is a perfect illustration of this fact; while providing a common mechanism for the evolution of species, it is also a testament to the astonishing variety of living creatures on our planet. If a unified theory of nature does turn out to be a pipe dream, we should celebrate the fact that whatever creating force was responsible for the evolution of the universe chose to make it more interesting than we imagined. The lack of a unifying theory would be a perfect embodiment of Haldane's quote that "the universe is not only queerer than we suppose but it's queerer than we can suppose". Our failure at finding a unified theory would only mean our success in discovering that the universe is an inexhaustible source of riches. For this we should be grateful.

The views expressed are those of the author and are not necessarily those of Scientific American.

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