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Physics + MathPhysics & Math

Why Is Gravity Such a Weakling?

ByPaul HalpernThe Nature of RealityThe Nature of Reality

We think of gravity as weighty—its omnipresent grasp pulling us down to the ground. Try to lift a piano up a flight of stairs and you can feel gravity’s resistance. (

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Laurel and Hardy showed this best!) Yet in a match with the other fundamental forces of nature—electromagnetism, the weak force and the strong force—gravity gets pummeled.

You can see gravity’s relative weakness simply by using an ordinary bar magnet to pick up paper clips from a desk. Battling the gravitational pull of all of Earth, the tiny magnet wins! In fact, gravity is a staggering 10

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40 times weaker than electromagnetism. But why, among the fundamental forces, is gravity the runt of the litter? Explaining gravity’s relative feebleness is a profound challenge for physics, and an essential milestone on the road to a unified theory of all four forces.

Uniting the four fundamental forces into a single unified theory is a longstanding scientific dream. On the face of it, these forces are very different. They each operate across different distances, with different strengths, determined by the properties of a special class of particles, called “exchange particles,” whose job it is to convey the forces.

Exchange particles are like Frisbees thrown between particle players; the process of tossing the Frisbee brings ordinary particles together—or in some cases pushes them apart. In electromagnetism, for example, electrons interact by exchanging photons. Because the photons have no rest mass, they travel through the vacuum at the speed of light, making electromagnetism a long-range force. Long-range means that it can operate over great distances. For example, terrestrial receivers can pick up radio signals (a type of electromagnetic radiation) transmitted by Voyager 1, situated at the edge of the solar system more than 11 billion miles away. The weak force, in contrast, is conveyed by massive exchange particles called the W+, W- and Z bosons. Because these exchange particles are so heavy, particles feel the weak force only on very short ranges—within atomic nuclei. The strong force, too, operates only on short ranges. But gravity, which theorists believe is carried by particles called gravitons traveling at the speed of light, is a long-range force.

Physicists have made great strides toward unifying electromagnetism with the weak interaction and, to some extent, with the strong interaction, by looking at how the forces behave at very high energies—energies that existed just moments after the Big Bang. Theoretical and experimental discoveries of the past few decades suggest that at these energies—above about 100 GeV (gigaelectronvolts)—the weak and electromagnetic forces behave as a single type of interaction, called electroweak, with identical range and strength. During this brief, hot period, the “Frisbees” that convey the weak force had no mass at all. But as the universe cooled, interactions with the Higgs field caused the W+, W- and Z bosons to acquire mass, differentiating them from massless photons and splitting what was once one force, the electroweak force, into two, electromagnetism and the weak force.

Although physicists have yet to develop a “grand unified” model that includes the strong force, they believe that, at even higher energies, it too may merge with the weak and electromagnetic forces.

But what about gravity? If you could draw the evolutionary family tree of the physical forces, you might see the split between electromagnetism and the weak force as something like the division of primates into various species. Gravity, though, represents a far more radical diversification. Reconciling gravity along with the other forces is something like showing how viruses and whales have common ancestry. Spanning the differences is possible, but tricky.

How far up the energy scale must we climb to find a point at which gravity could be unified with the other forces? The answer is a number called the Planck energy: around 10 28 eV. That’s about 10 17 times greater than the energy of electroweak unification—an enormous difference. One would need a machine almost a quintillion times more powerful than the Large Hadron Collider or Fermilab’s (retired) Tevatron to probe the Planck energy, putting experimental tests of this kind of unification well out of reach for the conceivable future! The sheer magnitude of the Planck-to-electroweak energy ratio, related to the stark weakness of gravity, is called the hierarchy problem.

String theorists have proposed an innovative solution to the hierarchy problem: Perhaps gravity is weakened through its ability to travel across an extra dimension. What sounds like science fiction has become an active branch of scientific inquiry called the “braneworld hypothesis.” The braneworld hypothesis suggests that the observable universe lives within a four-dimensional (three dimensions of space and one dimension of time) membrane, or “brane.” Beyond this brane, extended along a fifth dimension, is a region called the “bulk.” Unique among exchange particles, gravitons are free to wander the bulk; everything else is stuck on our brane. So while most particles are like ants confined to the surface of a wooden picnic table (the brane), gravitons are like termites that can bore within (and visit) the bulk. (In the language of string theory, the difference is that gravitons are represented by closed strings; other particles are open strings and have ends that stick to our brane like a curved handle attached to a door.) Because photons cannot enter the bulk, it remains invisible.

An advantage of explaining gravity’s weakness through its dilution into the bulk and making the brane the venue for the other forces is that unification can take place at energies not much higher than the electroweak scale, rather than at the Planck scale, rendering the search for a unified theory much easier.

There are a number of variations of the braneworld idea. One model , proposed in 1998 by physicists Nima Arkani-Hamed, Savas Dimopoulos and Gia Dvali envisions a “large extra dimension” of about one millimeter throughout which gravity is spread. (String theorists are typically concerned with such tiny size scales that one millimeter does indeed qualify as “large.”) A second brane, parallel to ours, would constitute the opposite boundary of the bulk, confining gravitons to the region between the two limits. You can imagine this second brane as something like the underside of the picnic table. The extra dimension would then comprise the thickness of the table—the distance between its top and bottom—limiting the graviton “termites” to travel through a finite amount of wood.

However, this proposal modifies the law of gravity in measurable ways, which have since been ruled out experimentally. Another version , proposed by physicists Lisa Randall and Raman Sundrum, includes only one brane and posits that the warping of the structure of the bulk, along the direction of the extra dimension, would be enough to confine gravity to a limited region and dilute its strength. The theory predicts a measurable leakage of gravitons from our brane into the warped bulk, which could potentially be detected in collisions at the Large Hadron Collider through unexpected energy loss that finds no other explanation. Researchers have sought such telltale clues to test the Randall-Sundrum idea and other braneworld approaches. The tricky part is using statistical models to rule out more mundane effects that could mimic the leakage of energy (for example, the release of neutrinos). While LHC results have not yet confirmed the braneworld idea, the jury is still out as to whether or not gravity’s weakness is a result of its slick ability to leave the visible universe and travel through a higher dimension.

Go Deeper
Editor’s picks for further reading

CERN Courier: The Nobel path to a unified electroweak theory
In this article, CERN marks the anniversary of the 1979 Nobel Prize in physics, which honored the foundations of electroweak unification.

The Particle Adventure: What holds it together?
Explore the physics of force-carrying particles on this interactive web site.

Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions
In this book, physicist Lisa Randall explores extra dimensions, braneworlds, and the bulk.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.