Large Extra Dimensions (1998): Why Gravity Might Be So Weak

The ADD model, proposed in 1998 by Nima Arkani-Hamed, Savas Dimopoulos and Gia Dvali, suggested that gravity looks weak because it leaks into extra spatial dimensions that could be as large as a millimeter. Ordinary particles would stay stuck to our four-dimensional world while gravity spreads into the hidden space. The idea made extra dimensions testable.

What the paper found

• A new answer to the hierarchy problem. Gravity is vastly weaker than the other forces: its natural energy scale, the Planck scale of about 10¹⁹ GeV, sits far above the weak scale of about 100 GeV where the other forces meet. Explaining that gap is the hierarchy problem. The authors proposed that the true strength of gravity is comparable to the other forces at the weak scale, and only looks feeble to us because it is diluted in extra dimensions.
• At least two extra dimensions. With one extra dimension the scheme would require a dimension about 10¹³ centimeters across, roughly the size of the solar system, which would change gravity on planetary scales. That case is ruled out. With two or more, the dimensions can be small enough to have escaped every test.
• A millimeter-scale prediction. For two extra dimensions, their size comes out between about 100 micrometers and 1 millimeter. Below that distance, gravity between two masses would fall off as 1/r⁴ instead of Newton’s 1/r².
• Particles stuck to a surface. The particles and forces of the Standard Model must be confined to a four-dimensional “membrane” in the extra-dimensional space. Only gravity, carried by gravitons, travels freely into the extra dimensions.
• Collider signals. At the energies of the Large Hadron Collider, quantum gravity could become strong, and particles could be kicked off our membrane into the extra dimensions, carrying energy away unseen.

How they did it

The paper is theoretical. Its key relation connects the familiar strength of gravity to a more fundamental gravity scale in 4 + n dimensions and the size of the n extra dimensions. If the fundamental scale is set near the energy of the weak force, about a trillion electron volts (1 TeV), the equation tells you how large the extra dimensions must be. The authors then checked which sizes survive known experiments and sketched a concrete model in six dimensions.

Why it mattered

Before 1998, extra dimensions were usually assumed to be curled up at unimaginably small scales, as in Oskar Klein’s 1926 picture, and therefore untestable. ADD showed they could be large enough to affect experiments that were already being built. That turned a theoretical idea into a program for tabletop gravity tests and particle colliders.

It also prompted a rival proposal a year later: the warped extra dimension of Randall and Sundrum, which solves the same problem with a single small dimension. Both ideas trace back to Kaluza’s fifth dimension of 1921.

What we know now

No sign of large extra dimensions has been found, and the simplest versions are now tightly squeezed:

Test	Result	Source
Torsion balance, 2007	Inverse-square law holds down to 56 micrometers; an extra dimension must be smaller than 44 micrometers	Kapner et al., Phys. Rev. Lett. 98, 021101
Torsion balance, 2020	No deviation down to 52 micrometers; the largest extra dimension must have a radius below 30 micrometers	Lee et al. 2020
LHC, ATLAS monojet search, 2021	Fundamental gravity scale above 11.2 TeV for two extra dimensions, above 5.9 TeV for six	ATLAS 2021

Since the original motivation was a fundamental scale near 1 TeV, these limits have pushed the model away from its most natural form, though not ruled it out for larger numbers of dimensions. Gravitational-wave data constrain a different kind of extra dimension: GW170817 showed that gravitational waves are not leaking into large, uncompactified ones.

The full picture, separating what is established from what is speculative, is in our explainer on the fourth dimension and extra dimensions.

Who wrote it

Nima Arkani-Hamed and Savas Dimopoulos were at SLAC and Stanford University; Gia Dvali was at ICTP in Trieste. The model is known by the authors’ initials, ADD, and the scale it introduced, the fundamental gravity scale written M_D, is the quantity collider experiments still quote their limits on.

Read the original

Arkani-Hamed, N., Dimopoulos, S., and Dvali, G. (1998). “The hierarchy problem and new dimensions at a millimeter.” Physics Letters B 429, 263-272. DOI: 10.1016/S0370-2693(98)00466-3. Free to read on arXiv (hep-ph/9803315).