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Section 9: Gravity: So Weak, Yet So Pervasive

The electromagnetic, strong, and weak interactions fit nicely into the Standard Model, and unify into a single theory at high temperatures. Gravity is still an outlier, in more ways than one. It is the first force to have a quantitative model thanks to Isaac Newton, and it happens to be the weakest force at the particle level. The electric force that binds a proton and electron into an atom is 10,000,000,000,000,000,000,000,000,000,000,000,000,000 (1040) times larger than the gravitational force that attracts them.

Despite its weakness, gravity has a significant impact at macroscopic distances because of one crucial unique feature: All matter has the same sign gravitational charge. The charge for the gravitational force is mass, or energy in the full theory of general relativity. The gravitational force between two massive particles is always positive and it always attracts. Thus, unlike say electromagnetism, in which opposite charges attract and can thus screen the long-distant effects, gravitational charge always adds, and large objects can produce large gravitational fields.

Schematic of a laser interferometer that can detect gravitational waves.

Figure 32: Schematic of a laser interferometer that can detect gravitational waves.

Source: © LIGO Laboratory. More info

General relativity, Einstein's theory of gravity and its current best description, works in effect as a theory of a gravitational field coupled to matter. In the full quantum theory, one would expect the existence of a particle associated with the field—the graviton—to be the force carrier. Nobody has yet detected an individual graviton. Nor is anyone likely to, owing to the extremely small likelihood that gravitons will interact with matter. However, astrophysicists have mounted several experiments to detect gravitational waves, which represent clusters of many gravitons. The most prominent, as we shall see in Unit 3, involve the use of lasers to measure how gravitational waves stretch space.

The graviton and gravitational coupling

In the absence of experimental evidence, theorists have devised a general picture of the graviton's characteristics. According to that picture, the graviton resembles the photon more closely than other force carriers, as it has no mass and is not confined at low energies, meaning that it can travel long distances freely. It is distinct from the photon in three ways. First, it is a spin-2 rather than spin-1 particle, though it still only comes in two types, analogous to left-handed and right-handed particles. Second, like the gluon, the graviton itself carries (gravitational) charge, in the form of energy (mass). Thus, gravitons attract each other. However, this does not lead to a constant force at arbitrarily long distances. The force still falls off with one over the square of the distance between objects as happens in QED. Third, while the QED coupling is a dimensionless number, the gravitational coupling to matter, Newton's constant, carries the dimensions of meters cubed divided by kilograms times seconds squared. The fact that it carries dimensions is important because it suggests that there is a fundamental mass, energy, length, and duration associated with gravity.

Physicists call the characteristic energy scale for gravity the "Planck scale," whose value is approximately 1019 GeV. Using a simple approximation to estimate the cross section, the probability of gravitational scattering of two particles at energy E would be proportional to E4/MPl4c8. At the energies the LHC will produce, that amounts to about 10-60—so small as to make it totally irrelevant. That means if a trillion LHCs were packed onto a trillion different planets and they ran for a trillion years, it would still be extremely unlikely for any of them to see the gravitational scattering of two particles.

Energies, sizes, and temperatures in physics, and in nature.

Figure 33: Energies, sizes, and temperatures in physics, and in nature.

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Thus, at energies of experimental particle physics, now and anytime in the foreseeable future, one can include gravitons in the Feynman diagram calculations, but their effect is negligible. However, it also suggests that for scattering close to the Planck energy, the gravitons become very important and cannot be neglected. In fact when the coupling (which could be interpreted as E/MPlc2) is large (much bigger than one), then the simplest Feynman diagrams are no longer the biggest, and one would in principle need to calculate an infinite number of diagrams. It is again the case that the theory becomes nonsense, and a new theory that incorporates quantum theory and Einstein's general relativity must be found. The leading candidate for such a theory is called "string theory," which will be explored in Unit 4.

If one were actually able to build a collider that could scatter particles at the Planck energy, then the simplest assumption, and prediction of general relativity, is that the two particles would form a particle-sized black hole. In a quantum theory, even a black hole will decay, as predicted by British physicist Stephen Hawking. One would in principle study those decays and hope information about the quantum theory of gravity was contained in the spectrum of particles that came out.

However, while a simple estimate points to the energy scale of 1019 GeV, we have never probed experimentally beyond energies of about 103 GeV. In fact, because gravity is so weak, we have not probed gravity beyond energy scales on the order of 10-2 eV, which corresponds to wavelengths or distances shorter than about 10 microns, which is one of the motivations for the ongoing experimental program exploring gravity at short distances described in Unit 3. Thus, while the Planck scale represents the first guess at and simplest picture of the region in which quantum gravity becomes strongly coupled, it may be wrong-headed to assume that Einstein's theory of gravity continues to work between 10 microns and 0.00000000000000000000000000001 microns, the Planck length. We will discuss alternatives at the end of this unit.