Warped Passages - Lisa Randall [138]
General relativity works only when there are smooth gravitational fields encoded in a gradually curving spacetime. But quantum mechanics tells us that anything that can probe or influence the Planck scale length has huge momentum uncertainty. A probe with sufficient energy to probe the Planck scale length would induce disruptive dynamical processes, such as energetic eruptions of virtual particles, that would dash any hope of a general relativity description. According to quantum mechanics, at the Planck scale length, instead of a gradually undulating geometry, there should be wild fluctuations and loops and handles of spacetime branching off, the sort of topography that the futuristic Ike encountered. General relativity cannot be used in such untamed territory.
Nor does general relativity step aside to give quantum mechanics free rein, for at the Planck scale length gravity exerts a substantial force. Although gravity is feeble at the particle physics energies we are accustomed to, it is enormously powerful at the high energies required to explore the Planck scale length.* The Planck scale energy—the energy needed to explore the Planck scale length—is exactly the energy at which gravity is no longer dismissible as a feeble force. At the Planck scale length, gravity cannot be ignored.
In fact, at the Planck scale energy, gravity constructs barriers that make conventional quantum mechanical calculations impossible. Anything sufficiently energetic to probe 10-33 cm would be snapped up into a black hole that imprisons whatever enters. Only a quantum theory of gravity can tell us what is really going on inside.
At tiny distances, quantum mechanics and gravity cry out for a more fundamental theory. Given the conflict between them, there is no choice but to bring in an external arbiter as an alternative to both. The new regime must allow quantum mechanics and general relativity free rein in their undisputed home territories, but have adequate authority to govern the disputed region where neither of the older theories is in control. String theory might be the answer.
The incompatibility of quantum mechanics and gravity also reveals itself through conventional gravity’s nonsensical predictions for the high-energy interactions of a particle called the graviton—the particle that communicates the gravitational force in a quantum theory of gravity.
According to classical gravitational theory, gravity is communicated between massive objects through a gravitational field in much the same way that, according to Maxwell’s classical electromagnetic theory, electromagnetism is communicated from one charged particle to another via a classical electromagnetic field. But quantum electrodynamics (QED), the quantum field theory of electromagnetism, reinterprets this classical electromagnetic force in terms of the exchange of a particle, the photon.* QED, the theory of the photon, is the extension of the classical theory of electromagnetism that incorporates quantum mechanical effects.
Quantum mechanics dictates that, similarly, there must be a particle to transmit the gravitational force. That particle is the graviton. In a quantum theory of gravity, the exchange of a graviton between two objects reproduces Newton’s law of gravitational attraction. Although gravitons have not been directly observed, physicists believe that they exist because quantum mechanics tells us they do.
Later on, the distinctive spin of the graviton will be important to us. Because gravitons communicate gravity, a force inherently connected with space and time, they have a different spin from all other known force carriers such as the photon. We will not delve into the reasons here, but the graviton is the only known massless particle whose spin is 2—not 1, as for other gauge bosons, or ½, as for quarks and leptons. The fact that it has spin-2 is important when it comes to finding convincing evidence of extra-dimensional theories. And, as we will soon see, the graviton’s spin was also the key to recognizing string