The Gravitational Harmony of Quantum Fields

These three terms are all interconnected in my head. While I was about to quit Grad school in theoretical physics, I stumbled across a quantum field theory book on a classmate's desk which, upon reading the introduction, enticed me to finish up. Let me paraphrase the beginning of the book's intro: "The new paradigm of physics describes the totality of nature as an ensemble vibrating fields that interact with each other… in that sense the universe is like an orchestra and we are a result of eons of harmonies, rhythm and improvisation" (I added in the improvisation part). It helped that I was also a student of jazz theory at the time.

As I continued to study quantum field theory over the years (and now teach the subject), I am amazed at the concise parallels between the quantum field paradigm of nature, music and improvisation. Connected to this theme is one of the coolest things I've learned; an idea that was pioneered by a true master in quantum field theory, Leonard Parker. The basic idea is that when we combine Einstein's discovery that the gravitational force arises from the curving of spacetime with the field paradigm of matter we get a very neat physical effect—which underlies Stephen Hawking's information loss paradox and the emergence of matter from the early universe that is devoid of stars and galaxies.

Last month I had the pleasure to finally meet Parker at the University of Wisconsin, Milwaukee. After a seminar on gravitational wave physics, Leonard took me to his office and revealed the pioneering calculations in his PhD dissertation, which established the study of quantum fields in curved spacetime—I'll refer to the effect as the Parker Process.

In quantum field theory, we can think of all matter as a field (similar to the electromagnetic field) that permeates a large region of space. A useful picture is to imagine a smooth blanket of magnetic fields that fills our entire galaxy (which is actually true). Likewise the electron also has a field that can be distributed across regions of space. At this stage, the field is "classical", since it is a smooth, continuous distribution.

To speak of a quantized field means that we can imagine that if the field vibrates, only discrete bundles (quanta) of vibration are allowed, like an individual musical note on a guitar. The quanta of the field are identified with the creation (or annihilation) of a particle. Quantum field theory has new features that classical field theories lack; perhaps the most important one is the notion of the vacuum. The vacuum is a situation where no particles exist, but one can "disturb" the vacuum and create particles by "exciting" the field (usually with an interaction). It is important to know that the vacuum depends on the space-time location of an observer who can measure no particles.

On the other hand we know from General relativity, space-time is curved and observers don't see the same curvature at different places in general. What Parker realized was that in space-times of cosmological interest, such our expanding universe that Hubble discovered, that existed in a state of zero particles would create particles at a later time due to the very expansion of the space. We can think of this effect occurring because of the wave-like nature of particles (a quantum effect).

The quantum matter fields that live in the vacuum also interact with the expanding space-time field (the gravitational field). The expansion acts on the vacuum in a manner that "squeezes" particle quanta out of the vacuum. It is this quantum-field effect, which is used to explain the seeds of stars, and galaxies that now exist in the universe. Similarly, when black holes evaporate, the space-time also becomes time-dependent and particles are created, but this time as a thermal bath of matter/radiation. This physical feature of quantum fields in curved spaces raise the philosophical questions about the observer dependence of particles or the lack of them.

As you read these words, don't try to imagine some strange observer in some far region of the universe that will swear that you don't exist; and don't blame it on Leonard.