The academic year just started at Harvard University. As I entered the classroom, it was humming with many new students. The class I teach this semester is the only mandatory class for all graduate students at the Harvard Astronomy department. But there were three times more students, including undergraduates as well as students from the Harvard Chemistry and Physics departments and other universities, such as MIT.
The class, titled “Radiative Processes in Astrophysics,” covers the fundamentals of electromagnetism which are essential for interpreting the data we collect from observations of the Universe through telescopes. Just over the past decade, astronomers started using a new non-electromagnetic messenger from the cosmic horizon, namely gravitational waves sourced by the collisions of black holes.
Gravity allows us to detect dark objects such as black holes or dark matter. I disclosed to the students that everything to be discussed in my class applies to merely 15% of the cosmic matter budget, because dark matter does not interact with light. Humans are made of atoms of ordinary matter that interact electromagnetically, and so we naturally care about this sector of the cosmic mass budget the most. One can imagine a classroom with students made of dark matter, where the instructor teaches a completely different mandatory class about the dark sector. Since the attendees of this hypothetical class represent 85% of cosmic matter, they deserve more credit than I do for describing most of the Universe.
I started by mentioning that the electric repulsion between protons is 36 orders of magnitude larger than their gravitational attraction. Why is it then that gravity dominates the scene on cosmic scales? The answer is simple: protons and electrons have positive and negative charges that screen each other, whereas gravity is only sourced by positive masses. Incidentally, if there were negative masses, we could have built a time machine.
After defining radiation intensity, energy density and pressure, I explained that pressure is force per unit area. A knife is simply a device that transmits the force from our hand to a tiny area at its sharp edge until the pressure exceeds the material strength of the material it cuts.
Then I went on to mention five surprising coincidences:
(i) The pressure of an isotropic radiation field is one third of the energy density because we live in three spatial dimensions. If we had lived in four dimensions, radiation pressure would have been a quarter of the energy density.
(ii) Our eyes are sensitive to visible light because survival of the fittest implies using the most abundant photons sprayed on Earth by the Sun. If we had lived near a black hole, natural selection would have favored X-ray eyes.
(iii) The cross-section per unit mass for scattering light by free electrons and protons follows the “rule-of-thumb”: it is 0.4 centimeter-squared per gram, similar to the area per unit mass of a thumb. By coincidence, this also happens to be the inverse of the mass per unit area of matter throughout the Universe, out to when the first generation of galaxies formed. Gladly, 85% of the cosmic mass budget is dark matter which does not scatter light and allows the Webb telescope to observe the first galaxies. If all cosmic matter was free electrons and protons, the images of the first galaxies would have been hidden behind a dense fog that scatters light. A gram per centimeter squared is also the critical mass per unit area needed to produce multiple images by gravitational lensing across cosmological distances. The inner parts of galaxies have exactly this mass per unit area, making them gravitational lenses.
(iv) Intensity is constant along a light ray. This is a manifestation of the conservation of phase-space density, in line with Heisenberg’s Uncertainty Principle of quantum mechanics where phase space volume is discretized into cubes of Planck’s constant in size. Photons are social particles (Bosons) and prefer to occupy the same phase-space state, as in the case of a laser. Many of them with the same frequency and phase make for a classical electromagnetic wave.
(v) Without Heisenberg’s Principle, atoms would not have had their characteristic size. Newtonian gravity allows for the Earth to get arbitrarily close to the Sun because reducing the Earth’s orbital radius by some factor does not increase the Earth’s velocity by the same factor. The Earth is a classical object with a momentum and spatial extent whose product is huge compared to the Planck constant. In contrast, an electron becomes unbound if it is localized to a smaller region than the Bohr radius around a proton. This radius defines the size of a hydrogen atom.
The study of hydrogen has been a long tradition at Harvard. Theodore Lyman IV discovered in 1906 the Lyman series of spectral lines of the hydrogen atom. The tradition continued with Cecilia Payne-Gaposchkin who discovered in her 1925 PhD thesis that the most abundant chemical element on the surface of the Sun (and as it turns out, the Universe!) is hydrogen. Later, Ed Purcell and George Field laid the foundation for what is now called “21-centimeter cosmology”, namely the use of a spin-flip spectral line of hydrogen with a wavelength of 21-centimeter to map the three-dimensional distribution of hydrogen atoms throughout the Universe. Ed, with Doc Ewen, by virtue of discovering the Milky-Way’s 21-centimeter signal from a window in the Physics department in 1951, and George by deriving the relevant physics (including the role of Lyman-alpha photons in coupling the spin temperature to the kinetic temperature) in the context of the intergalactic medium.
As the final item in my class, I derived the radiative transfer equation which is foundational not only to the 21-centimeter signal but also the propagation of radiation through any medium. The Sun, for example, is a nuclear fusion reactor held together by gravity. Its core produces primarily X-rays, and the radiation propagates to the surface from where it escapes to space. Why is the Sun emitting visible light, similar to that of a candle, when its core emits mostly X-rays?
The answer can be found by solving the radiative. Transfer equation. The Sun is opaque and we can see only its outer skin. The radiation is processed through scattering and absorption in the solar interior, but from outside we can only see its outer surface at a temperature of 5,800 degrees Kelvin.
The same is true about looking back into the Universe. As we look farther away, we probe the Universe when it was younger. We cannot see through to earlier than 400,000 years after the Big Bang (or equivalently a cosmological redshift above 1,100) because the denser Universe was opaque at earlier times. We are therefore surrounded by a cosmic photosphere at 3,000 degrees Kelvin, comparable to the temperature of the photosphere of the Sun or the flame of a candle. The only difference is that the cosmic photosphere surrounds us in a spherical shell, as we were embedded in a cosmic womb. This defines the finite volume of space that we can see. What lies beyond our cosmic horizon is a matter of speculation.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, was published in August 2023.
