I’m a phenomenologist, which means I take my cues from experimental data rather than from first-principles theory. In my opinion, the most robust collection of data we have to guide particle physics research is the evidence for the existence of dark matter. Read on for some background on the implications of these measurements, and check out the other pages under “Research” for particular projects addressing these issues.

While my primary research direction has been dark matter for the past decade, I have become increasingly interested in studying neural networks from a theoretical physics perspective. These complex systems can perform feats that were unimaginable a decade ago, but their enormous number of parameters has made it difficult to understand their inner workings in an explainable way. However, the perspective of a phenomenologist is quite valuable here: the data comes from performing numerical experiments on ensembles of neural networks, all of which are governed by known microscopic laws (we wrote the code!), and we would like to build principled and predictive models to test our understanding. I think this is a very exciting area of research which is highly complementary to more traditional topics in particle physics, and brings in a lot of interdisciplinary collaborations, just like dark matter experiments do.

Dark Matter – beyond WIMPs

Of all the mass energy* in the universe, the particles comprising everything we’ve ever measured or observed directly — stars, planets, interstellar gas, all life on Earth — make up only 15% of the cosmic pie chart. The vast majority of the mass of the universe has only been observed indirectly, and has been dubbed dark matter. Despite this, the gravitational effects of dark matter are numerous and profound, and many independent measurements have all converged on a remarkably consistent story:

  • Rotation curves. By observing how fast stars rotate about the centers of their galaxies, we can infer how much total mass exists inside the galaxy. This is a fun calculation which uses only first-year physics and Newton’s Law of Gravity, and is the same calculation which determines the orbital radius of satellites traveling at a given speed, knowing the mass of the Earth. Lo and behold, the calculation tells us there is much more matter than we can observe through electromagnetic radiation (microwave, infrared, visible light, or X-rays), and amazingly, this “halo” of dark matter extends far beyond the last stars of the galaxy.
  • Structure formation. The universe has been expanding since the Big Bang, and hence all atoms have been flying apart from one another since they were created. So how did enough matter collect in one place to form galaxies, stars, and planets? Gravity makes things clump, and the more stuff there is in one place, the more other stuff tends to clump around it. Dark matter can provide the “seeds” for structure formation by clumping first, after which ordinary matter will be gravitationally attracted, eventually forming stars and galaxies. Without dark matter, the primordial nuclei would have been moving too fast to have time to clump. This is entirely consistent with the observed “halos” described above.
  • CMB power spectrum. The universe took a selfie at the tender young age of 380,000 years (that is, almost 14 billion years ago), and we now have the technology to develop the image. In the early universe, charged particles were so hot and dense that light couldn’t travel any appreciable distance before being deflected or absorbed. But once the universe had expanded and cooled sufficiently, light could travel unimpeded, and the “surface of last scattering” 380,000 years after the Big Bang is a snapshot formed by light escaping from this cosmic soup which we see today as the cosmic microwave background (CMB). Tiny temperature variations in these photons from different parts of the sky track density variations at that point in cosmic evolution: hotter photons means more stuff was there.** Dark matter’s distinctive property is that it carries mass but doesn’t interact with photons, so it contributes differently to the behavior of the CMB. Measurements of correlations between CMB temperatures at different points in the sky (the power spectrum) agree precisely with the presence of a significant component of dark matter, and allows us to determine that it makes up 82% of the mass of the universe.

In summary, dark matter is not an arbitrary fudge factor physicists have added to their equations to tweak some puzzling observations. It is a single ingredient which, in one fell swoop, explains vastly disparate properties of the universe from the earliest times until today, through independent measurements, in a consistent picture. This is the best kind of result in science: a theory that keeps on giving! Of course, not every observation agrees perfectly with the theory and work is still ongoing, but the broad picture is firmly in place.

The problem is, we know nothing about dark matter apart from the fact that it’s there. How much does it weigh? Does it interact with itself, or weakly with ordinary particles? Are there multiple species of dark matter, perhaps analogous to the proton, neutron, and electron which make up ordinary matter? Much effort has focused on a particular scenario: dark matter weighing about as much as an atomic nucleus, interacting with atomic nuclei via the weak nuclear force, and consisting of just a single particle species. This kind of dark matter is known as a WIMP, or “weakly-interacting massive particle,” and it’s a beautiful theory: with a minimal number of moving parts, it predicts exactly the right amount of dark matter, and is tied to both the Standard Model and supersymmetry. Alas, the simplest explanation is not guaranteed to be the correct one.  Dozens of experiments have searched for this particle — passing through the Earth, annihilating at the center of the galaxy, or being produced in particle colliders — to no avail. The WIMP scenario is certainly not ruled out, but it is becoming highly constrained.

I’m interested in exploring theories of dark matter beyond the WIMP: lighter particles (MeV-scale or sub-eV scale, in particle physics units), particles with different interactions (a dark photon rather than the weak nuclear force, or with electrons rather than nuclei), or multiple species of particles. Each of these theories would give different experimental signatures, and my research is focused on proposing experiments to look for these different kinds of dark matter. I’m especially drawn to the creativity and open-mindedness required to find just the right experimental avenue to detect these particles, and also to the possibility of collaboration between different fields of science (neutrino physics, condensed matter, physical chemistry, plasma physics, materials science) to develop the right equipment to build the experiment. I believe discovering the identity of dark matter is the most pressing question in particle physics which is likely to be resolved on a 50-year timescale, and I want to help cover all the bases in case dark matter is hiding in a place we least expected it.

*for the experts, I’m deliberately leaving out dark energy. My perspective is that the dark energy problem is not “what is dark energy?” but “why dark energy?” All observations are consistent with dark energy behaving like a cosmological constant, so its identity is not really in doubt. The harder questions are why the observed dark energy density is so fantastically small compared with theoretical expectations (the cosmological constant problem), and why it’s an order-1 fraction of the total energy density of the universe today, rather than being vanishingly small or completely dominant (the coincidence problem). I will leave these fascinating questions to the cosmologists, for the time being, and eagerly follow their progress.

**also for the experts, there are competing effects on the photon temperature: adiabatic perturbations work as advertised, but there is also the Sachs-Wolfe effect, where photons in overdense regions have to climb out of a deeper potential well and hence appear colder. Which effect dominates depends on the angular scale of the fluctuations. CMB physics is beautifully complicated!

Further reading

Machine Learning and Theoretical Physics

What is going on inside a neural network? Right now, very little is known: the tool works, so why ask too many questions? For one, if we would like to use these tools to do data analysis for physics experiments, we need to have some idea of the systematic uncertainties of the output with respect to the input parameters. Another important reason is that principles from physics, like Lorentz invariance, can be baked into the network architecture from the beginning, which is much more efficient than forcing the network to discover these symmetry principles from scratch each time it is trained on new data. Finally, there are many tantalizing analogies between neural networks and situations we encounter in all branches of physics. The interactions of a large number of entities which give rise to simple collective behavior is strongly reminiscent of statistical mechanics and condensed matter physics, and in many common situations, the equations by which the weights and biases are optimized are analogous to equations of motion from classical mechanics with stochastic force terms. Finally, physics data is qualitatively and quantitatively different from data “in the wild”, because it typically comes from manifolds, which are continuous spaces that you can put coordinates on. For example, I don’t know how to define the manifold of cat images, but a collection of elementary particles can always be described by a list of energies and momenta that define a point in Lorentz-invariant phase space.

All of these observations suggest that physicists may bring a unique perspective towards understanding neural network architectures and algorithms (“physics for AI”), while at the same time helping to develop new tools (or modify existing ones) for specific physics applications (“AI for physics”). This area is fertile ground for new explorations, and I am always on the lookout for new collaborations or interesting numerical experiments to try.

Further reading