Making your way to the cutting edge of any field is a daunting challenge. But especially when the edge of the field is expanding; and even harder still when the rate of expansion is accelerating. John recently helped *Physics World* create a special 25th anniversary issue where they identified the five biggest breakthroughs in physics over the past 25 years, and also the five biggest open questions.

***Neutrino Mass:** *surprisingly, **neutrinos have a nonzero mass, which provides a window into particle physics beyond the standard model. *THE STANDARD MODEL has been getting a lot of attention recently. This is well deserved in my opinion, considering that the vast majority of its predictions have come true, most of which were made by the end of the 1960s. Last year’s discovery of the Higgs Boson is the feather in its cap. However, it’s boring when things work too perfectly, because then we don’t know what path to continue on. That’s where the neutrino mass comes in. First, what are neutrinos? Neutrinos are a fundamental particle that have the special property that they barely interact with other particles. There are four fundamental forces in nature: electromagnetism, gravity, strong (holds quarks together to create neutrons and protons), and weak (responsible for radioactivity and nuclear fusion.) We can design experiments which allow us to observe neutrinos. We have learned that they are electrically neutral, so they aren’t affected by electromagnetism. They are barely affected by the strong force, if at all. They have an extremely small mass, so gravity acts on them only subtly. The main way in which they interact with their environment is through the weak force. Here’s the amazing thing: only really clunky versions of the standard model can allow for a nonzero neutrino mass! Hence, when a small but nonzero mass was experimentally established in 1998, we gained one of our first toeholds into particle physics beyond the standard model. This is particularly important today, because to the best of my knowledge, the LHC hasn’t yet discovered any other new physics beyond the standard model. The mechanism behind the neutrino mass is not yet understood. Moreover, neutrinos have a bunch of other bizarre properties which we understand empirically, but not their theoretical origins. The strangest of which goes by the name neutrino oscillations. In one sentence: there are three different kinds of neutrinos, and they can spontaneously transmute themselves from one type to another. This happens because physics is formulated in the language of mathematics, and the math says that the eigenstates corresponding to ‘flavors’ are not the same as the eigenstates corresponding to ‘mass.’ Words, words, words. Maybe the Caltech particle theory people should have a blog?

**Shor’s Algorithm:** *a quantum computer can factor N=1433301577 into 37811*37907 exponentially faster than a classical computer.* This result from Peter Shor in 1994 is near and dear to our quantum hearts. It opened the floodgates showing that there are tasks a quantum computer could perform exponentially faster than a classical computer, and therefore that we should get BIG$$$ from the world over in order to advance our field!! The task here is factoring large numbers into their prime factors; the difficulty of which has been the basis for many cryptographic protocols. In one sentence, Shor’s algorithm achieves this exponential speed-up because there is a step in the factoring algorithm (period finding) which can be performed in parallel via the quantum Fourier transform.

***Accelerating universe :** *the universe is expanding, and the rate of this expansion is increasing.* This result has been the source of an incredible number of misconceptions. First, how do we know this is happening? In the 1920s astronomers discovered that some of the really faint ‘stars’ that we see in the night sky are actually distant galaxies. Shortly thereafter, it was discovered that these galaxies are actually moving away from us, and away from each other. Astronomers had discovered that the universe is expanding. Now, remember that photons travel at a fixed speed, the speed of light. So the photons that hit our telescopes coming from a galaxy 1 billion light years away, have been traveling for approximately 1 billion years (you have to correct for the expanding universe, so yes, we make assumptions and build a model.) Also, type IA supernovas have the special property that different instantiations produce a consistent peak luminosity, so we can use this fact to accurately determine their distance. In 1998, by studying type IA supernovas, astronomers were able to compare the rate of expansion of the universe between galaxies of very different ages. From this, they learned that galaxies are moving away from each other much faster now, than billions of years ago, and therefore the rate of expansion is accelerating.

The question becomes, how does this happen? The short answer is that we don’t know, but we think the answer should be called “dark energy”, and we’ll talk about this below. Another thing to point out is that Einstein’s equations of general relativity naturally included a term () which retrospectively, appropriately describe the physics of an accelerating universe. Einstein and other physicists were famously unsettled by this term at the time. Another point is that there’s a whole web of interrelated ideas, which have tricky names, and this interplay oftentimes trips people up. Some of these ideas include: inflation, accelerating universe, cosmological constant, big bang, vacuum energy, dark energy, etc. Here is my CliffsNotes-style overview:

*The Big Bang.*The universe started somehow. It was probably some type of quantum fluctuation.*Inflation.*During the first few moments after the big bang, the universe, which is synonymous for a ‘spacetime manifold’, expanded INCREDIBLY RAPIDLY! This was a short-lived phenomenon and it is different than the ‘accelerating universe.’ One of the major surprises about this period of inflation is that, spacetime CAN expand FASTER THAN THE SPEED OF LIGHT! It’s like having a box, where anything that lives within the box has an upper bound on how fast it can travel, but the box itself can change sizes, and in particular, it can expand faster than the upper bound of local travel speeds for the particles within. I had nightmares as a child trying to reconcile these ideas. You can ask my mom, she’ll verify! These ideas start to make sense after you’re able to play with the FLRW metric. This has all kinds of crazy consequences about our observable universe and the cosmological horizon. Inflation is still speculative but it has made many experimentally verified predictions, most notably about the structure of the cosmic microwave background (CMB), and explains why the universe is so homogeneous, isotropic and flat. Another interesting question is, what is the global geometry of our universe?*Accelerating universe.*After the initial inflationary period, the universe continued to expand, and this rate of expansion has been increasing. This is very well tested experimentally. The mechanism for this has many different names: dark energy, the cosmological constant, vacuum energy, etc.

**Extrasolar Planets:** *over the past two decades, we have detected ~1000 planets outside of our own solar system. *As a prerequisite for finding extrasolar life–unless they find us first–we need to discover candidate homes. We’ve only had the capability to find planets outside of our solar system for the past two decades or so. The pace of these discoveries quickened as space based observatories like Kepler and COROT came online. The methods we use to detect exoplanets are extremely cool. Caltech is heavily involved in these efforts. Unfortunately, as of this past August, 2 out of 4 of Kepler’s reaction wheels are no longer operational. Here’s an idea for an ambitious Intel Science and Engineering Fair (ISEF) project: propose a new mission plan for Kepler. Bonus points if it involves finding exoplanets. Double word score if the mission gets flown. Triple word score if you find an exoplanet. You are my hero if there is life on said exoplanet.

***Higgs Boson: ***quantum field theory is hard to explain in one sentence. The Higgs “field” permeates all of space; excitations in this field are interpreted as particles (Higgs bosons); these particles give other particles mass. *What can I say that hasn’t been said infinitely more eloquently over the past month?

**Quantum Error Correction (QEC):** *we want to protect quantum information from noise.* We also face this challenge with classical computers. However, things are more difficult with quantum computers/information for at least two reasons. The no-cloning theorem tells us that we cannot copy unknown quantum information, which is a necessary step for many classical error correction protocols, such as encoding the bitstring 01011 into 000111000111111. We can’t do that with quantum information. It also turns out that our enemy is formidable: we are battling decoherence. One way to think about decoherence is that every quantum system interacts with its environment, creating entanglement between the two – since we can’t control the environment (it both large and unknown), we lost control of our quantum system. It’s hard to imagine a better place to learn about QEC than from John’s notes. These ideas are also starting to infiltrate other areas of physics, such as the way that people think about black holes.

**Topological Insulators (TIs): ***we’ve known for a long time that **solids, liquids, gases and plasmas aren’t the only phases of matter; but only recently, we’ve unexpectedly discovered a huge new class of phases. *How can you distinguish different phases of matter, such as: liquids from solids; ferromagnets from antiferromagnets; or nematic liquid crystals from smectic liquid crystals? This is a tricky problem and you should think about it the next time you fly cross country on an airplane! However, for the phases mentioned above, there is a nice classification simply based upon local observations. Imagine putting each of these materials under a microscope. You can differentiate the phases simply via the local observations you get from looking through the window. For example, in its liquid phase, H2O molecules are densely packed, but in a random fashion. In its solid phase, the H2O molecules are densely packed, but arranged in a regular crystalline pattern. Before topological phases, we classified phases based upon their local symmetries. In the early 1980s, experimentalists discovered quantum hall systems, which were the first materials whose ground states couldn’t be differentiated by only using a local description. Entanglement allows different phases to look the same locally, even though they are different globally. It’s kind of like an ant trying to tell you whether it lives on a mobius strip or a simple chain. The ‘phases of matter can’ had a few dents in it, but the lid was blown sky-high when topological Insulators were discovered in 2006. These materials have bizarre properties; they provide the foundation for a multitude of cousin systems; they are shedding light on questions from fundamental physics; and they will probably be widely utilized in the electronics of the 21st century. Topological insulators can be constructed from certain homogeneous slabs of material, such as bismuth telluride. Imagine a cube of this material. Despite having a homogenous composition, the cube would be electrically insulating on the interior, but conductive on the surface. Moreover, the mechanism for how electric charge is carried on the surface is different than in conventional insulators. Namely, it is SYMMETRY protected, and this makes it so that charge carrying particles don’t want to scatter off of impurities. This is one of dozens of properties that makes these materials interesting.

**AdS/CFT:** *there is a mapping between gravitational problems in n+1-dimensions and critical quantum system in n-dimensions; maybe the universe is holographic? *This is one of my personal favorites, and something that I’ve devoted the past few months towards understanding. These ideas are incredibly deep and mathematical, but I’d like to argue through analogy. Imagine you are sitting on a balcony in Malibu, CA overlooking the vast Pacific Ocean (I was asked about this at a 4th of July BBQ and that’s how I came up with this analogy.) By only looking at the surface, how much do you think you could predict about the complicated fluid dynamics below? Obviously, you wouldn’t have enough information to predict the behavior of the biology, and we know that jellyfish, for example, move tons of water. However, I’d argue that with complete enough information about the surface waves and a powerful enough computer, you’d be able to solve the corresponding inverse problem and learn quite a bit. AdS/CFT, which sometimes gets called the holographic principle, is basically a mathematical toolkit which says that in certain situations, there is an exact correspondence between gravity problems in n+1-dimensions and strongly correlated electron systems in n-dimensions. Sometimes it’s easier to think about black holes in two spatial dimensions + time, or to think about electrons living in a system undergoing a phase transition in two dimensions (such as the fractional quantum hall system or superfluids.) AdS/CFT provides a mapping which allows you to convert problems back and forth between these settings. String theorists and the black hole information community originally came up with these ideas, but they are also connected to many other areas of physics.

Here is an example of how holography has been useful. The concept of entropy has been remarkably successful and has permeated many areas of science: from the second law of thermodynamics to designing codes used in computers. However, entropy is usually defined in terms of closed systems, and when dealing with quantum mechanics, entanglement implies that systems are very rarely closed. This has made generalizing the ideas of entropy to quantum systems very difficult. We call this generalization ‘entanglement entropy’. It’s easy to write down the definition, but exact calculations have only been carried out in a handful of settings, and mainly only when the tools of conformal field theory can be brought to bear. However, Ryu and Takayanagi conjectured that there is a geometric interpretation, called holographic entanglement entropy, which is oftentimes extremely easy to compute. Faulkner, Lewkowycz and Maldacena recently showed that Ryu and Takayanagi’s conjecture isn’t exactly right in all settings, but these holographic ideas are still very powerful. Entanglement entropy is also related to other deep ideas from the past 25 years or so, such as the c and a-theorems.

***Bose Einstein Condensates (BECs):** *quantum experiments that we can see with our eyeballs (more factually, by looking at images from microscopes.) *People all over the place are constantly talking about how weird quantum mechanics is. Hence, building systems where we can see quantum effects with our eyeballs is incredibly helpful. How do BECs work? Here are a few stepping stones. First, I mentioned above that symmetry is incredibly important in physics. For example, point particles (perfect spheres), have rotational symmetry. We then plug this fact into the mathematical machinery involved with quantizing a classical theory, and this rotational symmetry gets turned into a ‘representation theoretic‘ fact that particles have ‘spin.’ Every particle has a spin number associated to it. These numbers are integers or half integers. We call particles with integer spin bosons, and half integer spin fermions. The spin-statistics theorem then tells us that bosonic particles can stack on top of each other, as many as we’d like. On the other hand, no two identical Fermions can occupy the same region of space. BECs are a laboratory demonstration of our predictions about bosons. One of the original BEC experiments involved cooling thousands of Rubidium atoms to extremely low temperatures (a few nanokelvin above absolute zero), at which point their behavior is described by quantum mechanics. The Rubidium atoms behave as predicted, where the thousands of atoms coalesce into a very small area. Moreover, the Heisenberg uncertainty principle tells us that we cannot know BOTH the atoms’ exact locations and momenta, so the atoms are localized, but also moving at a slow speed. This interplay is right up against the limits provided by the Heisenberg uncertainty principle.

***Quantum Teleportation:** *using off-the-shelf quantum and classical resources, and strategically positioning them in advance of a task, we can then teleport custom quantum states anywhere in the universe, only governed by our ability to send pulses of laser light to the same location. *I’ve already written a series of blog posts about this! Why is this amazing? Well, teleportation would certainly be amazing, but that’s a bit of a misnomer, and a point I tried to clarify in my posts. Quantum teleportation IS NOT an all-purpose teleportation protocol. But it is incredibly awesome, and will undoubtably have major technological significance someday. Basically, it’s easy to send photons all over the universe (we are very good at building and operating lasers), but it’s very hard to send more exotic forms of matter, especially when the matter is supposed to stay in a specific quantum state. Quantum teleportation allows us to first spread entangled matter throughout space. Then, at a later time, we can exploit this resource to move delicate quantum states to the location of our entangled matter. Better yet, we don’t need to use quantum information in order to do this, we can simply send a classical signal describing the outcome of a measurement at the base station (00, 01, 10 or 11). Another reason why quantum teleportation is so important, is because it’s one of those rare revolutionary ideas, from which thousands of other amazing ideas have been built. It’s counterintuitive, but it works, and we do experiments verifying this on a regular basis.