How we explore unanswered questions in physics

James Beacham: How we explore unanswered questions in physics


There is something about physics that has been really bothering me since I was a little kid. And it’s related to a question that scientists have been asking for almost 100 years, with no answer. How do the smallest things in nature, the particles of the quantum world, match up with the largest things in nature — planets and stars and galaxies held together by gravity?
As a kid, I would puzzle over questions just like this. I would fiddle around with microscopes and electromagnets, and I would read about the forces of the small and about quantum mechanics and I would marvel at how well that description matched up to our observation. Then I would look at the stars, and I would read about how well we understand gravity, and I would think surely, there must be some elegant way that these two systems match up. But there’s not. And the books would say, yeah, we understand a lot about these two realms separately, but when we try to link them mathematically, everything breaks.
And for 100 years, none of our ideas as to how to solve this basically physics disaster, has ever been supported by evidence. And to little old me — little, curious, skeptical James — this was a supremely unsatisfying answer.
So, I’m still a skeptical little kid. Flash-forward now to December of 2015, when I found myself smack in the middle of the physics world being flipped on its head. It all started when we at CERN saw something intriguing in our data: a hint of a new particle, an inkling of a possibly extraordinary answer to this question.
So I’m still a skeptical little kid, I think, but I’m also now a particle hunter. I am a physicist at CERN’s Large Hadron Collider, the largest science experiment ever mounted. It’s a 27-kilometer tunnel on the border of France and Switzerland buried 100 meters underground. And in this tunnel, we use superconducting magnets colder than outer space to accelerate protons to almost the speed of light and slam them into each other millions of times per second, collecting the debris of these collisions to search for new, undiscovered fundamental particles. Its design and construction took decades of work by thousands of physicists from around the globe, and in the summer of 2015, we had been working tirelessly to switch on the LHC at the highest energy that humans have ever used in a collider experiment.
Now, higher energy is important because for particles, there is an equivalence between energy and particle mass, and mass is just a number put there by nature. To discover new particles, we need to reach these bigger numbers. And to do that, we have to build a bigger, higher energy collider, and the biggest, highest energy collider in the world is the Large Hadron Collider. And then, we collide protons quadrillions of times, and we collect this data very slowly, over months and months. And then new particles might show up in our data as bumps — slight deviations from what you expect, little clusters of data points that make a smooth line not so smooth. For example, this bump, after months of data-taking in 2012, led to the discovery of the Higgs particle — the Higgs boson — and to a Nobel Prize for the confirmation of its existence.
This jump up in energy in 2015 represented the best chance that we as a species had ever had of discovering new particles — new answers to these long-standing questions, because it was almost twice as much energy as we used when we discovered the Higgs boson. Many of my colleagues had been working their entire careers for this moment, and frankly, to little curious me, this was the moment I’d been waiting for my entire life. So 2015 was go time.
So June 2015, the LHC is switched back on. My colleagues and I held our breath and bit our fingernails, and then finally we saw the first proton collisions at this highest energy ever. Applause, champagne, celebration. This was a milestone for science, and we had no idea what we would find in this brand-new data. And then a few weeks later, we found a bump. It wasn’t a very big bump, but it was big enough to make you raise your eyebrow. But on a scale of one to 10 for eyebrow raises, if 10 indicates that you’ve discovered a new particle, this eyebrow raise is about a four.
I spent hours, days, weeks in secret meetings, arguing with my colleagues over this little bump, poking and prodding it with our most ruthless experimental sticks to see if it would withstand scrutiny. But even after months of working feverishly — sleeping in our offices and not going home, candy bars for dinner, coffee by the bucketful — physicists are machines for turning coffee into diagrams —
This little bump would not go away. So after a few months, we presented our little bump to the world with a very clear message: this little bump is interesting but it’s not definitive, so let’s keep an eye on it as we take more data. So we were trying to be extremely cool about it.
And the world ran with it anyway. The news loved it. People said it reminded them of the little bump that was shown on the way toward the Higgs boson discovery. Better than that, my theorist colleagues — I love my theorist colleagues — my theorist colleagues wrote 500 papers about this little bump.
The world of particle physics had been flipped on its head. But what was it about this particular bump that caused thousands of physicists to collectively lose their cool? This little bump was unique. This little bump indicated that we were seeing an unexpectedly large number of collisions whose debris consisted of only two photons, two particles of light. And that’s rare.
Particle collisions are not like automobile collisions. They have different rules. When two particles collide at almost the speed of light, the quantum world takes over. And in the quantum world, these two particles can briefly create a new particle that lives for a tiny fraction of a second before splitting into other particles that hit our detector. Imagine a car collision where the two cars vanish upon impact, a bicycle appears in their place —
And then that bicycle explodes into two skateboards, which hit our detector.
Hopefully, not literally. They’re very expensive.
Events where only two photons hit out detector are very rare. And because of the special quantum properties of photons, there’s a very small number of possible new particles — these mythical bicycles — that can give birth to only two photons. But one of these options is huge, and it has to do with that long-standing question that bothered me as a tiny little kid, about gravity.
Gravity may seem super strong to you, but it’s actually crazily weak compared to the other forces of nature. I can briefly beat gravity when I jump, but I can’t pick a proton out of my hand. The strength of gravity compared to the other forces of nature? It’s 10 to the minus 39. That’s a decimal with 39 zeros after it.
Worse than that, all of the other known forces of nature are perfectly described by this thing we call the Standard Model, which is our current best description of nature at its smallest scales, and quite frankly, one of the most successful achievements of humankind — except for gravity, which is absent from the Standard Model. It’s crazy. It’s almost as though most of gravity has gone missing. We feel a little bit of it, but where’s the rest of it? No one knows.
But one theoretical explanation proposes a wild solution. You and I — even you in the back — we live in three dimensions of space. I hope that’s a non-controversial statement.
All of the known particles also live in three dimensions of space. In fact, a particle is just another name for an excitation in a three-dimensional field; a localized wobbling in space. More importantly, all the math that we use to describe all this stuff assumes that there are only three dimensions of space. But math is math, and we can play around with our math however we want. And people have been playing around with extra dimensions of space for a very long time, but it’s always been an abstract mathematical concept. I mean, just look around you — you at the back, look around — there’s clearly only three dimensions of space.
But what if that’s not true? What if the missing gravity is leaking into an extra-spatial dimension that’s invisible to you and I? What if gravity is just as strong as the other forces if you were to view it in this extra-spatial dimension, and what you and I experience is a tiny slice of gravity make it seem very weak? If this were true, we would have to expand our Standard Model of particles to include an extra particle, a hyperdimensional particle of gravity, a special graviton that lives in extra-spatial dimensions.
I see the looks on your faces. You should be asking me the question, “How in the world are we going to test this crazy, science fiction idea, stuck as we are in three dimensions?” The way we always do, by slamming together two protons —
Hard enough that the collision reverberates into any extra-spatial dimensions that might be there, momentarily creating this hyperdimensional graviton that then snaps back into the three dimensions of the LHC and spits off two photons, two particles of light. And this hypothetical, extra-dimensional graviton is one of the only possible, hypothetical new particles that has the special quantum properties that could give birth to our little, two-photon bump.
So, the possibility of explaining the mysteries of gravity and of discovering extra dimensions of space — perhaps now you get a sense as to why thousands of physics geeks collectively lost their cool over our little, two-photon bump. A discovery of this type would rewrite the textbooks. But remember, the message from us experimentalists that actually were doing this work at the time, was very clear: we need more data. With more data, the little bump will either turn into a nice, crisp Nobel Prize —
Or the extra data will fill in the space around the bump and turn it into a nice, smooth line.
So we took more data, and with five times the data, several months later, our little bump turned into a smooth line. The news reported on a “huge disappointment,” on “faded hopes,” and on particle physicists “being sad.” Given the tone of the coverage, you’d think that we had decided to shut down the LHC and go home.
But that’s not what we did. But why not? I mean, if I didn’t discover a particle — and I didn’t — if I didn’t discover a particle, why am I here talking to you? Why didn’t I just hang my head in shame and go home?
Particle physicists are explorers. And very much of what we do is cartography. Let me put it this way: forget about the LHC for a second. Imagine you are a space explorer arriving at a distant planet, searching for aliens. What is your first task? To immediately orbit the planet, land, take a quick look around for any big, obvious signs of life, and report back to home base. That’s the stage we’re at now. We took a first look at the LHC for any new, big, obvious-to-spot particles, and we can report that there are none. We saw a weird-looking alien bump on a distant mountain, but once we got closer, we saw it was a rock.
But then what do we do? Do we just give up and fly away? Absolutely not; we would be terrible scientists if we did. No, we spend the next couple of decades exploring, mapping out the territory, sifting through the sand with a fine instrument, peeking under every stone, drilling under the surface. New particles can either show up immediately as big, obvious-to-spot bumps, or they can only reveal themselves after years of data taking.
Humanity has just begun its exploration at the LHC at this big high energy, and we have much searching to do. But what if, even after 10 or 20 years, we still find no new particles? We build a bigger machine.
We search at higher energies. We search at higher energies. Planning is already underway for a 100-kilometer tunnel that will collide particles at 10 times the energy of the LHC. We don’t decide where nature places new particles. We only decide to keep exploring. But what if, even after a 100-kilometer tunnel or a 500-kilometer tunnel or a 10,000-kilometer collider floating in space between the Earth and the Moon, we still find no new particles? Then perhaps we’re doing particle physics wrong.
Perhaps we need to rethink things. Maybe we need more resources, technology, expertise than what we currently have. We already use artificial intelligence and machine learning techniques in parts of the LHC, but imagine designing a particle physics experiment using such sophisticated algorithms that it could teach itself to discover a hyperdimensional graviton.
But what if? What if the ultimate question: What if even artificial intelligence can’t help us answer our questions? What if these open questions, for centuries, are destined to be unanswered for the foreseeable future? What if the stuff that’s bothered me since I was a little kid is destined to be unanswered in my lifetime? Then that … will be even more fascinating.
We will be forced to think in completely new ways. We’ll have to go back to our assumptions, and determine if there was a flaw somewhere. And we’ll need to encourage more people to join us in studying science since we need fresh eyes on these century-old problems. I don’t have the answers, and I’m still searching for them. But someone — maybe she’s in school right now, maybe she’s not even born yet — could eventually guide us to see physics in a completely new way, and to point out that perhaps we’re just asking the wrong questions. Which would not be the end of physics, but a novel beginning.
Thank you.


“We understand a lot about [quantum mechanics and gravity] separately, but when we try to link them mathematically, everything breaks.”

Quantum field theory describes, shockingly well, the realm of particles moving at near the speed of light, and general relativity is our mind-bendingly good description of gravity at the scales of planets and galaxies (the predictions of which are still being successfully confirmed, such as the first observation of gravitational waves by the LIGO and Virgo collaborations in 2016), but the quest for — and lack of — a coherent description of quantum gravity that’s supported by experimental evidence has been keeping physicists awake at night for decades. Sabine Hossenfelder wrote a good description of the problem for PBS, called, “Why Quantize Gravity?”

“CERN’s Large Hadron Collider”

The LHC is the biggest experimental project at CERN, and is a search for evidence of physics beyond the Standard Model, such as dark matter, quantum black holes, extra dimensions, supersymmetry, and exotic Higgs bosons, among other research goals. The animation used in the talk can be seen here, and a different version with more detail is here

“superconducting magnets colder than outer space”

The LHC electromagnets attain the special property of superconductivity — the only thing that enables us to bend protons around the 27-km tunnel at such speeds — when we cool them down to 1.9 K, colder than the 2.7 K of outer space. We suspect that this makes the LHC the coldest extended object in the universe.

“collecting the debris with huge detectors”

There are four large experiments on the LHC ring, ATLAS, CMS, LHCb, and ALICE, and two smaller ones, LHCf and TOTEM. Huge means huge. For example, ATLAS is buried 100 meters underground and is six stories high and 40 meters long.

“Its design and construction took decades of work by thousands of physicists from around the globe.”

CERN is truly a worldwide science project, encompassing women and men of all races, languages, physical abilities and sexual orientations, around 12,000 scientists from over 70 countries and 120 different nationalities.

“the highest energy humans have ever used in a collider”

In 2015 the LHC began colliding protons at 13 TeV, a much higher center-of-mass energy than we particle physicists have ever used in a laboratory setting, but much, much lower than what nature achieves all the time with cosmic ray collisions. We would love to use a beam of ultra-high energy cosmic rays under controlled laboratory conditions, but it’s beyond the scope of humanity at the moment.

“an equivalence between collider energy and particle mass, and mass is just a number put there by nature”

In particle physics, energy and rest mass are two sides of the same coin, related by Einstein’s famous equivalence relation, E = mc^2, and wonderfully described by my colleague Matt Strassler.

“2012 led to the discovery of the Higgs particle and to a Nobel prize for the confirmation of its existence”

The Higgs boson was the last missing piece of our wildly successful Standard Model of particle physics, and its discovery was announced by the ATLAS and CMS collaborations in July of 2012 and published later that year. It was predicted in the 1960s as a consequence of something called spontaneous electroweak symmetry breaking, a necessary ingredient of the Standard Model. But the problem was that the Standard Model didn’t predict the mass of the Higgs boson. Thus, we simply had to explore higher energies until we found it or something that did its job in the Standard Model. After the discovery, the 2013 Nobel Prize in Physics was awarded to theorists François Englert and Peter Higgs, while the 2010 J.J. Sakurai Prize had been awarded to them and to T. W. B. Kibble, Gerald S. Guralnik, Carl R. Hagen, and Robert Brout, the others responsible for the development of the mechanism that predicted the particle.

“almost twice as much energy as we used when we discovered the Higgs particle”

The Higgs boson was discovered in data that was taken while colliding protons at 7 and 8 TeV, instead of the 13 TeV milestone we achieved in 2015.

“if ten indicates that you’ve discovered a new particle, then this eyebrow raise was about a four”

In particle physics, we look for significant deviations from what we expect from our backgrounds. But our backgrounds can fluctuate, and occasionally these fluctuations can look, at first glance, like bumps. Anytime we see a deviation, a bump, there’s a possibility that it’s a fluctuation. That’s why we set an extremely high bar for stating that we’ve discovered a new particle, known as the five-sigma guideline. This means that the significance of a bump must be at least five standard deviations away from our mean expectation, or, equivalently, that there’s only a 1-in-3.5 million chance that the bump is a fluctuation of the background. The bump we found in 2015 was around two-sigma. Intriguing, but not yet a discovery.

“arguing over this little bump with my colleagues, poking and prodding it with our most ruthless experimental sticks”

In science — particle physics, genomics, climatology; all of it — we deliberately try to knock down our ideas and our results to see if they stand on their own, to make certain that they’re real. We eagerly seek out, examine and admit our experimental uncertainties and question our assumptions, because we want to minimize the possibility that we’ve been tricked into thinking something is true that is actually false. But after we’ve done that, and after our result is sturdy, we accept our conclusion as the best one. In this case, the two-photon bump result stood up: We had a slight excess and we required more data to either verify it as evidence of a new particle or to show it was a fluctuation of the background.

“physicists are machines for turning coffee into diagrams”

“A mathematician is a machine for turning coffee into theorems.” — Alfréd Rényi, page 155 of My Brain is Open, by Bruce Schechter.

“So a few months later, we presented our bump to the world”

We held a big seminar at CERN on December 15th, 2015, where the ATLAS and CMS collaborations announced our first results from the small amount of data we’d taken at 13 TeV, this new energy frontier. The room was packed, since, while the two collaborations work independently and have stringent internal vetting procedures before making results public, rumors had been flying around the particle physics world already.

“the world ran with it anyway”

Part of the reason the excess captured the attention of the physics world in the way it did is that both the ATLAS and CMS experiments reported a small excess at about the same place in their independent (but equivalent) two-photon data analyses. This was coincidentally suggestive, to be sure, but neither of the bumps was very significant on their own at the time. Humans love to see patterns where there are none, and emotions run high when exploring the unknown, but nature doesn’t really care about our emotions. Data talk, desires walk.

“theorist colleagues wrote 500 papers about it”

Mihailo Backović is updating a chart here.

“two particles can briefly create a new particle that lives for a tiny fraction of a second before splitting into particles that hit our detector”

According to quantum field theory, the things that are the same before and after a particle collision are not the total number, names or labels you give to the particles but conserved quantities such as total energy, momentum, and charge. This can lead to some conclusions that may initially seem counterintuitive and weird to the non-specialist but, once you study them for a while, you see their power and elegance.

“What if the missing gravity is leaking into in an extra spatial dimension that’s invisible to you and me?”

Lisa Randall, from 2003:

“[Randall-Sundrum warped geometry theory with two branes] has exciting experimental implications, since it applies to a particle physics scale—namely, the TeV scale. In this theory’s highly curved geometry, Kaluza-Klein particles—those particles with momentum in the extra dimensions—would have a mass of about a TeV; thus there is a real possibility of producing them at colliders in the near future. They would be created like any other particle and they would decay in much the same way. Experiments could then look at their decay products and reconstruct the mass and spin that is their distinguishing property. The graviton is the only particle we know about that has spin 2. The many Kaluza-Klein particles associated with the graviton would also have spin 2 and could, therefore, be readily identified. Observation of these particles would be strong evidence of the existence of additional dimensions and would suggest that this theory is correct.”

“[the graviton] is one of the only hypothesized particles that has the special quantum properties that could give us our little two-photon bump”

The quantum property is called spin angular momentum, and particles can have it in either integer values or half-integer values. Particles with integer values of spin follow special rules. A photon has spin 1, and, according to the Landau-Yang theorem, another particle with spin 1 cannot decay to two photons. This makes it impossible for our two-photon bump to be produced by a heavier cousin of the Z boson, called a Z’ (Z-prime) (which we also search for at the LHC), because the Z’ would have spin 1, as well. So that leaves two possibilities: a spin 0 particle that would be a heavier cousin of the Higgs boson (also spin 0) or a spin 2 particle, which would have to be a graviton. I chose to emphasize the graviton possibility here, but, honestly, an exotic cousin of the Higgs boson would be completely amazing, too.

“New particles can either show up immediately as big, easy-to-spot bumps, or they can only reveal themselves after months of data-taking.”

When charting out our brand-new 13 TeV energy frontier, searching for revolutionary new particles, we have two main directions or axes on our blank map that define where we have to look: Collision energy and rate of interaction. Nature controls the masses of the elementary particles and our job is to find them, but nature also controls the rate at which these particles are produced in collisions or, equivalently, the coupling strength of the new particles to our known particles. This means that if you’re lucky, the new particle will have a large coupling to known particles — a high rate of production in collisions — and it will show up as a big bump with only a little bit of data, and if you’re not-so-lucky the new particle will have a small coupling — a low rate of production — and you’ll have to collide protons and collect data for several years before seeing a detectable effect.

“Planning is already underway for a 100-kilometer tunnel colliding particles at ten times the energy of the LHC.”

A future circular collider will be hosted at CERN or — in a slightly smaller but still very-high-energy guise — in China.

“We already use artificial intelligence and machine learning techniques in parts of the LHC, but imagine building a particle physics experiment with such sophisticated algorithms that it could teach itself”

We use neural networks and machine learning in a variety of ways when we analyze our LHC data, but they are still operated and directed by physicists. For example, our ability to look at a given blob of energy that hits our electromagnetic calorimeters and determine whether this blob came from a photon or from a spray of hadronic particles (a “jet”) is greatly aided by artificial neural networks, which were used in the ATLAS search for the Higgs boson. And when we try to locate very subtle signals buried under large backgrounds in our data, we routinely combine several variables of varying degrees of discrimination power into a single, much more powerful discriminant using boosted decision trees, a form of machine learning. But we suspect that the future, with larger colliders and exponentially more data, will require independently-running deep learning techniques already used in pattern recognition in images, such as convolutional neural networks.

“We’ll be forced to think in completely new ways. We’ll need to go back to our assumptions and determine if there’s a flaw somewhere.”

The LHC was built to operate at 13 TeV — the as-yet highest energy ever — because we had quite a lot of experimental and theoretical suggestions that some new things would be right around the corner, within its energy reach, namely the Higgs boson and evidence of beyond-the-Standard Model (BSM) particles that would help explain unanswered questions such as why gravity is so weak compared to the other forces of nature. We discovered the Higgs boson, which is a fantastic triumph. And so far no BSM particles have shown up at the LHC — with the caveat that, as mentioned in the talk, right now, in 2016, we have just begun our two decades of exploration at the 13 TeV energy frontier. It’s a magnificently exciting time to be working at the LHC, because we’re at the mapping-out-the-mapping stage, discussing how to best use our detectors to ensure that we don’t miss the new discovery wherever it may be hiding, such as with long-lived particle signatures or atypical detector objects.

However, “right around the corner” in theoretical terms really means “at the TeV scale,” and 13 TeV is on the low range of “the TeV scale” compared to a hundred or a few hundred TeV that could be reached with the next generation of colliders. Our current duty as physicists is to explore as much of the TeV scale as we can, meaning a larger collider operating at higher energy.

But if, after all of that, in fifty or a hundred years from now, the Standard Model reigns supreme and we still find no dark matter, no evidence for supersymmetry, no hyperdimensional gravitons, it may mean that new physics may be a bit farther away than we think. Not a few hundred TeV away, but perhaps sixteen orders of magnitude away at something called the Planck scale, the smallest and highest-energy scale defined by quantum mechanics. It’s totally ridiculous to underestimate human ingenuity and to claim that we will never be able to reach the Planck scale, but it will require advancements in technology beyond what we have available.

At that point, it will be necessary to simultaneously really interrogate our basic assumptions. As it stands, we have no reason to think that the bases of all of physics and nature — things like Lorentz invariance, the renormalization group equations, and charge-parity-time (CPT) conservation — are flawed or wrong. But without a way to merge quantum field theory and general relativity, the only conclusion is that something is missing. We may find it at the LHC. We may find it at the next generation of collider. Or our current understanding may be superseded by a larger, more universal theory of which our current theory is only a subset. This doesn’t mean that our current versions of physics are wrong; they’re clearly completely correct up to the limits that we’re able to test. But we’ve now reached the point in the history of particle physics where we have no more guaranteed results, no more ace-in-the-hole particles that have been necessarily predicted and must be found or our current models make no sense, as with particles like the charm quark or the W and Z bosons, in the past. We’re right now at the point where whatever we discover at the LHC and beyond will be revolutionary — even if we discover nothing. The rest of physics begins now.

Reading List

Books for non-specialists
Warped Passages

Lisa Randall
Harper Perennial, 2006

Lisa Randall developed some of the key ideas about how gravity could live in extra dimensions, and this book is a gripping and accessible account of branes, spacetime, Kaluza-Klein theory and general relativity from the world’s expert. This book has inspired more than a few skeptical little kids to become physicists.
The Elegant Universe

Brian Greene
W. W. Norton & Company, 2010

If you’re not satisfied with the possibility of only one or two extra dimensions of space, perhaps you’d prefer the ten (or twenty-five?) of string theory. Brian Greene’s electrifying account of the journey physicists took from thinking about elementary point particles to considering that there may be another level of substructure below that — that all particles are vibrating loops of string — remains one of the best explorations of the biggest open questions of physics and our inventive attempts to answer them. I wouldn’t have gone into physics if it weren’t for this book.

You can also watch Brian’s talks here and here
Deep Down Things

Bruce Schumm
Johns Hopkins University Press, 2004

The Standard Model of particle physics is one of the greatest intellectual achievements of humankind, and there are lots of great books that describe it in a non-technical and qualitative way. But to really understand and appreciate it, you need to dive into the mathematics behind it, that of gauge groups and quantum field theory. This can be intimidating to many non-specialists. That’s why Bruce Schumm’s book is so good, since it presents the math of the Standard Model without the math, describing the concepts behind the mathematical structures — and how they map into the physical world — without overwhelming the reader with equations. An unparalleled book for getting a deeper sense of what particle physics is all about without getting a PhD (although I also suggest you get that PhD).
“The Pleasure of Finding Things Out” with Richard Feynman

BBC Horizon, 1981

Essential viewing for anyone who wants to understand why physicists do what we do: because we’re insatiably curious. Feynman was a couple of orders of magnitude smarter than most physicists (including me), but here he tells stories, gives his views, and ends up displaying the attributes so many of us share: a love of problem-solving, a dedication to empiricism, a healthy and deep-seated distrust of asserted authority, and the recognition that science is simply the best set of methods and tools that we have for determining truth from falsehood — and that physics, in its purest form, is inherently fun.
“Beyond the Standard Model: Theory, Introduction and Motivation”

Natalia Toro
Lecture at the Perimeter Institute, 2015

My close colleague — and recipient of the 2015 New Horizons in Physics Prize, part of the Breakthrough Prizes — Natalia Toro is one of the deepest thinkers in physics right now. This talk is actually for graduate students in theoretical physics, but it’s a masterpiece of how contemporary particle physicists think about the world and, even more fundamentally, how we organize our thinking to push the boundaries of what we know and find where our current understanding breaks down — which often opens up opportunities to make progress.
In Particular

Tova Holmes, Laura Jeanty and Larry Lee

Founded by my colleagues Tova Holmes, Laura Jeanty and Larry Lee, In Particular is a wonderful, personable look at the people we work with at CERN every day featuring fantastic first-person accounts of the research we do.

Advanced reading for those who want to be physicists

Introduction to Electrodynamics

David J. Griffiths
Pearson Education, 2015

The Classical Theory of Fields

Landau & Lifshitz
Butterworth-Heinemann, 1975

Introduction to Quantum Mechanics, 2nd ed.

David J. Griffiths
Pearson Prentice Hall, 2004

Advanced Quantum Mechanics

J. J. Sakurai
Addison-Wesley, 1967

Introduction to Quantum Field Theory

Peskin & Schroeder
Westview Press, 2015

PCT, Spin and Statistics, and All That

Streater & Wightman
Princeton University Press, 2000

Gravity: An Introduction to Einstein’s General Relativity

James B. Hartle
Pearson, 2003

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