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The aim of physics is to understand the world we live in. Given its myriad of objects and phenomena, understanding means to see connections and relations between what may seem unrelated and very different. Thus, a falling apple and the Moon in its orbit around the Earth. In this way, many things “fall into place” in terms of a few basic ideas, principles (laws of physics) and patterns.

As with many an intellectual activity, recognizing patterns and analogies, and metaphorical thinking are essential also in physics. James Clerk Maxwell, one of the greatest physicists, put it thus: “In a pun, two truths lie hid under one expression. In an analogy, one truth is discovered under two expressions.”

Indeed, physics employs many metaphors, from a pendulum’s swing and a coin’s two-sidedness, examples already familiar in everyday language, to some new to itself. Even the familiar ones acquire additional richness through the many physical systems to which they are applied. In this, physics uses the language of mathematics, itself a study of patterns, but with a rigor and logic not present in everyday languages and a universality that stretches across lands and peoples.

Rigor is essential because analogies can also mislead, be false or fruitless. In physics, there is an essential tension between the analogies and patterns we draw, which we must, and subjecting them to rigorous tests. The rigor of mathematics is invaluable but, more importantly, we must look to Nature as the final arbiter of truth. Our conclusions need to fit observation and experiment. Physics is ultimately an experimental subject.

Physics is not just mathematics, leave alone as some would have it, that the natural world itself is nothing but mathematics. Indeed, five centuries of physics are replete with instances of the same mathematics describing a variety of different physical phenomena. Electromagnetic and sound waves share much in common but are not the same thing, indeed are fundamentally different in many respects. Nor are quantum wave solutions of the Schroedinger equation the same even if both involve the same Laplacian operator.

Along with seeing connections between seemingly different phenomena, physics sees the same thing from different points of view. Already true in classical physics, quantum physics made it even more so. For Newton, or in the later Lagrangian and Hamiltonian formulations that physicists use, positions and velocities (or momenta) of the particles involved are given at some initial instant and the aim of physics is to describe the state at a later instant. But, with quantum physics (the uncertainty principle) forbidding simultaneous specification of position and momentum, the very meaning of the state of a physical system had to change. A choice has to be made to describe the state either in terms of positions or momenta.

Physicists use the word “representation” to describe these alternatives that are like languages in everyday parlance. Just as with languages, where one needs some language (with all equivalent) not only to communicate with others but even in one’s own thinking, so also in physics. One can use the “position representation” or the “momentum representation” (or even some other), each capable of giving a complete description of the physical system. The underlying reality itself, and most physicists believe that there is one, lies in none of these representations, indeed residing in a complex space in the mathematical sense of complex versus real numbers. The state of a system in quantum physics is in such a complex “wave function”, which can be thought of either in position or momentum space.

Either way, the wave function is not directly accessible to us. We have no wave function meters. Since, by definition, anything that is observed by our experimental apparatus and readings on real dials, is real, these outcomes access the underlying reality in what we call the “classical limit”. In particular, the step into real quantities involves a squared modulus of the complex wave functions, many of the phases of these complex functions getting averaged (blurred) out. Many so-called mysteries of quantum physics can be laid at this door. It is as if a literary text in its ur-language is inaccessible, available to us only in one or another translation.

What we understand by a particle such as an electron, defined as a certain lump of mass, charge, and spin angular momentum and recognized as such by our electron detectors is not how it is for the underlying reality. Our best current understanding in terms of quantum field theory is that there is a complex electron field (as there is for a proton or any other entity), a unit of its excitation realized as an electron in the detector. The field itself exists over all space and time, these being “mere” markers or parameters for describing the field function and not locations where the electron is at an instant as had been understood ever since Newton.

Along with the electron, nearly all the elementary particles that make up our Universe manifest as particles in the classical limit. Only two, electrically neutral, zero mass bosons (a term used for particles with integer values of spin angular momentum in terms of the fundamental quantum called Planck’s constant) that describe electromagnetism and gravitation are realized as classical electric and magnetic or gravitational fields. The very words particle and wave, as with position and momentum, are meaningful only in the classical limit. The underlying reality itself is indifferent to them even though, as with languages, we have to grasp it in terms of one or the other representation and in this classical limit.

The history of physics may be seen as progressively separating what are incidental markers or parameters used for keeping track through various representations from what is essential to the physics itself. Some of this is immediate; others require more sophisticated understanding that may seem at odds with (classical) common sense and experience. As long as that is kept clearly in mind, many mysteries and paradoxes are dispelled, seen as artifacts of our pushing our models and language too far and “identifying” them with the underlying reality, one in principle out of reach. We hope our models and pictures get progressively better, approaching that underlying reality as an asymptote, but they will never become one with it.

Headline Image credit: Milky Way Rising over Hilo by Bill Shupp. CC-BY-2.0 via shupp Flickr

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By Tom Lancaster and Stephen J. Blundell

Sometimes it’s the fly in the ointment, the thing that spoils the purity of the whole picture, which leads to the big advances in science. That’s exactly what happened at a conference in Shelter Island, New York in 1947 when a group of physicists gathered to discuss the latest breakthroughs in their field which seemed at first sight to make everything more complicated.

Isidor Rabi reported experimental results from Columbia University that showed that the g-factor for the electron, a property reflecting its magnetic moment, was not precisely two, as Paul Dirac’s beautiful theory of the electron had predicted, but came out to be a messy 2.00244 (though the modern value is very slightly lower than this). And Willis Lamb, also at Columbia, explained how two energy levels in the hydrogen atom which were supposed (again according to Dirac) to be coincident were very slightly displaced from each other (an effect now known as the Lamb shift).

These were apparently messy, annoying and disruptive results that ruined a pure, dignified and elegant theory. But physicists like a challenge, and the conference attendees included Hans Bethe, Julian Schwinger, and Richard Feynman, all three of whom would attack the problem. The key insight was to realize that there are a multitude of quantum processes that can occur, and which had been forgotten. An electron is not just an electron, but is surrounded by a cloud of virtual particles: photons, electrons, and antielectrons, popping in and out of existence. These higher order processes are most pictorially described by Feynman diagrams, simple cartoons containing dots, arrows and wiggly lines, each one a shorthand for a mathematical term in a complex calculation but summarizing a physical interaction in an elegant form.

These diagrams can be used to show how the basic interaction between electrons and light is altered by quantum processes, an effect which tweaks its magnetic moment. This slightly shifts the “g-factor” and gives a prediction which has been verified experimentally to many decimal places. It also affects the way in which the spin and orbital angular momentum behave and this can be used to explain the Lamb shift. These tiny effects signal a vacuum that is not empty but teeming with quantum life, myriad interactions shimmering around every particle

Feynman diagrams first appeared in print sixty-five years ago this year, so they have now reached statutory retirement age. But rather than being put out to grass, Feynman’s cartoons are still used to make calculations and describe physical processes. They are at the foundation of modern quantum field theory, and if we ever figure out how to make a theory of quantum gravity, it is pretty likely Feynman diagrams will be in the description. It’s a reminder of why detailed measurements are needed in physics. Those little discrepancies can lead to revolutions in understanding.

Tom Lancaster was a Research Fellow in Physics at the University of Oxford, before becoming a Lecturer at the University of Durham in 2012. Stephen J. Blundell is a Professor of Physics at the University of Oxford and a Fellow of Mansfield College, Oxford. They are co-authors of Quantum Field Theory for the Gifted Amateur.

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Frank Close, OBE, is Professor of Physics at Oxford University and a Fellow of Exeter College. He was formerly vice president of the British Association for the Advancement of Science, Head of the Theoretical Physics Division at the Rutherford Appleton Laboratory, and Head of Communications and Public Education at CERN. He received the Institute of Physics’ Kelvin Medal in 1996, awarded for outstanding contributions to the public understanding of physics. He is the author of The Void, Very Short Introduction to Particle Physics, The Particle Odyssey and many more.  Also, look for Antimatter in January, Close’s newest book.

We asked Close to explain the importance of the Large Hadron Collider to us.  He kindly sent us the post below and the following analogy, comparing the journey for answers about the origin of the universe to sewing a tapestry:  “The quest is like sewing a tapestry, but one where the picture is only revealed as you do so. First you have to make a needle, then feed it with thread and then finally start sewing. It took 20 years to design and build the needle. Last Wednesday we started to put thread through the needle’s eye. It will take some time before we have enough thread, tightly enough wrapped and in sufficient colors to start sewing. That will be later this year or next spring. If we are lucky there may be some parts of the picture where the image quickly comes clear; other parts of the picture may take a lot of time and careful work before the images can be discerned.”

Keep reading to find out the answers this tapestry may hold.

Only nature knows what happened in the long-ago dawn of the Big Bang; but soon humans will too. The visions of the new world will hopefully be tomorrow’s stories. If you want a machine to show how the universe was in the moments of creation, you don’t find it in the scientific instrument catalogs: you have to build it yourself. And so scientists and engineers around the world pooled their knowledge to build the Large Hadron Collider (LHC).

Immediately there were problems. Beyond the ability of a single continent, this became a truly global endeavor; unparalleled in ambition, in political and financial challenges. At its conception, the state of the art in cryogenics, magnets, information technology, and a whole range of technologies was far short of what would be required for the LHC to work. The whole enterprise relied on the belief that bright ideas would emerge to solve problems, any one of which could have proved a show-stopper. There were many who feared that particle physics had bitten off more than it could chew; that the LHC was over-ambitious; that this would be the end of physics.

Now we are almost there. Wednesday, Sept 10 when the current was turned on, and for the first time a beam of protons circulated through the vacuum tubes colder than outer space, was just the start. The next step will be to send two beams, in opposite directions – well, that’s been done but not yet intensely enough to smash into one another and produce data. That is still for the future. At first, and for some months, they are likely to be too diffuse and low energy to produce anything of great use to science. Only later when high energy intense beams collide, and the debris from those mini-bangs pour through the gargantuan detectors, which in turn speed signals to the waiting computers, will the moment we’ve waited for have arrived. A year or two accumulating data and the first answers to the big questions will begin to emerge.

The seeds of matter were created in the aftermath of the Big Bang: quarks, which clustered together making protons and neutrons as the newborn universe cooled, and the electron, which today is found in the outer reaches of atoms. We and everything hereabouts are made of atoms. In the sun and stars intense heat rips atoms apart into their constituents, electrons, protons and neutrons.

By colliding beams of particles, such as electrons or protons, head-on, it is possible to simulate the high-energy hot conditions of the stars and the early universe. At CERN (European Council for Nuclear Research) in the 1980s a machine called LEP (Large Electron Positron collider) collided electrons and their antimatter analogues, positrons, fast enough that they mutually annihilated and created for brief moments in a region smaller than an atom, the conditions that occurred within a billionth of a second of the Big Bang. Trying to reach time zero is like finding the end of the rainbow, and the LHC will take us ten to a hundred times further than ever before. At the LHC the beams of protons will pack a bigger punch and their collisions will show how the universe was at its infancy and perhaps give us some insight to how the universe evolved.

Within a billionth of a second after the Big Bang, the material particles from which we are made, and the disparate forces that act on them, had become encoded into the fabric of the universe. However, the events that led our universe to win the lottery of life were decided earlier than this. Some of them we believe occurred in the epoch that is now within our reach. That is what the LHC promises to reveal.

As the 21st century begins, physics can explain almost all of the fundamental phenomena revealed in the search for our origins, yet there are niggling loose ends. We see hints of a unified theory vaguely in the shadows, but what it is and how the structures that led to the particles and forces that molded us are still perceived only vaguely.

Why are there three spatial dimensions; could there be more? Cosmology suggests that “normal matter” is but one percent of the whole, and that we are but flotsam on a sea of “dark matter”. What that dark sea consists of, how it was formed, why there is any matter at all rather than a hellish ferment of radiation, are unknown.

Why is there structure and solidity to matter when our theories would be happier if everything flitted around at the speed of light? Theorists believe that all structure and ultimately the solidity of matter are the result of a field of force that today permeates the universe known as the Higgs field. This can be made to reveal itself if the conditions are right. For example, as an electromagnetic field can be stimulated to send out electromagnetic waves, so can the Higgs field create waves. However to create these waves requires huge energy. The LHC has been designed to achieve these conditions. As an electromagnetic wave comes in quantum bundles, particles known as photons, so the Higgs waves will come in the form of particles known as Higgs bosons.

There is also the question: why there is anything at all? In the beginning there was nothing: “there was darkness on the face of the void”. Then came a burst of energy: “let there be light and there was light”, though from where it came no-one knows. What we do know is what happened next: this energy coagulated into matter and its mysterious opposite, antimatter, in perfect balance. Anti-matter destroys anything it touches in a pyrotechnic flash. So how did the early universe manage to survive self-annihilation between the newly born matter and antimatter? Something as yet unknown must have occurred in those first moments to upset the balance. For several years we have glimpsed a subtle asymmetry between arcane forms of matter and antimatter made from “strange” and “bottom” quarks and antiquarks. One of the goals of the LHC will be to produce large numbers of particles of bottom matter and their antimatter counterparts in the hope of finding the source of the asymmetry between matter and antimatter.

Ultimately however, this is a voyage of discovery into a world that once existed but was lost in the sands of time, 13.6 billion years ago. Like some astonishing Jurassic Park, the LHC will show once more what that epoch was like. We have ideas of what is to be found, and there are certainly questions, such as those above, whose answers we crave. But in focusing on them like this we are getting ahead of ourselves. We are at the stage of witnessing remarkable engineering, and it is those we should be applauding; as for discoveries in fundamental science – watch this space.

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