When most people think of physics, they think of what they learned in high school physics: that the world is fundamentally predictable. Given the position and velocity of a particle in space, it should be possible to predict its position at any moment in the future, right? Though this was thought to be true for thousands of years, recent developments in the field of physics have shown that this isn't actually true. Instead of being fundamentally predictable, the universe is fundamentally unpredictable. However, this doesn't seem to make sense. What happened to the centuries of physics developed by Newton, Bernoulli, and Lagrange? Well, as it turns out, they weren't actually wrong. Their equations were actually an approximation of a formula called the wavefunction, which is the "Newton's Laws" equivalent for modern physics. In this paper, we'll take a look at this peculiar wavefunction and why our intuition about the world is completely wrong.
When most people think of physics, they think of what they learned in high school physics: that the world is fundamentally predictable. Given the position and velocity of a particle in space, it should be possible to predict its position at any moment in the future, right? Though this was thought to be true for thousands of years, recent developments in the field of physics have shown that this isn't actually true. Instead of being fundamentally predictable, the universe is fundamentally unpredictable. However, this doesn't seem to make sense. What happened to the centuries of physics developed by Newton, Bernoulli, and Lagrange? Well, as it turns out, they weren't actually wrong. Their equations were actually an approximation of a formula called the wavefunction, which is the "Newton's Laws" equivalent for modern physics. In this paper, we'll take a look at this peculiar wavefunction and why our intuition about the world is completely wrong.
I suppose one could imagine laws of physics which would dictate that a world be exactly so, and not otherwise, allowing no detail to be varied. But what could dictate that those laws of physics be ‘the’ laws of physics? By considering a spectrum of possible laws, one could again consider a spectrum of possible worlds. In fact the laws of physics of our actual world, as presently understood, have no such dictatorial character. So that even with the laws given, a spectrum of different worlds is possible. There are two kinds of freedom. Although the laws say something about how a given state of the world may develop, they say nothing (or anyway very little) about in what state the world should start. So, to begin with, we have freedom as regards ‘initial conditions’. To go on with, the future that can evolve from a given present is not uniquely determined, according to contemporary orthodoxy. The laws list various possibilities, and attach to them various probabilities. The relation between the set of possibilities and the unique actuality which emerges is quite peculiar in modern ‘quantum theory’ – the contemporary all-embracing basic physical theory. The absence of determinism, the probabilistic nature of the assertions of the theory, is already a little peculiar… at least in the light of pre-twentieth-century ‘classical’ physics. But after all everyday life, if not classical physics, prepares us very well for the idea that not everything is predictable, that chance is important.
In classical physics there is, in accordance with common sense, an objective world ‘out there’. That world evolves in a clear and deterministic way, being governed by precisely formulated mathematical equations. This is as true for the theories of Maxwell and Einstein as it is for the original Newtonian scheme. Physical reality is taken to exist independently of ourselves; and exactly how the classical world ‘is’ is not affected by how we might choose to look at it. Moreover, our bodies and our brains are themselves to be part of that world. They, also, are viewed as evolving according to the same precise and deterministic classical equations. All our actions are to be fixed by these equations - no matter how we might feel that our conscious wills may be influencing how we behave. Such a picture appears to lie at the background of most serious 1 philosophical arguments concerned with the nature of reality, of our conscious perceptions, and of our apparent free will. Some people might have an uncomfortable feeling that there should also be a role for quantum theory - that fundamental but disturbing scheme of things which, in the first quarter of this century, arose out of observations of subtle discrepancies between the actual behaviour of the world and the descriptions of classical physics. To many, the term ‘quantum theory’ evokes merely some vague concept of an ‘uncertainty principle’, which, at the level of particles, atoms or molecules, forbids precision in our descriptions and yields merely probabilistic behaviour. Actually, quantum descriptions are very precise, as we shall see, although radically different from the familiar classical ones. Moreover, we shall find, despite a common view to the contrary, that probabilities do not arise at the minute quantum level of particles, atoms, or molecules - those evolve deterministically - but, seemingly, via some mysterious larger-scale action connected with the emergence of a classical world that we can consciously perceive. We must try to understand this, and how quantum theory forces us to change our view of physical reality.
Ed hai corragio di traitor scherzando un negozio si serio? [And you have the nerve to joke about so serious a business?] – Susanna My amiable friend Professor Mozart dropped by the other day. Now that his NSF grant has been cut way back, he has more time to think about things, and it's a pleasure to chat with him. Some of his views, though, are more than a little peculiar, as the following conversation clearly reveals. “I have to admit,” Mozart began sadly, “that particle physics over the last 40 or 50 years has been a disappointment. Who would have expected that in half a century we wouldn't learn anything really profound?” “Nothing profound?!” I exploded. “What about parity nonconservation? What about the breakdown of time-reversal symmetry?” “To be sure,” sighed Mozart, “we've learned that left can be distinguished from right and that time past is different from time future. But most ordinary people knew the difference between left and right all along, and who except the most highly trained physicists—temporarily, it now turns out—ever doubted for a moment that they could tell the future from the past? So establishing that the asymmetry is really there after all is certainly commendable. But about really serious problems we've discovered nothing—nothing whatsoever about the central puzzle.” “And just what might that puzzle be?” I urged, for he seemed in danger of succumbing to an attack of melancholia. He revived. “All particle physics has taught us about the central mystery is that quantum mechanics still works. Perfectly, as far as anybody can tell. What a letdown!” “Letdown? It's a triumph!” “Letdown!” he insisted. “Think of the previous half-century, when we went down from the macroscopic by seven or eight orders of magnitude. What delicious confusion! All the verities of the preceding two centuries, held by physicists and ordinary people alike, simply fell apart—collapsed. We had to start all over again, and we came up with something that worked just beautifully but was so strange that nobody had any idea what it meant except Bohr, and practically nobody could understand him . So naturally we kept probing further, getting to smaller and smaller length scales, waiting for the next revolution to shed some light on the meaning of the old one. But what happened? For 65 years, since 1925, we've been probing, at finer and finer levels.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You then measure the dynamical properties (say position or energy) of that object at a later time and compare those measurements with the prediction using Isaac Newton's laws of motion. Newton's laws directly predict what those quantities should be at that later time, so the comparison is straightforward. However, the microscopic laws of physics, quantum mechanics, aren't so simple. The quantum concepts are so alien and counterintuitive that the language used to describe the mathematics and physics is often ambiguous and confusing. Therefore, for you to \emph{really} understand what is going on, some mathematics must be used. This is my attempt to explain some "weird facts" using a minimum of mathematics, yet eliminating as much ambiguity as possible.
“Anyone who is not shocked by quantum theory has not understood it.” Since Niels Bohr said this many years ago, quantum mechanics has only been getting more shocking. We now realize that it’s not really telling us that “weird” things happen out of sight, on the tiniest level, in the atomic world. Rather, we can now see that everything is quantum: our everyday world is simply what quantum becomes at the human scale. But if quantum mechanics is right, what seems obvious and right in our everyday world is built on foundations that don’t seems obvious or right—or even possible. An exhilarating tour of the contemporary quantum landscape, Beyond Weird is a book about what quantum physics really means—and what it doesn’t. Science writer Philip Ball offers an up-to-date, accessible account of the quest to come to grips with the most fundamental theory of physical reality, and to explain how its counterintuitive principles underpin the world we experience. Over the past decade it has become clear that quantum physics is less a theory about particles and waves, uncertainty and fuzziness, than a theory about information and knowledge—about what can be known, and how we know it. Discoveries and experiments over the past few decades have called into question the meanings and limits of space and time, cause and effect, and, ultimately, of knowledge itself. The quantum world Ball shows us isn’t a different world. It is our world, and if anything deserves to be called “weird,” it’s us.