Entries in quantum (32)
In the 16th century, Kepler and Brahe founded a field that was to become one of the most important disciplines of our times: Physics as we know it today, the mother of all the Sciences. Since then we learned a great deal about the world around us. Still, physics amounts to only a handful of beautiful and profound ideas - in Einstein’s words, “God’s thoughts”... We will present a bird’s eye view of physics - with the benefit of hindsight - and talk about a few key principles upon which our modern understanding of the physical world is based.
But what are these ideas or divine thoughts? Are they the same or of the same kind as the first principles discussed by Aristotle? This is where philosophy will step in to clarify—and, of course, to further complicate—the role and the place of physics. We will call upon both Plato and Aristotle to discuss the most fundamental principles of knowledge, in the sense in which knowledge has been conceived in the West. But we will also talk about mythos, or thinking based on ambiguity that challenges the so-called rational, or scientific discourse.
This lecture will be a conversation between philosophy and physics in a different way than the previous ones.
First, we will discuss what string theory is. It purports to be the ultimate unifying framework of the physical laws. This theory emerged as a response to several overwhelming puzzles that arise within traditional physics—the puzzles that suggest that the laws of physics we love and rely on are logically inconsistent; that they are incompatible with each other. In recent years string theory made a great deal of progress in understanding black holes, in cosmology, and particle physics. We will review these advances and present a simple, powerful, and yet preposterous story of what string theory is. We will also discuss the importance of experimental evidence as opposed to logical and conceptual consistency.
Next, we will consider whether or not philosophy is useful. In doing so, we will return to its origins in Ancient Greece, and in particular, to Plato and Aristotle, but also draw on ideas of a contemporary French philosopher Gilles Deleuze. We will also have to confront the question of what philosophy is, as well as what makes one a philosopher.
Finally, we will comment on the convergences and the differences between these two kinds of knowledge.
Optical microscopes are familiar instruments to visualize the world of small things, like cells and bacteria. The basic principle at work in a microscope is transmission/scattering of light through a material; and the use of lenses to magnify the image. Visible light however has an inherent size, a wavelength, that limits its resolution. Think of trying to probe a small hole in a wall by throwing a basketball through it: it won't work. You need to use perhaps a tennis ball instead. In this spirit, you need a probe with a smaller size to explore smaller things. Use of visible light in an optical microscope allows one to see things about the size of bacteria, about 1 millionth of a meter, or a micrometer (one can go down to around 0.2 micrometer if things are really pushed to the limit). The same principle however can be used to build an electron microscope: replace light photons with electrons, and lenses with magnets. The wavelength of electrons is typically shorter, and hence allows one to see smaller things; about one thousand times smaller than an optical microscope.
The state of the art of visualizing the world of small things was however achieved in 1981 with the invention of the scanning tunneling microscope. This device consists of a tiny needle hovering a few nanometers above the surface of the subject of interest. A voltage difference is applied between the tip of the needle and the surface of the subject. Because of quantum mechanics, electrons in the needle can "tunnel" through the empty gap between the needle and the surface! See previous post on quantum tunneling. This creates a measurable electrical current in the needle that one can use to infer the distance between the needle's tip and the surface. As the needle scans over the surface, it can then image the topography - bumps and ditches on the surface. The resolution of this device: a fraction of a nanometer! that's the size of an atom, ten thousand times smaller than a cell! This has allowed physicists to image for the first time the fuzzy quantum world of atoms and electrons. The device can also be used to manipulate atoms individually using the needle as a tweezer! Check out the accompanying videos and photos for an amazing visual tour of the quantum world.
The first video shows the workings of a traditional electron microscope. The second one that of a scanning electron microscope. The third video describes the quantum mechanical principles underlying the workings of a scanning tunneling microscope (STM). The final video shows a portable STM in action! The last picture shows the manipulation of atoms with an STM: iron atoms on the surface of copper. The ripples are actually the copper electrons...
This post requires reading a previous post titled "Finding The Exit".
Imagine the world of physical systems as an imaginary landscape of lengths, times, and masses - a vast three dimensional expanse where every point corresponds to a particular physical phenomenon, with an associated characteristic length, time, and mass; an abstract space that visually organizes all natural phenomena we are capable of ever observing. Three fundamental constants of Nature delineate this magical space. They define boundaries that cannot be crossed - three planes that form a pyramid without a base, in-between which the laws of physics confine all our observations of the world…
One boundary is determined by the speed of light: we may not observe any phenomenon involving speeds faster than that of light… That's the statement of Special Relativity, discovered in 1905.
Another boundary is set by Newton's gravitational constant. If we land on this boundary, we are looking at physical systems that have collapsed under their own weight to form black holes… Beyond the boundary, we are studying physics inside a black hole - a mysterious place disconnected from the rest of the universe, a region where space itself comes to an end. Our understanding of this physical realm started with Newtonian gravity in 1687 and ended with General Relativity in 1915.
The last boundary is defined by Planck's constant of Quantum Mechanics. Beyond it, we are not allowed to peek since even Nature itself does not know what goes on… This is the crazy realm of uncertainties - the world of Quantum Mechanics -formulated by 1927.
The three walls of this pyramid intersect in three lines - one between each pair of planar boundaries. And the three intersection lines intersect at a single point - the tip of the pyramid. The junction between the Quantum and Special Relativity planes is captured by a set of physical laws collectively known as Quantum Field Theories. The small world of particle physics - of electrons, quarks, and the sort - lies in this region of our magical landscape. The junction between the Special Relativity and the Gravitational walls is described by the framework of General Relativity - also known as Einsteinian gravity. It is the realm of astrophysics and cosmology - the large scale structure of space. Quantum Field Theory and General Relativity together form the basis of all the laws of Physics that we can currently write down to describe our entire world; and they do so with much success, perhaps a little too much...
But this still leaves us with one junction - the one between the Quantum and Gravitational planes. Physical phenomenon in this region require the use of the laws Quantum Mechanics and of General Relativity… While this is possible, any attempt at understanding phenomena in this region - such as the physics near the surface of a black hole - quickly leads to puzzles and inconsistent conclusions. Quantum Mechanics and General Relativity do not fit together! It is safe to say that the theoretical framework for understanding this region - formally known as Quantum Gravity - is still work in progress…
How about the apex or tip of the pyramid? Near this region, we have a confluence of all the laws of physics that we know - a region where gravity, quantum mechanics, and special relativity are all simultaneously important… We know with certainty that this is a realm that we simply do not yet understand - a realm that probes the tear in the fabric of space and time at the center of a black hole!
The field of String Theory purports to capture all the physics inside our pyramid of physical phenomena - even the junction of Quantum Gravity, and all the way up to the enigmatic tip of the pyramid. To do so, String Theory has to render a judgement with respect to the following grand question: if Quantum Mechanics and General Relativity do not fit together, at least one of the two is to blame; if so, which one? String Theory proposes that it is General Relativity that is at fault. It adopts wholeheartedly the frameworks of Quantum Mechanics and Special Relativity - that is the frameworks underlying Planck's constant and the speed of light. But it rejects the framework of General Relativity, proposing instead that General Relativity - along with its gravitational constant - is an approximate theory; a theory that is not fundamental and that needs to be replaced with a more fundamental framework if it is to make sense in conjunction with Quantum Mechanics.
Hence, String Theory starts with the premise that there are three fundamental constants in Nature: the speed of light of Special Relativity, Planck's constant of Quantum Mechanics, and a new third scale in lieu of Newton's gravitational constant. Newton's constant is then proposed to be a derived concept, built up from the new third fundamental constant. We will call this new third fundamental constant, cryptically, "the tension"...
We just described the first of two postulates that underly the subject of String Theory. The second postulate is a simple one, yet surprisingly powerful and restrictive. It is proposed that all observables in the physical world should be dynamical and computable. That is, we do not allow for any additional scales in Nature beyond the three fundamental constants: the speed of light, Planck's constant, and the "tension". After two decades of hard work by hundreds of lonely and isolated string theorists, these two postulates lead to the proposition that the building blocks of all energy in the world consist of membranes flopping around in a ten dimensional world… And the "tension" constant introduced earlier is simply the stretching tension of these membranes - a measure of their stiffness. We call this theory "Membrane Theory" or "M-theory" for short. In many computationally practical situations however, these membranes appear collapsed as strings - hence arises the alternative historical name of our new theory, "String Theory" - along with a constant known as the "string tension".
We now need to describe two main aspects of this new framework: (1) How does the three dimensional world that we see around us possibly arise from such a (putting things mildly) crazy suggestion?; (2) How does this framework take us beyond what we already know? In particular how does it resolve the original problems and inconsistencies between Quantum Mechanics and General Relativity? Stay tuned for answers to these questions in future posts… In the meantime, have a look at the remaining four parts of video that present a historical narrative of the subject.
The process of discovery in physics comes in two basic flavors. Imagine you are thrown in a large and totally dark room, and you are asked to map it out - or even to find the exit door to leave it. You can adopt one of two basic strategies. You could start from a nearby object you can touch and feel, and go from there around the room discovering one adjacent bit of the room at a time. Alternatively, you could "shoot in the dark" by walking towards a random direction until you hit something; if nothing interesting is found, just head into another random direction; and repeat until perhaps you would luck out and even find the door.
This large dark room represents the physical world around us. The first method of exploration corresponds to a process of meticulous experimentation, discovering bit by bit new phenomena - often from a basis of already well established physics. The second method starts with a pen and paper, without any urgent need for explaining new and exotic data from some experiment. It is driven by logical and sometimes esthetic considerations, and lots of imagination. The first method is robust and the norm for all the sciences, including physics. The second method is rarer and leads mostly to disappointments; but, when it works, it leads to a revolution, to a sudden leap of knowledge perhaps worth centuries of traditional work - to finding the room's exit door, to great enlightenment.
In the history of physics, both methods have played crucial roles in bringing us to our current state of knowledge of the world. The first method is well known and appreciated; the second less so since it often leads to nowhere. However, its impact on physics is immense. The most dramatic example of a revolutionary leap driven by theoretical considerations was the development of the theory of Special Relativity, and soon after that, the theory of General Relativity by Einstein. In both cases, experiments only followed the theories to quickly confirm the counter-intuitive predictions that were implied by the theories. Soon after these developments, quantum mechanics was formulated in a tour force of physical ingenuity through the first method of physics exploration - through meticulous experiments and ideas developed to explain the results. The beginning of the 20th century thus consisted of a two punch discovery extravaganza - first with theory leading experiment, then experiment leading theory.
String theory is an exercise of "shooting in the dark" akin to General Relativity. It is motivated by strong indications that our current best understanding of the gravitational force - given by the theory of General Relativity - is logically (and ironically) inconsistent with quantum mechanics... Experimentally, we do not currently have the technology to demonstrate and understand this paradoxical inconsistency. However, theoretical considerations rather overwhelmingly force us to accept that General Relativity cannot be a fundamental description of gravity and spacetime; rather, it must be an approximate framework that would fail to describe the real world correctly when one looks at gravity at very small distances - distances of the order of ten to the power minus 33 centimeters...
Historically, string theory was developed with very different motivations. In a series of posts - of which this is the first introductory one - I will try to give an overview of string theory with the benefit of historical hindsight - using a chain of logic instead of a historical thread. Hence, let's put history aside and talk about this very intriguing new framework of theoretical physics with an attitude that we are attempting to take a giant leap, find the exit, and reach enlightenment that brings unity to all pillars of modern physics: gravity, quantum mechanics, and special relativity. Until the next post in this sequence, have a look at the accompanying four part videos about the subject - presented from a historical perspective.