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Friday
Nov262010

The M(other) Theory, part 1 

 

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.

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