A Theory of Everything

Introduction

Many people know that Einstein spent most of the latter part of his life searching for a 'Theory of Everything'.  What this means, more or less, is that he - and many others - have spent a great deal of time looking for a way to unify Relativity and Quantum Mechanics.  Ideally, the result, when they find it, will be an equation which can fit onto a t-shirt, although they would be grateful for any equation which does the job.  It has been described as the 'Holy Grail' of physics - although, to be fair, several things have been described this way, and the relevance of any of them to the Grail of Arthurian legend is debatable.

Suffice it to say that this quest is incredibly difficult, some believe it to be impossible, and all the lines of inquiry which have been explored so far have been complicated.

An Overview

While the details of any Theory of Everything must be horribly complicated - or it would have been found long ago - the big picture summary of what it must be like is surely far simpler than most of the articles suggest.

Around 1900, physicists thought they had everything sewn up, more or less.  There were a few outstanding details, some minor niggles, remaining to be resolved, but - given the progress they had already seen - pretty much everybody was confident that these details would be cleared up reasonably quickly.  Then Einstein came along, and wrecked it: the universe turns out to be very different from our expectations.  It turns out that Newton was wrong - after every experiment for centuries had confirmed his equations.

But Newton was only wrong in a very specific way: he was very, very nearly right when things are going at the speeds we are familiar with - when we run, when we drive, when we fire guns and missiles.  What Newton did not know is that there is a limit to speed, a maximum speed which cannot be exceeded.  Everything he said was correct, in effect, until you start to approach that maximum speed.  And the closer you get to the maximum speed, the more things deviate from the way Newton described them.  This deviation is described by the theory of Relativity, and the important thing about Relativity is that it describes both what happens at very fast speeds, and also what happens at much slower speeds -  when it gives you, to an extremely close approximation, the same result as Newton.

There is something else that Newton did not know: just as there is a limit to speed, there is also a limit to size - nothing can be smaller than the Planck length (about 1.6x10^-35m).  The objects we are familiar with operate in certain ways, but the closer you get to the smallest size the more things deviate from the way we expect: this deviation is described by Quantum Mechanics.  The weakness of Quantum Mechanics, as we currently formulate it, is that it only operates at very small sizes, or when we are not looking: an electron may be in many places at the same time, but when you throw a tennis ball, it is only in one place at a time.

What we need, first of all, is a formulation of Quantum Mechanics which applies both to the very small and to larger objects.  Just as Reletivistic effects become less obvious the further you get from the speed of light, so too must Quantum effects become less obvious the futher you go from the Planck length.

It is often said that Relativity and Quantum Mechanics are incompatible, but at this level of detail, there is no obvious contradiction between them: Relativity describes the effects which come into play when you are intrested in the very fast, and Quantum Mechanics describes the effects which come into play when you are interested in the very small.  Speed and size are quite distinct attributes of matter.

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