Minimum sizes and uncertainties

Before we go on to explain the phenomenon of inertia, let us first relate our theoretical framework concerning distances and time to the real world we live in.

The first thing to note is that we, and everything we directly interact with, are made up of inertial matter. This has consequences when it comes to how we measure things, not because of any technological shortcomings, but because of real world limits.

Suppose we want to measure distance. To do this, we will need a ruler. Such a ruler must naturally be made of inertial matter. Otherwise, it would be flying about at the speed of light. The smallest possible bit of stable inertial matter that we can use as a ruler, at least in theory, is therefore the electron. Noting that the electron is a balloon-like net, it does not have a stable cross-section, even if well inflated. The most reliable measure we can use is therefore its circumference.

To measure time as precisely as theoretically possible, we take the electron, and define a tick of our super-precise clock as the time it takes a photon to traverse its circumference. The reason we cannot  arbitrarily choose a shorter distance is that our clock must necessarily register the tick. Something physical has to happen to the electron. It has to go from one state to another. For this to happen, energy has to be moved into or out of the electron. Either way, the process involves the photon and the entirety of the electron.

We now have our real world unit length and unit time, corresponding to the theoretical unit length and unit time described initially in this book. No distance shorter than 1 unit length can ever be measured with certainty. Similarly, no time shorter than 1 unit time can ever be pinned down. Our unit distance and unit time are:

1. 1 unit distance = the circumference of an electron
   
2. 1 unit time = 1 unit distance / speed of light

Photon traversing the circumference of an electron

In our physical existence, there is a limit to how precise we can be. There is therefore an inescapable uncertainty related to everything. Since we have no way of pinning down exactly where and when things happen, we cannot make any predictions with absolute precision.

Furthermore, things that happen faster than 1 unit time, cannot be registered in any way as being anything but instantaneous. No matter how we try to measure such super-fast events, we will end up with missing information about the state of things between each tick of our clock. Such events will appear as being one moment in one state and the other moment in a different state. This does not mean that nothing takes place in the intermediate time. It only means that whatever takes place cannot in any way be properly measured or registered. While it is possible to spot an intermediate state, quite by chance, such states cannot be reliably interpreted. They will be indistinguishable from completely random noise.

On a final note, we must at all times keep in mind that the unit length and unit time described here are real physical entities, with real physical implications. All forces and energies are implicated by this. When we later in this book start to investigate phenomena related to time and space, it is important to remember that there is no difference between measured time and physical time. If our unit time speeds up or slows down relative to other clocks in other locations, we're dealing with different realities, all adhering to the same physical laws, but observably different from one vantage-point to another.