A theory of incomplete measurements (ePub)

For over a century, physics has been in a strange situation: in order to correctly describe the universe, we need not one, but two theories, known as quantum mechanics and general relativity.

These two theories, which emerged almost simultaneously at the turn of the XXth century, were true conceptual revolutions, upturning our understanding of time, space and fundamental bricks that make up our universe. Since their inception, both were experimentally tested time and time again. We know for certain today that both are remarkably accurate.

However, there is only one universe. It seems superfluous to need two theories to describe it. This is the reason why a number of highly regarded physicists dedicated so much effort into building a "unified theory" of the universe, meaning a theory that combines the best aspects of relativity and quantum mechanics, starting with Einstein's unsuccessful "unified field theory".

Unfortunately, quantum mechanics and general relativity proved to be mathematically incompatible. Theories combining both do not work. Consensus is therefore that the problem is very difficult. This book offers an improbable solution to this problem, both extremely simple and frighteningly complicated. The core idea is to extend the principle of relativity to all forms of measurement. That extended principle simply require that we must be able to do physics regardless of the physical measurement apparatus being used, including one that is imperfect, defective or did not complete its measurement. This requires a precise definition of what a measurement is.

This leads to a new way of doing physics, where there are no variables, no equations, no real numbers, no continuity, and where even space and time have to be replaced with discrete measurements of space and time. Most surprising, we are already doing it that way, in digital cameras or in 3D video games. In the theory presented here, the numerical representation of a digital picture is the discrete equivalent of a wave function, recording or predicting the probability of presence for photons at every pixel.

Videos giving an overview of the theory.