MOTION MOUNTAIN

the quest for precision and its implications 305
Vol. VI, page 102
Challenge 316 s
In daily life we also observe that nature is separable and a whole at the same time.
It is a ‘many that can be thought as one’: in daily life nature is a set. Indeed, the basic
characteristic of nature is its diversity. In the world around us we observe changes and
differences; we observe that nature is separable. Furthermore, all aspects of nature belong
together: there are relations between these aspects, often called ‘laws,’ stating that the
different aspects of nature form a whole, usually called the universe.
In other words, the possibility of describing observations with the help of ‘laws’ followsfromourexperienceoftheseparabilityofnature.Themorepreciselytheseparability
is specified, the more precisely the ‘laws’ can be formulated. Indeed, if nature were not
separableorwerenotaunity,wecouldnotexplainwhystonesfall downwards.Thuswe
areledtospeculatethatweshouldbeabletodeduceall ‘laws’ fromtheobservation that
nature is separable.
In addition, only the separability allows us to describe nature at all. A description is a
classification, that is, a mapping between certain aspects of nature and certain concepts.
All concepts are sets and relations. Since the universe is separable, it can be described
with the help of sets and relations. Both are separable entities with distinguishable parts.
A precise description is commonly called an understanding. In short, the universe is
comprehensible only because it is separable.
Moreover, only the separability of the universe makes our brain such a good instrument.
The brain is built from a large number of connected components, and only the
brain’s separability allows it to function. In other words, thinking is only possible becausenatureisseparable.
Finally,onlytheseparabilityoftheuniverse allows us to distinguish reference frames,
and thus to define all symmetries at the basis of physical descriptions. And in the same
way that separability is thus necessary for covariant descriptions, the unity of nature is
necessary for invariant descriptions. In other words, the so-called ‘laws’ of nature are
basedontheexperiencethatnatureisbothseparableandunifiable –thatitisaset.
These arguments seem overwhelmingly to prove that the universe is a set. However,
these arguments apply only to everyday experience, everyday dimensions and everyday
energies. Is nature a set also outside the domains of daily life? Are objects different at
all energies, even when they are looked at with the highest precision possible? We have
three open issues left: the issue of the number of particles in the universe; the circular
definition of space, time and matter; and the issue as to whether describing nature as
made of particles and void is an overdescription, an underdescription, or neither.These
three issues make us doubt whether objects are countable at all energies. We will discover
in the final part of our mountain ascent that indeed, objects in nature cannot be counted
at high energy. The consequences will be extensive and fascinating. As an example, try
to answer the following: if the universe is not a set, what does that mean for space and
time?
Does the universe exist?
connectedwith thatofquantumtheory.
“Eachprogressive spirit isopposed bya
thousandmenappointed toguardthepast.
MauriceMaeterlink”
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net