__The Nature of Space - A Sideways View__

Einstein
rightly abhorred the idea of "action at a distance". We know that if two
particles some distance apart interact then that interaction is mediated by the exchange
of other particles. A commonly quoted example is the electrostatic force due to the
exchange of photons.

The fly in the ointment of
this touchy feely view of the universe is quantum entanglement. This is the phenomenon
where the act of observation of a property of a particle, that property being known to be
indeterminate until the observation, instantaneously determines the state of the same
property of a second particle no matter how far away it is. This effect has been verified
in experiments and is not just some theoretical construct.

In order to avoid citing
action at a distance by way of explanation one is forced either to assume that
"something" has traveled between the entangled particles far faster than the
speed of light or that our concept of distance needs thought. So how do we define distance
and our familiar three spatial dimensions?

Einstein taught us to think
of the distance between two observers in terms of the time it takes light to pass from one
to the other. If we restrict ourselves to thinking about the distance between two
particles in terms of the time it takes one to interact with the other through the
mediation of a third particle, such as a photon, then we have a universe with one spatial
dimension.

We can define the two
particles as being at rest with respect to each other if repeated interactions take the
same time. In all of what follows the interacting (as opposed to mediating) particles I
consider will be at rest with respect to each other in order to keep the thought
experiments simple. So, rushing ahead, if we add other particles at rest with the first
two along the same spatial dimension the times/distances are all neatly additive. Bring in
our experience of the universe and we know that if we have three such directions all
pointing along different axes then we have modeled the three dimensions of space and one
of time. Job done!

Maybe not. Let us drop back
to the case of interactions between just two particles as mediated by a third particle. We
have defined distance in terms of time but not said how we measure time. The only
non-metaphysical way to do so in the simple universe we are constructing is to assume a
clock where the distance between two particles which are its 'works' is *defined* as
unchanging. Such a clock ticks at the rate it takes successive interactions between the
two particles to occur. This is standard stuff and we can again be comfortable that we
have defined distances along our first spatial dimension - or can we? There is a hidden
assumption here that we have any need to produce this first spatial dimension at all.

So far we have used distance
as a way to explain why there is a time delay between the interaction of a pair of
particles if, for example, they exchange a photon. Biologically we *need* to think in terms of spatial dimensions and even
our language almost forces us to do so. To try and escape this straight-jacket consider
the above system of two interacting particles as one where both particles are in *exactly
the same place*. We now use the idea of
distance just as a placeholder to explain the potentially variable time delay between the
interactions of such pairs of collocated particles. Hold on to this thought - distance is
just a placeholder for the time delays between particle interactions.

As above we can, in our
thought experiment, add more particles on top of the first two 'collocated' particles and
see that all the time delays are neatly additive. But what if we had added a third
particle to our initial universe of two interacting particles and find that the time delay
between interactions of particles 1 & 2 added to the time delay between particles 2
& 3 does not equal the time delay between particles 1 & 3. Such inequalities in
the combination of time delays are all we need to define the extra degrees of freedom
which we perceive as extra spatial dimensions.

Mathematically, what I have described above provides
no predictions, testable or otherwise, about the universe and so is not a scientific
theory. However I believe that it can provide a useful perspective on the nature of space.
Spatial dimensions are now defined in terms of the way in which time delays between pairs
of interacting particles combine within a set of such particles. As such, spatial
dimensions have no independent existence outside such a set of interacting particles. In a
sense, space doesn't exist at all!

To see why this perspective
is useful let us return to quantum entanglement. Some people are uncomfortable with this
because on the one hand the particles, as observed using photons, are separated by a
significant distance and yet they also have properties which behave as though the
particles are in the same place. If we just consider this in terms of time delays then all
we have is a pair of particles which interact in one way with a predictable time delay and
which interact in another way with no delay at all. We don't have to get hung up with the
idea of trying to construct some weird geometry of spacetime to explain how particles can
apparently be separated and yet in the same place.

So, in the macroscopic
universe, which we directly experience, the reality of just three spatial dimensions (or
four, ten or eleven dimensional spacetime if you prefer) may just be an illusion. Thinking
just in terms of time delays between interactions resolves the contradictions which
spatial dimensions impose on the reality of quantum entanglement. This begs the question
of whether there are any other classes of particles in the universe which share different
time delays for different types of interactions. One which immediately springs to mind is
dark matter.

Astronomers know that the
universe is littered with dark matter but can't see it except through its gravitational
interaction. By analogy, if we were only able to experience the universe directly by means
of the interactions of quantum entanglement we would be amazed at the wider universe
evidenced through electromagnetic interactions. While we can only experience dark matter
though its gravitational interactions maybe it is part of a something larger which is
quite astonishing.

###### Copyright © 2005 Bob Andersson. All rights reserved.