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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.