Thought for this day.  2 July 2015

I have always been fascinated and bemused by the property associated with the Pauli Exclusion Principle and Quantum Entanglement as I understand it, namely that every particle in the universe is aware In some inexplicable way of the quantum state of every other particle. That is, communication between particles concerning their spin, charge, momentum etc, would within the stochastic/uncertainty limitations of spacetime be instantaneous. Accordingly each particle adjusts its Quantum State to accommodate state changes in other particles no matter how far apart they are, thus appearing to violate the cosmic speed limit for massless particles. This seems like experimental evidence looking for a theory. My musings are an attempt to propose a candidate theory.

Applying Occam’s Razor to the problem. If the particles are in such close communication, then in some sense they must be physically close together. The only way I could think of this being possible was that spacetime was crumpled up in another dimension, in the form of a double fanfold structure as described and developed below.

The relatively small spacetime curvature associated with mass would act in the normal way gently undulating spacetime in the fourth spacial dimension. The fan folding could take place in a fifth spacial dimension which would not be influence by the distribution of matter at all. The closeness of the folds would only be restricted by perhaps fluctuations in the quantum vacuum.

To think through the feasibility of this hypothesis consider an analogy which limits the number of dimensions to three so we may visualise the situation in our three dimensional limited brains.

Consider a colony, no matter how Impractical, of one dimensional beings living within the confines of a straight line. Further consider that matter within this one dimensional space causes the line to curve, (reference: general relativity) requiring a second spacial dimension to curve into. This can be imagined as a wiggly pencil line drawn on a flat sheet of paper(see fig1). The one dimensional beings would still be confined to their linear lifestile and be unaware of the curvature providing that the radius of curvature were sufficiently large. If this two dimensional Universe, modelled by a flat sheet of paper were now fan folded first in one direction (figures 2 & 3) and then again in an orthogonal direction (fig4), every point on the pencil line will be brought close to every other point on the line. It is simple to construct our own model with pencil and paper to see the simple logic behind the hypothesis. The degree of closeness would only depend on the width of the folds and the thickness of the fanfolded stack (fig4). The folding would of course require a third spacial dimension to fold up into. The movement of our one dimensional creatures, light rays etc would follow the long route along the surface of the sheet, not aware of their zig-zag motion around the folds of this convoluted space. Information relating to the quantum state of individual particles would take the very short route directly through the folds appearing instantaneous within the limits of any measurements that our one dimensional creatures were capable of making.

The idea can of course be scaled up to include our four dimensional spacetime world with an additional fifth dimension to accommodate the fanfold structure described above. Additional folded up dimensions required to accommodate other mathematical models, such as string theory, could be additional to or include that necessary for the fan-folding.

Other possibilities and thoughts arising from the hypothesis.

If it could be established that the fan folded up universe were the lowest energy configuration, then maybe the universe started off in a planar (relating to the two spatial dimensional analogy) form and over time coiled (crumpled) up into the lower energy fan-fold configuration releasing the excess energy as Radiation? Normal Matter? Dark Matter? Dark Energy? Could this be linked into the inflation model.

If the early universe were not initially fan folded, then consider the consequences to the Pauli principle and the lack of energy/momentum balance or quantum entanglement. Would these consequences push the universe in the direction of fan folding to stabilise itself?

Is the fanfold geometry the only feasible configuration or just one of an infinite number of possibilities? Would entropy dictate that the folding be random, more like a crumpled/screwed up piece of paper? The more random folding would not destroy the mechanism suggested, because the infinitesimally thin sheet would bring all particles into close proximity no matter how the crumpling occurred, providing the widest dimension were small enough for apparent instantaneous particle communication.

Could the lack of, or delay in, communication between particles in the prefolded up phase result in the known but unexplained initial inbalance between matter and antimatter particles in the very early stages of the Universe? That is, without entanglement matter antimatter creation may have got out of step.

Could this Inperceptual weaving about, this zigging and zagging in the fifth dimension have consequences which we call inertia? And could it also set an upper limit to the speed of massless particles?

Could the double slit experiment be explained in terms of convoluted spacetime? If the probability wave function of the particle after passing through the slit were still in close communication with its value prior to passing through the slit.

Could multidimensional geometry, seen differently by different matter and force particles, be the key to everything?

The width of the fanfold stack must be relatively small to produce the illusion of instantaneous communication between particles within the tolerance limits of our measuring capability. Ultimately the limitation imposed by the uncertainty principle would create a lower bound of the order say one plank length. However, in the real Universe it could be much larger than this and still meet the criteria imposed by practical observation.

Would the expansion of the universe (space time expansion) involve adding an integral number of folds per unit time essentially a digital process, that is a jerky rather than a smooth expansion?

What would be the consequence of adjacent folds coming into physical contact?

My mathematical skills are no longer good enough (if ever) to sort out the feasibility (or not) of these ideas. But then it has always been my opinion that a description of anything real within science should at least in the broadest terms stand alone without the aid of complex mathematics. After all it was Einstein that said “Everything should be made as simple as possible, but not simpler”. Mathematics may strengthen and support and expand an idea but should not be the only basis for a practical description.

Brian Kershaw.

Note

The first draft of this document was written Nov 2012

Copies to Prof Brian Cox, Dr Chris Lintott, Dr Martin Rees,

Prof Niel Turok and Brian Green.