Ultrafilters And Creation (ZPE?)
Now, where can we start with the idea of ultrafilters and creation? There is the idea in pseudo-science that the vacuum of space contains enough energy or potential energy to supply our every need, if we were but able to extract it. There is often quoted a mysterious factor of 1/2 in the physics that leads some to say the quantum model is to be interpreted as demonstrating a whole half of all energy in the universe is present in the vacuum of space, (or so it is said.)
Is all this hooey?
For now, It would be best to have two A4 sheets of paper and some scissors to hand.
Cut one sheet in half and lay both halves on top of the whole sheet that remains. Now, if we consider the uncut A4 sheet as the "observable" universe or as that which we may consider "classical euclidean space" then our two halves which from this point on we consider to intersect (overlap) in only "one quanta" or "atom" (so that they are overlapping each over to the tune of 1 atom only), then the new space, which may in "potential" overlap 100% - I.e. to fill the space of up to two whole sheets of A4 upon our classical space - our unused sheet (of three). (Hence the factor of 1/2) Our two half-sheets represent the minimum energy of a particle, and the observable universe sees just this one particle, although we may have a "potential overlap" of up to two sheets of A4 in our "quantum" overlap, filling the whole observable universe with that one particle.
We have the axioms for the ultrafilter as should now be familiar to us. First, the empty set is not a member (as we assume we always have an overlap of at least one "quanta".) Any possible overlap contains at least that one quanta and possibly more we may assume. (say, a particular particle or quark etc must always be present.)
The intersection of two overlaps (as three or four plus sheets) that contain the same quanta or elementary particles may be considered as exactly the same two sheets, - but separated merely by time and momentum. (As larger structure in a different state).
So
1) {} is not in U (The empty set is not part of creation. There is always some "overlap".)
2) if A is in U and A ⊆ B then B is in U, (They both have the same generative quanta)
3) if A is in U and B is in U then A∩B is in U. (Two structures that contain the same basic particles (quanta) are technically interacting "in the same state" and merely separated by space and time (energy/momenta)
4) Any particle is either in U or not in U. We may intuitively state then that all electrons belong in the same class (I.e. U[1]) and all photons in another, say U[2], and others another still.
Is there any U, the union of all U[i]?
A good question... one I presently don't have a chance of understanding myself! I can figure that an electron is largely the invention of mathematics, one made in order to make good sense of observed experimental data. I can also state quite happily that there is no need for God to use more than one "equation" say for each type of particle and therefore one "U[i]". The complexity of the union of all these separate particles, their combining states and the constructions in the universe around us is quantum theory and as such are not my concern.
But I figure that that factor of "1/2" is still very interesting! For an electron has; (as the smallest and simplest example present) the potential to be everywhere without being thus observed at any time, or observed somewhere at a particular time. If that accounts for the complete range of potential states of a universe containing one model for just one electron, then I would consider that that "overlap" of one quanta is as the half-energy of the universe's full potential (i.e. as potentially 100% overlap) - to be entirely compatible with the notion of an ultrafilter used in creation.
Psa 19:1 To the chief Musician, A Psalm of David. The heavens declare the glory of God; and the firmament sheweth his handywork.
(KJV)
When would the uncertainty principle show its face? Clearly in the miniscule,.. and we may surely expect strange effects at the quantum level. We should be able to explain at least the wave/particle duality if there is any sense to be made of this... If we really identify the position of a particle, then we do so in a four vector. If we measure the particle's energy then we do so with respect to momentum.
What we have in essence is a medium for these quantum waves, without the need for that medium to move or sweep with the observer, i.e. as it is filling the whole universe already (our two half sheets), within which only the interface or the "overlap" or the "generative quanta" is in motion in this universe. That is, no information is transferred from the measurable universe to the overlay, or vice versa.. so that *all* information is preserved within the measurable universe as some form of interface present in the overlay. This could allow a basis for the conservation laws.
There is then in the miniscule a problem with the nature of the interface or "generative quanta". On the large scale we see a connected trace of the quanta in space time, a continuous curve in the four vector that we may measure. At the very small and isolated case we would truly expect to find problems, since we would have the interaction of more than one U[i] allowing us to measure momentum or position.
But waves and particles should seamlessly mix: If we imagine only the propagation of waves, then at the measurement of the particle the wavefront may "burst" to give away it's position to the tune of each "quanta". "Particles" are a consequence of quanta, not energy - there at present is no "reason" why the particles are then quantized, unless that intersection of the overlay or "interface" is in some way, "finite" rather than infinitesessimal.
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