Holistic Dimensionality
If it is possible that there are extensions with other dimensions. Spaces of this kind, however, cannot stand in connection with those of a quite different constitution. Accordingly, such spaces would not belong to our world, but must form separate worlds. ~ German philosopher Immanuel Kant
Our experience of Nature is ostensibly limited to 4 dimensions: 3d space and a time vector. 4D is a natural province for chemistry, as elemental and molecular interactions may be sufficiently understood in the ambient; sufficient in the sense of workable predictability.
Historically, 4D had been the home stomping grounds for physics. But physics is a discontented discipline in its striving to be a know-it-all. Modern physics peeled back the 4D veneer and delved deeper, where it encountered uncomfortable unknowns.
There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say, we know there are some things we do not know. But there are also unknown unknowns: there are things we do not know we don’t know. ~ American bureaucrat Donald Rumsfeld
4D exists in a higher-dimensional envelope. Extra dimensions (ED) exist. Holistic dimensionality (HD) is the realm of actuality as it is, not as we perceive it.
HD = 4D + ED
ED has long been regarded as the “spirit plane.” There are many spiritual attributions throughout history for an HD existence, focused on ED as a piece not to be left out of the picture in perceiving Nature.
Some live an HD actuality. The spiritually sensitive feel the energy of their chakras flow. ED-resident presences may be sensed 4D. Those less aware easily dismiss such.
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There is nothing sacrosanct about dimensionality. ~ Paul Wesson
In declaring gravity as a curvature of spacetime, Einstein unwittingly made the case for extra dimensionality. If gravity distorts spacetime, there must be more than 4 dimensions. Warping 3d space geometrically requires at least 1 extra spatial dimension; an obvious implication which Einstein refused to acknowledge out of religious conviction for naïve realism.
Further, general relativity predicted black holes; a most massive curvature that appears planar only because visibility cannot extend beyond a black hole’s event horizon. Surely the massive volumes of matter/energy sucked into a black hole go somewhere. Such singular sinks must be beyond 4D.
Even on the rim of black holes are HD dynamics. Hawking radiation is the predicted black-body radiation emitted from a black hole’s event horizon. The gravitational force is so strong as to spontaneously produce 4D photons (light energy), and even mass-laden particles. Small-scale experimentation has demonstrated this dynamic. This black hole evaporation is necessarily an example of HD interaction.
Dimensions must not be multiplied beyond necessity, but a multiplicity of dimensions is absolutely unavoidable. ~ French – American mathematician Benoît B. Mandelbrot
In 1921, German mathematician and physicist Theodor Kaluza extended general relativity to a 5d spacetime, thereby unifying electromagnetism and gravitation, the forces relevant to general relativity. Einstein was impressed by the math, but was discomforted with the idea of unseen dimensions, as were many of his contemporaries. To them the notion of ED smacked of mysticism. Welding time to 3d space was as much tinkering as Einstein could abide.
The non-mathematician is seized by a mysterious shuddering when he hears of “four-dimensional” things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more commonplace statement than that the world in which we live is a 4-dimensional spacetime continuum. ~ Albert Einstein
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A cosmological issue is how the universe developed its HD existence with 4D as a predominant scale. Somehow our 4D diverged from ED while leaving an integrated HD.
One proposal has been that a quantum energy fluctuation near the start of the emerging universe broke the symmetry of the dimensions, with 3 of space to blossom in scale, resigning other spatial dimensions to less than Planck length; meanwhile, leaving time as the eternal illusion of passage.
In 1926, Swedish physicist Oskar Klein extended Kaluza’s 5d concept with compactification. Klein proposed that the 4th space dimension was curled up: existing at a wavelength beyond measure (i.e., shorter than Planck length).
The Kaluza–Klein theory is exemplary of models extending the number of dimensions and defining ED characteristics, such as whether the extra dimensions are curled or flat.
In their search for a unified field theory, Lisa Randall and fellow theoretical physicist Raman Sundrum developed 2 braneworld models in 1999 (the Randall–Sundrum models). Both braneworld models construe a universe of 5 dimensions using warped geometry, with the force of gravity (via gravitons) emanating from the 5th dimension. RS1 has a small (10–31 cm) 5th dimension, but not compact; instead, merely phase-shifted from 3d space. RS2 was bolder, with a warped 5th dimension that is infinitely large.
As Randall–Sundrum suggests, the path of peeling ED from 4D does not necessitate compactification. The problem remains in properly characterizing the geometry of HD.
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However HD may be shaped – with ED either compact, small, or large – all modern physics’ models require more than 4 dimensions. Though relativity and the Standard Model (SM) of quantum physics require extra dimensions, theorists of both those models have often stayed silent about ED, spooked by the implications of supporting spooky action dimensionally.
SM is replete with examples of higher dimensionality. The separation of matter (fermions) from fundamental interaction forces (bosons) requires extra dimensions.
3 dimensions of space provide only sufficient mathematical room for fermions. No dimensional room is left over for bosons to instantaneously act. If limited to 4D, bosonic fields have no means to instantaneously impose their coherent forces on fermions.
The uncertainty principle itself is an extra-dimensional cry for help. Explaining nondeterministic quanta in a 4D harness can’t be done. Actuality as a probability matrix must be a constrained view, leaving the basic gyre unexplained. In other words, exhibition of inherent uncertainty suggests an underlying determinism, as light refraction illustrates.
Wave-based interpretation of particle momentum is hard to adjudge as a mere 4D mathematical construct when quantum entanglement, as well as much less exotic effects, demand an extra-dimensional vehicle. Nonlocality is sheer magic if existence is constrained to 4D.
Virtual particles present a most pressing case for HD. These little bits make constant cameo appearances 4D. There is no other way to explain their comings and goings except via extra-dimensional shifts. Virtual particles must have active HD lives.
Virtuality as fleeting is a peephole 4D perspective. The notion that particles pop in and out of existence is ridiculous, beginning with the issue of where they could possibly come from. Yet that is the stance that SM modelers typically take for virtual particles.
Further, SM posits ghost fields that give rise to virtual particles – a mathematical necessity treated with contempt by not granting the possibility that those fields are actual.
Ghost fields are as unsavory to SM physicists now as uncertainty was to Einstein. The incongruity of begrudging acceptance of virtual particles, while maintaining denial for the ghost fields from which the particles supposedly emanate, is virtual irrationality: self-contradiction between cause and effect.
The energy of virtual particles – vacuum energy – is figured to be enormous. Yet vacuum energy appears not to impact 4D in a rip-roaring way. That can only make sense if vacuum energy is mostly tucked away ED, with fleeting 4D appearances via virtual particles. But virtual particles do carry considerable 4D heft.
An electron is an elemental fermion, but it is overstatement to say that an electron has no constituents. An electron travels with an entourage, dragging a cloud of virtual particles around. The virtual cloud literally defines the electron, contributing to its mass, volume, and charge.
That the electron has an HD existence is known for several electromagnetic quantum phenomena, including near-field effects, such as induction, the Casimir effect and van der Waals force, and the quantum energy fluctuation known as the Lamb shift.
The photon is another self-standing elemental, a light-giving boson well known for its HD qualities. Virtual photons are behind static electricity (Coulomb force).
Bodies in motion create quantum vacuum fluctuations, causing photons to be emitted while dissipating the body’s motional energy. This is an example of the Casimir effect, which characterizes physical forces arising from a quantized field.
The Casimir force can, as a function of distance, oscillate between attractive and repulsive, and it can be tuned by application of an external magnetic field. ~ American theoretical physicist Frank Wilczek
Magnetic fields are caused by the exchange of virtual photons via vacuum polarization. Magnetricity flows like electricity.
When vacuum polarization happens, a background electromagnetic field produces virtual electron–positron pairs which change the charge and current distributions that generated the original electromagnetic field. Vacuum polarization is the self-energy of the photon. Generally, a particle’s self-energy is its contribution of energy or effective mass in HD interactions.
The strong nuclear force between quarks is an interaction outcome of virtual gluons. Likewise, exchange by virtual W & Z bosons results in the weak force.
All these expressions of virtuality poignantly prove that Nature is a front propped up by extra dimensions.
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Spontaneous emission is the process where an atom or molecule transitions from an excited state to one with a lower energy, emitting a photon as a tell. This everyday experience is another HD event.
Extra dimensions really exist. They’re part of Nature. ~ Edward Witten
In the macroscopic world, photosynthesis and animal sensory perception work with astonishing efficiencies, as do other natural processes at the subcellular level, including genetics. Such energy economies in organic processes are HD dynamics.
There is something beyond that which we call the visible universe; and that individual consciousness is in some mysterious manner related to, or dependent upon, the interaction of the seen and unseen. ~ Scottish physicists Balfour Stewart & Peter Tait in 1874
3D
Space is nothing else than the form of all phenomena of the external sense, that is, the subjective condition of the sensibility, under which alone external intuition is possible. ~ Immanuel Kant
No physics theory demands 3 dimensions as the nominal spatial construct. Why then does existence appear in 3D?
Nature’s love of diversity withstanding, economy is a cardinal facet of existence. All of physics pronounces it: from classical thermodynamics to quantum mechanics. Chemistry cogently coheres about energy parsimony guiding reactivity, despite the plethora of ways in which reactions may transpire.
Time is a single vector. No one questions why there are not 2 dimensions of time, because it is inconceivable how that would work.
Following Occam’s razor, the snappiest answer for 3D space as spot-on is adequacy: 3 dimensions are the fewest that can create a rich life experience.
Extra dimensions may be necessary to explain quantum and cosmological mechanics, but ambient 3D is opulently textured in a way that flatland (2D) could never approach, at the expense of only a single extra dimension.
Conversely, experiencing more than 3 spatial dimensions would create an entirely new level of complexity in experiential existence, and in so doing contravene Nature’s proclivity for economical sufficiency.
