A Heuristic, Non-Mathematical Approach to Superstrings/M-Theory

By David Sears Schroeder

Premises

  1. That nature's fundamental particles, and associated fields, are inherently mutable in symmetrical ways, as evidenced by antimatter and hypothetical magnetic monopoles, and that this reflects underlying symmetries within superstring theory.

  2. That in each of the above field transformations the symmetry corresponds to a role transposition, the latter (magnetic monopole) being more complex than the former - entailing a role transposition of the electric and magnetic variables of the electromagnetic field.

  3. That higher order field transformations along the same lines - correspond to the long conjectured supersymmetric partners, that it is hoped will be detected at the Large Hadron Collider during the 2015 - 2018 run.

  4. That these higher order field transformations will entail the transposition of the roles of the fundamental forces of nature, which collectively form the components (or variables) of the superforce, and that, consequently, supersymmetry is more generic1 than supposed.

  5. That the role transposition of any pair of fundamental forces leads to a new pair of fundamental forces with unique properties. The transposition operation is therefore non-commuting.

  6. That, to preserve symmetry, the role transposition of any pair of fields entails: 1) a reciprocal trade of force strengths, and: 2) each field coupling to the other field's type of force. The first condition is surmised to correspond to a form of duality, while the second condition is regarded as the physical manifestation of fermionic/bosonic spin shift.

  7. That the fundamental forces of nature reduce to three (strong, electroweak, gravity) when seen from the vantage point of the electroweak unification scale, and above.

  8. That the total number of transpositions (permutations) with three elements is equal to six (N!, where N=3), and that these six principle field restructurings of the superforce correspond to the six subtheories of M-theory - the framework of superstrings (M-theory consists of five ten dimensional string theories, and eleven dimensional supergravity).

  9. That each of the three fundamental forces (as defined in 7) is characterized by three primary degrees of freedom, and three secondary degrees of freedom, that internally relate to one another via local gauge symmetries (see text). This equalization of degrees of freedom must enable nature to rationalize the role transpositions between the three forces.

  10. That there is a hierarchy of lower order transpositions, as a consequence of the multiple degrees of freedom per force, so that each of the six facets of M-theory has numerous variants. It's surmised that this hierarchy of transpositions reflects the recently discovered non-commutative matrix nature of M-theory, at the fundamental string geometry level.

  11. That the hierarchy of field transpositions is always present in the quantum background as virtual vacuum fluctuations, influencing the behavior of matter. It's presumed that there exists six principle sub-theories of M-theory that constitute the lowest energy transpositions, and are therefore first order contributors to these vacuum fluctuations.

  12. That the transposition of the electro-magnetic (primary-secondary) degrees of freedom with the space-time (primary-secondary) degrees of freedom (encompassed within the electroweak/gravity transposition) gives rise to an equivalent pair of fields with extraordinary properties. This transposition is assumed to be first order.

  13. That one of the two fields devolving from the transposition in 11 would be a direct analogue of our space-time continuum in its intrinsic strength and structure, except that, this field's space and time variables would possess electric and magnetic properties. As such, this field is denoted as the electric magnetic continuum (emc).

  14. That the other field devolving from the transposition in 11 would be a Maxwell type field in it's intrinsic strength and structure, but in which, the electric and magnetic variables are replaced by space and time variables. This novel field is dubbed the spatiochronetic (SC) field (where chronetic is derived from the Greek word chronos for time).

  15. That the SC field (in conjunction with the emc) corresponds to the supergravity subtheory embraced within M-theory. Since the SC field is gravitational in character, strongly coupled, and bipolar it possesses the correct properties to account for the cancellation of divergences in the quantization of gravity.

  16. That, by virtue of being embraced within the supergravity family, the photon of the putative SC field must possess considerable mass (supersymmetry energy scale: 50GeV - 1 TeV), restricting its maximum range to several orders of magnitude less than the weak force. This SC photon is identified as the gravitino in the supergravity field theory.

  17. That virtual SC waves (in the form of SC photons) will be especially prominent in proximity to elementary particles, in consequence of the extreme concentration of mass/energy, and that this group of SC waves will possess a mean wavelength determined by the mass of the particle. This "wave packet" will be highly localized as a consequence of interference between waves and the finite range of the SC photon.

  18. That SC waves constitute a sinusoidal expansion/contraction of space in phase with a sinusoidal expansion/contraction of time, both of which average out to zero, and that these oscillations correspond to the "internal periodic phenomena" intrinsic to all fundamental particles, as predicted by Louis deBroglie in 1923.

  19. That the reciprocal force trade asserted in 6 imposes an intrinsic strength, for the spatial and temporal variables of the SC field, 42 magnitudes larger than the warpage of space-time embodied in ordinary gravity. In consequence, the vacuum enveloping fundamental particles - that is, within the range where the flux of virtual SC photons are present - should be subject to immensely strong fluctuations in curvature that must, nonetheless, average out to zero, or flat space. These curvature fluctuations of the metric should be highly localized, by virtue of the limited range of the SC photon's field.

  20. That, during the expansion phase of these fluctuations, the spacetime curvature would clearly need to be positive, so that there would be a mismatch between the externally measured volume and the internal volume. During the contraction phase the spacetime curvature would necessarily go negative, so that overall curvature fluctuations average to zero. Such expansions and contractions could potentially be superluminal, depending on their absolute magnitudes3 and duty cycles.

  21. That the intense localized oscillations in metric curvature, due to vacuum derived SC photons enveloping every fundamental particle, will equate to a cyclical motion of regression and advancement relative to external reference frames e.g. other particles. This cyclical change in effective distance between quantum particles should, in turn, lead to a desynchronization of clocks sync shifts (relativity of simultaneity), part of the suite of Lorentz transformations. To distinguish it from its macroscale counterpart it is labeled the quantum sync shift

  22. That the quantum sync shift being bipolar like its source - the SC field - will induce a sinusoidal forward/backward oscillation through time in all fundamental particles, as seen from other particles. This is in contrast to the temporal component of the SC field, which would induce a cyclic slowing/accelerating of the rate of temporal passage. A direct result of the influence of the quantum sync shift in the microworld is that the present moment for every fundamental particle will always be in flux, oscillating between the past and the future, but averaging to the local present, or zero.

  23. That the cyclic quantum sync shift - a derivative of SC oscillations, and modified by observer dependent relativistic time dilation - is the essence of deBroglie matter waves, and therefore, a vital ingredient underlying the Schrodinger wave equation, and thus wave mechanics4.

  24. That, the potentially huge cyclic variations in spatial volume, within a microscopically confined region about every fundamental particle, can account for the enormous disparity between typical deBroglie wavelengths, and the observed physical size of fundamental particles.

  25. That, if deBroglie waves correspond to cyclic displacements in time, as proposed in 24, they cannot involve the transport of energy from place to place, as Louis de Broglie surmised in his original 1923 Comptes rendus paper.

  26. That the dominant axis of virtual SC wave oscillations, enveloping a quantum particle, may coincide with the spin axis of the string composing that particle. And, since the SC field replicates the geometry of the electromagnetic field (on a microscopic scale), the sync shift may not be asymtotic, but exhibit a preferred axis. Spin alignment would then be a necessary condition to optimize coordinated temporal interactions between multiple particles.

  27. That a Bose-Einstein Condensate (BEC) is possible because of the temporal distribution of its constituent elements. In a BEC thousands, (or millions) of bosonic, integer spin atoms share the same quantum wave function - a common set of deBroglie matter waves. The physical size of a true (lowest energy state) BEC is the same as a single atom. To account for the absense of mutual electrostatic repulsion tearing such an ensemble of atoms apart, it must be concluded that the individual atoms are uniformly distributed temporally along their commonly shared deBroglie matter wave such that they are spacelike separated, and thus do nots electric fields.

  28. That the Pauli Exclusion Principle operating among a group of particles may, in part, arise from the condition of spacelike separation between the particles, as a function of their regular temporal spacing along their individual deBroglie waves.

  29. That the sinusoidal forward/backward oscillation through time experienced by all elementary particles induces a corresponding modulation of the particles positions in 3D space, which in conjunction with the temporal oscillations leads to their wavelike nature (interference, etc.).

  30. That, should it some day be possible to synthesize (in sufficient quantity) the conjectured spatial charges (selectrons, squarks), and combine them into stable supersymmetric matter, then it should, in principle, be possible to create large scale quantum effects. Presumably, reactionless physical motion could be induced in macrosized objects. This might be accomplished by enveloping the object in a skin of conducting supersymmetric matter (the supersymmetric analogue of a metal in ordinary matter), and maintaining this 'skin' at cryogenic temperatures. It would then only be necessary to manipulate the relative phases and amplitudes of large scale spatial 'currents', within this skin, at various locations around the object.

    Text of The Field Interchange Hypothesis

    FOOTNOTES

    1. By 'generic' is meant that every transposition of a pair of fundamental forces is assumed to correspond to a supersymmetry operation. This notion would seem to be at variance with supersymmetry theory, which predicts a single set of supersymmetric partners that differ by a half unit of spin from their standard model counterparts. The resolution of this apparent paradox is that spin is surmised to be a function of perspective. If the observer is physically composed of one of the other field transposed types of matter, then another one of the six basic field structures embraced within M-theory will correspond to his supersymmetric matter.
    2. Intriguingly, the form of the conjectured SC wave mimics the acceleration free character of the Alcubierre warp metric, at certain points along the wave. An electron entrained between a minima node and maxima node of an SC standing wave would be continuously preceded by a region of contracting spacetime, and trailed by a region of expanding spacetime. This is precisely the recipe for an Alcubierre warpdrive, in which a hypothetical spaceship, enveloped in such a modified space-time metric, would experience a free fall geodesic, even as the whole disturbance is undergoing acceleration relative to external space-time. This may be significant for the absense of synchrotron radiation from orbiting electrons in quantized, standing wave Bohr orbits, except that the imputed range of the SC field is many orders of magnitude smaller than the circumference of a typical atomic orbit.
    3. If the magnitudes of such expansions and contractions were sufficiently large, the resulting forward/backward displacements in time for every fundamental particle would span the entire age of the universe. Assuming such temporal displacements modulate the physical positions of particles in 3D space with equal magnitude, the particles will take every possible path in space, weighted by a probability function - a result that parallels Feynman's Path Integral formulation of quantum mechanics.
    4. It's notable that Schrodinger suggested that the wavefunction for deBroglie matter waves is analogous to the field variables in electromagnetic waves. The SC field is modeled as a Maxwell field with space and time variables, but confined to short range, because of the mass of its photon.