Interpretations of Quantum Mechanics
And Superstring Theories

By: Dr. Sam Vaknin

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The Science of Superstitions

The Decoherence of Measurement

The Quantum of Continuity

E. Particles

Every physical theory postulates physical entities, which are really nothing more than conventions of its formalism. The Standard Model (SM) uses fields. The physical properties of these fields (electric, magnetic, etc.) are very reminiscent of the physical properties of the now defunct pre-relativistic ether. Quantized momenta and energy (i.e., elementary particles) are conveyed as ripples in the field. A distinct field is assigned to each particle. Fields are directional. The SM adds scalar fields (=fields without direction) to account for the (directionless) masses of the particles. But scalar fields are as much a field as their non-scalar brethren. Hence the need to assign to them Higgs particles (bosons) as their quanta. SM is, therefore, an isotropy-preserving Quantum Field Theory (QFT).

The problem is that gravity is negligibly weak compared to the enormous energies (masses) of the Higgs, W, Z and Gluon particles. Their interactions with other fields are beyond the coupling strengths (measurement energies) of today's laboratories. The strong and electroweak forces get unified only at 10 to the 16th power GeV. Gravity - at 10 to the 18th power (though some theories suggest a lower limit). This is almost at the Planck scale of energy. There is an enormous gap between the mass of the Higgs particles (200 Gev) and these energies. No one knows why. Supersymmetric and "Technicolor" solutions suggest the existence of additional forces and particles that do not interact with the SM "zoo" at low energies.

But otherwise SM is one of the more successful theories in the history of physics. It renormalized QFT and, thus, re-defined many physical constants. It also eliminated the infinities yielded by QFT calculations. Yet, it failed to renormalize a gravitational QFT.

The result is a schism between the physics of low energies and the physics of high and ultra-high energies. Particle theories look totally disparate depending on the energies of the reactions they study. But, luckily, the reactions of massive particles are negligible in low energies - so renormalizable QFT (e.g., SM) is a fair approximation, althesame. At low energies, the combination of Special Relativity Theory (SRT) and any quantum theory is indistinguishable from a renormalizable QFT. These are the fundaments of a possible unification. Unfortunately, these theories break down at high energy and, though very effective, they are far from being simple or aesthetic (i.e., classic). Too many interactions yielded by the formalism are arbitrarily suppressed below this or that energy threshold. Most of these suppressed interactions are figments of the imagination at the energy scales we are accustomed to or which are attainable in our labs. Not so gravitation - also a non-renormalizable, suppressed (though extremely weak) interaction. Other suppressed reactions threaten to unsettle the whole edifice - yielding such oddities as unstable photons, or neutrinos with masses.

Hence the intuitive appeal of string theories. The vibratory modes of strings appear to us as particles. Gravitation is finally made a part of a finite theory. The drawbacks are the extra-dimensions, which seem to unparsimoniously run contra to Occam's razor - and the outlandishly high energies in which they are supposed to reveal themselves (uncurl). M Theory tries to merge QFT with the classic string theories - but this alleviates only a few marginal issues.

The more philosophically and aesthetically inclined reject the operationalism which characterizes modern physics ("if it works - I am not interested to know WHY it works or even HOW it works"). They demand to know what is the underlying PHYSICAL reality (or at least, physical PRINCIPLE). The great pre-QM (Quantum Mechanics) theories always sprang from such a principle. The general Relativity Theory (GRT) was founded on the principle of the equivalence (i.e., indistinguishability) of gravity and inertia. Even the SM is based on a gauge symmetry. Special Relativity Theory (space-time) constrains QFTs and is, therefore, their "principle". No one is quite sure about string theories.

Arguably, their most important contribution is to have dispensed with Perturbation Theory (PT). PT broke down quantum processes into intermediate stages and generated an "order of complexity". The contributions from simpler phases were computed and added up first, then the same treatment was accorded to the contributions of the more complex phases and so on. It worked with weak forces and many theories which postulate stronger forces (like some string theories) are reducible to PT-solvable theories. But, in general, PT is useless for intermediate and strong forces.

Another possible contribution - though highly theoretical at this stage - is that adding dimensions may act to reduce the energy levels at which grand unification (including gravity) is to be expected. But this is really speculative stuff. No one know how large these extra dimensions are. If too small, particles will be unable to vibrate in them. Admittedly, if sufficiently large, new particles may be discovered as well as new force conveyance modes (including the way gravity is transmitted). But the mathematical fact is that the geometrical form of the curled dimensions determines the possible modes of vibration (i.e., which particle masses and charges are possible).

Strings also constitute a lower limit on quantum fluctuations. This, in due time and with a lot more work (and possibly a new formalism), may explain why our universe is the way it is. Unconstrained quantum fluctuations should have yielded a different universe with a different cosmological constant.

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