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Discrete Quantum Gravity  
spacetime is not always everywhere!

Quantum gravity needs to couple the two systems of representing the world we experience at the level of particles. One represents the way reality is and the other the way reality will be—what we experience now and what comes next. Observed reality is described using the principles of locality and geometry. By contrast, those two principles do not apply to what comes next, before it has arrived; they do not govern the transition from what is to what follows. Therefore, the classical geometry of spacetime and locality emerge concomitant with the arrival of what comes next. It is as though what comes next, for a particle, begins in a geometry-free (background independent) state then arrives in a state which is subject to the principles of geometry and locality.

The discrete scheme models the particle as a non-classical oscillator. The rationale for the oscillator has its origin in the Dirac equation for the electron. The non-classical, or quantum nature of the oscillation arises from the the unreal physical consequences of the equation viz. negative energies, motion at c of the electron and an equal role for space and time in its description

Mass, Inertia and Gravity
Why bother to try to quantize gravity? The answer adopted here has to do with mass. Since mass is the source of momentum for quantum mechanics and it is the cause of gravity, intuition suggests that the behavior of the mass of an elementary particle, such as an electron, should be the cause of gravitational and inertial effects. Indeed, the equivalence principle demands the unification of inertia and gravitation. The question is: how does mass behave that makes it turn out that way? It is not without interest that for Einstein the new concept of mass was the most important consequence of Special Relativity.

A discrete theory of the action of mass might show the connection between quantum mechanics (QM) and General Relativity (GR). It has often been said that if QM is to be coupled in a single theory with GR the concept(s) of space and time will have to undergo a major overhaul. QM will have to be recast in a framework of background independence. That requirement is no simple matter. A fundamental element of quantum field theory is that quantum systems move in a background of curved space. Such a theory cannot be divorced from that framework.

Discrete Space and Time
In the discrete scheme, space and time are quite different from the usual picture in GR and yet when coupled, spacetime turns out to be background independent and gives elementary particles (e.g. the electron) a framework to act quantum mechanically and manifest classically. On one hand, Einstein insisted that the gravitational field was the spacetime which relates objects. They are identical and DQG agrees fully with that proposition. This is crucial for the discrete scheme because it rules out one spacetime sitting on or in another. There is no spacetime-nesting in the discrete scheme. Einstein also asserted that in the absence of matter there is no spacetime or gravitational field. Mass/energy is the cause of the gravitational field and therefore it is the cause of spacetime. If this is not an empty proposition, with respect to microscopic reality, then it is possible that under some conditions there is no spacetime or matter. This consequence of GR cannot be understood physically in continuous theories, whether of gravitation or anything else. It is clearly problematic, even though it is a necessary corollary of the identity of gravity and spacetime! But can it be physically realized?

From the perspective of the present scheme, the absence of spacetime and matter is a logically necessary condition of discrete spacetime. For if discrete spacetime pieces are not simply floating in a background of continuous spacetime, or seamlessly stitched together in some way, they form a physically contiguous series as distinct from a single continuum. If seemingly continuous space and time are in reality contiguous regions of discrete spacetime then perhaps the absence of spacetime separates the discrete regions.

The distinction between continuity and contiguity of spacetime is crucially important for any theory of discrete microscopic reality; everything else is secondary. It is so important that the theory must hinge upon how to distinguish the two possibilities. Empty space and vacuous time are in principle undetectable, but contiguous discrete spacetime must differ from continuous spacetime. This becomes a major philosophical problem: vacant spacetime is undetectable and we need to determine whether its apparent continuity is or is not a consequence of spacetime contiguity. The theory must either make testable predictions, that depend upon the contiguity of discrete spacetime 'pieces' and are impossible in the alternative geometry, or have considerable explanatory power. An example of the unexplained might be a principle from which quantum mechanics arises naturally—if there is one.

Einstein’s assurance that the absence of spacetime means the absence of matter, introduces a problem for Planck size pieces of spacetime which have to accommodate electrons that are twenty orders of magnitude larger. Electrons whose mass and charge are continuous in time must not extend across gaps devoid of spacetime; they cannot survive such a transition. The usual way of dealing with this type of problem is to retreat from reality into the Platonic world of mathematics, where support can be found for almost anything. But that won't do for a theory of microscopic realism which applies to the physical world but rejects continuity.

The discrete scheme has no use for the ether that Einstein made redundant 100 years ago and neither has it a use for objective spacetime which is either empty or preexisting. The 150 year old field concept is also unnecessary. The most that can be retained of what was the nineteenth-century field concept is an immaterial region of influence, not something that moves and interacts and has a life of its own. Electrons, protons and photons are all particles in the theory and they each oscillate between actual and potential states.

On the Quantum Gravity of the Electron

In the search for a coherent theory of quantum gravity we investigate the discrete model of the electron from the perspective of its autochthonous geometrical framework. The form of the model is a minimalist oscillation out of which evolves a continual serial transition between quantum and classical behaviour. The postulated oscillation reduces the electron of continuous physics to a series of discrete motionless events (the classical part). The geometric relations among events are energetically created by the nonlocal behaviour of the electron (the quantum part). Here we show that the discrete model provides a framework within which a coherent explanation of the cause of gravity is possible. In an ideal two-electron universe the geometrical relations of the enduring particles exhibit the features of classical gravitation. The locus of each motionless event arises from nonlocal quantum mechanical action which is subject to initial conditions that derive from the geometric relations of its immediate antecedent. The serial relative positions occupied by each electron describe curved geodesics which are deviations from their discontinuous inertial motion, in the form of reciprocal free-fall acceleration. The rate of acceleration is independent of the mass of the object. The magnitude of the gravitational effect varies as the inverse square of the distance and is proportional to the mass of the attractor. Gravitation is geometry in action; it is instantaneous, repetitious and background independent.

PACS numbers: 04.60.-m, 12.90.+b, 13.40.Dk, 14.60.Cd

Full Text
is here

A more detailed description of the electron in a quantum mechanical and background independent framework, can be found here in two preprints.

Comments and questions are welcome to pjf@it.net.au

© Peter Fimmel 2002-2008

Last page update 15/08/2008