 SPACE CONCEPT  DISCRETENESS  BACKGROUND IDEAS  PROCESS  ORDER  Web Site 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 geometryfree
(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 nonclassical oscillator. The rationale for the oscillator has its origin in the Dirac equation for the electron. The nonclassical, 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
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 nineteenthcentury 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. Title Abstract
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 twoelectron
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 freefall 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 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 20022008 Last page update 15/08/2008
