Bernard,
In my essay I asked myself: How can a universe create itself out of nothing, without any outside intervention?, so I cannot but agree with your statement that
''If the Universe is emerging from nothing, not only the stuff (matter, particles) but also the physical laws .. and space-time must emerge from nothing.''
We can only understand a universe rationally if it obeys the conservation law which says that what comes out of nothing must add to nothing, so such universe has no physical reality as a whole, but only exists as seen from within. A Self-Creating Universe (SCU) then must be like a zero splitting itself continuously in positive and negative numbers, their sum always staying nil, a perpetuum mobile which yields as much as it costs: nothing. This conclusion has all kinds of interesting consequences for physics.
A Big Bang Universe (BBU) is supposed to have been popped up from one moment to the next, all particles properties calibrated to the last decimal, as if there has been a previous calculation as to what properties and constants might work, something which is hard to do before the existence of anything, of a physical calculator.
Since in a SCU particles must create themselves, each other, particles and particle properties must be as much the product as the source of their interactions, so here you'd expect particles and the laws ruling their behavior to evolve in a trial-and-error process. In a SCU particles don't causally precede stars and galaxies nor vice versa: processes in stars and galaxies are part of the of the creation of particles, the design of particle properties, of their evolution, which is a calculation in progress.
In a study (see www.quantumgravity.nl) (where my essay is a very short and incomplete summary of), I propose a (qualitative) mass definition based on the Uncertainty Principle (UP): the less indefinite the position of a particle (or mass center of an object) is, the greater its mass is. If forces upon a particle can be stronger as they are more exactly equal from all directions, and they are more precisely equal within a smaller area as these forces are stronger, which they are as the mass of the particle is greater, then its position is less indefinite as its mass is greater and vice versa. As the force on it and definiteness in its position also depends on the mass and mass distribution in its environment, its mass in this definition automatically is a relative quantity. Indeed, if particles are both the product as the source of the force between them, then we cannot really distinguish mass from the force it exerts, unlike a BBU where mass is thought to be only the cause of gravity, as if mass can precede gravity. If a larger distance between particles is a less definite distance, and particles can only exchange energy (see below) at a frequency the definiteness of which corresponds to the definiteness in their distance, then the frequency they exchange energy shifts to red at larger distances, which agrees with the fact that clocks in a SCU are observed to run slower as they are more distant even if they are at rest relative to the observer. In another chapter ('The color of light') this definition is shown to be consistent with relativity theory. Though this is just a first, cursory analysis, I expect that it is possible to derive relativity theory from the UP, using the proposed mass definition. As in a SCU particles are product and source of their interactions, here forces never become infinite, so we don't get the infinite self-energies of QED not the singularities of a BBU-based GR.
If, as I argue, the 'speed' of light c doesn't refer to a (finite) velocity but to a property of spacetime (which is something else entirely) then the communication between particles at different spacetime points is instantaneous. So the 'hidden variables' Einstein needed to avoid indeterminism, can be identified as the energy exchange by means of which particles express and preserve each other's properties, its instantaneousness making self-evident things like the EPR paradox, entanglement and the results of the double-slit experiment.
However, the unpredictability Einstein wished to eradicate remains since (in a SCU) particles and particle properties are as much the effect as the cause of their interactions. It is because the exchange of energy, of info between particles is unobservable as long as they are in equilibrium that we have been able to remain ignorant of it: because we've always assumed that particles have passively been created, so only can be the cause of fields and forces. This exchange only becomes observable when their equilibrium is disturbed and net energy is emitted or absorbed.
The UP is interpreted to say that virtual particles can appear by borrowing the energy to exist from the vacuum, for a time inversely proportional to their energy. From the UP it is but a small step to a SCU where real particles can be thought of as virtual particles which by alternately borrowing and lending each other the energy to exist, force each other to reappear again and again after every disappearance, at about the same place. The smaller, the less indefinite their distance, the higher the frequency they exchange energy at, the higher their energy is. As in this view particles express and preserve each other's mass by continuously exchanging energy (the sign of which then alternates), the origin of mass is obvious, as is the equality of inertial and gravitational mass. A SCU therefore has no use for Higgs particles, string theory, nor does it need a big bang, a cosmic inflation and dark energy to explain observations.
As to the arrow of time, in the study and essay I try to show that time is powered by gravity, that gravity is the expression of the inherent property of mass to keep creating itself: the existence of gravity, in fact indicates that we live in a SCU, not in a BBU.
Anton