Part 2,
We might distinguish two kinds of time: the kind involved in the preservation of the state of particles, the kind which keeps them oscillating at a constant frequency about some zero-time point, alternately moving in opposite time directions, the kind which on its own would show a universe frozen in time, all lights out. The second is an accumulative kind of time, produced by or producing changes in the energy of particles, couples to the continuing creation, evolution of the universe. Is the first kind like a sewing machine zig-zagging without thread at the same piece of cloth without advancing, pricking in the same holes over and over again at a constant frequency, in the second kind the needle speeds over the cloth, stitching events to each other, the rhythm of the needle varying locally and changing in time, dragging the zero-time point with it.
That we experience time as proceeding in the direction mass accumulates is because mass, gravity, is a machine or process which by preserving itself in time, tends to accumulate in time, and, in turn, keeps time going, a process powered by, powering the expansion of the universe. A SCU then doesn't so much evolve in time, but rather creates the time as it evolves, as it continues to create itself.
As to integrating over the future, if a SCU can have no beginning nor end, then future and past states are rooted in each other (see my reply to Steve dd 17 oct), making it less strange that such calculations yield usefull results without our universe having to be predetermined. If, like energy, time is an ambivalent quantity, if there's no clock outside the universe, no point in time and space which is more special than any other, then terms like past and future, beginning and end have a less absolute meaning than they would have in a causal, caused universe. If things only exist to each other as far as they interact and have no reality outside the universe, then they have a more fictitious or virtual character than we've always assumed and are comfortable with. So we shouldn't be too surprised if our ideas about causality, past and future only have a limited, local significance. Though we may not like this noncausality, if we live in a SCU which unavoidably has a paradoxical character, then we need to find ways to handle it if we are to comprehend its mechanics.
'Space and distance do not have a direction.'
Though this may be true for a mathematician who isn't part of his equations, a physicist cannot even in his imagination see how his universe may look like from the outside, as even a fictitious observation requires the specification of his physical relation to what he observes. As 'outside the universe' is defined as 'having no physical relation to what's inside', he would, of course, see nothing at all. As the scientist physically is part of the equation, the world he investigates, to him space, the distance to what he observes does have a direction if only because he sees processes proceed slower at increasing distances.
'The natural zeros of radius and elapsed time, makes these quantities directed ones. Positive elapsed time is the distance of a past event seen from now.' 'Temperature, length, mass, energy, entropy, elapsed time, virtually all basic physical quantities can be reduced to a onesided ones with an absolute zero.'
Though zero values are useful in physics, as a physical quantity is absent when it is zero, this number doesn't describe a physical quantity. A zero value is as unattainable for a physical quantity as the maximum number of an infinite series. In nature a zero radius corresponds to an infinite energy, a zero mass means that we talk about something which doesn't exist etcetera. It is as impossible for a massive object to have a velocity which exactly is zero as it is to reach the speed of light, so a zero can be approximated in physics but never reached. Similarly, if cooling particles to a temperature near (an also unattainable) 0 Kelvin isolates them from changes in energy and only the energy exchange to preserve their energy remains so their state is frozen in time, then their position with respect to objects outside the cooler becomes much less definite. Less affected by outside changes, they tend to coordinate their exchange, forming a collective, their indentity suppressed. If we could cool them to exactly 0 degree Kelvin, we would annihilate them.
[1] Perhaps you might say that the change in the energy of the particle (and, as seen by the particle, that of the objects of its world) is what makes the particle move in time, and, as its world changes as its own energy changes, what makes time pass to the particle. As the particles of its world also oscillate, alternate their energy sign, and we opposite energy signs correspond to opposite time directions, then the particle and its world move alternately in opposite time directions, be it at different frequencies.
