... X Y Z T X -1 0 0 0 Y 0 -1 0 0 Z 0 0 -1 0 T 0 0 0 +1
A particle moves in a straight line in this Fundamental Metric, where there is no time dilation; where the time-time element g44 = +1, which is an invariant 1 s/s rate in all frames, the same rate we each experience in our inertial frame as we evolve along our worldline. It represents a null gravitational field. Though a useful tool in GR, Einstein admits this metric most likely cannot exist in finite space. If it did, there would just be a single, infinitesimal, particle, and it would have a zero velocity, regardless of the X, Y, Z components of the metric, as there would be nothing to relate its motion to. Space would appear flat and have no dimensions as there would be nothing else to relate distance to. He considers this situation to be in vacuo. In saying this state probably cannot exist in a finite region, he is confirming the author’s conjecture that the spacetime continuum is energetic. It cannot be otherwise.
This isn't true, you can have motion in Minkowski spacetime (the flat space whose metric you are referring to as "the Fundamental metric") it just doesn't have gravity.
Re: questions on review process, thoroughness, etc.
What Captcass is saying makes no sense, so this is more for the interest of others.
Do you know that in quantum mechanics an "observer" doesn't have to be a conscious being but anything that gets in the way and thus resolves a property of the particle in question? Like hitting an electron momentarily resolves the question of position of another particle.
What exactly qualifies as an observer is currently not entirely resolved. We do have some results suggesting that there are issues with applying QM to other observers directly, but this is an ongoing area of research.
Electrons don't have a position, so really you aren't resolving that property when you observe it. It's more that you make the electron report a position to you, or as some physicists like David Mermin say "give you a position experience". QM doesn't actually describe what microscopic objects are like, it describes what reactions they give to observers when observers probe them.
Quantum Theory predicts probabilities for a how a system will react to certain kinds of questioning/probing/measurements/way of looking at it given: (a) What way you are measuring it (b) The results of previous measurements, along with what exactly those measurements were.
Once you get a reaction to your measurement it then provides rules for updating your expectations of future reactions (those rules were once called "collapse", but today we say "state reduction" or "Bayesian updating")
However note that the predictions depend on what you've witnessed before, so different users of quantum theory can disagree on the probabilities. Probabilities are subjective
Also the different ways of looking at the system don't cohere or make sense together. It's just a collection of incompatible subjective "impressions" of the system that can't be made sense of together. Impressions are subjective
Obviously these two forms of subjectivity are not what one normally wants in a fundamental theory, but it seems to be the way the world is. Quantum theory deals with your probabilities for reactions you might receive from micro-systems.
What happens for classical things like a stone is that Quantum Theory says that every way of looking at it makes sense together and that they can be combined into one cohesive picture. The probabilities are also definitive and don't depend on the observer.
Thus it says there will be inter-subjective agreement. All observers should expect to see the same reactions for each given way of probing and all ways of probing make sense together. Thus you can detach the observer from the description and speak of what the stone is "actually like" independent of any observer.
Since you can now speak of the stone without reference to anybody, i.e. as it is in itself, you are then able to have equations for the stone that predict what it will be like in the future and was like in the past. In other words its history and predictions for its future.
Since we can't detach observers from the description of micro-systems we can't really speak about their past which is a bit of difficulty for cosmology in some areas. It also means statements like "the protons in your body were once in stars" are not strictly true.