It is not about calculations, as in the standard 'shut-up-and-calculate' interpretation of Quantum Mechanics. We want to identify the physical reality at the fundamental level. We need quantum gravity, after Albert Einstein.

The task can be explained by recalling the relation of a map to the real territory: we are interested in revealing the real territory.

Let me first briefly explore the map-territory metaphor, and then I will try to explain the suggestions for improving our map.

We know that a planet orbiting around the Sun doesn't solve differential equations. We do, with our 'map'. The latter, however, contains a clear idea of a 'trajectory', which tallies to the real one in the 'territory'. All of our maps in the modern theoretical physics contain some clear ideas of what we believe could be the 'real territory' of Mother Nature, as well as some purely mathematical tools which may or may not have direct relevance to the real territory. In the case of a planet orbiting the Sun, the distinction between the two is quite obvious. Not so in the case of quantum gravity: it is still 'under construction'.

How can we improve our map without knowing the real territory? Here's a brief presentation of the method adopted by the author of these lines.

1. Take lessons from history. Some of the greatest discoveries, such as the discovery of the quantum of action by Max Planck, have been made by solving the puzzle of some immense catastrophe that hasn't happened. Thus, instead of indulging ourselves with calculations of what could happen if we're still incredibly lucky to avoid such catastrophes, we should seriously zoom on the reason why we're still alive to make these calculations. Examples: naked singularities and negative mass.

2. Hit the nail on the head. Give highest priority to all unsolved puzzles which clearly call for new physics, such as the puzzles of the vacuum energy density and cosmological constant.

3. Adopt some general strategy which could address the unresolved puzzles from both Quantum Mechanics and General Relativity.

Exactly how are we supposed to do that? Here one can hardly argue about some consensus among physicists, but since the two theories differ dramatically in their treatment of spacetime, perhaps we need to start with some new ideas on the nature of spacetime.

From now on, the choice of particular approach could be very different. It is perhaps a matter of taste or some vague aesthetic inclinations, or even a gut feeling. Here's my choice.

3.1. Start with the treatment of continuum of "points" at the scale of tables and chairs. The puzzle there is very old, since the time of Lucretius. We just have to solve it. Since the target is quantum gravity, we need some generic quantization of spacetime, which is scale-independent, and hence serves as the ‘backbone’ for constructing a background-free version of quantum gravity that is embedded in the 4-D continuum of Einstein's General Relativity ab initio. In other words, we have to start with the solution to the crucial task of the background-free quantum gravity.

3.2. Find some 'common denominator' for puzzles from Quantum Mechanics and General Relativity. How? Again, take lessons from history.

First, recall that the metaphysical idea of 'time' refers to some object which exists and changes its state 'in time'. We can think of changes in time if we have at least two "successive" states separated by a gap in which the object does not exist. This is the metaphysics of the phenomenon of transience. If there were no gaps of non-existence, there would be only one state of the object, which will not be allowed to change 'in time'. Instead of 'time', we would be living in one instant stretched to infinity which is nothing but 'eternity', after St. Augustine.

But what could be the nature of these gaps of non-existence? There is a very old idea about the nature of physical reality, which perhaps can be traced back to Chuang-Tzu: Before Zen, a tree is a tree and a mountain is a mountain. During Zen, a tree is not a tree and a mountain is not a mountain. After Zen, a tree is again a tree and a mountain is again a mountain.

Thus, we need two modes of spacetime: a local mode for the tree and the mountain, and a global mode for the gap of Zen. In the local mode, we have a perfect continuum of facts, while in the global mode we have a very different kind of reality, which is known since the time of Aristotle and Plato.

We find this gap in the so-called non-local interactions, as implied in Quantum Mechanics, and in the bi-directional "talk" between matter and geometry, as implied in Einstein's General Relativity. We also find this gap in the so-called mind-brain problem, as well as in some special "topology change" (J. Baez).

This gap still poses tremendous problems in understanding the limitations of QM formalism, the transition of quantum to classical regime, as well as some of the basic notions in Einstein's General Relativity, since November 1917.

The solution cannot be trivial. We cannot simply drop the content of this gap onto the local mode of spacetime, pretending that there is only one kind of reality. In the global mode of reality, things do exist, but they belong to the realm of potentiality. They can be 'both up and down', both 'inside and outside', and most importantly 'both one and many'. They cannot be modeled with any denumerable set, because the gap of Zen can potentially absorb everything. It is a bona fide case of actual infinity. Here's some very crude explanation of the gap of Zen:

[actual infinity] + 1  <=>  [actual infinity] + 2

As noted by Heraclitus of Ephesus, the puzzle is not in the flux of reality; it is in the bold fact that the reality is stable. Hence we need something that does not change and could make the world of facts stable: the content of the gap of Zen, in the global mode of reality. It is always [actual infinity] and hence can handle any change in the local mode of spacetime. Surely if something can carry the states of a physical system along a continual line of points, then the carrier itself must not change. Example: the gap of Zen in the human brain. Its "proper time" would be stand-still, as if you were riding a photon. It is the Unmoved Mover of Aristotle, which can act on itself, just as the human brain does act on itself: we think about our brain, with our brain.

To sum up, we use our current map, do our calculations, and if the map is correct, we verify successfully our calculations by experiments. Although we don't know the 'real territory', we can at least try to think of the real territory through our map.

What in the bi-directional "talk" of matter and geometry corresponds to the real territory of Mother Nature? It cannot be all purely mathematical tool, and nothing but pure math. There should be something real in this "talk", otherwise Einstein's theory would have never worked. Where is the Unmoved Mover (Karel Kuchar) in Einstein's General Relativity?

On the one hand, Einstein was right in his belief that "spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field". On the other hand, I believe there are many arguments in favor of some prior-geometry media (the gap of Zen) facilitating the emergence of time and space in quantum gravity. It is, however, "ferociously difficult to understand their emerging, or even some aspects of them emerging, from 'something else'" (Chris Isham and Jeremy Butterfield). We certainly shouldn't start with some non-dynamical, Riemann-flat metric à la Nathan Rosen's bimetric theory of 1974. Perhaps we should question the fundamental postulate that spacetime and the gravitational field are 'the same things': the very fact that the Riemann curvature tensor has 256 components from which we identify "just" 20 that are mathematically independent of each other (Warren Davis) is an alarming evidence that the notion of 'spacetime curvature' needs a much better presentation; see S. Carlip.

One way to demonstrate the pitfalls in the philosophy of Einstein's GR is to recall that the reality of the alleged "points" in the spacetime manifold is being determined exclusively by their fleeting physical content: it is the collective property of physical events which defines the physical spacetime manifold and its geometry. The metaphysical assumption implied here is that there are no 'empty points' (the gap of Zen) waiting patiently 'out there' to be filled with some physical content, as we calculate the 'observables' with our current Diff(M)-invariant recipe. Physically speaking, a "point" in spacetime is defined as an 'event' with some unique address in the manifold (Sten Odenwald), valid for the particular Diff(M)-invariant calculation only. Thus, in order to elaborate a physical definition of all potential points in our 4-D spacetime, and proceed to the ultimate question of the emergence of spacetime, we need the 'empty points' of the gap of Zen.

Perhaps "during" the gap of Zen we live in a special absolute reference frame or ether, which has a metric tensor equal to zero: all physical points are merged into ONE, and there is no physical distance "between" these potential "points". This is the state of physical non-existence, which is needed for the description of the phenomenon of transience, as we know from St. Augustine. Then we make the next huge step: elevate the gap of Zen into the potential future of the putative universal time arrow, and get the common media for quantum and gravitational waves, in which things are in a special Holon state, 'both one and many'. Otherwise we simply cannot understand how the human brain and gravity can 'interact with itself', how could the gravitational waves "propagate" within themselves and with respect to themselves, and most importantly the nature of 3-D space which is being stretched by some dark energy with constant acceleration. In what inertial frame would you place the ubiquitous smooth dark energy? It's absolutely everywhere, and yet 'outside' spacetime. If the spacetime were, as Einstein believed, nothing but a structural quality of the gravitational field, there will be no room left for any 'dark stuff' which constitutes 96 per cent of the stuff in the universe, and we may never understand the emergence of spacetime from 'something else': the gap of Zen elevated in the Holon (global mode of spacetime). Perhaps all we need is a bare mathematical "point" which could be the ultimate source of 'absolutely everything'. More on these very old ideas here.

One last word: I'm not a physicist, and I certainly won't be nominated for a Nobel Prize for my "advanced math" above. I need to know much more about quantum gravity in order to improve my brain training and, hopefully, develop some skills of healing people. It's very easy to move some light propeller in a sealed glass jar, but the task of sealing a gap in the spinal cord is immensely difficult, and far more complicated. Can't do it. And yet it should be possible. Perhaps many of what we call diseases are nothing but reversible functional disorders. Remember, we have two modes of reality here, and our brain might have direct access to the gap of Zen. The complete spectrum (actual infinity) of future possibilities in the gap of Zen cannot be normalized, hence the future is open up to the 'unknown unknown'. If brand new possibilities for future events can indeed be created ex nihilo, out of a bare mathematical "point", we could speculate about some universal time arrow, and then everything would be possible, the creation of the universe included. Just imagine that you can run the putative universal time arrow backwards, along the deflation time, and all actualized possibilities would be quietly fainting back into the same 'ultimate source', until you reach [John 1:1]. Only there is a catch: you cannot actually reach The Beginning, since the very same ultimate source is quietly residing 'inside' the instant 'now' (logical infinity).

So, can we develop a complete theory of quantum gravity in line with Einstein's dictum Der Herrgott würfelt nicht? Can we improve our life by influencing our common potential future? If you want it, you can make it happen, sources say.

Well, maybe. More at EPS13 in Bern.
 

Dimi Chakalov
Good Friday, 2004
Latest update: Friday, May 20, 2005