The emergence of spacetime

Der Herrgott würfelt nicht!
(God casts the die, not the dice)

I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are details.

Albert Einstein



Your Global Time is ZERO


This site will be officially announced on March 14, 2004, to commemorate Albert Einstein's 125th birthday. If the universe is ONE entity evolving along a putative universal time arrow, there is no room for 'playing dice', since this ONE state will choose one state of all sub-systems, one-at-a time. The rest of the possible potential states will be kept available for the next step of the universal time arrow.

Let's not be frighten by this ONE state. It can be derived with the same notion of infinity, which we use for calculating any "point-like" value of physical quantities or probabilities. It is the notion of infinity that we use, without any hesitation, to pass from physics to geometry. If we use it again, "in the limit" everything could be ONE. We just don't know. What we do know, however, is that if we use geometrical "points" to describe the physical world, there is no ban for using the notion of infinity to derive 'the universe as ONE'. In the context of Hindu catechism, The One is an unbroken Circle (ring) with no circumference, for the circumference is nowhere and the center is everywhere. There's nowhere where God is not.

What if this ONE state is alive as well? Welcome to 'Einstein and PHI'! Our goal is to discover the quantum gravity of He Who Does Not Play Dice. The task looks very simple: discover the mechanism of selection and actualization of one possibility amongst many. However, it's not 'one out of 101230 possibilities', as suggested by R. Penrose, but 'one out of UNcountable infinity of possibilities'. Think of the latter as some virtual dough of quantum propensities, much like the amplitude density in Feynman's path-integral approach to QFT. Moreover, the mechanism of selection and actualization of 'one possibility' must also provide an answer to the question of what happens with 'the rest of possibilities'. In other words, we are talking about some cosmological version of Schrödinger's cat, albeit the cat states do not, and cannot form a set, since they are in a special holistic mode of UNcountable infinity of possibilities. The end result is well-known: we live in a 4-D spacetime, the objects around us have well-defined, point-like location, and we can teach our kids how to apply the notion of infinity in, say, calculating the circumference of a circle, after Archimedes.

I don't think this task can be achieved with any probabilistic physics whatsoever. We need the quantum gravity of He Who Does Not Play Dice.

Einstein wanted to know 'His thoughts', and wanted to discover the phenomenon which can determine exact, point-like values of all physical quantities. I call 'His thoughts' causal field, and suggest that the whole universe evolves like a human brain along a hypothetical universal time arrow which runs the human brain as well. If we model the universe as a human brain, the brain correlates of what we call 'context' -- not their subjective presentation in our mind -- should be sought in our current Weltbild. Hence the 'context' of the universe-as-a-brain is called causal field. It is produced from the whole universe as ONE, which enables all sub-system to "talk to each other" and correlate their evolution along the universal time arrow: think globally, act locally. This is, in plain words, the interpretation of 'His thoughts'.

The causal field is a new kind of reality, potential reality. It is a physical stuff. Just think of the whole universe as a huge brain, and put aside the question of its mental or spiritual correlates: quantum gravity should be able to answer the question of the physical correlates of God as ONE, but nothing else. If God is ONE, we should be able to identify His physical correlates/imprint in modern theoretical physics, but nothing else. (If we were able to prove the existence of God, all our religious beliefs, anti-theism included, would be reduced to science and math.) The determinism emerging from such Weltbild is identical to the determinism in living matter: it does involve the flexibility of choosing one possibility amongst many. How many? The upper bound, if any, would be infinitely many. I mean, actual infinity, since the 'chooser' is 'everything else in the universe' stored in the hypothetical causal field. Then we can enjoy "points", and build the 4-D continuum of the Theory of Relativity. It all started with the seminal paper by A. Einstein, which he filed on June 30, 1905.

I anticipate severe resistance from the established physical community, since I strictly follow Einstein and do not talk about God with anthropomorphic concepts. We're talking science here. God could be a bare mathematical "point" hidden inside the instant 'now' from the universal time arrow. Always been there, always will. Unlike religion, this statement can indeed be verified. It's a matter of math and clear thinking. Nothing else. "The rest are details" (A. Einstein).

The importance of Einstein's heritage to the project of PHI (Physics of Human Intention) is enormous. The link can be revealed in the postulated two modes of spacetime, global and local. We can understand the global mode of spacetime with the help of a simple experiment, which everyone can perform with her/his brain. From the perspective of the local mode of spacetime, the frozen static "holder" of the unchanging human self corresponds to a timeless static world, which does not change in the local mode of spacetime. The time read by an inanimate physical clock corresponds to this local mode of reality, and such inanimate physical clock will read the intrinsic "time" of the global mode of reality as zero, just as if we were riding a photon. We can picture the global mode of spacetime as a pocket of propensities attached to each and every "point" from the local mode of spacetime, and from this pocket of propensities one, and only one, next state is being actualized, in line with the rule "think globally, act locally". Just like the human brain.

Hence the local mode of spacetime is being build from the propensities kept in the global mode: a perfect (not coarse-grained) continuum in the local mode, and a discrete lattice in the global mode, which is totally hidden (or rather transparent) in the local mode due to the "speed" of light. However, in present-day theoretical physics, there is no room for the potential future of the universal time arrow and the global mode of spacetime.

The confusion is very old. The solution is very simple: the nature of gravity requires these two modes of spacetime. They can be revealed in both General Relativity and Quantum Mechanics. The predictive power of GR and QM can be explained with the global mode of reality which can indeed be calculated for one, and only one, instant in the local mode of spacetime. Then we 'run the wheel' and calculate "trajectories", and since the global mode of reality will be converted into a local mode in the future anyway, in many cases our calculations predict correctly the probabilities for occurrence of physical events in the future. Regrettably, this creates an erroneous impression that the Newtonian time has something to do with the "time parameter" in the Schrödinger equation.

Then there is a great puzzle with the so-called gravitational waves and black holes, which many people persistently ignore. The input from the global mode of spacetime cannot be 'swept under the carpet' anymore. It strikes back as the puzzle of dark mass & energy and cosmological constant. Going back to the 1917 debate between Einstein and Levi-Civita, we can understand why both men were right: they were implying different modes of reality, global and local.

From the perspective of the local mode, Einstein was right: if the total energy-momentum of a closed system would always be equal to zero, this would not allow the existence of the system under whatever form in the local mode of spacetime (reference here).

On the other hand, Levi-Civita was also right: the correct mathematical model of the gravitational waves has to be cast in the global mode of reality, since these "waves" do not, cannot, and should not impose any physical force whatsoever: 'His thoughts' are not physical (there is a subtle issue here; please see below). These gravitational waves "propagate" in the global mode of spacetime, along with the quantum waves, and their joint "evolution" is strictly non-unitary, thanks to which they can explicate -- in the local mode of reality -- infinitely many (actual infinity) quantum propensities, one-at-a-time, and with unit probability.

But in the 4-D spacetime of the local mode of reality, both waves are physically nonexistent. They simply don't exist there for more than one instant, as read by your (inanimate) clock. Of course we can calculate this instant, but then we wrongly assume that the gravitational waves would propagate along some trajectory. There is no background time parameter in the local mode of reality, which could time the "ripples" of the metric of that same local mode of reality. We cannot, even in principle, pin down the time parameter of this trajectory, as we were playing Frisbee on the beach. My dog can, LIGO cannot. Increasing LIGO's sensitivity -- that's the magic word, isn't it? -- won't help with detecting the global mode of reality. More on this issue here.

"Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve", says John Wheeler. This bi-directional talk "takes place" in the global mode of spacetime. The ultimate 'chooser' in the quantum ream is "placed" there, too.


Note that in the bi-directional talk between matter and geometry, the input from the matter fields has to be cancelled by the opposite input from its "just-created" gravitational field, or else the metric won't by dynamical but will display some preferred reference frame in the local mode of reality, in sharp violation of the principle of general covariance. However, this mutual cancellation cannot be actually accomplished; it is merely a dynamical cancellation process that tends asymptotically toward its dead-end -- the mathematical "point".

Thus, when we say that 'His thoughts' are not physical, we imply this last stage of total cancellation (see 'the grin of the cat'), which is not physical at all, in the sense of Einstein's argument above. It pertains to the global mode of reality. I think this is the only way we could 'have our cake and eat it', by keeping both the general covariance and energy conservation. If we confine ourselves to the local mode of spacetime only, the conflict between the diffeomorphism freedom and energy conservation is severe, to say the least.

Perhaps the most important issue here is the dynamical nature of the cancellation process and the 'vanishing small' (=tending asymptotically toward zero) cosmological constant, since we have to solve the coincidence problem and the cancellation puzzle in one stroke.

The cosmological constant problem is produced from the erroneous search for the global mode of reality in the local mode, and all we can say, after Feynman, is that "we're missing something in our formulation of the theory of gravity." Sure, but instead of exploring the global mode of spacetime, which boldly shows up in the "timeless" mode of 'the only truly isolated system' in the Wheeler-DeWitt equation, most of the physicists are trying, one way or another, to eliminate it (a notable exception is Bill Unruh). How can we eliminate 96 per cent of the universe consisting of some "dark matter" and "dark energy", after the cosmological constant? How can we eliminate 'His thoughts'?

In a letter to P. Ehrenfest on 4 February 1917, Einstein wrote about his attempt at introducing the cosmological constant: "I have again perpetrated something relating to the theory of gravitation that might endanger me of being committed to a madhouse. (Ich habe wieder etwas verbrochen in der Gravitationstheorie, was mich ein wenig in Gefahr bringt, in ein Tollhaus interniert zu werden; English translation by N. Straumann)"

It was, in fact, a brilliant guess. Now, all we have to do is to spell it out with math. As a bonus, we could develop a theory of the brain, since all these ideas have originated from brain science and psychology.

I sincerely hope that we can complete this project by 30 June 2005, to celebrate Einstein's Annus Mirabilis.

Now is the time to get ready for GR17. We certainly don't want to make him feel as a shoemaker on his 125th birthday, and during the celebration of his Annus Mirabilis in 2005.

D.C., March 14, 2004, 3:01:25 AM GMT
Last update: May 20, 2005
I should not want to be forced into abandoning strict causality without defending it more strongly than I have so far. I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.

A. Einstein, Born-Einstein Letters, 29 April 1924


The local and global modes of spacetime in pictures:
The infinitesimal segment AB


Fig. 1


Fig. 2


Fig. 3
Fig. 4

What follows is an outline of my intended oral contribution to EPS13.

Suppose you travel by train (say, from London to Brighton), and your wristwatch reads the duration of the whole trip as being composed by infinitely many and infinitely small segments AB (cf. Fig. 1). I will picture the global mode of spacetime with  Z  (from 'the gap of Zen'), and will decompose the infinitesimal timelike displacement AB into 'beginning' at A (Fig. 2) and 'end' at B (Fig. 3). The state of the train in the gaps of the global mode is both "timeless" and "spaceless", and your inanimate wristwatch would read its duration  AB  or  AAz  as zero (Fig. 4). It has to be read as zero by your wristwatch, because your trip is along a continuous trajectory in the local mode of spacetime.

Thus, we postulate a new degree of freedom of the spacetime continuum, modeled with  Z , which springs 'from inside' the infinitesimal  AB .

Please note that in the local mode we have a perfect continuum: we postulate that the gaps in the global mode, along the  Z  line, are hidden due to the so-called speed of light (to be explained in my oral contribution to EPS13). Very briefly: Consider a hypothetical source of points, call it {X}, which generates points/events, {E}, by some hypothetical mechanism of absorption-and-emission of single discrete photons in the local mode {E}. What matters here is to suggest an explanation of the "gaps" in {E}, which are totally transparent "inside" {E}, hence making the latter a perfect continuum: the local mode of spacetime.

Imagine an observer in {E} equipped with a clock. At some instant t0, she records retrospectively an event  t0  that has already been produced by the emission of a photon from {X} and its absorption by {E}. The intrinsic "duration" of this absorption/emission is strictly zero, according to the observer in {E}. The next emission of a photon from {X} and its absorption by {E} will produce the next "neighboring point" (a.k.a. the infinitesimal timelike displacement,  AB , cf. Fig 1) in {E}, call it  t1, and so on.

Hence {X} literally builds up the 3-D space {E} by "expanding" the number of points in it: t0, t1, t2, ..., tn, ...  [ad infinitum]. All these points have zero dimensions and are "separated" by zero "intervals" in the local mode of spacetime, hence perfect Euclidean continuum, perfect "clock" with elementary steps  AB , and a scale-independent 'back bone' for canonical quantum gravity. In turns, the very expansion of the 3-D space produces "time", and the observer in {E} will say: hey, I can draw a "temporal" axis orthogonal to my 3-D space, so I actually live in a 4-D spacetime! Sure. But this additional "temporal axis" is just the coordinate time in STR, which loses its meaning in Einstein's GR, and completely and totally disappears in all background-free theories of quantum gravity. Most importantly, this new "temporal axis" is orthogonal to both the 3-D space {E} and  Z

For illustrational purposes, I have reduced the dimensionality of  {E}  to 1-D space in the drawing here, and have denoted the expansion of points with [x]. I hope the reader will immediately notice that her/his coordinate "time" is missing. It isn't interesting anyway. Some people, however, are trying to detect the "gravitational waves" only and exclusively only along the local mode of spacetime {E}. Yes, it is a perfect continuum, but -- no, you cannot detect these "waves", since they live in the global mode, as modeled with  above. The two modes overlap only "inside" the apex of the light cone.

I will also try to explain the issue of relativistic "collapse", will argue that the only possible way for such event to be embedded into Minkowski spacetime would be if the relativistic "collapse" enters all reference frames through the apex of Minkowski cone from the Holon in the global mode,  Z. In the case of Einstein's GR, similar considerations hold for the so-called dark energy. The intrinsic dynamics of the infinitesimal transition  AB  is explained with the notion of relational reality (see also the so-called donkian Hamiltonian here).

Note that the misfortunate, and highly misleading, decomposition of spacetime in geometrodynamics into 1-D "time" and 3-D "space" is rooted on the seemingly simple, and also highly misleading, case depicted on Fig. 1. (This latter case is valid for classical mechanics and Special Relativity, such as the dynamics of a train, and for objects not larger than the size of a planet such as Earth or Mercury, because the effect of the Holon is negligible and can be safely ignored: no "dark matter" effects nor 'initial value problems' can be detected at this scale.) As acknowledged by A. Ashtekar, we are doing "grave injustice to space-time covariance that underlies general relativity". Not surprisingly, the temporal evolution was found to be frozen (the problem of time in canonical quantum gravity), and there is no solution, not even phenomenological, to the task of the timeless and spaceless emergence of spacetime. (If you click on Fig. 4 above, you will read an outline of the emergence of spacetime along the  Z  axis of the global mode of spacetime; more about Einstein's GR here and here.)

In a nutshell, I will try to outline a scale-independent "backbone" of the whole physical world: a perfectly continual and fully deterministic local mode of spacetime. It fully preserves the principle of locality, since all physical systems "proceed" from  A  to  B  "after" their next state is fully negotiated with 'the rest of the universe', via their common Holon kept in the global mode of spacetime: think globally, act locally. This is the rule of 'relational reality'. Let me stress that the "negotiation" takes place within each and every infinitesimal "point"  AB  from the trajectory, and at each and every instant it fixes (or rather explicates) different states of the system stored in its Holon state (global mode). Philosophically speaking, you could not step twice into the same river, as stressed by Heraclitus, but the genidentity (Kurt Lewin's Genidentität) or "sameness" of the river will not be jeopardized from your steps, because it is being kept in the global mode of spacetime.

Physically, in order to have a genuine dynamical evolution, there must exist an infinitesimal timelike displacement  AB "during" which the system in consideration does not exist in the local mode of spacetime -- the so-called gaps of non-existence in the global mode of spacetime (cf. Fig. 4). These "gaps" constitute the ultimate "background" of the whole universe: a Holon state which can continuously affect the dynamics of the system while remaining unaffected by it. Hence all sub-systems of the universe can "negotiate" their next state in the local mode, by the rule "think globally, act locally", while the ultimate "chooser", as a genuine non-Archimedean reality, remains unaffected in the global mode of spacetime. It can absorb infinitely many (actual infinity) UNspeakable cat states, and its "proper time" will be read by an inanimate physical clock in the local mode as being totally frozen, just as the brain state corresponding to the human self. If we toss a ball or calculate the trajectory of a planet such as Mercury, the effect of this non-Archimedean Holon state can and should be neglected, because at this scale its "dark" effects are still vanishing small. However, if we are interested in the so-called God particle or are studying the dynamics of systems of the size of our Milky Way, the situation is entirely different. The best way to understand these issues is to recall the problems of relativistic "collapse", "gravitational wave" astronomy, inflationary cosmology, and quantum cosmology in general. All these issues have a common origin: the clash between classical physics and quantum theory. The problem has been identified by Erwin Schrödinger in 1931, and four years later, in his seminal 1935 paper "Die gegenwärtige Situation in der Quantenmechanik", Sec. 15, he stressed "that "sharp time" is an anomaly in Q.M.", and yet seventy years later people still neglect this ultimate puzzle (cf., e.g., the decoherence functional for the quantum history theory here), and claim that the concept of time may not be fundamental but should instead "emerge" only in some "semiclassical approximation". If we brush aside the warning from Erwin Schrödinger, we will never discover the "backbone" of the physical world, and all efforts to quantize 'the grin of the cat' are doomed to fail. This the reason for my efforts to unravel the "backbone" of the whole physical world, with the putative two modes of spacetime. Needless to say, this "backbone" cannot be rooted on any probabilistic physics: Der Herrgott würfelt nicht!

It is quite a different matter that we cannot know the precise states of all sub-system in the universe, and hence our description of the negotiation process in the global mode of spacetime will be inevitably incomplete, hence will display some "probabilistic touch" in computing the relational state of a given quantum system at a given instant from its trajectory. I believe Albert Einstein would have been quite happy with this purely epistemological uncertainty.


Full text at


Download the abstract from here. An email with the acceptance or refusal of my oral contribution to the Conference “Beyond Einstein – Physics for the 21st Century” (EPS13) will be sent to me after May 1, 2005. I very much hope that will be given the chance to defend Einstein's dictum "Der Herrgott würfelt nicht!" at EPS13.

I am fully prepared to compete with all participants, but I need to speak. Poster presentation is not acceptable, and will be considered as an insult to Albert Einstein. He shouldn't feel as a cobbler, and I sincerely hope that will be given an opportunity to defend his belief.

D. Chakalov
March 14, 2005
Last update: May 11, 2005


My talk was rejected. Feel like having my mouth shut with duck tape, again. Just like in communist Bulgaria. What a shame.

The topics of my talk were outlined here. I suppose we will celebrate Einstein's General Relativity in 2015. I have ten more years.

D. Chakalov
May 4, 2005
Es ist schwieriger eine vorgefasste Meinung zu zertrümmern, als ein Atom.
Albert Einstein

Du bist (neben Laue) unter den zeitgenössischen Physikern der einzige, der sieht, dass man um die Setzung der Wirklichkeit nicht herumkommen kann - wenn man nur ehrlich ist. Die meisten sehen gar nicht, was sie für ein gewagtes Spiel mit der Wirklichkeit treiben.

Albert Einstein to Erwin Schrödinger, 1950