"I wish you wouldn't keep appearing and vanishing so suddenly; you make one quite giddy!"
"All right", said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.
"Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!"

Lewis Carroll, Alice's Adventures in Wonderland


 
 

ABOUT POINTS, IF ANY*





The dynamical nature of the infinitesimal is attributed to a hypothetical 'local mode of spacetime', while its completion or 'end point' is reserved for a hypothetical 'global mode of spacetime'. The latter (i) serves as the 'breaking point' of the perfect continuum of "points" in the local mode of spacetime, (ii) provides the "gaps" of non-existence needed for the phenomenon of transience, and (iii) carries the genidentity or 'sameness' of the physical systems through these gaps. Thus, it is suggested that in each and every transition from matter to geometry, all physical systems in the universe pass through an 'end point' in the global mode of spacetime, resembling the creation of the universe. The implications of such Phoenix Universe for quantum gravity are briefly discussed, with emphasis on some practical issues, such as gravitational wave astronomy. The theological implications of the 'end point' interpreted as 'pure light and cognition' [John 1:1] are not addressed, and will be explored in another paper.
 
 
 
 

The most curious thing we see in our life is the transition from matter to geometry: a grin of a cat without the cat, as observed by Alice. But do we actually see those geometrical "points" to which we attribute point-like numbers, for example, in calculating the circumference of a circle? We cannot literally see them, but the world around us indicates, at least at the scale of tables and chairs, that objects have fixed, point-like position in space and time. This is the mystery of "points", regardless of the numbers we attach to them and the precision in their calculation, as required by our engineering needs. Perhaps without recognizing it, we employ a very spooky phenomenon in differential calculus and in the derivation of probability, which we call 'actual infinity'. At first glance, it seems that this phenomenon does not belong to the world of tables and chairs around us. And yet we need it and employ it without hesitation for very mundane purposes, say, for calculating the circumference of a circle or a tangent vector that belongs to a dimensionless "point" stripped from any orientation in spacetime, as every engineer and physicist knows very well [Penrose, 2004].

What if the existence of these "points" requires a phenomenon that does not belong to the realm of "points", and does not live in the spacetime of events presented with points? What if we are dealing with a unique holistic object, a Holon which is literally everywhere, like a transcendental tachyon, hence there is no room left to go, no further place to move, and no time to make this move? If it is everywhere-at-no-time, like the Aristotelian Unmoved Mover, it can reach the "end" of any non-divergent infinite series, hence deliver some nice "points" to build the geometry of our world, making us happy but also deeply amused. This is certainly one of the most curious thing we ever see in all our life.

I will argue that the emergence of points, which we use as geometrical presentation of events, requires (i) a holistic object known as 'the atom of Lucretius', and (ii) a universal Heraclitian time pertaining to Lucretius' atom, which refers to the dynamical emergence of points: in order to move from one point to the nearest one, we need a special gap separating these points. Keeping the points and their gaps is the prime job of Lucretius' atom living in its Heraclitian time: Panta rei conditio sine qua non est. The resulting physical picture (Weltbild) suggests that the 4-D spacetime continuum of Einstein's General Relativity (GR) could be embedded in Lucretius' atom. The latter serves as a holistic 'context', as with words in a sentence: the meaning of the words is being fixed by both their individual properties and their holistic context. Thus, the 'context' would facilitate the bi-directional talk of matter and geometry (J. Wheeler), and would enable the final stage of converting matter to geometry, in which we have the geometrical "points" from 'the words in the sentence'. Possible implications for the problem of quantizing spacetime in background-free versions of quantum gravity are discussed at the end of the paper. For now it suffices to say that currently we cannot, even in principle, quantize the very 'grin of the cat' [Loinger, 2003]. Put it differently, the quantization of spacetime requires to 'hold on something' during the quantization process. We need a new reference object -- not 'the words in the sentence' which have gone down to geometrical points, but their omnipresent holistic context. Needless to say, it could be a very peculiar "dark" background.

Let's insert it "between" every two adjacent points, and see what we can make with this new "third" point. The textbook lore of quantum mechanics (QM) says that the source and the mechanism of generating quantum waves are unknown. Quite a nettlesome situation, I must say. For if we do not reveal the origin of quantum waves, how are we supposed to unify them with 'the grin of the cat' and develop a complete theory of quantum gravity?

[To be continued]
 

===


 

If between any two points in space there is always a third point, can anything touch anything else?

[To be continued]

===

The first thing we have to do is to ground our work on rocks. Some hints from the human brain could be very elucidating, I hope, for unraveling the dynamics of quantum-gravitational systems, as prescribed by their Hamiltonian constraints. The guiding idea is to model the whole universe as a brain, and seek the physical manifestation of its holistic organization. Once we solve the paradox of continuum, we may hope that all pieces from the jigsaw puzzle of quantum gravity will stick together in a coherent picture of our world. Then it is very likely that we will discover new puzzles and will have to move further: Nur die Fülle führt zur Klarheit, und im Abgrund wohnt die Wahrheit (Friedrich von Schiller).

Let's begin with the problem of time in canonical quantum gravity [Isham, 1993]. There is a very simple explanation of the "freezing" of Hamiltonian dynamics: the notion of 'time' in present-day theoretical physics does not include the phenomenon of transience, and hence the resulting "dynamics" is inevitably frozen, in blatant contradiction with everything we observe in the world. I believe this is an artifact from the essentially incomplete mathematical models used in current quantum gravity research, and does not represent some genuine 'disappearance of time'. The explanation of this artifact is with the notion of 'relational reality': if we use only one kind of time, the resulting dynamical evolution will be inevitably halted, a bit like the famous Buridan donkey.

The difference is that the donkey doesn't move and starves to death because it cannot choose between two equidistant piles of hay, while in our case the 'donkey' is a member of a totally interdependent herd of 'donkeys', such that each and every donkey has to determine its next 'pile of hay' relationally, by 'the rest of donkeys', before it can make any move. Hence none of the donkeys could have its next 'pile of hay' determined by 'the rest of donkeys', none can move in any direction, and the resulting 'donkian Hamiltonian' will be frozen, just as in the case of Wheeler-DeWitt equation. To be specific, if a given donkey (pictured above), at instant t0, looks for its next pile of hay at a later time t1, then this next pile of hay has to be determined by 'the rest of donkeys'; however, each and every donkey that belongs to 'the rest of donkeys' needs to have its own next pile of hay determined by the first donkey. Since none of the donkeys can proceed to their next pile of hay before the latter being fixed, none of them can move either. (To make this possible, the donkeys would perhaps need to introduce an absolute reference frame for all members of the herd, and correlate their Hamiltonians "online" with tachyons, which is not very likely.)

Thus, before making the move to its next pile of hay, the donkey has to produce time, which can be done only by 'the rest of donkeys'; but in order to produce time, 'the rest of donkeys' need to have the initial move of the donkey (pictured above) fully completed. Of course, this kind of 'next/before paradox' never happens with donkeys, they are smart enough to solve such Catch 22 paradox in their 'relational reality', but what can we do to solve the problem of time in quantum  gravity? Here again comes a hint from human brain dynamics, since we keep nearly 100 billion neurons bootstrapped in a perfect 'relational reality' that is being updated at least 1014 times per second. If we model the whole universe as a brain, perhaps we can understand the Hilbert space/inner product problem, as well as explain why it is impossible to develop some inanimate quantum computer that would harness the phenomenon of entanglement.

Clearly, we need to enrich the notion of time, particularly its topology, and the first-off task will be to solve the Schrödinger cat paradox. Recall that an inanimate physical clock can read only and exclusively only a trajectory of states in the phase space of classical mechanics. Such a clock belongs exclusively to the realm of 'objective reality out there', and cannot read simultaneously some multi-fingered time that pertains to all possible superposed cat states. We need a new kind of multi-fingered time that would accommodate infinitely many cat states, since in quantum cosmology the "number" of all possible cat states/donkeys may be unlimited, that is, there could be an uncountable infinity of solutions to the 'next/before paradox' above, all of which has to be considered en bloc, as a holistic relational reality.

Thus, the postulated multi-fingered time (called 'global mode of spacetime') has to be placed literally "outside" the smooth manifold employed in Einstein's General Relativity, hence allowing the manifold of spacetime to "pack an uncountable infinity of events into a finite spacetime volume" [Mallios A., Raptis I., 2004] without any physical singularity. We simply operate with a new kind of reality, a holistic relational reality. Put it differently, in order to have one happy donkey that has found its pile of hay at a fixed location in spacetime, we need to consider a 'holder' of infinitely many -- actual infinity -- potential states of this pile of hay. Let's examine the case of Schrödinger cat, in which this 'holder' would keep just two potential states, |live cat> and |dead cat>. Here the 'chooser' of the state, either live cat or dead cat, is not 'the rest of donkeys', but the problem is by no means easier to solve. Once we observe one of the manifestations of the cat, we face the problem of the relativistic description of this "process": how did it happen, and what happened to the other manifestation of the cat [Bloch, 1967]? We have a Hilbert space, not Hilbert spacetime, while the so-called time parameter in the Schrödinger equation pertains to an "isolated system". Let's attach our multi-fingered time to this "isolated system", and think of the latter as 'the quantum state of the cat', only in a special mode, that of Wheeler's 'cloud'.

Consider the issue of relativistic "collapse" [Bloch, 1967]. Bloch has argued that the hypersurface on which the state reduction may be taken to 'have occurred' can be chosen arbitrarily, since that choice will not affect the probability distribution of all local observables. On the other hand, many people believe that "immediately prior" to the observation/collapse, the quantum system "has been" in some "prepared state".

I think the phrase "immediately prior" [Gillespie, 1973] is poetry. Hence my confusion: what hypersurface we should choose for this "prepared state", how did the quantum system "get there", how "fast", and from where. Once you perform the "collapse", you might say -- retrospectively -- that it 'had occurred' along a spacelike hypersurface which has contained the measurement event in your reference frame. But "immediately prior" to this event, people speculate that the quantum beast is in some already prepared, smoky-dragon-like state, and is patiently waiting to be collapsed, in line with the rule of eigenvalue-eigenstate link.

Where is the quantum beast hanging around, like Wheeler's 'cloud'? In what "history" (consistent, decoherent, etc.) would you accommodate it, along with your brain?

I believe addressing the issue of 'quantum reality' is the first-off step toward quantum gravity, because we cannot 'sweep the garbage under the rug' with the standard (mis)interpretation of QM, according to which the wave function describes some "knowledge" that can emerge from some previously "collapsed" state and fade out instantaneously in the next "collapse". The only viable road toward canonical quantum gravity seems to be with the so-called relational interpretation of QM. However, none of these interpretations can cope with the undisputable problem that QM does not describe the occurrence of facts. Facts are fixed reality in our past light cone, while Wheeler's 'cloud' is neither 'inside' nor 'on' the light cone. It simply doesn't live there, as we know since the time of Plato.

How does the 'cloud' enter Minkowski's cone? Maybe only "through" the apex of the cone. Maybe it is being driven by the Aristotelian final cause and Jungian synchronicity. Obviously, developing a theory of quantum gravity on these grounds would be a very tough challenge.
 

[To be continued]

===

Sec. 3. Einstein's General Relativity and Quantum Gravity

There are a number of ideas in Einstein's General Relativity [Einstein, 1917], which are crucial for the quest for quantum gravity.

As a prerequisite, let's recall the stipulation launched here that the quantum waves are effect of the Holon, and hence their "source" cannot be pinpointed, cannot be related to any concrete physical stuff in the universe. If we look at a centipede, we will notice that its legs are correlated like a wave, because (supposedly) each leg chooses its next state by following the rule of 'His thoughts': think globally, act locally. Thus, our first task will be to unravel the non-local, or "wave-like" behavior of matter coupled to gravity, and subsequently the problems in its description by purely local concepts. I will try to examine the non-tensorial nature of the gravitational stress-energy pseudo-tensor [Hoefer, 2000]: there is no fixed, local, unique, and intrinsic 'amount of stuff' in any "point" from cat's grin, as Alice would have probably said. If Einstein's GR was formulated on the basis of some wave equation, similar to Schrödinger's equation for Quantum Mechanics, perhaps the corresponding "gravitational waves" would have smeared the 'amount of stuff' in any point from the geodesic lines of material bodies, and the latter would be correlated just as centipede's legs. Of course, we cannot pick up a reference frame outside spacetime to watch the "wave-like" evolution of gravitational systems, but we can infer the possibility for such effect by recalling that its alternative explanation ultimately fails: the issue of energy transport by these gravitational "waves" makes no sense in Einstein's GR, since the very concept of energy has lost its meaning there [Stephani, 1990; Weyl, 1951]. These gravitational "waves" are therefore 'empty waves', just like the empty waves produced by the Holon, which we call 'quantum waves'.

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth", says Arthur Conan Doyle. In what follows, I will use the same indirect method of deriving arguments, based on some simple math: 2-1=1. It means the following: there are two, no more and no less than two, possible descriptions of the dynamics of gravitational systems. One of them is supported by the experts in this field (despite the problems its carries; see [Weyl, 1951]), while the alternative possibility is based on the Holon or 'His thoughts', and is not supported by the experts. In one of the alternatives fails, we will explore the remaining possibility.

There is no 'empty spacetime' in Einstein's GR: "Space-time does not claim existence on its own, but only as a structural quality of the field" [Einstein, 1917]. If we remove the cat, there will be no grin, as Alice would have said. But the transition from matter to geometry, or from the cat to its pure cat-less grin, is by no means trivial. It involves the notion of infinity, which in turns is plagues with many paradoxes. And yet in Einstein's equation, the cat (matter) is related to its pure cat-less grin (geometry of space). Even more: these two entirely different entities are engaged in constant "online" negotiation. Here I refer to the famous statement by John Wheeler: "Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve". However, neither of the two parties can take care of the timing of this bi-directional talk. Hence we will attribute it to the Holon, and seek some 'have our cake and eat it' solution to the problem of dynamics of General Relativity.

The next indirect argument is produced by zooming on the dynamics of the gravitational systems, namely, the initial data problem for Einstein equations, known as the Cauchy problem in Einstein's GR. In the absence of the Holon, the dynamics will expose its various pathologies, which are well-know to all experts. We don't know exactly how a centipede walks, but we can try to solve the fifty-year old Cauchy problem with the dynamics of the human brain, which too is based on the Holon.
 

[To be continued]

===

Sec. 4. Generalized Quantum Dynamics*

Ensuing from the solutions to the problem of time in canonical quantum gravity and the Schrödinger cat paradox, I will try to outline the common ground for Quantum Theory and General Relativity, which will be called Generalized Quantum Dynamics (GQD). I will try to suggest the basic ideas of Virtual Geodesic Paths formulation of GR. The model should be capable of accommodating UNcountable potential states kept in the Holon, as explained above by examining the dynamics of the human brain.

To find the common denominator of Quantum Theory and General Relativity, the first off task will be to suggest a description of the Holon, which can accommodate the quantum-and-gravitational "waves". The first obvious obstacle from our current models of gravitational systems is that they are strictly kinematical: the genuine dynamics of GR cannot be found there. Perhaps the missing 'wave degrees of freedom' can be recovered by enriching the phase space of GR with field degrees of freedom, that is, two gravitational wave polarizations and their time derivatives. What we need to introduce in GR has been hinted in Cramer's interpretation of QM, and now we have to find the GR-implementation of the "localization" of the state of gravitational systems in a frozen, point-like state. Obviously, a direct analogy with the Born rule cannot be productive.

Let's examine a toy model of another animal, a centipede with four legs, and see how the four legs can make one joint step. We will think of the potential states of the legs as residing in two virtual worlds with inverted spacetime basis, in the sense that what is "1-D time" in one of the worlds is "3-D space" in the other. These two virtual worlds 'run against each other' in the Holon, and select one localized state for every gravitational system (here - four legs) from the whole spectrum of their potential states, in line with the rules of 'relational reality'. This selection is nothing but cancellation of all but one state valid for one step of the centipede, so we need to work out the phase of these brand new quantum-and-gravitational waves.

Perhaps the first objection to this conjecture would be along the following lines: Einstein's General Relativity is a classical theory, and there is nothing "virtual" in it. However, if we interpret 'virtual' as the opposite to 'classical objectivity', then the famous Hole Argument can be used to demonstrate that the absence of 'physical points' -- and hence absence of 'classical objectivity' -- implies that the physical content of these "points" is indeed virtual.

To explain the notion of 'classical objectivity' (and later the opposite notion of 'virtual'), let's look in Chris Isham's "Lectures on quantum theory" [Isham, 1995, p. 57]:

"Properties are intrinsically attached to the object as it exists in the world, and measurement is nothing more than a particular type of physical interaction designed to display the value of a specific quantity."

Thus, a measurement in classical physics is merely 'copy&paste' of the value of a specific quantity at a specific "point" from, say, a trajectory of a ball. Hence in classical physics at each and every "point" we have some intrinsic physical content that makes these "points" unique. They are like different individuals chained along a trajectory, and each of them is endowed with concrete physical content. Thus, the "points" cannot be 'moved around'; they are fixed by their physical content.

However, if we allow this same physical content to be influenced by the very 'grin of the cat', it becomes a genuine dynamical entity that cannot 'stay quiet at one point', nor the "points" can be endowed with any intrinsic physical content. It isn't intrinsic anymore; it has became virtual.

This is what Einstein meant by 'physical objectivity' when he wrote that "the requirement of general covariance takes away from space and time the last remnant of physical objectivity". Regarding the Hole Argument, Jeremy Butterfield and Chris Isham wrote the following [Butterfield J., Isham I., 1999, p. 33]:

"Suffice it to say that: (i) the argument applies not just to general relativity, but to any generally-covariant theory postulating a spacetime manifold; and (ii) according to the argument, general covariance (that is: the diffeomorphism-invariance of the theory), together with spacetime points being physical objects, implies a radical indeterminism: and such indeterminism is unacceptable -- so that we should conclude that points are not physical objects.

"That is, the points occurring in the base sets of diffrerentiable manifolds with which general relativity models spacetime should not be reified as physically real."

Hence we can ask in the framework of Einstein's GR the following question: what could be physically real before we apply the rules of diffeomorphism-invariance? Unlike classical physics (cf. C. Isham above), properties are not intrinsically attached to the object as it exists in the world. These properties "emerge" only after we apply the rules of diffeomorphism-invariance. Put it differently, we can see only covariant derivatives, only 'John's jackets' cast on a fixed hypersurface.

Thus, the very rules of diffeomorphism freedom presuppose a virtual reality from which a fleeting set of "points" with a fleeting physical content can be actualized. This crucial issue can be made particularly clear if we examine the non-tensorial quantities in Einstein's GR, from which we "project" some observable, temporary "localized" physical properties.

Note that these efforts at modifying Einstein's GR are by no means purely academic exercise: there is an outstanding puzzle of the dynamical adjustment of the so-called dark energy, as revealed in the bundle of cosmological constant problems. Moreover, the perfectly smooth dynamical dark energy needs to be explained by a new theory of all "dark" constituents of the universe, the "clumsy" cold dark matter included.

It is agonizingly clear that we need to modify Einstein's GR, and the approach suggested here is to look for the virtual component of gravity, such that it can be dynamically adjusted to its real counterpart (matter) throughout the whole history of the universe. Surely we are talking about a manifestly non-unitary Generalized Quantum Dynamics (GQD), in which the two "dark" constituents of the universe are presented as effects of the Holon in the global mode of spacetime. If we model the Holon with two virtual worlds (cf. above), it may cast two dynamic blueprints on the local mode of spacetime: cold dark matter and dark energy. These two blueprints from the (CPT-invariant?) Holon are diametrically opposite in the sense that the cold dark matter refers to implosion (hence the speculations about some black holes, dark matter galaxies, and "blackholic energy"), while the smooth ubiquitous dark energy refers to expansion of the whole universe.

To cut the long story short, we shouldn't blame on Einstein that his 1915 theory of gravitational field was not flexible enough to accommodate 96 per cent of the stuff in the universe, dark energy & dark matter. He was fully aware that his GR theory is essentially incomplete: "The right-hand side includes all that cannot be described so far in the Unified Field Theory, of course, not for a fleeting moment, have I had any doubt that such a formulation is just a temporary answer, undertaken to give General Relativity some closed expression. This formulation has been in essence nothing more than the theory of the gravitational field which has been separated in a somewhat artificial manner from the unified field of a yet unknown nature."

Perhaps the 'unknown nature' refers to the effects of the Holon, which are always "dark" in the local mode of spacetime. Recall that the "dark" effects of the Holon are introduced in quantum theory from the outset: we never question the source and the origin of quantum waves, and are fully aware of the peculiar fact that the quantum potential has no "external source". But in Einstein's GR we speculate that the gravitational potential can be "produced" from a massive body in space, and we happily point to some massive body 'out there', and say -- look, this is what makes the spacetime curvature. Fine, but what if the spacetime curvature is being fixed not only by some massive body 'out there' but also from the Holon of the whole universe? This latter component will be inevitably "dark", and may produce genuine "dark" effects at scales larger than the size of the solar system. It can create the effect of a whole 'dark galaxy', and can shape the "neural" pattern of visible galaxies as well. That's the virtual component of gravity. Just as in the case of the "collapse" in QM, we project an instantaneous snapshot from the bi-directional talk of matter and geometry in the asymptotical Minkowski limit of Einstein's GR; these are the "collapse" rules of the linearized approximation of Einstein's GR. Hence in the local mode of spacetime we inevitably wipe out the virtual component of gravity, just as we wipe out the Holon as the source of quantum waves with the "collapse" of von Neumann.

Now, if we keep the initial idea to represent matter with a tensor, we should at least try to elucidate the question of what could be the dynamics of all non-tensorial quantities in Einstein's GR, namely, how do they "emerge" as some observable localized stuff in the local mode of spacetime.

Consider the so-called cosmic equator, which shows up in WMAP data, and the hypothetical space rotation symmetry.
 


The effects of the Holon are always "dark", as in the case of the so-called dark matter and dark energy. Could it be that the cosmic equator is a 3-D blueprint from the space rotation? If yes, what could be "the opposite" blueprint from space rotation? What is the "spin" of the universe? Perhaps we shall find answers to these puzzles only after we understand the virtual reality in Einstein's GR. What makes this reality virtual is that it belongs to 'the universe as a whole' but cannot be pinpointed, because it comes from the Holon in the global mode of spacetime. Needless to say, it is both virtual and completely "dark".

The situation is truly paradoxical: on the one hand, we are banned from speaking about any absolute reference frame in which we can talk about 'the universe as a whole', but on the other hand we're faced with the dynamics of the ubiquitous, and perfectly smooth, "dark energy" (the coincidence problem), which is "embedded" within each and every spacetime point/event, hence constituting the absolute reference frame of the global mode of spacetime.

[To be continued]
 
 

Sec. 6. Acknowledgements

I am grateful to Prof. Chris Isham for inviting me to present these ideas at a seminar in Imperial College, which was scheduled for November 27, 2002. The title of my talk was "About points, if any". The seminar was very well advertised but there was virtually no interest on behalf of theoretical physicists, and I decided to cancel it, with utmost regret. The reason for my efforts was my naïve hope that I might qualify for a job at IC Physics Department (headed by Prof. Peter L. Knight, FRS). Since Prof. C. Isham has already been fully acquainted with my speculations, there was no sense to repeat them, and push for a seminar that was born dead, sit venia verbo.
 
 

D. Chakalov
--
In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and the cobbler.

Albert Einstein

 

References and notes

Bloch I., Some relativistic oddities in the quantum theory of observation, Physical Review 156, 1377-1384 (1967).

Butterfield J., Isham I., Spacetime and the Philosophical Challenge of Quantum Gravity, gr-qc/9903072.

Einstein A., Relativity: The Special and The General Theory, translated by Robert W. Lawson, Three Rivers Press, Crown Publ., 1995. (Original title: Über die spezielle und allgemeine Relativitätstheorie, gemeinverständlich, 1917.)

Gillespie D., Quantum Mechanics Primer: An Elementary Introduction to the Formal Theory of Non-Relativistic Quantum Mechanics, New York: International Textbook Co., 1973, pp. 49-58.

Hoefer C., Energy Conservation in GTR, Stud. Hist. Phil. Mod. Phys., 31(2) 187 (2000); pdf file from here.

Isham C.J., Prima Facie Questions in Quantum Gravity, gr-qc/9310031.

Isham C.J., Lectures on quantum theory. Mathematical and structural foundations, London: Imperial College Press, 1995.

Loinger A., "Quantum gravity": an oxymoron, physics/0308042.

Mallios A., Raptis I., Smooth Singularities Exposed: Chimeras of the Differential Spacetime Manifold, gr-qc/0411121 v1, pp. 10-15.

Penrose R.,The Road to Reality, Jonathan Cape, London, 2004, pp. 61-62, p. 230, and Fig. 6.8 on p. 117.

Stefani H., General Relativity: An Introduction to the Theory of the Gravitational Field, Cambridge University Press, Cambridge, 1990, p. 142.

Weyl H., Space-Time-Matter, Fourth Edition, translated by H. L. Brose, Dover Publ., New York, 1951, p. 270.
 
 
 

More at


 


 


Addendum


I wrote above the following:

"I am grateful to Prof. Chris Isham for inviting me to present these ideas at a seminar in Imperial College, which was scheduled for November 27, 2002." True, because his invitation made me think very carefully about the practical implications from my work, and one year later I filed a proposal at the 2004 Rolex Awards for Enterprise.

What I didn't mention above was the bold opinion of Chris Isham from Wed, 23 Oct 2002 19:24:15 +0100, which he still hasn't backed with any evidence whatsoever. Thus, I can't take it in any way but as an insult. There may well be some stupid ideas at this web site, but to claim (emphasis added) that I "do not know enough theoretical physics to help with any research in that area", and then not providing any evidence for my stupidity, up to this day (29.03.2008), is a sheer insult.

I also wrote above: "The title of my talk was "About points, if any"."

True, but the ideas in this web page, and the whole web site, are kept strictly philosophical, and are very loosely related to the scope of my intended talk at Imperial College on 27 November 2002: notice that I was hoping to work at "IC Physics Department". I suppose nobody would expect from me to discuss anything but 'philosophy of physics' at this web site. Discussing the practical and experimental work is quite a different subject, which I wasn't able to deliver on 27 November 2002: the seminar was "born dead, sit venia verbo."

Let me finish with the following statements: I do not need quantum gravity to practice PHI3. The theoretical ideas are very simple, yet it took me full sixteen years to learn them, from January 1972 to May 1988 (I'm not smart). All my efforts to suggest some ideas on quantum gravity are dictated by my strong desire to distinguish myself from all people who practice parapsychology, and to test my theory of PHI (just 'physics of human intention') by elaborating on its implications for quantum gravity.

If you want parapsychology, watch David Blaine. If someone is interested in PHI3, we should first discuss the ideas proposed here. First things first.

Subsequently, if my ideas on quantum gravity are wrong, there will be strong possibility that the theory of PHI3 (not explained at this web site) is also wrong, since one third from it would be proven wrong. Which would in turn mean that I may indeed be just some parapsychologist and door-to-door salesman. Alternatively, if my ideas on quantum gravity are correct, there might -- just might -- be some possibility that the whole theory of PHI3 (again, not explained at this web site) could also be correct. I am quite confident about the other two pieces, 'physiology of human intention' and 'psychology of human intention', because everything there is directly grounded on indisputable and widely accepted facts. The case of 'physics of human intention' and its predictions for quantum gravity, however, is still totally unclear, and I really wanted, very much indeed, to "qualify for a job at IC Physics Department".

Well, you never know what you lose when you win, and the other way around.
 


D. Chakalov
March 29, 2008