Dear Dr. Piechocinska,

I read with great interest your recent paper, "Wholeness as a Conceptual Foundation of Physical Theories" [Ref. 1], and am deeply impressed by your ambitious goals,

http://www.teknik.uu.se/ftf/staff/barbara.html

My efforts are to convince the established theoretical physics community that the atom of Lucretius has not been discovered,

http://God-does-not-play-dice.net/Magueijo.html#note

and that it is the only logical solution to the paradox of continuum,

http://God-does-not-play-dice.net/Pestov.html#continuum

In psychology, it shows up as 'context',

http://God-does-not-play-dice.net/Knuth.html

Its physical manifestations are far from clear to me,

http://God-does-not-play-dice.net/energy.html

Please see the imaginary valued time introduced by Giovanni Modanese and Giorgio Fontana [Ref. 2], and the efforts to revive the tachyons as 'dark energy' by S.K. Srivastava [Ref. 3].

As to quantum gravity, see an interesting point made by Giovanni Modanese and Giorgio Fontana [Ref. 2]: "These findings open new questions; for instance, if imaginary time is required to keep the probability to find the particle constant in time, does imaginary time
really exist in the physical world?"

The problem is well-known,

http://God-does-not-play-dice.net/Shimony.html#Ashtekar

I hope you and your colleagues can investigate it further, and bring us closer to the correct formulation of the ubiquitous phenomenon of wholeness.

Wishing you and your colleagues all the best,

Dimi Chakalov
--
http://God-does-not-play-dice.net

References

[Ref. 1] Barbara Piechocinska, Wholeness as a Conceptual Foundation of Physical Theories, physics/0409092 v1,
http://xxx.lanl.gov/abs/physics/0409092

"IV. MATHEMATICAL FRAMEWORK

"In order to provide a mathematical foundation that is capable of expressing features of wholeness at the very fundamental level, it is suggested that we start with set theory, since most of mathematics can be expressed in terms of it, and add the Wholeness Axiom introduced by Corazza [19] to the normal axioms of set theory. The normal axioms of set theory are the Zermelo-Fraenkel set of axioms and the Axiom of Choice, abbreviated ZFC [20], [21], [22]. For approximatively eighty years it has been known that most of mathematics is derivable from them. These axioms refer to sets and are formulated in the formal language {E}. This means that the only relation used in the formulation of the axioms is the membership relation,  E .

"The mathematical theory within which we shall attempt to describe a theory from wholeness will contain the ZFC set of axioms together with the Wholeness Axiom and will be referred to as ZFC+WA. We will now proceed to see what the Wholeness Axiom is and what features of wholeness ZFC+WA is capable of expressing.
...

"Let us now continue by outlining, step by step, a possible way of further developing the mathematics so as to establish a correspondence with physical phenomena. A detailed exposition of the following presentation will be published elsewhere by the author."
 

[Ref. 2] Giovanni Modanese, Giorgio Fontana, Effect of the Vacuum Energy Density on Graviton Propagation, physics/0409098 v1

"The possibility of Faster-Than-Light travel is based on a class of postulates regarding the significance of the speed of light, the validity of Special Relativity and General Relativity near and beyond c, the possibility of travelling in imaginary valued time, etc. Neither science fiction nor current scientific literature clearly explains "what" can really do that "jump in hyperspace" that will enable the exploration of the galaxy. Nevertheless if an object or a particle is found to be characterized by some suitable properties, then Faster-Than-Light travel is no longer science fiction, but a fact. Studying graviton propagation in spacetimes with a cosmological constant we have found superluminality or unitarity of the graviton wavefunction only in imaginary time. Imaginary valued time is equivalent to a spatial coordinate, therefore under these circumstances the graviton is somehow locked in time and propagates in a space with 4 space-like coordinates.

"These findings open new questions; for instance, if imaginary time is required to keep the probability to find the particle constant in time, does imaginary time really exist in the physical world?"
 

[Ref. 3] S.K. Srivastava, Tachyon as a Dark Energy Source, gr-qc/0409074 v1

[From the abstract]: It is demonstrated that dark energy, driven by tachyon condensates, decays to cold dark matter in the late universe. It is found that this phenomenon yields a solution to "cosmic coincidence problem."
--

Note: Key word here is "minimal coupling with gravity" and Born-Infeld lagrangian: "Using this lagrangian, it is argued that tachyon scalars may be able to explore more physical situations than quintessence [10]."
 

Note: Regarding the question of the physical nature of imaginary time (cf. above), it seems to me that this very special "time" is related to (i) the so-called mysterious time (or why not spacetime?) of Bill Unruh, and (ii) the nature of "regions" from which we get "points", in Chris Isham's research in quantum gravity. Perhaps this "imaginary time" is simply UNspeakable.

To explain this conjecture and shed some light on the phenomena of wholeness and context, let's recall that, in the path-integral approach to QFT, we tend to think of those virtual "paths" as 'possible alternative classical trajectories' in some 'configuration space'. We believe the latter is just purely mathematical abstraction, a calculation tool that bears no resemblance to the world of tables and chairs. And yet we think of these virtual "paths" as 'alternative classical histories', hence contaminating this purely quantum concept with the notion of 'something that has been laid out' and has become a 'history', a history being a path in this configuration space.

As explained by Roger Penrose (The Road to Reality, Jonathan Cape, London, 2004, pp. 667-668), "the complex amplitude to be assigned to that particular history is then given by the deceptively simple formula [XXX]. Part of the deception, in the simplicity of this formula, lies in the fact that the 'amplitude' is not really a (complex) number, here (which, as written, would have to have unit modulus), but some kind of density. (...) But here we have a continuous infinity of classical alternatives. Our above 'amplitude' thus has to be thought of as an 'amplitude density' (...). But the bad news here is that the 'space of classical paths' will almost certainly turn out to be infinite-dimensional." (See [Ref. 5].)

If we toss a dice, we certainly do not think of probabilities as some kind of density. We operate with real numbers that nicely sum up to unity. In QM, we operate with complex numbers, but we again push them to sum up to unity, because by default QM describes only what we can observe (with inanimate measuring devices) at the scale of tables and chairs. Hence the notorious measurement problem. I think it is rather a measurement paradox, because what we do is something like 'looking at a yellow flower through blue glasses'. By measuring quantum particles with inanimate devices, we impose some sort of a filter -- the evolution of 'quantum states' should be unitary and "local", as implied by the Schrödinger equation, and we strictly insist on Boolean logic: "Philosophically speaking, we can assert that the quantum world is being perceived through Boolean reference frames, regulated by our measurement procedures" (Elias Zafiris, quant-ph/0202057).

However, in QFT, the situation cannot be simplified anymore. We have some kind of 'amplitude density', and the 'history' can "wiggle up and down in time if it wants to" (R. Penrose, op. cit., Fig. 26.3, p. 668; emphasis mine -- D.C.). In what time? This is what we need to clarify, since the major problems of quantum gravity are rooted on the different notions of 'time' in quantum theory and GR, as explained by Claus Kiefer in his recent monograph Quantum Gravity. See also the Hilbert space problem here and here.

The story of this (imaginary?) time shows up in many more cases, like a song being played with different musical instruments. Barbara Piechocinska has composed a beautiful song, crisp and clear. Let's see what she can achieve in solid state physics. To quote from her web site, "A description based on wholeness is expected to prove particularly interesting in solid states physics, which is largely concerned with collective phenomena, as it may lead to new insights in their understanding." I like solid states physics (this was my last job in the BG Academy of Sciences), but prefer quantum gravity and the human brain.

Perhaps quantum gravity will change drastically our current QFT, we will know how to "attach" gravity to quantum fields, thanks to which no divergences and non-renormalizable mussiness will occur, as they certainly don't occur in the phenomenon of wholeness. Why am I optimistic? Because the nature of gravity reveals the phenomenon of self-acting, which is possible only and exclusively only if the 'whole is more than the sum of its parts', in such a way that the 'parts' can act on themselves via gravity defined by 'the whole' and its context. Just as the context of a sentence defines the meaning of all words (=matter, fields, etc.), and all worlds are "self-coupled" by their common context (=gravity). Look again at the Einstein's equation here.

More from Emilio Elizalde [Ref. 4], he has made a beautiful song too. Pay attention to 'the grocer being put into the bag'. As I mentioned above, the problem is well-known,

http://God-does-not-play-dice.net/Shimony.html#Ashtekar
 
 

D. Chakalov
September 22, 2004
 

[Ref. 4] Emilio Elizalde, COSMOLOGY: TECHNIQUES AND OBSERVATIONS, gr-qc/0409076 v1.

See Sec. 2: "More about this point in lesson 3, where a number of such expressions will be explicitly used in the calculation of the contribution of the quantum vacuum fluctuations to the cosmological constant."

Also Sec. 4.2.1, On the meaning of Einstein’s equations:

p. 37: "On April this year I had to explain some couple of aspects of Special and General Relativity to the mixed TV audience of a Thursday evening. I decided to start with the most famous equation E = cm². "Look", I said to the imposing camera in front of my face, "with this equation Einstein’s genius put on the same footing matter and energy, which had been always thought to be non-matching quantities. All of us have been told at primary school that apples and oranges don’t match: no way to add 3 apples and 4 oranges. Since, what the result would be? Seven, ... but seven what? However, we go to the grocer’s or the supermarket every week and we buy not only fruit, but all sort of different things, and the owner or the cashier just puts all items inside a bag and then ... he does it! precisely what we were told it was impossible to do: adds for us everything together and says ‘this makes $14.76’. But this is exactly what Einstein did: to find a conversion factor for the different quantities, which in his case was the velocity of light and for the cashier it’s just the price per pound of every item. Easy, isn’t it? Einstein, as the grocer’s, was not constrained by what we learn at school. In Einstein’s case this opened the way to the possibility of converting matter into energy, and vice-versa, what was soon put to test.

"And then I went on, "Now let’s turn to GR. This is actually rather more difficult to grasp and no shop owner or cashier on Earth would have guessed the answer this time.

p. 38: "That’s very different from the rest of terms, since it means that the reference system itself gravitates, that there is no ‘outside reference system’. In other words and following with the same example as before, what Einstein did here was to put the grocer himself inside the bag together with the rest of the things we bought! Who now will do the sum for us?

"Actually the first to guess our Universe could behave in this remarkable way was Ernst Mach (1838-1916). And Einstein found out the precise equations to try to confirm such extraordinary idea.

p. 39: "Any mathematical reference will also ‘gravitate’, that is, it will be unavoidably subject to the influence of all the masses in our Universe, and their rotation. In plain words, ‘the grocer himself will have to be put into the bag, indeed, and nobody will be able to do the sum for us.’ This is what we learn from looking at our Universe."
 

[Ref. 5] Roderich Tumulka, Feynman's Path Integrals and Bohm's Particle Paths, quant-ph/0501167 v2.

p. 3: "Finally, I address mathematical rigor. There is a mathematical problem with path integrals when both the time axis and configuration space are taken to be a continuum, a problem that is absent when either one is taken to be a discrete set. The problem is that there exists no analogue to Lebesgue measure, in other words no natural notion of volume, on the space of all paths, because this space is infinite-dimensional. Such a measure D_y, however, is assumed in the path integral formalism. This problem is not cured by Bohmian mechanics, and, as far as I can see, the problem will never be cured because it is simply a mathematical fact that there is no Lebesgue measure on infinite-dimensional spaces."