Sometimes physicists prefer to remain anonymous. I would like to comment on the opinion of a leading theoretical physicist who was not, to the best of my knowledge, a student of Wolfgang Pauli, but would certainly prefer to remain anonymous. I will refer to this person as 'Professor X'.Humana anima non est forma in materia corporali immersa, vel ab ea totaliter comprehensa, propter suam perfectionem Here is the opinion of Professor X sent to me by email on Wed, 23 Oct 2002 19:24:15 +0100: "You do not know enough theoretical physics to help with any research in that area." What area? I am trying to follow the steps of Wolfgang Pauli who suggested a solution to the mind-matter problem in January 1948, and has published numerous papers and monographs co-authored by Carl Jung. All of them consistently ignored and forgotten by the established theoretical physics community. These efforts of mine resulted in a new framework for mind-brain relations, which I called trialism, since it presupposes not two but three ontologically different entities. The idea is not original at all, the only new element in it is the conjecture about a universal time arrow, which serves as the physical basis of the psychological time arrow. Hence the task boils down to pinpointing the problems in modern theoretical physics, which would require the universal time arrow for their unique solutions. If there are such solutions already proposed, then mine will be redundant, and I will consider them wrong. (I tried to explain the proposal for two modes of time in the universal time arrow in my email to Todd Brun, Tito Vecchi, and Carlos Castro.) I had many conversations with Professor X in the past four years, but the only piece of information relevant to the task stated above was the following text sent to me by email on Fri, 25 Oct 2002 16:46:34 +0100: "As for time, wrist-watches and Diff(M), one of the key things that emerged from all the discussions on the problem of time was that although it is true that, because of the Diff(M) action, no physical meaning could be attached to a point on the space-time manifold, a physical meaning *can* be attached to specifying a space-time location by the values of various physical quantities. Karel Kuchar is probably the person who has done most work on this, but it is something that number of people have remarked on in recent years. For example, \phi is a scalar field on the manifold and $X$ represents the space-time coordinate of a particle, then although \phi(x) has no physical meaning (if x is a point in the space-time manifold) nevertheless $\phi(X)$ *does* have a meaning: ie you can talk in a Diff(M)-invariant way about the value of a field where a particle 'is', and similarly for a trajectory. And, after all, general relativity does seem to work well as a theory, and yet I can certainly read the time on my wrist watch!" Now, if this
is an answer, what could have been the question? Amazingly, the question
had nothing to do with the answer! My request to Professor X, send by email
on Thu, 24 Oct 2002 20:34:51 +0300, was the following: "To prove me wrong,
please explain to me what kind of time is implied by 'moving points around'
in Diff(M)-invariance, and how can your wristwatch read it." The reply
I got from Professor X was more than elusive, to say the least.
To comment on the notion of "trajectory" in the email above: while it may be true that "... $\phi(X)$ *does* have a meaning: ie you can talk in a Diff(M)-invariant way about the value of a field where a particle 'is', and similarly for a trajectory", the whole truth behind the seemingly innocent adverb "similarly" is that the so-called trajectory belongs to a dead frozen block universe, firstly, and secondly -- it belongs to a single solution of the GR equations of motion (a single solution of the GR equations of motion determines 'a spacetime', where a notion of proper time is associated to each timelike worldline, C. Rovelli), which has somehow emerged from the whole spectrum of all possible (infinitely many) solutions in quantum gravity, much like a single trajectory (C. Rovelli) of a quantum particle emerges from the quantum "dough" in QFT (R. Penrose). The notion of 'proper time' associated to such trajectory is unphysical (Butterfield & Isham), in the sense that there is no 'natural' way to single out some preferred or global 'proper time', due to the absence of any background "grid" (called here 'global mode of spacetime') in present-day in GR. Therefore, if Professor X wishes to "talk in a Diff(M)-invariant way about the value of a field where a particle 'is' ", the first off task is to explain the alleged "unobservable" (not Diff(M)-invariant) proper time [tau] along spacetime leaves (called 'global mode of time'), and answers the question in my email from Thu, 24 Oct 2002 20:34:51 +0300: "what kind of time is implied by 'moving points around' in Diff(M)-invariance, and how can your wristwatch read it." Regrettably, my opponent chose to evade this question (perhaps because it came from "just another crank"). However, the question shows the greatest mystery of GR: the nature of "points" in the context of the principle of general covariance, after Einstein. The æther comes back again, alive and well, being placed ] between [ the points of the underlying manifold. It is completely hidden in present-day GR, hence the alleged "dynamics of GR" is entirely generated by constraints: "The dynamical data do not explicitly include a time variable" (Karel Kuchar). And we face two insurmountable problems in quantum gravity: 'the embarrassment of richness' (the multiple choice problem) and 'the embarrassment of poverty' (the global problem of time), after Karel Kuchar. I believe my opponent was familiar with these issues, at least because Karel Kuchar spent a sabbatical year at Imperial College. Now, let's zoom on the particular example from Professor X.
My opponent talks about some scalar field
\phi on the manifold (see above), and examines two entirely
different situations: (i) x as a "point" in the spacetime
manifold, and (ii) $X$ as the spacetime coordinate of a
particle, endowed with a fleeting "meaning" by $\phi(X)$ . Although
in case (ii) the
spacetime coordinate of a particle has been fixed --
after being 'moved around by Diff(M)-invariance'
-- at a point in the spacetime
manifold, it is only the particular scalar field
\phi that converts case (i) into case (ii). (The explicit dynamics of this
conversion, in both gravitational and quantum realms, was
indeed the subject of my talk at Imperial College, scheduled on
27 November 2002; see below.) NB: Notice the immediate consequence from the requirement for active diffeomorphism: the 'building' must exist as some form of reality (potential reality), in order to preserve its "sameness" (cf. Kurt Lewin) under all possible coordinate transformations (cf. Mihaela Iftime). It can't exist 'out there' (classical determinism), because it will impose a fixed background spacetime in GR. Einstein was fully aware of these consequences from the principle of general covariance, and was trying for full three years, from 1913 to 1915, to avoid the principle of general covariance, because it "takes away from space and time the last remnant of physical objectivity". Thus, we need 'potential reality' to understand the requirement for active diffeomorphism. In present-day GR, this new (to theoretical physics) form of reality is missing. To elaborate further on the metaphor of 'building displayed on a map', the only way to observe a building in GR is through some map (=spacetime), hence the building will inevitably acquire some fictitious "coordinates" in that map, but these "coordinates", and the coordinate "time" in which the building may evolve, are unphysical, because such definitions of time "provide no hint as to how their time might be measured or registered" (Butterfield & Isham). In the case of classical determinism the ontological status of the building would be 'objective reality out there', in which case the points from its "spacetime" would be the fundamental constituents of such classical determinism. These "points" will of course be re-labeled (or "colored" with nail varnish; see below) in different maps with which the same building would be displayed, but the invariant structure that would remain unchanged upon such (passive!) transformations would be 'the same building' as 'objective reality out there' ('bare finger nails', see below), and subsequently the bare spacetime "points" would be dead fixed as well. If that was the case chosen by Mother Nature, the localization of energy would be 'simple' (compare it with the case studied by Tullio Levi-Civita in 1917), and there would be no "quasi-local" complications from non-tensorial quantities due to the Equivalence Principle, as explained by Hermann Weyl in 1922. In fact, the problem of defining energy in GR was recognized by Hilbert even before Einstein formulated -- with the crucial help from Levi-Civita -- the basic principles of GR. To sum up, GR cannot in principle be formulated on the basis of classical determinism, because it will inevitably lead to an aether pertaining to such dead fixed spacetime points, as well as absolute reference frame, as implied in the non-relativistic cosmological picture here.
The fundamental lesson from GR is that such classical
determinism is not even a convenient approximation to the
potential reality of spacetime "points". The potential
reality may be ignored only in those cases in which
quantum or
gravitational effects (cold dark matter or dark energy) are vanishing small.
This new form of determinism is completely different from the old
fashioned determinism you used to derive the first option, so it may take
some time for you to understand it. Just keep in mind the
rule of 'relational ontology': the necessary and
sufficient conditions for something, call it A, to exist at a given instant
(local mode of spacetime) consist of negotiating and correlating its
instantaneous state with 'not-A', or 'everything else in the universe'. The
latter is the only remaining possibility to define rigorously an object in GR,
because there is no fixed "grid" we can 'hold
onto': the paths in GR are only created dynamically, by
'walking'.
Your brain
can do it, too. This is how the "brain" of Mother Nature adjusts the
global "context", hence fixes the 'inertial mass'
of all physical bodies in the universe (recall that a truck requires more energy
to be accelerated in ten seconds from zero to 100 km/h than your mom's car, so in this sense
the truck has more 'inertial mass'). But this "fixing" of the inertial mass
(along with the "cold dark matter") is still a great mystery, because the "gravitational
field" is not like the field that sticks the magnets on the fridge in
the kitchen: the "gravitational field" is 'pure geometry' and hence has no
intrinsic energy. In a way, the energy is delocalized and belongs to "the
forest" itself, yet it can show up only through some particular "tree".
Got a headache? Don't worry, it's natural. I can show you dozens of academic studies dedicated to some ad hoc postulated mysterious "scalar field" through which the so-called "dark energy" enters spacetime, and you'll get a real headache. But let me try to explain the puzzle with two actors, who you know very well: George Clooney and Robert De Niro. The former would always play 'George Clooney', whether it is Emergency Room (IR), or Ocean's Thirteen, or a Nespresso commercial, say. Quite the opposite with Robert De Niro: if he presents a character, it is always an entirely different person who has nothing to do with 'Robert De Niro'. He is indeed a great actor, and if you try to grasp his personality, it would be like trying to determine the "intrinsic" camouflage color of an octopus. In this sense, Robert De Niro is a good metaphor for the "dark energy", while George Clooney is more like that "scalar field" mentioned above. Capiche? (To be specific, the "crack" through which the holistic or "dark" effects of "the forest" get smuggled in GR (producing the "colored octopus") can be revealed by recalling that no genuine Dirac observable can exist in GR: the set that is supposed to encode the complete gauge invariant information by Diff(M)-related configurations cannot exist in principle, just as the complete (or global) presentation of a quantum system by a set of all observable (or local) states of that same quantum system, for Hilbert space dimension greater than two, cannot exist in principle, as we know from Ernst Specker. Briefly, in QM and GR we do not have a well-defined notion of 'set': metaphorically, "the forest" that defines the 'set of trees' cannot be completely described with the properties of the "non-local" or "quasi-local" trees. Stated differently, we are not dealing with 'countable infinite' (denumerably infinite) colored pieces shaken in a kaleidoscope.) Going back to your finger nails, all this means that the infinitely many possible "colors" of your nails are engaged in perpetual negotiation and correlation 'outside the train' (compare it to the emergence of a single "trajectory" in QFT; cf. R. Penrose above). And since you're confined 'inside the train', you cannot witness the infinitely many negotiating steps taken 'outside the train', which are "projected" into one instant from your (local) time, as read by your wristwatch (cf. Macias & Hernando). You might only notice that this relational ontology produces quasi-local effects 'inside the train', and that the train gains more fuel by accelerating its speed, being driven by the "dark energy" of the stuff 'outside the train'. The latter is the last remaining 'relational background' with respect to which the "brain" of Mother Nature can produce the quasi-localized explications of 'His thoughts' inside 'the train' (local mode of spacetime). Otherwise the task of producing the "picture" of your train will be impossible (we need to answer the question 'with respect to what?'), because it will be like "trying to paint a painting without any canvas". Capiche? Let's go back to the 'building displayed on a map'. On the one hand, GR allows for the genidentity (Genidentität, cf. Kurt Lewin) of the building -- 'the building per se' -- to be preserved and sustained in all maps, provided the building is Diff(M)-invariant (see the principle of maximal permutability, John Stachel). But on the other hand, the building does not exist like 'objective reality out there' (classical determinism), because in GR there is no unaffected flat spacetime in which the constituents of the building would be tied/fixed to particular points from that fixed underlying spacetime. In this sense, the reality of 'the building in GR' is completely different from the (fake, strictly speaking) case of 'objective reality' in classical physics and STR. Yes, 'the building in GR' is real, but it only casts its different perspectives or "shadows" in different maps (context-dependant presentations), while 'the building per se' has become totally illusive in GR (as Plato would have said). To recover 'the building per se' and unveil the physical objectivity in GR, we need to recover the true dynamics of GR, and the first step is to recover the hidden "grid" of the global mode of spacetime, which Karel Kuchar dubbed Perennial, since it refers to an "all time [tau]" that is "eternally present". Then the next step will be to build a brand new "trajectory" of states of the building, each of which will be a brand new, re-created, instantaneous snapshot of 'the building per se' in a brand new, re-created, 4-D spacetime -- in the same vein as the dynamically build 'quantum phase space' and Heraclitian time of Unruh & Wald (cf. K. Kuchar (1992), Time and interpretations of quantum gravity, kvk.pdf, p. 40). And speaking about the dynamics of GR, it's worth remembering the simple metaphysical considerations from St. Augustine: there must be a state of "non-being" ]between[ the points from the spacetime manifold, such that these "points" can be individuated and labeled 'in time', or else they will fuse into one single point of eternity, which people call 'block universe'. Hence we need Kuchar's Perennials and an "all time [tau]" that is "eternally present" (global mode of spacetime).
It is very important to stress that Bill Unruh
prefers to talk about an "explicit (but unmeasureable) time", which
Marco Spaans could perhaps demonstrate with
a triplet of three-space regions, hence making the 3-D space time-orientable
from the outset, by showing that every "point" from 3-D space is endowed
with a time-orientable mechanism: it has a "history" and a "future". Hence we
need three (not two) states. It remains to be seen whether
Marco Spaans will implement the
Bayes' learning rule to "orient" an arbitrary point in 3-D
space toward its "history" and "future". Bottom line here is
to reveal the blueprint from the phenomenon of transience
cast on the 3-D space, because it is impossible to deduce it from the matter
fields we drop later on that 3-D
space (P. Joshi). In my just-another-crack opinion, this is the genuine dynamics of GR: the "trajectory" will pass through infinitely many re-created maps (3-D hypersurfaces), and the resulting dynamics will be totally different from the current "block universe". We cannot derive the dynamics of GR from just one instantaneous 'state of the building' for which we've solved the Einstein field equations, and have "collapsed" the 'building per se' onto one spacetime only. We can do that only in classical mechanics: once you capture an instantaneous state from the trajectory of your Frisbee, you can recover (approximately) the whole history and future states of your Frisbee along that trajectory, because you have an underlying unaffected flat spacetime that you can 'hold onto'. Once we accept the principle of general covariance (after Einstein) and its modern Diff(M)-formulation (cf. J. Stachel), both the building and the map will lose their status of 'objective reality out there' (classical determinism). Einstein struggled with this painful situation long before he formulated GR in 1915 -- with the crucial help from Levi-Civita -- and finally chose to adhere to the principle of general covariance, at the expense of losing "the last remnant of physical objectivity". In my just-another-crank opinion, the only way to keep the principle of Diff(M)-invariance and recover the 'physical objectivity' of GR is to move to a broader level of reality, called 'potential reality'. It is designed from the outset to include the "non-tensorial" variables in GR, which are interpreted as effect of the Holon, hence will inevitably look "dark" in present-day GR. Let me again stress that the Diff(M)-group needs to be extended by including brand new transformations pertaining to 3-D space. Unlike in STR, where the metric acts as a background structure given a priori, in Einstein GR the metric is treated as a field which not only affects, but also is affected by, the other fields present. The resulting relational presentation leads to "disappearance of time" in background-independent theories (cf. John Baez), in the sense that the 'time of facts', which we know from classical mechanics and STR ('classical determinism'), is not valid for the whole trajectory, but pertains to just one instant from it; hence the frozen "block universe". And because there is no background spacetime in present-day GR, we cannot derive the "trajectory" from that single instant. The non-linear, bi-directional "talk" (J. Wheeler) continues at every instant from the non-tensorial "time" [tau] (cf. C. Rovelli and B. Bolen), as depicted with the lake metaphor here, and at each of these instants the non-tensorial "time" [tau] is being dynamically converted into an 'observable time of facts', in such a way that you can say "yet I can certainly read the time on my wrist watch!", after Professor X. But again, due to the active diffeomorphism freedom, the geometrical "points" cannot be identified by any fixed material content of 'objective reality out there', as explained by J. Stachel and Butterfield & Isham: there are no fixed paths in GR, because "paths are made by walking" (Antonio Machado). To be specific, if all Type I matter fields (P. Joshi) could have been presented in present-day GR as "smooth objects" and "thus ‘well defined’ on any point of space" (Corichi & Zapata), the "walk" would be well-defined at any point of 3-D hypersurface and up to its "boundaries", and subsequently no "singularities" and Cauchy problems would have ever emerged in GR. Notice again that the "walk" is inherently relational and quasi-local. It is also flexible, hence cannot be derived from 'the laws of an instant'. If we choose to collapse this quasi-local "walk", we will inevitably face the Cauchy problem for the Einstein equations (J. Stachel) and many other discrepancies, chief among which is that there is no natural way to embed in GR the holistic (or "dark", as some people call it) energy of the Holon. Briefly, if we wish to understand the dynamics of GR (instead of using some slippery poetic expressions such as "... and similarly for a trajectory"; cf. above), we need quantum gravity to explain (i) the whole spectrum of all possible "spacetimes", and (ii) the selection mechanism that singles out one possible solution (=spacetime) in the context of some particular scalar field \phi : Mother Nature does not suffer from Cauchy problems. The bold statement by my opponent -- "yet I can certainly read the time on my wrist watch!" (cf. above) -- tells nothing about the mystery of GR. (Does his wristwatch read the proper time [tau] along the stack of spacetime "leaves", in ADM presentation? Is the cosmological time, as read by his wristwatch, some "Dirac observable"? How would he cook up a time-orientable spacetime in the first place?) Another bold statement was his opinion on my knowledge in theoretical physics (see above), which he reformulated on October 12th this year, again without providing even a shred of evidence. With the benefit of the hindsight, it is clear that my decision to cancel the talk at Imperial College, scheduled for 27 November 2002, was right. My opponent, Professor X, kindly invited me to talk under his roof, but informed me that only "three, maybe four people" have shown interest in it. Which makes me wonder, how was the talk advertised by him in the first place. It was certainly not announced at Imperial College web site in October 2002. Perhaps it cannot be ruled out that my opponent had privately told his colleagues that some crank wishes to speculate on GR. Anyway. My next talk
is scheduled for Sunday, 21 September 2008 (read a
brief introduction here), and will be
delivered in Munich. I will certainly invite all my
opponents, but it is not
clear whether Professor X would act as a
gentleman, by placing
his cards on the table prior to 21 September 2008. D. Chakalov The whole story was about a well-known problem of reconstructing a classical spacetime from nonlocal diffeomorphism-invariant observables. We can not use the trajectory obtained with the recipe described above for solving any of the problems of quantum gravity. This trajectory gives us nothing but the pathologies of the classical spacetime manifold. It can not, even in principle, gives a hint to some fixed instant of time, simply because in canonical classical GR we do not have any background. The only entity we could 'hold on' is the global mode of time and space. I believe this is a new road toward quantum gravity. I hope my CD ROM "Physics of Human Intention" will live long enough to find some open-minded theoretical physicists who would like to explore the heritage from Pauli and Jung, as well as my efforts. The reward could be enormous. We might be able to develop not only a complete theory of quantum gravity but also learn to use our brains far more effectively, by exploring the phenomenon of Synchronicity. There are some staggering problems in the immediate future. It is an open future, up to the unknown unknown. The phrase 'this is a local problem' is already an oxymoron. We are interdependent. We have to help each other. The world is not the same after 9/11. However, Professor X says: "You do not know enough theoretical physics to help with any research in that area." So be it.
Dimi Chakalov dimi@chakalov.net Monday, October 28, 2002, 23:59:11 GMT --
We know from textbooks that the only truly isolated system is 'the whole universe', which raises the question: isolated with respect to what? Isolated from what? From some mirror "negative" word maybe? Not really, the task is far more subtle than constructing a mirror world with one spatial and three temporal "dimensions". Let's keep in mind one of the cosmological constant problems: the cancellation of all but one part in 10120. (Read about vacuum energy here.) That's how the negative world should be coupled to 'the whole universe', i.e., to the only truly isolated system. This peculiar 'truly isolated system' might not have any physical beginning. It could be infinite in the past and future, singularity-free, and without particle horizon (George Ellis and Roy Maartens, gr-qc/0211082, Fig. 1). Moreover, the ultimate fate of the universe is undecidable (Paul Frampton and Tomo Takahashi, astro-ph/0211544; Hitoshi Kitada, gr-qc/9910081): "Time is Nature's way to keep everything from happening all at once" (John Wheeler). Our potential future is open up to the 'unknown unknown', hence our possible states do not, and can not form a set. These possible states exist in the form of propensities or potentialities, and can not be normalized, which leaves a window for totally new things to emerge in the future by creatio ex nihilo. This is the physical basis of our non-unitary free will: everything is possible. If you want it, you can make it happen. I've sent the email printed below
and the link to it to many theoretical physicists, hoping to receive their
critical comments and suggestions. Meanwhile I will try to read some physics
textbooks, as suggested by Mr. Walter Polansky from U.S. Department of
Energy
eight and a half years ago. Dimi Chakalov dimi@chakalov.net Tuesday, November 5, 2002, 21:29:47
GMT
==
Dear Colleagues, May I ask a question. Is it possible that the acceleration of the universe is caused by some pool of negative mass, along the lines suggested by Sir Hermann Bondi [Negative Mass in General Relativity, Reviews of Modern Physics 29, 423 (1957)]? It seems to me that if we need to find some uncancelled forces and free acceleration, the hypothetical pool of negative mass could fit the job: it will be attracted to the positive mass of the universe, while the latter will be repelled by it, hence the system [pool of negative mass] & [physical universe] will accelerate the physical universe, in violation of Newton's third law, without limit and with constant acceleration. I will highly appreciate your comments and suggestions. The reason for asking this question can be found at my web site. Thank you for your time, as read by your clock. Regards, Dimi Chakalov
--
D.C.
Subject: History as sequential conjunction
RE: Smaragda Kessari, Affine histories
in quantum gravity: introduction
May I ask a question. I wonder what would happen to the sequential conjunction " a_1 is true at time t_1, and then a_2 is true at time t_2, and then ..., and then a_n is true at time t_n " if the alleged truth values of propositions are 'neither true nor false but somewhere-in-between', after C.J. Isham, Is it true; or is it false; or somewhere in between? The logic of quantum theory. Contempory Phys., 46(3), 207-219 (2005) Aren't such truth values UNdecidable à la Gödel? I will appreciate the opinion of your colleagues as well. BTW my efforts to follow Chris' program (type-IV scheme, gr-qc/9310031) can be read at http://www.god-does-not-play-dice.net/Xiao.html#outline Kindest regards, Dimi Chakalov
==============
Subject: Re: History as sequential conjunction
Subject: Re: History as sequential conjunction ===== Note: Perhaps the reader has already noticed the "link" between topos truth value 'somewhere-in-between' and Gödel's undecidable propositions: they are identical. The theories from which they have been derived are drastically different, of course. In the case considered by Chris Isham, the problem originates from the well-known statement of Erwin Schrödinger about the realism in quantum theory, which can be read here. As to the undecidable propositions, Kurt Gödel stated "... that a complete epistemological description of a language A cannot be given in the same language A, because the concept of truth of sentences of A cannot be defined in A. It is this theorem which is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic" (S. Feferman, Kurt Gödel: Conviction and Caution, Philosophia Naturalis 21, 546-562 (1984), p. 554). Thus, in both cases we have undecidable, 'somewhere-in-between-true-or-false' propositions. Big mess. Perhaps the undecidable truth value of propositions in the topos approach to quantum theory would be cleared in a meta-theory such as quantum gravity, which contains A (=quantum theory) as a limiting case. Only in such meta-theory (=quantum gravity) the concept of truth of sentences of A (=quantum theory) can be made comprehensible. Otherwise he and his younger colleagues "will get "down the drain" into a blind alley from which nobody has yet escaped" (Richard Feynman). Not surprisingly, Chris Isham says that I "do not know enough theoretical physics to help with any research in that area." It's dead obvious that I can't help him with these undecidable, 'somewhere-in-between-true-or-false' propositions. Sorry.
=================
Alternatively, if all examples you can think of
can indeed be reduced to 'single-valued truth
assignment' in some meta-theory, then there will be no difference between
the two cases, yours and Gödel's. They would look different on paper only. It
happens.
Note: Notice the linked text above: it will bring you to the "number" [phi], which "enumerates" the potential explications of the Holon. These potential explications are both 'many' (hence the 'multi-valued truth assignment') and ONE, because the Holon is ONE entity as well. This is the meta-theory referred to above. In the framework of this meta-theory, there are no "undecidable" nor "multi-valued truth" assignments to propositions, thanks to the dual nature of the Holon. This is the crux of the new form of reality, called 'potential reality'. This was also the subject of my first talk with Chris Isham on November 13, 1998. Fifty-two months have passed since Chris Isham delivered his opinion on my knowledge in theoretical physics, yet he still haven't found some spare time to support it with any fact against the potential reality. I've urged him twice, in private conversations and very politely, to put his arguments on the table. He refused, politely. Now I am trying to play the game 'his way', without even having a clue what he and his younger colleague, Andreas Doering, have written in their forthcoming four papers "that will be hitting the web in the next few days", as he put it above. All I am asking is for one physical example that would support Chris Isham's view on that 'multi-valued truth assignment', and prove that I am indeed a moron who, after working in this field since 1972, still does not know "enough theoretical physics to help with any research in that area." After waiting 52 months, I believe can say 'enough is enough'.
==============
===================
The other issue we discussed was the "truth value" YAIN. There are a number of reasons to insist on YAIN, as opposed to the proposed toposification of quantum theory, producing a spectrum of truth values "totally true -- something in between -- totally false" (see above). Firstly, the summation over all truth values yields YAIN. I believe this is clear to both Andreas Döring and his eminent co-author, so if they wish to proceed with their project, I believe they should totally redesign the topos theory, to make it applicable to quantum theory. In my just-another-crack opinion, such task is not feasible. As of today, Isham & Döring cannot explain even the superposition of states (Paper II, pp. 31-32): "This is clearly an area in which further research is necessary. In particular, we would like to know if there are any generic properties of a truth object as an element in (XXX). Or, to put it another way, is there an analogue for truth-objects of the superposition of states? This is a very important subject for future research." And also an endless math jungle, resembling the one of Alain Connes. Forget it. Perhaps Chris Isham believes there are no insurmountable problems with the normalization procedure in his approach, but I haven't seen 'the proof of the pudding'. Just try the Schrödinger cat -- the interference pattern with "negative" regions, in Wigner presentation, here. The second reason for insisting on YAIN can be grasped by pondering on the nature of 'potential reality' and the "oranges <--> apples" transition: unitary transformations between the two realms are impossible. Forget it. And the third reason is that the "truth" value of Gödel's UNdecidable propositions (read Hitoshi Kitada) is indeed UNdecidable, or simply YAIN. Notice that this third issue is very complex, since it goes straight to non-unitary transitions of 'the universe in its local mode of spacetime', along the universal/master cosmological time arrow: read John Wheeler. The future is open, up to 'the unknown unknown'. So, if you ask Chris Isham whether he will write an update on the prima facie questions in quantum gravity by 21 September 2008, he will probably respond with YAIN. The last paragraph of Chris Isham's Lectures on Quantum Theory: Mathematical and Structural Foundations (reference here) reads: "The central issue in all this is really the phenomenon of quantum entanglement, and its striking contrast with the reductionist concepts of Western philosophy."
But how does this entanglement stuff
exist? Read the opinion of Chris Isham
above. Apart from that, he is indeed a charming person.
D. Chakalov
==============
Subject: Re: History as
sequential conjunction
=============
[Note: Perhaps Chris Isham wishes to imply that
"there may well be things that are wrong" in his
neo-realist paper, although their mathematical presentation could be
correct. But there is no need to make errors in both the key idea and its math
presentation -- the first error is enough. D.C.]
Note: As of today, 2 March 2007, the content of the four paper by Chris Isham and Andreas Döring, which "will be hitting the web in the next few days" (see above), is completely unclear. Once they appear on ArXiv.org server, I will certainly study them, with great scrutiny. What is known so far is the following statement by C. Isham, regarding the scope of these papers: "The key idea is to associate a formal language of a certain sort (a higher-order, typed language) with each physical system. One can then show that any theory of physics can be interpreted as finding a representation of this language in a topos. A lot of general issues can be discussed within this framework." Let me write the introductory section of my forthcoming review. I shall be very brief, for a number of reasons, one of which is that nobody is sponsoring my efforts (as opposed to those by C. Isham and A. Döring; see above).
of four papers by C. Isham and A. Döring
1. Introduction Recently, Chris Isham (Dean of Natural Sciences and Professor of Theoretical Physics at Imperial College, London) and Andreas Döring (Postdoctoral and Advanced Research Fellow at Dept of Physics, Faculty of Natural Sciences, Imperial College, London) have presented four research papers, entitled: [..........] .
Their intention is "to associate a formal language
of a certain sort (a higher-order, typed language) with each physical system. One can then show that any theory of physics can be interpreted as finding a representation of this language in a topos. A lot of general issues can be discussed within this framework."
(C. Isham, private communication) As stressed by Erwin Schrödinger in 1935: "The rejection of realism has logical consequences. In general, a variable has no definite value before I measure it; then measuring it does not mean ascertaining the value that it has. But then what does it mean?" Suppose we, and presumably the authors, wish to suggest some key ideas to reveal the unique nature of quantum realm, which is drastically different from 'the objective reality out there' from classical physics. What kind of 'quantum realism' can be derived from their four papers? Specifically, what kind of "formal language" can be associated with quantum systems, and what sorts of "general issues" can be discussed within their topos framework? What can we gain from their efforts, as compared to the current 'shut-up-and-calculate' interpretation of Quantum Mechanics? Let me begin by examining one concrete physical example provided by C. Isham and A. Döring. In their paper "..........", they wrote:
" .......... [the example is
still missing!] .......... " [To be continued]
D. Chakalov
The latest sequel dated 2 March 2008 (A. Doering,
C. Isham, 'What is a Thing?': Topos Theory in the Foundations of Physics,
arXiv:0803.0417v1
[quant-ph]) didn't offer any concrete example either, but it is worth
providing some excerpts, which I will leave without comments. Just follow the
links.
D. Chakalov Andreas Döring and Chris Isham, arXiv:0803.0417v1 [quant-ph]: p. 183: "Of particular interest is the problem with which we motivated the scheme in the first place: namely, to find tools for constructing theories that go beyond quantum theory and which do not use Hilbert spaces, path integrals, or any of the other familiar entities in which the continuum real and/or complex numbers play a fundamental role." p. 172: "A translation can at best give a faithful picture of an arrow, but it cannot possibly ‘know’ about the more complicated contextual structure of the larger category. Clearly, both technical and interpretational work remain to be done." p. 136, footnote 98: "The ideal monad has no windows."
p. 15: "Of course, as always these days, Google
will speedily reveal all that we have omitted."
This is the crux of the challenge: the Hilbert space has to be modified or perhaps even replaced by 'something else'. Erwin Schrödinger has explained the task in 1935; read his famous quote from Die gegenwärtige Situation in der Quantenmechanik above. In my opinion, we need to keep the quantum state as 'not possessing any definite, macroscopically describable state'. Stated differently, we have to preserve and
protect the quantum state -- before, during and after its
measurement/observation -- from being entirely and irreversibly converted into
some 'definite, macroscopically describable, state'. Which in turn means that we
have to deal with two things -- the quantum state and its fleeting
"projections". Which is why we need to modify the Hilbert space, or perhaps even replace it by 'something
else'. I opted for the latter. If we decide to 'copy' its value in the quantum realm and 'paste' it into the world of tables and chairs, we will encounter the puzzle explained by Erwin Schrödinger in 1935. In my opinion, we can only resolve it with 'potential reality'. We simply do not have any other option to explore. We need to keep the quantum state 'alive and kicking', as not possessing any definite (macroscopically describable) state before, during and after its measurement/observation. The human brain can do it (try it also here), and because the brain is a piece of matter, the quantum matter should do it as well (or maybe even better). Hence the motto of the so-called PR2 interpretation of QM: Dead matter makes quantum jumps; the living-and-quantum matter is smarter. I've been trying to explain it to Chris Isham ever since our first meeting on 13 November 1998. We are, in fact, dealing with three kinds of reality: physical reality, potential reality, and the ultimate reality of 'the monad without windows' or Aristotelian First Cause. It doesn't matter if people insult me, either politely, like Chris Isham, or not (like some LSC members). It doesn't matter if people keep quiet and totally ignore what they've learned from this web site. You just can't change Mother Nature.
There was a joke circulating in the established theoretical physics community at that time (probably originating from Niels Bohr's colleagues in Copenhagen), about how to catch a live elephant: we know that elephants are very curious animals, so all we need is to place a billboard at their path walk, explaining the Dirac Sea. The elephant will read it and will be so astonished that will drop down unconscious, after which we can safely catch the elephant. Well, Paul Dirac "blinked" in his publication and choose to talk about neutrons instead of positrons. And his colleagues were very gentle on him. Not so with Stanley Pons and Martin Fleischmann and their discovery dubbed cold fusion: they couldn't publish their experimental results in any high-ranked journal, and back in 1989 some established academic scholars even accused them in professional misconduct, until the undisputable evidence of the nuclear origin of cold fusion was demonstrated and published in Naturwissenschaften this year (reference here). To finish this gentle reminder on the "predictive power" of the established theoretical physics community, let me quote from Popular Mechanics, March 1949: "Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 tubes and perhaps only weigh 1 1/2 tons." And also Robert Millikan, Nobel Prize in Physics (1923): "There is no likelihood man can ever tap the power of the atom." But how to identify and separate sound and perspective ideas from the babblings of the cranks? It is actually quite easy: cranks make errors which every professional physicist can pinpoint (example here). All you have to do is to avoid what I called, after my personal experience, 'the Bulgarian logic': "the statement [A] is wrong, because it contradicts what was initially rejected by it." In the case under consideration, one concrete action would be to recall the basic basics of GR and immediately raise your voice against the Advanced LIGO and LISA, instead of keeping quiet, like the established theoretical physics community, Chris Isham included.
Another, and also very desirable, reaction to the
issues discussed here would be to examine under great scrutiny the textbook
version of QM, after Paul Dirac: "...a measurement always causes the system to
jump into an eigenstate of the dynamical variable that is being measured...''.
It definitely cannot even address the main challenge explained by Erwin Schrödinger in
1935, on which I tried to elaborate
above. Therefore: I hope Chris Isham will never wind up in a situation in which he could rely on math only, without being able to test the physical "output" from his topos models with some physical example, because this may drag him into an endless math jungle, similar to that of his colleague A. Ashtekar. In both cases, Loop Quantum Gravity and the toposification of Quantum Theory, there is indeed 'an essential germ of truth', which in the latter case can be clearly shown with the following excerpt from C. Isham's quant-ph/0508225 v1, p. 16:
"This is no problem in the conventional formalism
since, there, one never gets reduction to an eigenstate for which there is zero
probability of finding the associated eigenvalue. Or, more precisely: such zero
probability events are swept under the carpet as never happening." NB: We can reveal the "forest core" (potential reality) also in the primary object of geometry -- the point. The Holon in the global mode of spacetime is 'the universe as ONE', thanks to which it can "perform" an infinite (actual infinity) series of acts in one instant from the local mode of spacetime. Recall the Thompson's lamp paradox, and try to figure out what is the 'state of the lamp' at the limit '2 min': is it "on" or "off"? YAIN -- is the right answer, because the potential reality itself, residing "inside" the geometrical point, cannot be exposed in the physical world. The alternative option has far-reaching consequences, one of which is that there would be a fully scientific explanation of The Beginning, after which the whole theology would be annihilated, by being converted into science. Thank God, this is impossible. All this is widely known, and if Chris Isham wishes to express it with topos theory, it should be agonizingly clear to him that he simply can't do it. Suffice it to say that in topos theory you can't separate the UNspeakable "forest core" (potential reality) from its normalizable explications in the local mode of spacetime constituting the quantum phase space. The latter is dynamical, while the former is being rooted on the ideal monad (see below). It looks to us like an 'empty set' from which everything evolves in a strictly non-unitary, creatio ex nihilo fashion: read John Wheeler here. Can you express the "evolving" empty set of 'potential reality' in topos theory? Can you show the "darkness" of a room with a flashlight? Besides, every physical explanation is inevitably, by its very nature, teleological, hence it is impossible to describe a self-acting, ONE entity empowered by The First Cause. You should somehow insert a special "blank spot" into your theory, but you can't do it in topos theory. No way. Fuhgeddaboudit. To be specific, here is just the first pitfall (A Topos Foundation for Theories of Physics, Paper I, p. 2): "Propositions about the system are handled using Boolean logic. This requirement is compelling in so far as we humans think in a Boolean way." This requirement is certainly not "compelling". The calculations performed by computers are indeed based on Boolean logic, but we, humans, do not think exclusively in a Boolean way. Chris Isham should be fully aware of this faculty of the human brain, because I personally have explained to him the case of [YAIN], at least twice, in 2003 and in 2006. And since the brain can do it, the quantum matter should do it as well. Isn't this a simple argument?
Yet he choose to ignore it. And here's the result
(Paper II,
pp. 31-32): "This is clearly an area in which further research is necessary. In
particular, we would like to know if there are any generic properties of a truth
object as an element in (XXX). Or, to put it another way, is there an analogue
for truth-objects of the superposition of states? This is a very important
subject for future research." And also an endless math jungle,
resembling A. Connes' one. Anyway. In my just-another-crank opinion, Einstein's GR is essentially incomplete, because it provides only the necessary conditions for describing gravity, while the sufficient conditions should be delivered with the Aristotelian Connection. I will now finish this monologue and wait for the reaction of the readers of these lines (Chris Isham excluded, since he will never reply).
================================
Subject: Update?
I'm afraid Gerard 't Hooft is right about Chris Isham's efforts to change Quantum Theory. The task is known since 1935, and I don't believe topos theory is adequate to it. But since I "do not know enough theoretical physics to help with any research in that area", I will wait patiently to learn the professional opinion of Chris Isham, backed with facts or at least some arguments. As a second option, I asked Chris Isham to provide his professional opinion on the writings produced by his LSC colleagues: just follow the URL at the email above. If his LSC colleagues (490 distinguished GR scholars) are right, then I certainly "do not know enough theoretical physics to help with any research in that area". Of course, it would be preferable (although perhaps more difficult) if he could defend his opinion on my knowledge in theoretical physics by refuting the claim of Gerard 't Hooft, which I endorse. I believe have clearly explained my objection to Chris Isham's optimism regarding topos theory at our last meeting in Imperial College on March 9, 2006: the quantum reality cannot be modeled with the logic of propositions in topos theory -- 'neither true nor false but somewhere in between'. The logic of quantum reality is entirely different, since the question of whether 'the quantum state' is presented by one of the (infinitely) many classically-describable alternatives, smeared into some quantum dough (example from Einstein here), yields one and the same answer: YAIN. The truth value of 'YAIN' is an entirely different case, not covered in topos theory. It always emerges upon the development of specific observational context in which the latent observable acquires a definite "eigenstate", because we're dealing with an Onta, as stressed by Henry Margenau. Here's a simple illustration with the '20 questions game', courtesy from John Wheeler:
"There had been a plot not to agree on an
object to be guessed, but that each person, when asked, must give a truthful
answer concerning some real object that was in his mind, and which was
consistent with all the answers that had gone before." With only one
question left, John Wheeler guessed: "Is it a cloud?" The answer was "Yes!"
(John
and Marry Gribbin, In Search of Schrödinger's Cat, Black Swan, London,
1998, p. 209; quoted from: Quantum Theory and Measurement, ed. by J.A.
Wheeler and W.H. Zurek, Princeton University Press, Princeton, 1983, pp. 182-213). Perhaps the best way to explain the nature of 'potential reality' is by comparing it to something entirely different, namely, to some "hidden" quantum object which would exist 'out there'. Look at Claudia Schiffer below, and imagine that she is sitting in a dark room, but you can elucidate certain parts from her body with a narrow torch, resembling the eigenvalue-eigenstate link from your QM textbooks.
Suppose you wish to observe her knee. As a result from the preparation for such measurement, your torch would simply point to her knee, which you would imagine to be in some "eigenstate" prior to your observation. Then you turn on the torch for a fraction of a second, and obtain the knee-eigenvalue for this particular observation, with 50% chance for her left knee, and 50% chance for her right one. If you wish to observe her eyes (suppose eyes and knees are "complementary observables"), you could also claim that her knee-eigenstate did not exist before you set the corresponding measurement context, at the expense of being unable to observe her eyes, yet Claudia Schiffer were always sitting 'out there' in the dark room, so all you had to do was to orient your measuring device toward either her knee or eyes, to set the 'measurement context'. Even if you denounce the view of 'hidden reality out there' (e.g., Bohmian mechanics) and subscribe to the textbook version of QM, you would still think of Claudia Schiffer as Wheeler's smoky dragon which possesses the ability to exist in a "murky state of possibility -- to be anywhere, everywhere or nowhere at all -- until clicked into substantiality by a laboratory detector or an eyeball." Hence you'd reckon she is some "context-dependant reality", meaning some sort of "weakened" version of the objective reality we know from classical physics, yet still exists as 'physical reality out there'. Many people develop such twisted understanding of Kochen-Specker Theorem and QM in general, because they just cannot imagine that quantum reality may not at all exist as 'physical reality out there'. They are forced to choose between two alternatives: (i) Claudia Schiffer as some hidden objective reality or at least "context-dependant reality", or (ii) Claudia Schiffer emerging miraculously upon observation, like creatio ex nihilo. So, they choose the first alternative, as a "lesser evil", and stubbornly refuse to read and study Henry Margenau. And the prevailing interpretation of QM becomes 'shut up and calculate', based on the so-called 'classical notion of ignorance' (J. Hartle, arXiv:0801.0688v2, p. 11), because people can't even think of the case in which 'the quantum state' would freely fluctuate between non-settleable bets and settleable bets (ibid., p. 1 and Fig. 1). With the PR2 interpretation of QM, we have a third option for 'the universe as closed system', free from math pathologies: any time we look at Claudia Schiffer, we do not see the potential reality of Claudia Schiffer, but only her fleeting snapshot cast in our local mode of spacetime. Hence we always are dealing with two things -- (i) the potential reality of 'the quantum state', and (ii) its fleeting "projections". The second can be fitted in the Hilbert space (not without difficulties), but the first stays always outside it: see the interference pattern with "negative" regions, in Wigner presentation, here. I believe Mrs. Schiffer would grasp her Platonic idea effortlessly, even if she isn't versed in the math from our QM and GR textbooks. Again, the |
