ABOUT POINTS, IF ANY^{*}
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 everywhereatnotime,
like the Aristotelian
Unmoved Mover, it can
reach the "end" of any nondivergent 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. === If between any two points in space there is always a third point, can anything touch anything else? [To be continued] === 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 presentday 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 WheelerDeWitt equation. To be specific, if a given donkey (pictured above), at instant t_{0}, looks for its next pile of hay at a later time t_{1}, 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 10^{14}
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 quantum computer that would
harness the phenomenon of entanglement. 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. 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, smokydragonlike state, and is patiently waiting to be collapsed, in line with the rule of eigenvalueeigenstate 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? ===
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 "Suffice it to say that: (i) the argument applies not just to general relativity, but to any generallycovariant theory postulating a spacetime manifold; and (ii) according to the argument, general covariance (that is: the diffeomorphisminvariance 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." [To be continued] 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". However, there was virtually no interest on behalf of his colleagues, and at the end of October 2002 I decided to cancel the seminar, with utmost regret. The sole 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.
References and notes Bloch I., Some relativistic oddities in the quantum theory of observation, Physical Review 156, 13771384 (1967). Butterfield J., Isham I., Spacetime and the Philosophical Challenge of Quantum Gravity, grqc/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 NonRelativistic Quantum Mechanics, New York: International Textbook Co., 1973, pp. 4958. 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, grqc/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, grqc/0411121 v1, pp. 1015. Penrose R.,The Road to Reality, Jonathan Cape, London, 2004, pp. 6162, 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., SpaceTimeMatter, Fourth Edition, translated by H. L. Brose,
Dover Publ., New York, 1951, p. 270.
"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 (Fri, 4 Dec 2009) hasn't backed with any evidence whatsoever. Let's put aside all my speculations above, and focus of the solution proposed to the measurement problem in QM  the nonunitary “R” process  which was the crux of my intended talk at Imperial College on November 27, 2002. I borrowed the idea of 'latent observables' suggested by Henry Margenau. My input (if any) was about interpreting the way by which the latent observables are “not always there”. As Henry put it back in 1954: "I believe that they are “not always there”, that they take on values when an act of measurement (...) forces them out of indiscriminacy or latency." For if observables were in some form “always there” in the “U” process, the nonunitary “R” process is unavoidable (cf. Steve Adler, quantph/0004077v1, Sec. 1.3, 'Why the “R” Operation is Needed', Eq. 18). NB: Hence the key idea for resolving the nonunitary “R” process requires precise interpretation of Margenau's latent observables being “not always there”. Instead of thinking of 'quantum observables' as presented with a Hilbert space and some Hamiltonian "evolution" derived from the “U” process, consider Margenau's latent observables as 'shadows on Plato's cave' cast from their underlying source: you may "collapse" any of these shadows, yet their source (resembling Platonic ideas) will never experience any change whatsoever. (I explained this interpretation of 'latent observables' in a letter to Henry Margenau in 1990, during my stay in the United States, and Henry had no objections to it.) Hence the motto of this web site: Dead matter makes quantum jumps; the livingandquantum matter is smarter. Stated differently, the task for resolving the nonunitary “R” process leads to a new presentation of 'quantum reality': only part from it is presented with Hilbert space and the “U” process, while their ultimate source, resembling Platonic ideas, is 'never there'. If we wish to resolve the nonunitary “R” process, we have to offer a brand new presentation of 'quantum reality', because with Hilbert space and the “U” process we have no choice but the nonunitary “R” process. (Steve Adler has suggested quite a different solution to the nonunitary “R” process, which I was ready to discuss as well.) This was scope of my intended talk at Imperial College on 27 November 2002. The talk itself was based mostly on Schrödinger's 1935 paper and Henry Margenau's latent observables. My task was to demonstrate the ultimate, in my opinion, need for new presentation of 'quantum reality'. Discussing the practical and experimental work would have been quite a different subject, which I wasn't able to deliver on Wednesday, 27 November 2002 either  the seminar was "born dead, sit venia verbo." How did this happen? My recollection of the events from October 2002 is as follows: Prof. Chris Isham invited me to talk at his Seminar at Imperial College, and we agreed upon the title and the date. Soon I learned from him that there are actually only "three, maybe four people" interested in my talk, so he suggested to gather in his office room, and not in the designated Seminar Hall. Meanwhile I was checking every single day to see the announcement for my talk at the web page listing the upcoming Tuesday Seminar presentations. It wasn't showing up. Was this because Chris Isham had scheduled it for Wednesday, 27 November 2002? I got nervous and decided to email Dr. Dorje Brody (needless to say, my email was very polite), who was in charge of the Tuesday Seminar, as well as a few of his colleagues, hoping to learn if they would attend my talk on November 27, 2002. No reply whatsoever. Zilch. And at that point I smelled a rat. Why did Chris Isham invite me to talk in the first place? I emailed him and asked to set the record straight, namely, to state exactly how my ideas would/might connect to his field of expertise. He refused to do this by email, saying that we will talk on November 27th. But I firmly insisted, and explained briefly why I need clarity about his position regarding my ideas on quantum gravity. And at this point, he wrote back the following (Wed, 23 Oct 2002 19:24:15 +0100): "You do not know enough theoretical physics to help with any research in that area." Then I cancelled the socalled "seminar". Let me finish with the following statements: 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 by elaborating on its implications for quantum gravity. If you want parapsychology, watch C. Angel. If someone is interested in PHI^{3}, we should first discuss the ideas proposed here. First things first. Subsequently, if my ideas on quantum gravity are wrong, the whole theory of PHI^{3} (not explained at this web site) will also be wrong. Alternatively, if my ideas on quantum gravity are correct, there might  just might  be some possibility that the whole theory of PHI^{3} (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 experimental facts. The case of 'physics of human intention' and its predictions for quantum gravity, however, was (October 2002) 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. "just
another crank"
D. C.
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