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note: because important websites are frequently "here today but gone tomorrow", the following was archived from http://matpitka.blogspot.com/2013/05/how-sequence-of-quantum-jumps-could.html#comments on May 24, 2013. This is NOT an attempt to divert readers from the aforementioned website. Indeed, the reader should only read this back-up copy if the updated original cannot be found at the original author's site.
How a sequence of quantum jumps could give rise to
experience about continuous flow of Time
by Dr. Matti Pitkänen / May 24, 2013
Postal address:
Köydenpunojankatu 2 D 11
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URL-address: http://tgdtheory.com
(former address: http://www.helsinki.fi/~matpitka )
"Blog" forum: http://matpitka.blogspot.com/
I am trying to improve my understanding about the relationship between Subjective- and Geometric-Time. Subjective-Time corresponds to a sequence of quantum jumps at given level of hierarchy of selves having as correlates causal diamonds (CDs). Geometric-Time is the fourth space-time coordinate (General Relativity) and has real and p-adic variants. This raises several questions.
1. How do the subjective times at various levels of hierarchy relate to each other? Should/could one somehow map sequences of quantum jumps at various levels to real or p-adic time values in order to compare them (as Quantum-Classical correspondence indeed suggests)?
2. Subjective existence corresponds to a sequence of moments of consciousness: State function reductions at opposite boundaries of CDs. State function reduction localizes either boundary. But the second boundary is in a quantum superposition of several locations and size scales for CD.
We however experience Time as a continuous flow. Is this a problem or not? One could argue that it is not possible to be conscious about being unconscious so that gaps would not be experienced. But is this so simple? We are indeed able to experience the gap in sensory consciousness caused by sleeping overnight (this does not mean we have been unconscious; we just do not remember).
3. Subjective-Time is certainly not metricizable whereas Geometric-Time is and defines a continuum. But are moments of Consciousness well-ordered as the values of real variant of Geometric-Time are? This relates closely to the relationship of Subjective-Time to Geometric-Time. Certainly Subjective-Time does not allow any continuous measure in real sense as Geometric-Time does. One can however map moments of Consciousness to integers.
A. It would seem natural to be able to say about 2 moments of consciousness (call them A and B, whether A is before B or vice versa). Moments of consciousness would be well-ordered and could be mapped to real integers. But is this always the case? There is experimental evidence for the fact that consciously experience time ordering does not always correspond to the physical one. This was observed already by Libet (I have tried to understand these findings for the first time here).
B. What about p-adic integers as labels for moments of consciousness as suggested by the vision about p-adic space-time sheets as correlates for cognition and intention (as time reversal of cognition). Given p-adic integers m and n, one can only say whether the p-adic norm of m is larger than, smaller than, or equal to that of n. One can say that p-adic integers are weakly ordered.
p-Adic integers form a continuum in p-adic topology. Could one map the infinite sequence of quantum jumps already occurred to p-adic integers and in this manner to p-adic continuum instead of real one? Could the p-adic cognitive representations allow us to achieve this? If so, the experience about conscious flow ofTtime could be due to the p-adic topology for cognitive representation for the sequence of quantum jumps!
Could p-adic integers label moments of Consciousness and explain why we experience conscious flow of Time?
Next arguments give a more precise formulation for the idea that p-adic integers might label the sequence of quantum jumps at the level of conscious experience or rather reflective consciousness involving various representations realized as "Akashic records" [see => doc pdf URL-doc URL-pd ] and read consciously by interaction-free measurements (assuming that they make sense in TGD: NMP considerably modifies the standard quantum measurement theory).
1. Most p-adic integers expressible as n= ∑k nkpk are infinite in real sense and in p-adic topology they form a continuum. Suppose that the infinite sequence of moments of Consciousness that have already taken place can be labeled by p-adic integers and look what might be the outcome.
2. Sounds very strange in ears of the real analyst but it is true. The integers n and n+ kpN for N large are very near to each other p-adically. In a real sense, they are very far. This allows us to fill the gaps between say integers n=1 and 2 by p-adic integers which are very large in a real sense.
3. The p-adic correlate of the sequence of discrete quantum jumps/moments of Consciousness would define p-adic continuum which in turn can be mapped to real continuum by canonical identification.
This map sequence of moments of Consciousness to p-adic continuum would be nice but maybe tricky for anyone accustomed to think in terms of real topology!
This raises 2 questions:
A. p-Adic integers are not well-ordered. Could one induced the well-ordering of real time to p-adic context by mapping p-adic Time axis to real one in a continuous manner and in this manner achieving mapping of moments of Consciousness to real Time axis?
B. Could canonical identification ∑k nkpk → ∑k nkp-k map (or its appropriate modification) allow us to map p-adic integers to real numbers and in this manner induce real well ordering to the p-adic side. The problem is that real number with finite pinary expansion has second infinite expansion (1=.9999... is an example using decimal expansion) so that two p-adic time values correspond to any real time value with finite pinary digits. Should one restrict the consideration to integers with finite number of pinary digits (finite measurement resolution) and select either branch? Could the 2 branches correspond to real Time coordinates assignable to the opposite boundaries of CD defining 2 conscious selves in this scale?
What happens when I type letters in wrong order?
One can speak about sensory and cognitive orderings of events corresponding to reals and p-adics (for various values prime p or course). The cognitive ordering of events would not be well-ordering if cognition is p-adic. Is there any empirical support for this besides Libet's mysterious looking findings?
Maybe. For instance, as I am typing text I experience that I am typing the letters of the word in the correct order. But now-and-then it happens that the order is changed. Even the order of syllables and sometimes even that of short words can change. It is probably easy to cook up a very mundane explanation in terms of neuroscience or even electric circuits from keyboard to computer memory or the computer itself. One can however also ask whether this could reflect the fact that p-adic ordering of the intentions to type letter is not well-ordering and does not always correspond to the real number based order for what happened?
In the TGD Universe, the writing process involves a sequence of transformations of p-adically realized intention to type a letter to a real action (doing it). At the space-time level, it is therefore a map from p-adic realm to real realm by a variant of canonical identification crucial in the definition of p-adic manifold concept assigning to real preferred extremal of Kähler action a p-adic preferred extremal in finite measurement resolution (see this).
The variant of canonical identification in question defines chart maps from real to p-adic realm and vice versa and is defined in such a manner that discrete and rationals in a finite subset of rationals are mapped to themselves and defining the intersection of real and p-adic realms.
1. In the case of p-adic integers this subset is characterized by a cutoff telling the power of p below which p-adic integers and real integers correspond to each other as such. For the corresponding moments of Consciousness (now intentions to type letter), one has same ordering in both realms. For integers containing higher powers of p, a variant of canonical identification mapping p-adics to reals continuously is applied. In this case, ordering anomalies can appear.
2. Another pinary cutoff comes from physics. Real preferred extremals are mapped to p-adic preferred extremals and vice versa. Without the cutoff, the p-adic image of real extremal would be continuous but non-differentiable so that field equations would not make sense. The cutoff tells the largest power of p up to which the variant of canonical identification is performed for p-adic integers. Also now ordering anomalies appear if one regards p-adic integers as ordinary integers.
3. For the remaining integers, the map is obtained by completing the discrete set of points to a preferred extremal of Kähler action on both real and p-adic sides so that physics enters into the game. This assignment need not be unique and the most natural manner to handle the non-uniqueness is to form quantum superposition of all allowed completions with same amplitude. This effective gauge invariance would be very natural from the point of view of finite resolution and conforms with the vision about inclusions of hyper-finite factors as a representation for finite measurement resolution giving rise to the analog of dynamical gauge symmetry.
Could the strange inconsistencies between cognitive (sequences of intentions) and sensory time orderings (sequence of typed letters) reflect the fact that the ordering of p-adic integers as real integers is not the same as the ordering of their real images under canonical identification? Could it be possible to test this and perhaps deduce the prime p characterizing p-adic topology of cognitive representation in question?
Comments
1. At 11:10 AM, Plato Hagel said...
If you are a Platonist, it is much easier to reconcile?:)
I can further question this in relation to what you are asking. Who is the Clockmaker?
How does one ever begin to count? Pascal's triangle sets the emergence of a method to distinguish such counting?
Clock makers of the 4th dimension need a way in which to begin counting, yes?
2. At 7:40 PM, said...
I am a quantum Platonist. I assume no physical realities behind mathematical objects that I call zero energy states. There is no need for this since quantum jump between them causes the pain in my toe as I kick the stone.
Sequence of state function reductions at opposite boundaries of CD defines conscious clock at either boundary of CD. Conscious, non-conscious, conscious, nonconscious, ... it goes. At this level, one does not have any metric time.
The above questions are about how this non-metric Subjective-Time is mapped to a sequence of integers and then to a real valued space-time coordinate.
I do not need a clock-maker. Another manner to say this is that there is no eternal self, only self models defined by approximate invariants associated with quantum jumps as negentropically-entangled structures defining potentially conscious memories and future visions and thus self model via "Akashic records".
There is no beginning in Subjective-Time in the entire TGD Universe. For sub-CD born in quantum jump, there is the first state function reduction and its age is finite integer. In Geometric(relativistic)-Time ,there are boundaries of CDs at imbedding space level inducing end of space-time surfaces.
I have not said anything about how the correlation between Subjective-Time and Geometric-Time emerges here. I leave it as an exercise;-).
3. At 7:31 PM, Plato Hagel said...
The following comment may shed more light on what I am saying.
While one constructs the process toward some belief "when" is one truly convinced? So the idea here of visual reasoning is a culmination of sorts and quite revealing.
For a man like Dirac, he made good use of that process while analytically describing with the math. He writes:
When one is doing mathematical work, there are essentially 2 different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures.
Now, a good mathematician has to be a master of both ways of those ways of thinking. But even so, he will have a preference for one or the other. I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.
4. At 7:50 PM, said...
A natural identification for geometric and algebraic thinking would be in terms of visual and linguistic cognition (imagination and internal speech). A possible TGD-inspired consciousness theory interpretation would be in terms of dark photons and dark phonons decaying respectively to biophotons and biophonons (something new): visualization and internal speech.
Dark phonons could propagate along axonal membranes accompanying nerve pulses and potential waves and be due to the fact that cell membrane is an electret transforming electric to mechanical oscillations and vice versa.
There are indications that biophotons are associated with the right brain hemisphere. Could the left hemisphere be specified to internal speech by dark phonon communications? Why right/left hemisphere would have developed photon/phonon communications with very high value of hbareff? And does the dark photon make sense!?
[note: String-like objects at space-level connecting wormhole throats are a basic prediction of TGD and their oscillations define 2-particle excitation being thus analogous to sound waves which would however propagate with light velocity.]
Another possible interpretation is in terms of dark photons in 2 energy ranges: visible (biophotons) and those in IR near energy defined by cell membrane potential.
A third one in terms of membrane potential oscillations giving rise to Sine-Gordon-Soliton sequences having sequence of mathematical penduli oscillating in phase. Nerve pulses would result from perturbations putting one pendulum in full rotation. This perturbation would propagate and give rise to nerve pulse.