Friday, August 28, 2009

Did Boltzmann understand all about time?

Lubos Motl wrote a pedagogical review about the notion of time. The title of the posting is "The arrow of time: understood for 100 years". As a conservative Lubos believes that all interesting things about time were said by Boltzmann already before the birth of quantum theory. Second law would summarize all that is interesting. Lubos is also impatient about the fact that there are still people who feel that the nature of time is not fully understood.

The core of the Boltzmannian view about time is simple to summarize.

  1. The time development can be seen as analogous to Markov process. To continue, let us introduce discrete time tn = n×Δt. One could regard this as a technical simplification but will find that Δt has interpretation as time scale of quantum coherence.

  2. Physical events are identified as transitions from state i to state j taking place during time interval Δt and the probabilities P(i,j) characterize them. The probability of state i at time t=tn is given by p(i,tn) and once the probabilities p(i,0) for initial state are given by summing the probabilities over all paths j→k→...→i leading from j to i and calculating the average over the initial states

    p(i,tn)= ∑j (Pn)(i,j)× p(j,0).

    This formula leads to the second law stating the increase of entropy defined by Shannon formula.

There are several unpleasant questions that Lubos leaves out of consideration.

  1. Boltzmann's approach was developed before the advent of quantum mechanics but involves classical probabilistic approach not very natural in classical physics. Quantum theory indeed allows to calculate the transition probabilities p(i,j) from first principles. There are however deep interpretational problems. Can one say when quantum transition -state function reduction - breaking the deterministic Schrödinger evolution really takes place? How long is the period of non-determinism if it occurs? Is the non-determinism really assignable to the geometric time or could it be that the relationship between the geometric time and experienced time is what we do not actually understand? These are basic problems of quantum measurement theory which is a useful bag of calculational recipes but does not really deserve to be called a theory.

  2. At the technical level these problems are avoided by assuming that transitions take place during an infinitely long time interval. This idealization means that quantum coherence is present in infinitely long time scale. The resulting probability proportional to a square of energy conserving delta function is transformed to a rate by dividing with the length of this infinitely long time interval dividing away one delta function expressing the conservation of energy. One can feed the resulting rates to kinetic equations and assume that quantum coherence is present only in infinitely short time scales. Do not get frustrated: this is the situation! One can guess that there must be some finite time scale for which quantum coherence and sum over amplitudes makes sense and in longer time scales one must use Boltzmann's discretized approach and sum over probabilities.

There are also problems related to the justification of probabilistic approach.

  1. To some degree this picture could be formally justified by using path integral formulation of quantum field theory. What one must do is to replace the modulus squared for the path integral approximated with a sum over discrete paths with a sum in which all interference terms are neglected. This means a de-coherence. This kind of approximation can be defended by saying that due to the small value ofΔt in the example discussed. Do we really understand the origin and mechanisms of de-coherence? Could de-coherence have a more detailed description involving perhaps new physics?

  2. De-coherence assumption is rather strong in the many-sheeted space-time of TGD. TGD based view about dark matter as a hierarchy of phases partially labeled by Planck constant predicts macroscopic quantum coherence even in astrophysical time and length scales so that the Markovian view can be used only if one restricts the consideration to processes in definite time scale below the natural time scale characterizing the time intervals during which observations are made.

The basic problem of this approach is that the observer is not part of the Universe. In classical physics observer was a complete outsider and in quantum measurement theory the situation remains the same although the measurement interaction leading to state function reduction affects the measured system.

TGD inspired theory of consciousness can be seen as a generalization of the quantum measurement theory to resolve its basic paradox by making observer part of the Universe via the notion of self as well as to understand the differences and relation between the time of physics (geometric time) and experienced time by identifying the chronon of latter as quantum jump defining moment of consciousness.

  1. The outcome is what I call zero energy ontology. Zero energy states are pairs of positive and negative energy states localizable to the upper and lower boundaries of causal diamonds defined as intersections of future and past directed light-cones of Minkowski space (and taking Cartesian product with CP2). There are CDs within CDs and they form a hierarchy.

  2. The hierarchy of CDs is also a correlate for a hierarchy of conscious entities which I refer to as selves. CD represents the perceptive field of self. CD represents correlate for quantum jump identified as the chronon of experienced time and there is an infinite hierarchy of chronons. CD also defines also quantum coherence region inside which the sum over probabilities must be replaced with the sum over amplitudes so that Boltzmann's kinetic description fails.

  3. The notion of time measurement resolution reduces to the time scale of CD. If this time scale comes as powers of 2, p-adic length scale hypothesis follows. One would have a hierarchy of physics realized in different p-adic length and time scales characterized by primes near integer powers of 2.

  4. Although one has quantum coherence in a given time scale (CD), it is possible to have de-coherence in shorter time scale (sub-CDs). The description of hadronic reactions in terms of quarks and gluons using kinetic distributions defined in relatively short time and length scales and the description of hadrons using wave functions defined in considerably longer scales is a good example about de-coherence within coherence.

  5. This gives hopes about improved understanding of the second law in living matter. The essentially new notion is that of scale: when one speaks about second law one must specify the time scale in which it is applied. Only if applier is CD modeling what happens in the ensemble of sub-CDs this description works. If one tries to understand what happens in CDs characterized by time scale longer than the natural time scale of the observation- the approach fails. These CDs are expected to be highly relevant in biology.

I will not continue here further but give instead a link to the article About the Nature of Time and also a link to a video summarizing the recent view about the relation between geometric and subjective time: this includes explanation for the emergence of the arrow of time and for the fact that the contents of sensory experience are about very narrow time interval although one would expect that entire CD determines the contents of also sensory experience. I hope that I do not sound too authoritative and that my badly broken English is not too painful an experience;-).

Labels: , , ,

20 Comments:

At 11:08 AM, Blogger Ulla said...

Hi Matti

My friend Gabor and I have discussed evolution, and for instance an experiment made by Scripps Research Institute; Darwin in a test tube. (http://www.scripps.edu/news/press/042909.html). "A classic concept in Darwinian evolution known as "niche partitioning," which holds that when two species are competing for resources within a common environment, they become differentiated so that each species adapts to use different preferred resources."
Enzymatic RNA molecules that can continuously evolve in the test tube was used as organisms. There will be mutations and competition for "food".

"Then they placed the two RNA molecules together in a pot with five different food sources, none of which they had encountered previously. At the beginning of the experiment each RNA could utilize all five types of food—but none of these were utilized particularly well. After hundreds of generations of evolution, however, the two molecules each became independently adapted to use a different one of the five food sources. Their preferences were mutually exclusive, the molecules evolved different evolutionary approaches to achieving their ends, showing classic evolutionary strategies for survival."

The problem with this interpretation is in my opinion succession (change with time) with a lot of numerical small species that is making the "insurance" against sudden changes in the mileau. Also the specialzation of competiting spieces is problematic, and will in the long run means extinction when the surroundings change. One of the goals is complexity (as a cause of specialization) and differentation, which in essence is the same. Specialization can also be very fast and can be seen as opportunistic.

Over time, as these mutations accumulate, new forms emerge—some fitter than others. This is chaos and entropy that will form new information and negentropy. Maximation negentropy principle?

Organisms have solved this problem by taking some cells "out of time" and keeping them dedifferentated as germ cells and stem cells. Organisms have also created apoptosis and down-regulation as tools of regulation.

"These CDs are expected to be highly relevant in biology," you say. This is perhaps something like that?

What tells this about the principle behind evolution?
Why are the different spieces behaving like they do? What is their potential together?
This says clearly that competition is not the driving force, then one would have been put out of the game. Together they achieve a balance. Why? Behind the balance is laying a silent mechanism, achieving something together (more efficiency than alone). Or the Wallace principle. Think this is the bigger CD?

But you have also the p-adic in chaos and synchrony. Can you explain that?

 
At 12:47 PM, Anonymous Anonymous said...

There is no difference between
geometric and subjective time, why do you think so. I couldn’t
continue then, to explain. The
time was stopped, I wasn’t
frightened, I imagined one
hand will provide for me and it
was provided. It was the hand of
one orphan elder than me. Something more, when I was at five
in my native town there was a museum with a very beautiful
garden in it, in the Museum of The Liberation War in the end of
our street. One day it was in the morning, our group of two small and two elder children were talked over how to enter the beautiful garden from the river, where was was our secret entry at any time of the day or through the official entry, where the guard was our enemy. At the entrance we catch up with one family from Finland, father, mother, son and a daughter, they
had come to honour their ancestor died for our freedom.
We were very smart, we pretended as we have something to do with them and entered with them via the official entry. As children we loved them Russians, Romanians
and Finns because the museum had
proved something for us.Is the time only geometric, the time is also dynamic I think. To
not remember me for one my cousin
girl married in Finland.

 
At 1:43 PM, Blogger donkerheid said...

Dear Matti,

I liked your video :). It would be nice to see more of them coming :).

I've always wanted to ask this: how could one detect magnetic bodies?

thnq,

 
At 7:25 PM, Blogger Matti Pitkanen said...

To Ulla:

CDs within CDs picture would explain the evolution of the two RNAs species to utilize different food sources as guided by a Big CD corresponding to the "collective consciousness" associated with the two RNA species so that apparently opportunistic behaviors would have a hidden synergy. The Big CD would cheat the opportunistic little CDs to behave synergetically! Would give some hope in the recent opportunistic world!

There is also the p-adic aspect in dynamics: local chaos with characteristic long range correlations following from p-adic effective topology induced by p-adic space-time sheets representing cognition and intention. Intentions would induced the long range correlations.

As a matter fact, hbar hierarchy and p-adic length scale hierarchy suggest similar big picture and one can ask whether they are really independent of each other. I believe that this is the case although I have also considered the possibility that they might be equivalent.


To Anonymous:

There is difference between subjective and geometric time! Geometric time is irreversible, future and past exist simultaneously, there is no arrow of time, there is no free will type causality. Subjective time is irreversible, future does not exist, there is arrow, causality is that of free will.

To Donkerheid: Magnetic bodies consisting of ordinary matter could be detected by looking magnetic pulses created with the flux tubes (or more general flux quanta) of the magnetic body pass by the measurement apparatus.

Dark magnetic bodies (at different pages of the book like structure defined by the generalized 8-D imbedding space) containing dark matter could be "seen" by sending ordinary light which transforms with certain probability to its dark variant, scatters from the dark matter at the flux tube, and transforms back to visible light and goes to camera. Maybe Peter Gariaev has already done this for dark magnetic body of DNA.

See the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer of "Genes and Memes".

 
At 12:09 AM, Anonymous Anonymous said...

You are maybe right, but the vector of the free will can
make the geometric future come on earlier or later. Even as children
we played some simple games of
manipulating the future.

 
At 12:42 AM, Blogger Ulla said...

I like this picture very much. And yesterday I looked at Lubos posting and started to wonder about the entropy. It was low in the beginning after BigBang. And it shapes the time-picture, if I understood it right.

Can there have been both high negentropy (as a meaning or intention) and high entropy (as an explosive force) then at the same time. Once I learned they are mutually exclusive, but it what you say is true they can't be. And in fact this gives a much better picture according to me.

If you compare with a bomb, it has a meaning, a negentropy. Also its inner chemicals are quite ordened, that is negentropy. When the reaction starts it can't be stopped, that is intention. And with time the entropy grows, but this entropy was there already from the beginning, but silent, as sort of a kinetic energy?

Intentions would induced the long range correlations, you say. What kind of intention, and what long range correlations, if there is nothing in future? Whose intention?

Geometric time has no ordinary time, but all times together. That is also the end. Can this fatalistic intention make these correlations. Means we have free will to fight against (hard life), or just surrender and follow?

And we collect the negentropies to collect a new meaning, a new shell...

I saw a lot of diamonds all the night, in fact. My Ouroboros?

 
At 1:53 AM, Anonymous Anonymous said...

I read somewhere the dark matter
is coming with the big bang from some old universe or something like that. It can explain the
negentropy. But is the big
bang quite sure, there are already some suspections about
its happening.

 
At 2:03 AM, Anonymous Anonymous said...

Excuse me, I forget to ask you
what do you mean exactly
with the retina as intelligent
creature and what
is a role of the
biophotons in the case.
I’m trying to explain
something about the communicating
only with eyes.

 
At 2:09 AM, Blogger donkerheid said...

Can be a connection between CDs and succession in ecosystems?
And what you think is the role of hyper-genomes?

Greetings,
Gábor

 
At 9:18 PM, Blogger Matti Pitkanen said...

To Donkerheid:

Yes. Super, hyper- etc. genomes (I should have spoken just about hierarchy of genomes) would define collective genomes.

The basic argument "forcing" hypergenomes is quantization of magnetic flux at dark space-time sheets. The flux quantum is proportional to hbar and increases with hbar. If flux sheets going through DNA are in question then the length of DNA involved must increase with hbar to achieve enough flux. This leads to integration of DNAs of separate nuclei to super DNA.

This kind of hierarchy continues involving more and more genomes. Not only those of single organism but also several organisms so that one might speak even about genome of population. The common flux sheet would combine genomes to single thread and would make possible coherent collective gene expression.

 
At 9:51 PM, Blogger Matti Pitkanen said...

To Anonymous:

I am a firm believer in big bang;-): even fractal hierarchy of bangs. Perhaps CD as intersection of future and past directed light cones might be seen as analogous to a big bang followed by a big crunch. Could one see the moment of birth as analogous to big bang in some useful sense?


To the question of Anonymous about eye as an intelligent creature. If I believe in TGD inspired theory of consciousness, conscious intelligence is present at all levels of these big hierarchies. Eye is not an exception. Bacteria are intelligent, DNA and proteins are intelligent, and so on...

 
At 10:02 PM, Blogger Matti Pitkanen said...

To Ulla:

Ulla mentioned Negentropy Maximization Principle in some comment. Negentropy that I am talking about in this context and does not directly correspond to the negative of entropy as stastistical physicist defines it.

NMP in loose sense however implies second law. Suppose you have an ensemble of selves.

a) State function reduction minimizes entropy for individual self and guarantees maximal information gain in conscious experience.

b) Since the outcome of the quantum jump is not predictable, information about the state of ensemble decreases. If you have N conscious entities with free will (say your mental images!), forming a closed system (no metabolic energy feed) it is obvious that external observer (you) gradually loses information about what the state of ensembe (you get tired and lose control of your thoughts). This would correspond to increase of entropy in the sense of second law.

c) p-Adicity and cognition could bring in however something new. If one allows p-adic variants of entanglement negentropy, the situation changes. Real entanglement entropy is minimal for unentangled state. p-Adic variant can be maximum for entangled state. This would lead to a formation of entangled states with negative entanglement entropy and certain final states would be favored. The interpretation could be in terms of formation of coherent structures. Maybe living systems could be seen also from this perspective. Could this aspect of NMP relate to the larger CDs to which second law does not apply and to long range time correlations implied by p-adicity (cognition)?


There is a further interesting question related to NMP. If selves are "curious" and therefore induce arrow of time by shifting the quantum superposition of space-time surfaces to the direction of geometric past. Can one reduce this proposal to NMP? Could just the condition that the information gain in quantum jump is maximal explain "curiosity"?

Well , I am as confused as always. Seems to be my fate;-). It would be so wonderful to enjoy Lubosian state of mind in which everything is clear and well-understood;-).

 
At 10:26 AM, Anonymous Anonymous said...

Whether the second low of the
thermodynamics is valid
for the the dark matter
and in the same sense as
for the visible matter?
Because the negentropy is
coming from it if your theory
is right.

 
At 5:56 PM, Blogger Matti Pitkanen said...

Dear Anonymous,

thank you for a good question. Perhaps I will write about this a blog posting.

The resolution of cosmological entropy paradox relates to the relationship between subjective and geometric time.

a) It is *subjective* time with respect to which second law holds true. It corresponds to the geometric time of observer *only locally*.

b) One can apply second law only for to what happens inside 4-D causal diamond (CD) corresponding to the time scale of observations: in positive energy ontology second law is applied at fixed value of geometric time and this leads to problems. In cosmology this CD corresponds begins from moment of big bang and extends up to recent moment or even farther to future. The idea that entropy grows as a function of cosmic time is simply wrong if you accept zero energy ontology.

More concretely.

a) In each quantum jump re-creating entire 4-D Universe the entire geometric *future* and *past* changes.

b) Initial state of big bang in geometric sense(!)- the zero energy states associated with small CDs near the light-cone boundary corresponding to Big Bang- are replaced by a new one at every moment of subjective time. Hence the "subjectively recent" initial state of Big Bang can be assumed to have maximum entropy as also states after that when the time scale of observations (size of CD) is the age of the universe. Gradually the entire geometric past ends up to a maximum entropy state in time scales below the time scale characterizing the time scale of observations. Thermal equilibrium in 4-D sense rather than 3-D sense results and the paradox disappears.

Note: The breaking of strict classical determinism of Kahler action allowing CDs within CDs picture is essential mathematical prerequisite: otherwise this picture does not make sense. It makes possible also space-time correlates for quantum jump sequence rather than only for quantum states.

Note: One proposal for the resolution of entropy paradox could relate to generation of black holes with large entropy. In TGD framework this does not work since for gravitational Planck constant the value of black hole entropy is ridiculously small.

 
At 6:12 AM, Anonymous Anonymous said...

Today I flipped through two papers
by W. Tiller on
http://www.scientificexploration.org/journal.html and got totally
confused. But there is something
common with your work and as though only the dark matter
with its properties is missing.
You can post something there.
In the nowadays scaterred world
the promotions are very important.

 
At 6:36 AM, Blogger Matti Pitkanen said...

Dear Anonymous:


I think highly of William Tiller. I have commented his work in Bio-Systems as Conscious Holograms. These experimental findings provide support for the notion of magnetic body as intentional agent.

If I remember correctly, the model does not yet involve dark matter and hierarchy of Planck constants. It would be interesting to see what this notion adds to the model.

 
At 9:42 AM, Anonymous Anonymous said...

Yes, despite of the many uncleared
moments and the differences I
definitely became awared that such
interactions exist and that the magnetic body is playing the key role. It is very helpful as a direction for new findings. The information in the Internet is
too scaterred. I have a feeling
if people interested in some
problem really join their
efforts, they can solve it for
24 hours or less. But people’s inertion is great. I found information about the plasmoids
understood as such even from
1925.

 
At 9:54 PM, Anonymous Anonymous said...

P.S. I think the plasmoids and the rods are one direct proof
for your thesis about the dark
matter and as though there is an immediate connection with the dark plasma, but I’m not quite
sure for the last.

 
At 2:59 PM, Blogger Ulla said...

About the eye as an intelligent creature, see http://www.forskning.se/pressmeddelanden/pressmeddelanden/ogonfullproppademednervcellergerskarpsyn.5.250d5a1a12255a2b01380002153.html
(swedish text)"Ryggradsdjurens anfäder, som råkade ha en omvänd näthinna, hade en stor fördel. De utvecklade bättre synförmåga än sina konkurrenter och evolutionen började mot den stora och framgångsrika gruppen som finns idag."

Surprisingly at first sight, the retinal neurons are located between the lens and the light-sensitive parts of the photoreceptors. The tissue scatters some light, which leads to loss of light and image blur. The inverted retina has, therefore, long been regarded as inferior. Here, we provide evidence that the inverted retina actually is a superior space-saving solution, especially in small eyes. The inverted retina has most likely facilitated the evolution of image-forming eyes in vertebrates, http://www.sciencedirect.com/doi:10.10/j.visres.2009.07.001

 
At 6:46 AM, Blogger Thoughts said...

There is a need here to pin down what you mean by "consciousness" and "time" in the context of conscious experience. I would concentrate on describing conscious experience and the extended present moment. Whitehead, James, Bergson and others have taken this approach but their work seems to have been misunderstood. See Time and conscious experience.

 

Post a Comment

<< Home