Saturday, July 26, 2014

About the origin of Born rule

Lubos has been again aggressive. At this time Sean Carroll became the victim of Lubos's verbal attacks. The reason why Lubos got angry was the articles of Carroll and his student to derive Born rule from something deeper: this deeper was proposed to be many worlds fairy tale as Lubos expresses it. I agree with Lubos about the impossibility to derive Born rule in the context of wave mechanics - here emphasis is on "wave mechanics". I also share the view about many worlds interpretation - at least I have not been able to make any sense of it mathematically.

Lubos does not miss the opportunity to personally insult people who tell about their scientific work on blogs. Lubos does not realize that this is really the only communication channel for many scientists. For the out-laws of the academic world blogs, home pages, some archives, and some journals (of course not read the "real" researchers enjoying monthly salary) provide the only manner to communicate their work. Super string hegemony did good job in eliminating people who did not play the only game in the town: also I had the opportunity to learn this.

Ironically, also Lubos is out-of-law, probably due to his overly aggressive blog behaviors in past. Perhaps Lubos does not see this as a personal problem since - according to his own words - he has decided to not publish anything without financial compensation because this would make him communist.

Concerning Born rule I dare to have a different opinion than Lubos. I need not be afraid of Lubos's insults since Lubos as a brahmine of science refuses to comment anything written by inferior human beings like me and even refuses to mention their names: maybe Lubos is afraid of doing it might somehow infect him with the thoughts of casteless.

Without going to the details of quantum measurement theory, one can say that Born's rule is bilinear exression for the initial and final states of quantum mechanical transition amplitude. Bilinearity is certainly something deep and I will go to that below. Certainly Born's rule gives the most natural expression for the transition amplitude: demonstraing this is of course not a derivation for it.

  1. One could invent for the transition amplitude formal expressions non-linear in normalized initial and final states. One can however argue that the acceptable expressions must be symmetric in initial and final states.

  2. The condition that the transition amplitude conserves quantum numbers associated with symmetries suggests strongly that the transition amplitude is a function of the bilinear transition amplitude between initial and final states and norms of initial and final states. The standard form for non-normalized states - inner product divided by product of square roots norms - is indeed of this form. For instance, one could add exponentials of the norms of initial and final state norms.

  3. Projective invariance of the transition amplitude - the independence of the transition probabilities from normalization- implies that standard transition amplitude multiplied by a function - say exponential - of the modules square of the standard amplitude (transition probability in standard approach) remains to be considered.

  4. One could however still consider the possibility that the probability as given by Born rule are replaced by its function: pij→ f(pij)pij. Unitary poses strong constraints on f and my guess that f =1 is the only possibility.

Sidestep: To make this more concrete, the proponents of so called weak measurement theory propose a modification of formulate for the matrix element of an operator A to ⟨i|A|f⟩/⟨i|f⟩. The usual expression contains the product of square roots of the norms instead of ⟨i|f⟩. This is complete nonsense since for orthogonal states the expression can give infinity and for A =I, unit matrix, it gives same matrix element between any two states. For some mysterious reason the notion weak measurement - to be sharply distinguished from interaction free measurement - has ended up to Wikipedia and popular journals comment it enthusiastically as a new revolution in quantum theory.

Consider now the situation in TGD framework.

  1. In TGD framework the configuration space, "World of Classical Worlds" consisting of pairs of 3-surfaces at opposite boundaries of causal diamonds (CDs), is infinite-dimensional, and this sharply distinguishes TGD based quantum theory from wave mechanics. More technically, hyperfinite factors of type II (and possibly also III) replace factors of type I, in the mathematical formulation of the theory.

    Finite measurement resolution is unavoidable and is represented elegantly in terms of inclusions of hyper-finite factors. This means that single ray of state space is replaced with infinite-D sub-space whose states cannot be distinguished from each other in given measurement resolution. The infinite-dimensional character of WCW makes the definition of the inner product for WCW spinor fields extremely delicate.

    Note that WCW spinor fields are formally classical at WCW level and state function reduction remains the only genuinely quantal aspect of TGD. At space-time level one must perform second quantization of induced spinor fields to build WCW gamma matrices in terms of fermionic oscillator operators.

  2. WCW spinors which are fermionic Fock states associated with a given 3-surface. There are good reasons to believe that the generalization of the usual bilinear inner product defined by integration of the spinor bilinear over space (with Euclidian signature) generalizes but under extremely restrictive condition. Spinor bilinear is replaced with fermionic Fock space inner product and this bilinear is integrated over WCW.

    The integration over WCW makes sense only if WCW allows a metric which is invariant under maximal group of isometries- this fixes WCW and physics highly uniquely. To avoid divergences one must also assume that Ricci scalar vanishes and empty space Einstein equations hold true. Metric determinant is ill-defined and must be cancelled by the Gaussian determinant coming from the exponent of vacuum functional, which is exponent of Kähler action if WCW metric is Kähler as required by the geometrization of hermitian conjugation which is basic operation in quantum theory. One could however still consider the possibility that the probabilities given by Born rule are replaced by their functions: pij→ f(pij)pij but unitarity excludes this. Infinite-dimensionality is thus quite not enough: something more is needed unless one assumes unitarity.

  3. Zero Energy Ontology brings in the needed further input. In ZEO the transition amplitudes correspond to time-like entanglement coefficients of positive and negative energy parts of zero energy states located at the opposite light-like boundaries of causal diamond. The deep principle is that zero energy states code for the laws of physics as expressed byS-matrix and its generalizations in ZEO

    This implies that transition amplitudes is automatically bilinear with respect to positive and negative energy parts of zero energy state, which correspond to initial and final states in positive energy ontology. The question why just Born rule disappears in ZEO.

That ZEO gives justification also for Born rule is nice since it has produced a solution also to many other fundamental problems of quantum theory. Consider only the basic problem of quantum measurement theory due to determinism of Schrödinger equation contra non-determinism of state function reduction: Bohr's solution was to give up entirely ontology and take QM as a mere toolbox of calculational rules.

There is also the problem the relationship between geometric time and experienced time, which ZEO allows to solve and leads to much more detailed view about what happens in state function reduction. The most profound consequences are at the level of consciousness theory which is essentially generalization of ordinary quantum measurement theory in order to make observer part of the system by introducing the notion of self. ZEO also makes the physical theories testable: any quantum state can be achieved from vacuum in ZEO whereas in standard positive energy ontology conservation laws make this impossible so that at the level of principle the testing of the theory becomes impossible without additional assumptions.


Anonymous said...

I just saw 'A Thin Sheet of Reality' discussion ( My TGD shirt would say: scalable hbar.

Question in terms of the finite amount of 2D-surface planck area bits (too simplified in TGD terms I suppose, but lets play): Can "dark energy" in this context be defined as the push-effect of thin sheets of reality with lower hbar value than the one we can measure, and "dark" matter the gravity pull-effect of higher hbar-values?

Anonymous said...

Reality is the thin sheet between heart and mind. When our heart and mind are one, there is nothing we cannot achieve.

Anonymous said...

Buckminster Fuller said something very deep about gravity, and in his writings insisted using the correct language: in gravity there is no "up" or "down", just "inwards" and "outwards". I'm still having problems comprehending the notion "causal diamond" with it's ups and downs. If TGD finite measurement resolution is consistent with finite amount of planck surface bits of a state of classical world, we accept that no information can be lost, and that the most economical 2D surface is sphere, then the increase of information content of a given 2D-surface can only happen as exponential 4D quantum jump evolution? Is this even on the right track so far? So how and why the causal diamond enters the picture?

Anonymous said...

Anonymous said...

Anonymous, you are just babbling, are you a but just regurgitating comments? There is no such thing as an "exponential 4d quantum jump evolution". You might be in danger of descending into word-salad....

Anonymous said...

2 is quadratic root of 4, and 4 is square exponent of 2, is this correct? I'm not a physicist or a mathematician and producing precise English jargon is difficult for me, sorry if this creates unnecessary confusion.

However, if I'm not mistaken, the square root - square exponent relation manifesting also in Newton's inverse-square law is important also in TGD and values of hbar? Also, correct me if I'm wrong, 4D quantum jump that rewrites both history and future, is basic feature of TGD cosmology and evolution?

Is this just babble, and/or do you feel the need to try to insult and hurt others more? Are you hurting yourself for some reason, is everything not OK in your life? Or just the weather?

Matti Pitkanen said...

To the first Anonymous:

My view is that dark energy corresponds at "microscopic level" (many-sheeted space-time of TGD) to the (Kahler) magnetic energy of flux tubes
carrying monopole flux. Dark matter corresponds to ordinary particles at these flux tubes and have large Planck constant, much larger than standard Planck constant.

Cosmological constant emerges in GRT limit of TGD. This means that the sheets of many-sheeted space-time are replaced with single piece of Minkowski space endowed with effective metric which is sum of (empty space) Minkowski metric and deviations of induced metrics of sheets from Minkowski metric. Similar description applies to
various gauge potentials. Poincare invariance suggests that Einsteins-Yang-Mills equations with cosmological constant are satisfied for the resulting effective space-time time.

What TGD can thus give is "microscopic" explanation for dark energy and dark matter.

Matti Pitkanen said...
This comment has been removed by a blog administrator.
Matti Pitkanen said...

To Anonymous about causal diamond (CD):

I understand causal diamond and closely related zero energy ontology in terms of what they make possible.

CD makes possibly to formulate zero energy ontology (ZEO). ZEO is necessary to formulate TGD elegantly.

ZEO makes possible to formulate

* quantum theory in TGD framework where the strict determinism of basic action principle fails. Examples: -In ZEO brain is not 3-D but 4-D object
inside CD. - Self organisation is not for 3-D but for 4-D patterns: entire temporal evolution within CD is replaced in each quantum jump with a new
temporal evolution. This allows totally new view to say morphogenesis.

*number theoretical universality requiring p-adic variants of TGD can be formulated.

* conservation laws in length scale dependent manner. Conservation laws hold true inside given CD characterised by scale.

* genuine measure of information (negentropic entanglement). Standard physics allows only the notion of entropy and one can talk only about
reduction of information in some space-time region and say that information is gained when entropy is reduced. This is not enough in consciousness theory: information is more than reduction of dis-information.

Matti Pitkanen said...

Continuation to Anonymous:

In TGD I cannot assign to blackhole horizon bits of information. It is possible to assign with it entropy. I could assign with black hole negentropic entanglement with some other object or to a particle at the surface of blackhole negentropic entanglement with blackhole. That is information.

Negentropy Maximization Principle (NMP) is not present in standard physics: it says that negentropic entanglement -potential conscious information - is not conserved but increases. This would explain evolution. NMP implies second law for ordinary (entropic) entanglement. Second law applies to average member of ensemble. NMP to entanglement between systems of ensemble.

CD entires to the picture in ZEO because quantum jumps giving rise to increase of information/ negentropic entanglement happen for zero energy
states associated for it as repeated state function reductions at either boundary of CD. CD is also imbedding space correlate for self.

Matti Pitkanen said...

To Anonymous last questions about Newton's laws etc.

TGD predicts same things as Newton's theory in non-relativistic limit and long length scales. The stuff related to hierarchy of Planck constants is genuinely new and speculative for colleague.

In TGD Universe history is rewritten again and again much like in real world;-).

Matti Pitkanen said...

To Stephen:

Interesting claim. I do not know the details to comment the feasibility of the claim. In any case, I am not enthusiastic about Zero Point Energy (which might be involved as a theoretical background) because it it theoretically ad hoc and mathematically ill-defined.

Anonymous said...

Thank you. This state of TGD psychohistory evolution is not yet fully negentropically rewritten by what is emanating from the center of TGD quantum jumps as all linguistic messages send are not being fully received (negentangled) because I'm dumb. So allow me another stupid question: is the image of TDG that I can in my current state negentropically entangle and be informed by, the Russian doll of scalable values of hbar, 1) just wrong, 2) old history getting replaced 3) still somehow relevant with CD bipolarism? And: does ZEO CD together with strong holography imply that there is no hope for all the drama of "bipolar disorder", and it just can't be getting better?

Anonymous said...

Another question: does negentropic information mean that TDG information spreads, if it spreads, rather at heart level than at mind level of entropic 2D world maps?

A shaman said...

I am a shaman, so it easiest for me to map with "ylinen", "keskinen" and "alinen", and I have benefited from conversations with science and math that I have evolved to think and speak in 3D "outer", "middle" "inner". In my experience Inner, the road to the center of gravity, is where we meet our fears and find our strength. In this experience Outer is the space of creative imagination and soothing vibrations. Now I also see, thanks to your response, what was forgotten, that Middle, the claimed "thin" 2D layer is not a closed border (as in between 0 and 1 in the context of whole numbers) but open border on the level of rational numbers and their real and p-adic extensions. Thank you again. :)

As a shaman, it is also my job to listen the hearts desires of my peers, all sentient beings I communicate with, and let the 4D-quantum jumps happen as they happen in the emotional space time, informed and negentropically entangled by all heart felt desires.

What is your desire? That your scientific "peers" accept your 2D sheet-side of words and numbers as 1D either-or truth, traveling down in information content from 3D sheet to 2D map and 1D truth value? Or could the psychological and emotional spacetime of TGD be for some other purpose in your life. It is your life and it is not my responsibility to offer you advice, but if this question helps you and all of us with you to evolve, I will be even happier. You have all the answers you need in TDG and your brave heart. It is up to you what you do with all that information.

Matti Pitkanen said...

To Anonymous:

1) Seems that I have had some success in my communication effects;-)

2) Old history replaced: this is one of key ideas and especially interesting when one think the miracles of biological evolution at various levels. If something goes wrong at the beginning is not a catastrophe anymore. The whole
evolution hitherto can be replaced with a one in which never went wrong in the beginning. Hitler can be born again;-).

3) My original view about CD bipolarism was too simplistic: just single state function reduction to given boundary of CD and then to other boundary. The arrow of time would have changed all the subjective time. In elementary particle
scales the number of quantum jumps on single boundary might be small and this would explain why arrow of
time seems to absent in microscopic scales.

The realistic view is that a sequence of state function reductions occurs at same boundary of CD: meaning that the part of the zero energy state assigned with say "lower"/past boundary does not change - just as state does not change in repeated quantum measurement - whereas the part associated at the "upper"/future boundary changes. Arrow of time emerges as also self as sequence of the quantum jumps at same boundary. Something very obvious which took very long time to realise.

I am not sure in what sense you are using "bipolar disorder". As analogy or something concrete. In any case the sequence of reductions on given boundary would be self, and the lifetime of this self would correspond to the growth of the
distance of the "upper"/future boundary of CD.

In bipolar disorder the dominance period of particular brain hemisphere would be the life period of a self at some level of hierarchy. In bipolar disorder these competing self would kill each other alternately;-) instead of entangling to
bigger self.

Information is generated as entropic entanglement. Negentropic entanglement can be transferred/spread. It can be stolen, etc… I have considered the possibility that nutrients carry negentropic entanglement with entity which could be called Mother Gaia.

Question about negentropic information spreading. I would like to speak information creation and transfer. In living matter one could imagine flux tube with one end attached to nutrient and other end to some bigger and wiser space-time sheet- say that representing MG. The end of tube attached to nutrient is transferred to ATP molecule and from ATP to receiver molecule in ADP-ATP cycle. The transfer of metabolic energy would be thus transfer of negentropic entanglement with MG. Metabolism would be basically transfer of potential for moments of understanding.

A shaman said...

Most concretely we mean by 'bipolar disorder' the mood swings between happy enthousiasm and depressed inactivity, and in some cases shaman and poet and drunk forming "Swing of Gods" experiences that Eino Leino spoke about. A very common shamans way to spread and disrupt bipolar experiences and mechanisms are various healing rituals and their more civilized forms as drama and cathartic tragedy. Fear and love and new balance are the most basic elements.

Another very concrete and easy to comprehend form of bi-polar order parabolic curve and Law of diminishing returns. How to know that you have reached the ideal balance of ideal growth at the top of the gaussian curve of diminishing returns, and don't take a further step in the negative side to continue to deterministically fall back in towards the center of gravity, in the gaussian manner of the pendulum swings of Galileo and Newton?

I trust you now see why CD bi-polarism is approached very carefully and with healthy suspicion, out of still effecting fear of falling back to the trap of 1D ZEO bipolar codependence of happiness and misery?

Future as "up" and past as "down" is not easy for me to accept as the most coherent language I'm ready to receive, as in natural languages we speak and see them ahead and back, either way (e.g. Aymara sees past ahead and future is unseen behind the back), and metaphor and actuality of gravity suggest that out and in would be more precise language allowing also multidimensional view of the state instead of 1D up/down relation. Which has for me also very negative social connotations of upper class/lower class, "God Above", etc., which are not helpful for building a global peer-to-peer society. It is my hearts desire that we humans finally start to evolve towards new psychological and emotional level and learn to leave the past of shamanistic tribal ways behind.


Food from the God inside, from the Heart of the Mother, from the Fire of the Source in its both feminine and masculine aspects, is of course well known to shamans. DMT-plant molecules combined with ayahuasca vine for digestion is probably most potent such food known to us, and has distinct feminine aspect, which is why we call her Mother Ayahuasca. Can your formulas tell us something about why that particular brew opens such a strong nutritional flux tube between MG space-time sheet and a monkey brain and mind?

But let's remember, what was said about law of diminishing returns may quite likely apply also to the Food from Mother inside, She can point the way and offer much healing of traumas, but to stay in balance and evolve in good balance towards better and better without bi-polar mood swings, we can't depend from a single medicinal plant brew, or any other single growth factor molecule. In our selves we are all our relations.

A shaman said...

PS: as a token of gratitude I would like to offer this song for enjoyment. What the singer does in the middle turn point of the song is amazing and beautiful.

Anonymous said...

Anon, no hate, only love, I was just too too hungry before typing. Anyway, what you say is not too far off... with great power comes great responsibility, but yes you are realizing I think it is a communications problem in many ways. Peace, Crow

Matti Pitkanen said...

To Anonymous:

Concerning bipolar mood disorder and two other analogous disorders. I tend to identify the optimum situation as criticality. Dancing on the rope. In this state you are maximally sensitive perceiver and can rapidly change views about world.

In the totally stable state one has completely fixed world view and you become very serious scientist believing in text book truths and regarding those who do not as inferior organic stuff or rather waste;-). Both depression and mania represent these stable states.

In this view shamans are hang around critical point and can easily move between different states of consciousness. In stable state you would be hawk or dove, using political terminology.

In terms of Thom's catastrophe theory the shaman or creative person would be a someone who has developed third option besides the two bipolar options and thus does not fall for long times to depression or mania or does not become hawk or dove.

Concerning Ayahuasca, I do not of course have any formulas. Last autumn I wrote an article and also
blog text inspired by a book about shamanism interpreted as activating entanglement connections to distant parts of Universe and making possible to "meet" representatives of civilisation of distant galaxies. The propagation of signals in both time directions allowed by zero energy ontology allows to overcome the barrier posed by light velocity and communication becomes possible. DMT and some psychoactive drugs would activate communication line.

DMT molecules could have flux tube connections to very big magnetic bodies of cosmic size to which also representatives of distant civilizations could generate connections (ordinary nutrients could have connections to Mother Gaia).

As DMT like molecule attaches to a receptor in neuronal membrane, a Josephson junction generating Josephson radiation serving as signal sent to the distance receiver is activated. The signal to the ET would be neuronal signal. Same applies to the received signals. Very simple and economic.

Matti Pitkanen said...

To Anonymous about impossible engine.

I have considered models for so called free energy phenomena. Energy conservation suggests that
them to be transient phenomena so that perpetual mobiles are impossible.

It might be however possible to extract energy from environment. A related mechanism is transfer of energy between system and its magnetic body: something analogous to the proposals involving electromagnetic or even gravitational fields. This would make possible for system to gain momentum and its magnetic body or some larger magnetic body to get the compensating momentum in opposite direction.

A more natural mechanism is however the transfer of angular momentum between magnetic body and the system. The claimed spontaneous rotation of some magnetic system could be due to the spontaneous magnetisation of the magnetic body of the system giving it large spin (spin unit is h_eff and quite large now!) . The compensating angular momentum is obtained by the system and it starts to rotate.

The needed energy would come from the fact that spontaneous magnetisation gives negative and large (proportional to h_eff) energy for the dark matter at the magnetic body. The compensating energy goes to the rotational energy of the system. The transformation of rotational motion to translational one is standard operation.

A question left is how to "force" the transfer of energy and angular momentum between magnetic body and system. Here the fact that TGD predicts flux tubes carrying monopole magnetic flux and thus fields without current creating them is one promising possibility. How to realize this I leave as home exercize;-).

Pollack's experiments demonstrate that external radiation generates what he calls exclusion zones in water: EZ is negatively charged and there is electron potential difference between exterior and EZ and H1.5O is the stoichometry instead of H2O. This suggests that a fraction of protons goes to dark protons at the flux tubes outside EZ. If flux tubes spontaneously magnetize, one can imagine that rotational motion of say electrons is generated inside EZ. For instance supercurrents could be generated and Cooper pairs would have large binding energy if they have large h_eff.

A shaman said...

Hunger is good, friend, it feeds our thinking and learning.

Time is funny even in its one-dimensional aspect. Usually the real purpose of an action or event becomes revealed only afterwards. Maybe CD has something to do with that. Can feel bit weird at first, but then you get used to it and start to accept. Maybe the moment/quantum jump of purpose revealing itself has something to do with the fully saturated "top" point of the curve of diminishing returns also.

And as for communications problem, are there any other kinds of problems? :)

Ulla said...

Look at this about the weak measurements. I think this approach would fit the dam Schrödinger cat well, maybe even life itself?

Anonymous said...

Ulla, it looks like they finally implemented the quantum chaology stuff of Berry et. al. That is pretty cool stuff but not sure how it really applies to life..... periodic orbits, eigenfunction "scarring" etc. Even the vacuum propulsion thing tested by nasa the other day apparently relies on the Casimir effect which is one of the places in physics the Riemann zeta function appears.

Shaman, im not here to discuss my personal life.. maybe in a more private setting

Anonymous said...

This looks very interesting, novel mathematical derivation of SR with sound instead of light and inertial observer instead of inertial frame. Can this simplify TDG?

Matti Pitkanen said...

I did not have time to listen the who talk. It does not seem simple to me;-) . But what seems to go wrong is following on basis of general group theoretic considerations.

Special relativity is assumption about symmetries of space-time. Poincare group replaces Galilean group. This is a concise statement. If this model would allow to deduce special relativity, it should allow Lorentz group to act as symmetries of wave equations defining sound propagation.

Sound waves obey in the rest system of matter
formally the same wave equation as light but with sound velocity. This does not however mean that equations are invariant under special relativity with maximal signal velocity given by sound velocity. When one goes to a coordinate system moving with velocity v with respect to original one, the form of equations is *not* preserved.

Thus one cannot assume the basic transformation formulas of special relativity. Newtonian velocity addition formula is v=1_1+v_2. Special relativistic is non-linear and guarantees that v is not above light-velocity.

This fellow might of course have something different in mind.

Ulla said...
time has an order parameter due to transfer of energy... interesting. Does this also make time 3D?

Anonymous said...

You can easily create single observer clock with just ruler (affine geometry of parallel lines). If there are more than one observers, and two or more observers want to synchronize their clocks, also a compass is needed (projective geometry). Not to mention good will to do so (negentropy? ;)). The question is not about the quantity of dimensions, just about qualitative level of geometry (ruler -> ruler and compass).

Anonymous said...

Anonymous, why the hell would anyone want to synchronize a clock? That's just some bullshit anachronistic thing some white asshole made up to get people to do "work"

Anonymous said...

Stephen, that's a deep philosophical question relating to Hume's guillotine "no should from is". If someone likes to think about a general measurement theory and concludes that also a compass is needed to do so, that's an "is" and there is no obligation for other observers to participate and observe similarly, or obligation not to.

Ulla said... sterile neutrinos

Anonymous said...

"Entia non sunt multiplicanda praeter necessitatem."

AKA Occam's razor

Maybe it's still worth remembering?

Matti Pitkanen said...

Agree if "entia" correspond to basic principles. The outcome from these principles should be of infinite
complexity. Otherwise it would not be interesting.

Anonymous said...

Speculative houses of cards with feet of clay, and with interest on top, tend to grow until they fall down, and both processes can be very interesting.

And then with the help of the razor the spaces collapsed and vacuums left can be again filled with more rational structures build on solid foundations. And upon the more solid foundation to build new speculative houses of cards, to start to see what wonders the next biggest new prime and new beginning will show and allow to share and communicate.

It never ends and it's all good, the dance of creation and creative destruction.

This is how we are and interest each other in our infinitely unique complexity, all ready and all ways enlightened sources of light, no matter how much energy we put in thinking that we are not. :)

Anonymous said...

Ulla said...

Cyclotron-frequencies are basic to TGD.