söndag 30 augusti 2015

Quantum Information Can Be Lost

Stephen Hawking claimed in lecture at KTH in Stockholm last week (watch the lecture here and check this announcement) that he had solved the "black hole information problem":
  • The information is not stored in the interior of the black hole as one might expect, but in its boundary — the event horizon,” he said. Working with Cambridge Professor Malcolm Perry (who spoke afterward) and Harvard Professor Andrew Stromberg, Hawking formulated the idea hat information is stored in the form of what are known as super translations.
The problem arises because quantum mechanics is viewed to be reversible, because the mathematical equations supposedly describing atomic physics formally are time reversible: a solution proceeding in forward time from an initial to a final state, can also be viewed as a solution in backward time from the earlier final state to the initial state. The information encoded in the initial state can thus, according to this formal argument, be recovered and thus is never lost. On the other hand a black hole is supposed to swallow and completely destroy anything it reaches and thus it appears that a black hole violates the postulated time reversibility of quantum mechanics and non-destruction of information.

Hawking's solution to this apparent paradox, is to claim that after all a black hole does not destroy information completely but "stores it on the boundary of the event horizon". Hawking thus "solves" the paradox by maintaining non-destruction of information and giving up complete black hole destruction of information.

The question Hawking seeks to answer is the same as the fundamental problem of classical physics which triggered the development of modern physics in the late 19th century with Boltzmann's "proof" of the 2nd law of thermodynamics: Newton's equations describing thermodynamics are formally reversible, but the 2nd law of thermodynamics states that real physics is not always reversible: Information can be inevitably lost as a system evolves towards thermodynamical equilibrium and then cannot be recovered. Time has a direction forward and cannot be reversed. 

Boltzmann's "proof" was based an argument that things that do happen do that because they are "more probable" than things which do not happen. This deep insight opened the new physics of statistical mechanics from which quantum borrowed its statistical interpretation.

I have presented a different new resolution of the apparent paradox of irrreversible macrophysics based on reversible microphysics by viewing physics as analog computation with finite precision, on both macro- and microscales. A spin-off of this idea is a new resolution of d'Alemberts's paradox and a new theory of flight to be published shortly.

The basic idea here is thus to replace the formal infinite precision of both classical and quantum mechanics, which leads to paradoxes without satisfactory solution, with realistic finite precision which allows the paradoxes to be resolved in a natural way without resort to unphysical statistics. See the listed categories for lots of information about this novel idea.

The result is that reversible infinite precision quantum mechanics is fiction without physical realization, and that irreversible finite precision quantum mechanics can be real physics and in this world of real physics information is irreversibly lost all the time even in the atomic world. Hawking's resolution is not convincing.

fredag 28 augusti 2015

Finite Element Quantum Mechanics 4: Spherically Symmetric Model

I have tested the new atomic model described in a previous post in setting of spherical symmetry with electrons filling a sequence of non-overlapping spherical shells around a kernel. The electrons in each shell are homogenized to spherical symmetry which reduces the model to a 1d free boundary problem with the free boundary represented by the inter-shell spherical surfaces adjusted so that the combined wave function is continuous along with derivates across the boundary. The repulsion energy is computed so as to take into account that electrons are not subject to self-repulsion, by a corresponding reduction of the repulsion within a shell.

The remarkable feature of this atomic model, in the form of a 1d free boundary problem with continuity as free boundary condition and readily computable on a lap-top, is that computed ground state energies show to be surprisingly accurate (within 1%) for all atoms including ions (I have so far tested up to atomic number 54 and am now testing excited states).

Recall that the wave function $\psi (x,t)$ solving the free boundary problem, has the form
  • $\psi (x,t) =\psi_1(x,t)+\psi_2(x,t)+...+\psi_S(x,t)$         (1)
with $(x,t)$ a common space-time coordinate, where $S$ is the number of shells and $\psi_j(x,t)$ with support in shell $j$ is the wave function for the homogenized wave function for the electrons in shell $j$ with $\int\vert\psi_j(x,t)\vert^2\, dx$ equal to the number of electrons in shell $j$.

Note that the free boundary condition expresses continuity of charge distribution across inter-shell boundaries, which appears natural.

Note that the model can be used in time dependent form and then allows direct computation of vibrational frequencies, which is what can be observed. 

Altogether, the model in spherical symmetric form indicates that the model captures essential features of the dynamics of an atom, and thus can useful in particular for studies of atoms subject to exterior forcing. 

I have also tested the model without spherical homogenisation for atoms with up to 10 electrons, with  similar results. In this case the the free boundary separates diffferent electrons (and not just shells of electrons) with again continuous charge distribution across the corresponding free boundary. 

In this model electronic wave functions share a common space variable and have disjoint supports and can be given a classical direct physical interpretation as charge distribution. There is no need of any Pauli exclusion principle: Electrons simply occupy different regions of space and do not overlap, just as in a classical multi-species continuum model.

This is to be compared with standard quantum mechanics based on multidimensional wave functions $\psi (x_1,x_2,...,x_N,t)$ typically appearing as linear combinations of products of electronic wave functions
  • $\psi (x_1,x_2,...,x_N,t)=\psi_1(x_1,t)\times \psi_2(x_2,t)....\times\psi_N(x_N,t)$        (2)
for an atom with $N$ electrons, each electronic wave function $\psi_j(x_j,t)$ being globally defined with its own independent space coordinate $x_j$. Such multidimensional wave functions can only be given statistical interpretation, which lacks direct physical meaning. In addition, Pauli's exclusion principle must be invoked and it should be remembered that Pauli himself did not like his principle since it was introduced ad hoc without any physical motivation, to save quantum mechanics from collapse from the very start...

More precisely, while (1) is perfectly reasonable from a classical continuum physics point of view, and as such is computable and useful, linear combination of (2) represent a monstrosity which is both uncomputable and unphysical and thus dangerous, but nevertheless is supposed to represent the greatest achievement of human intellect all times in the form of the so called modern physics of quantum mechanics.

How long will it take for reason and rationality to return to physics after the dark age of modern physics initiated in 1900 when Planck's "in a moment of despair" resorted to an ad hoc hypothesis of a smallest quantum of energy in order to avoid the "ultra-violet catastrophe" of radiation viewed to be  impossible to avoid in classical continuum physics. But with physics as finite precision computation, which I am exploring, there is no catastrophe of any sort and Planck's sacrifice of rationality serves no purpose.

torsdag 27 augusti 2015

Finite Element Quantum Mechanics 3: Explaining the Periodicity of the Periodic Table

According to Eric Scerri, the periodic table is not well explained by quantum mechanics, contrary to common text book propaganda, not even the most basic aspect of the periodic table, namely its periodicity:
  • Pauli’s explanation for the closing of electron shells is rightly regarded as the high point in the old quantum theory. Many chemistry textbooks take Pauli’s introduction of the fourth quantum number, later associated with spin angular momentum, as the foundation of the modern periodic table. Combining this two-valued quantum number with the ear- lier three quantum numbers and the numerical relationships between them allow one to infer that successive electron shells should contain 2, 8, 18, or $2n^2$ electrons in general, where n denotes the shell number. 
  • This explanation may rightly be regarded as being deductive in the sense that it flows directly from the old quantum theory’s view of quantum numbers, Pauli’s additional postulate of a fourth quantum number, and the fact that no two electrons may share the same four quan- tum numbers (Pauli’s exclusion principle). 
  • However, Pauli’s Nobel Prize-winning work did not provide a solution to the question which I shall call the “closing of the periods”—that is why the periods end, in the sense of achieving a full-shell configuration, at atomic numbers 2, 10, 18, 36, 54, and so forth. This is a separate question from the closing of the shells. For example, if the shells were to fill sequentially, Pauli’s scheme would predict that the second period should end with element number 28 or nickel, which of course it does not. Now, this feature is important in chemical education since it implies that quantum mechanics can- not strictly predict where chemical properties recur in the periodic table. It would seem that quantum mechanics does not fully explain the single most important aspect of the periodic table as far as general chemistry is concerned. 
  • The discrepancy between the two sequences of numbers representing the closing of shells and the closing of periods occurs, as is well known, due to the fact that the shells are not sequentially filled. Instead, the sequence of filling fol- lows the so-called Madelung rule, whereby the lowest sum of the first two quantum numbers, n + l, is preferentially oc- cupied. As the eminent quantum chemist Löwdin (among others) has pointed out, this filling order has never been derived from quantum mechanics. 
On the other hand, in the new approach to atomic physics I am exploring, the periodicity directly connects to a basic partitioning or packing problem, namely how to subdivide the surface of a sphere in equal parts, which gives the sequence $2n^2$ by dividing first into two half spheres and then subdividing each half spherical surface in $n\times n$ pieces,  in a way similar to dividing a square surface into $n\times n$ square pieces.  With increasing shell radius an increasing number of electrons, occupying a certain surface area (scaling with the inverse of the kernel charge), can be contained in a shell. 

In this setting a "full shell" can contain 2, 8, 18, 32,.., electrons, and the observed periodicity 2, 8, 8, 18, 18, 32, 32, with each period ended by a noble gas with atomic numbers 2 (He), 10 (Neon), 18 (Argon), 36 (Krypton), 54 (Xenon),  86 (Radon), 118 (Ununoctium, unkown), with a certain repetition of shell numbers, can be seen as a direct consequence of such a full shell structure, if allowed to be repeated when the radius of a shell is not yet large enough to house a full shell of the next dignity. 

Text book quantum mechanics thus does not explain the periodicity of the periodic table, while the new approach am I pursuing may well do so in a very natural way.   Think of that.   

tisdag 25 augusti 2015

Ulf Danielsson om Klimathot, Hawking och Svarta Hål.

Strängfysikern Ulf Danielsson har startat en blogg med Stephen Hawking's besök vid KTH och föreläsning på Stockholm Waterfront som initiellt dragplåster. Ulf skriver gärna om svarta hål, som han verkar tro inneha verklig fysisk existens som "singularitet" till lösningar till Einstein's ekvationer. Ulf verkar även tro på kimatalarmismen som den predikas av IPCC:
  • När det gäller människogenererad klimatpåverkan är huvudslutsatsen klar: den finns där, och risken att den får betydande följder för den mänskliga civilisationen om inget görs är överhängande. Den senaste IPCC-rapporten gör det omöjligt att dra någon annan generell slutsats.
Vi skeptiker som granskat vetenskapen bakom IPCCs klimatalarmism, vet att Ulf i denna fråga blivit helt vilseförd. Frågan är om samma sak gäller för svarta hål? 

Om det nu är så att man kan hitta singulariteter hos lösningar till Einstein's ekvationer, vilket i sig kan diskuteras eftersom dessa ekvationer är hart när omöjliga att lösa, betyder det att dessa singulariteter också har fysisk realitet? 

Även om det finns massa i centrum på galaxer som man inte kan se, vilket observationer av galaxers dynamik verkar tyda på, så betyder det väl inte nödvändigtvis att denna osynliga massa utgörs av svart hål? 

Kan det vara så att IPCCs (farligt tjocka enligt Ulf) rapport utgör ett svart hål ur vilken ingen sann information förmår utstråla?

Finite Element Quantum Mechanics 2: Questions without Answers

Hans Primas formulates in Chemistry, Quantum Mechanics and Reductionism, the following basic questions left without answers in textbook quantum mechanics:
  1. Do isolated quantal systems exist at all?
  2. Is the Pauli Principle a universal and inviolable fact of nature?
  3. Does quantum mechanics apply to large molecular systems?
  4. Is the superposition principle universally valid?
  5. Why do so many stationary states not exist?
  6. Why are macroscopic bodies localised?
  7. Why does quantum mechanics fail to account for chemical systematics?
  8. Why can approximations be better than the exact solutions?
  9. Why is the Born-Oppenheimer picture so successful?
  10. Is temperature an observable? 
Despite now almost 100 years of giant efforts by giant scientific minds, no satisfactory answers to these basic questions have been delivered. There is no reason to believe that 100 more years will give any answers and the question must be posed if there is something fundamentally wrong with textbook quantum mechanics which prevents progress? 

Yes, I think so: The origin of all these questions without answers is the starting point of textbook quantum mechanics with a wave function 
  • $\psi (x_1,....,x_N,t)$ depending on $3N$ space coordinates and time,
  • satsifying a linear scalar wave equation in $3N$ space dimensions and time, 
for an atom with $N$ electrons as particles, with $\vert\psi (x_1,...,x_N,t)\vert^2$ interpreted as the probability that particle $j$ is at position $x_j$ at time $t$ for $j=1,...,N$.  

Such a wave function is both uncomputable (because of the many spatial dimensions) and unphysical (because an atom is not an insurance company computing probabilities, as little as an individual person paying an insurance). The fact that textbook quantum mechanics still after almost hundred years is stuck with such a hopeless scientific misconception, is nothing less than a scientific tragedy.

Hans Primas gives the following devastating verdict:
  • There is no general agreement about the referent (physical meaning) of pioneer (textbook) quantum mechanics.
  • Pioneer quantum mechanics has an agonising shortcoming: It cannot describe classical systems. 
  • From a fundamental point of view the only adequate interpretation of quantum mechanics is an ontic (realistic) interpretation.... Bohr's epistemic interpretation expresses merely states of knowledge and misses the point of genuine scientific inquiry...If we assume that pioneer quantum mechanics is a universal theory of molecular matter, then an ontic interpretation of this theory is impossible.
  • The Bohr Copenhagen (textbook) interpretation is not acceptable as a fundamental theory of matter. 
In other words, pioneer (textbook) quantum mechanics is a failed scientific project, and it is an open problem to find an ontic description of atomic physics by "genuine scientific inquiry", that is, in the spirit of the device of this blog, "by critical constructive inquiry towards understanding". 

Finite Element Quantum Mechanics 1: Listening to Bohm

David Bohm discusses in the concluding chapter of Quantum Theory the relationship between quantum and classical physics, stating the following charcteristics of classical physics:
  1. The world can be analysed into distinct elements.
  2. The state of each element can be described in terms of dynamical variables that are specified with arbitrarily high precision.
  3. The interrelationship between parts of a system can be described with the aid of exact casual was that define the changes of the above dynamical variables with time in terms of their initial values. The behavior of the system as a whole can be regarded as the result of the interaction by its parts.
If we here replace, "arbitrarily high precision" and  "exact" with "finite precision", the description 1-3 can be viewed as a description of 
  • the finite element method 
  • as digital physics as digital computation with finite precision
  • as mathematical simulation of real physics as analog computation with finite precision.
My long-term goal is to bring quantum mechanics into a paradigm of classical physics modified by finite precision computation, as a form of computational quantum mechanics, thus bridging the present immense gap between quantum and classical physics. This gap is described by Bohm as follows:
  • The quantum properties of matter imply the indivisibility unity of all interacting systems. Thus we have contradicted 1 and 2 of the classical theory, since there exist on the quantum level neither well defined elements nor well defined dynamical variables, which describe the behaviour of these elements.
My idea is thus to slightly modify classical physics by replacing "arbitrarily high precision" with "finite precision" to encompass quantum mechanics thus opening microscopic quantum mechanics to a machinery which has been so amazingly powerful in the form of finite element methods for macroscopic continuum physics, instead of throwing everything over board and resorting to a game of roulette as in the text book version of quantum mechanics which Bohm refers to.

In particular, in this new form of computational quantum mechanics, an electron is viewed as an "element" or a "collection of elements", each element with a distinct non-overlapping spatial presence, with an interacting system of $N$ electrons described by a (complex-valued) wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ of the form 
  • $\psi (x,t) = \psi_1(x,t) + \psi_2(x,t)+...+\psi_N(x,t)$,                             (1)
where the electronic wave functions $\psi_j(x,t)$ for $j=1,...,N$, have disjoint supports together filling 3d space, indicating the individual presence of the electrons in space and time. The system wave function $\psi (x,t)$ is required to satisfy a Schrödinger wave equation including a Laplacian 
asking the composite wave functions $\psi (x,t)$ to be continuous along with derivatives across inter element boundaries. This a is a free boundary problem in 3d space and time and as such readily computable. 

I have with satisfaction observed that a spherically symmetric shell version of such a finite element model does predict ground state energies in close comparison to observation (within a percent) for all elements in the periodic table, and I will report these results shortly.

We may compare the wave function given by (1) with the wave function of text book quantum mechanics as a linear combination of terms of the multiplicative form:
  • $\psi (x_1,x_2,...x_N,t)=\psi_1(x_1,t)\times\psi_2(x_2,t)\times ...\times\psi_N(x_N,t)$,
depending on $N$ 3d space coordinates $x_1,x_2,...,x_N$ and time, where each factor $\psi_j(x_j,t)$ is part of a (statistical) description of the global particle presence of an electron labeled $j$ with $x_j$ ranging over all of 3d space. Such a wave function is uncomputable as the solution to a Schrödinger equation in $3N$ space coordinates, and thus has no scientific value. Nevertheless, this is the text book foundation of quantum mechanics.

Text book quantum mechanics is thus based on a model which is uncomputable (and thus useless from scientific point of view), but the model is not dismissed on these grounds. Instead it is claimed that the uncomputable model always is in exact agreement to all observations according to tests of this form: 
  • If a computable approximate version of this model (such as Hartree-Fock with a specific suitably chosen set of electronic orbitals) happens to be in correspondence with observation (due to some unknown happy coincidence), then this is taken as evidence that the exact version is always correct. 
  • If a computable approximate version happens to disagree with observation, which is often the case, then the approximate version is dismissed but the exact model is kept; after all, an approximate model which is wrong (or too approximate) should be possible to view as evidence that an exact model as being less approximate must be more (or fully) correct, right?  
PS The fact that the finite element method has been such a formidable success for macroscopic problems as systems made up of very many small parts or elements, gives good hope that this method will be at least as useful for microscopic systems viewed to be formed by fewer and possibly simpler (rather than more complex) elements. This fits into a perspective (opposite to the standard view) where microscopics comes out to be more simple than macroscopics,  because macroscopics is built from microscopics, and a DNA molecule is more complex than a carbon atom, and a human being more complex than an egg cell. 

lördag 15 augusti 2015

Popper vs Physics as Finite Precision Computation

Today, physics is in a crisis....it is a crisis of understanding...roughly as old as the Copenhagen interpretation of quantum mechanics...(in 1982 Preface to Quantum Theory and the Schism in Physics)

Karl Popper's vision expressed in The Postscript to the Logic of Scientific Discovery (with the above book as Vol III), is a science of modern quantum physics which shares the following characteristics of classical physics:
  1. Realism
  2. Determinism                           (A)
  3. Objectivism.
Popper compares this paradigm of rationality with the ruling paradigm of modern physics being the exact opposite as an irrationality characterised by:
  1. Idealism
  2. Indeterminism                        (B)
  3. Subjectivism.
The crisis of modern physics acknowledged by all prominent physicists of today, can be viewed as an effect of (B). It is no wonder that (B) being an irrational opposite to a rational (A), has led to a crisis. 

The reason the paradigm (A) of classical macroscopic physics was replaced by (B) when Planck-Bohr-Born-Heisenberg shaped the ruling (Copenhagen) paradigm of modern physics, was a perceived impossibility to (i) explain the phenomena of black-body radiation by classical electrodynamics and (ii) to give the standard multi-dimensional (uncomputable) wave function of Schrödinger's equation describing microsopic atomic physics, a physical meaning.  

I have been led to a version of Popper's paradigm (A) viewing physics as
  • finite precision computation  
where (i) and (ii) can be handled in a natural way and the resort to the extreme position (B) can be avoided. This paradigm is outlined as Computational Blackbody Radiation and The World as Computation

In particular I have explored a computable three-dimensional alternative version of Schrödinger's equation conforming to (A) and I will present computational results in upcoming posts. In particular, it appears that this (computable) version explains the periodic table more directly than the standard (uncomputable) one. More precisely, an uncomputable mathematical model is useless and cannot be used to explain anything.

PS The crisis in physics rooted in the Copenhagen interpretation has deepened after Poppers 1982 analysis, following a well known tactic to handle a pressing problem, which appears to be unsolvable: make the problem even more severe and unsolvable and thereby relieve the pressure from the original problem. Today we can observe this tactic in extreme form with physicists flooding media with fantasy stories about dark matter, dark energy, parallel worlds and cats in superposition of being both dead and alive, all phenomena of which nothing is known. The Dark Ages appears as enlightened against this background.

tisdag 4 augusti 2015

Dystert Resultat av KTH-Gate = Noll: SimuleringsTeknik Läggs Ner

KTH-gate är benämningen på på den aktion som KTH riktade mot mitt verk som innebar att min ebok Mathematical Simulation Technology (MST) avsedd att användas inom det nya kandidatprogrammet i Simuleringsteknik och Virtuell Design (STVD), mitt under pågående testkurs under HT10 förbjöds av KTH (för en fullständig redogörelse för detta drama, som saknar motsvarighet inom demokratisk stats akademi, se här, härhär och här).

Resultatet av censuringripandet blev att kandidatprogrammet separerades från den grupp av lärare som initierat programmet med avsikt att driva detsamma och för detta fått KTHs stöd. Sålunda startade STVD HT12 på en grund av gamla kurser i numerisk analys under ledning av en annan grupp lärare i numerisk analys, detta utan marknadsföring och resultatet blev därefter: Noll intresse, noll söktryck, noll intagningsbetyg, noll aktualitet = noll resultat.

KTH insåg efter två år att det var totalt meningslöst att driva ett sådant program och HT14 fattade så Leif Kari, skolchef på skolan för Teknikvetenskap och huvudansvarig för censureringen av MST, det helt följdriktiga beslutet att lägga ner STVD (eller med omskrivning låta det vara "vilande") enligt denna offentliga handling (som registrator vänligt nog grävt fram då varken Leif Kari eller någon annan inblandad velat svara på mina upprepade frågor om status för STVD). Man kan i denna  skakande rapport läsa:
  • väldigt lågt söktryck
  • stora svårigheter för studenterna att klara studierna
  • förkunskaper alldeles för svaga
  • mindre an 20% klarar uppflyttningskraven. 
Så har då KTH lyckats med sitt uppsåt att stoppa ett alltför lovande initiativ från en alltför internationellt stark gruppering på KTH, under uppvisande av komplett inkompetens på alla nivåer. KTH har således genom censur förstört ett potentiellt högt värde och ersatt det med noll. Bra jobbat enligt KTHs rektor Peter Gudmundson, som aktivt deltog i bokbränningen 2010; när böcker bränns återstår bara aska.

Ironiskt nog har Leif Kari och Skolan för Teknikvetenskap dock inte låtit sig nedslås av detta dystra resultat utan arbetar nu aktivt för att uppgradera det havererade kandidatprogrammet i Simuleringsteknik till ett nytt civilingenjörsprogram i Teknisk Matematik enligt detta tilläggsbeslut. Fakultetsrådet har naturligtvis inte tillstyrkt inrättandet av detta program (se här 13d), då logiken saknas: Om KTH inte är kapabelt att driva en kandidatutbildning inom teknisk matematik/simuleringsteknik, är KTH (som landets främsta tekniska högskola) än mindre kapabelt att driva ett civilingenjörsprogram med samma inriktning.

PS Så här beskrevs programmet av KTH när det startade 2012:
  • Simuleringsteknik och virtuell design är ett nytt program på KTH som utvecklats för att möta det ökande behovet av datorsimulering. 
  • Utbildningen ger dig karriärmöjligheter inom många branscher, från verkstads- och processindustri, miljö- och energisektorn, via dataspel och animering, medicin och bioteknik till finansbranschen. 
  • Du kan exempelvis jobba som beräkningskonsult, expert på visualisering och informationsgrafik eller som programdesigner. 
  • Det nya kandidatprogrammet bygger på en mycket stark forsknings- och utbildningsmiljö inom detta område på KTH och är unikt i Sverige.
Ja, det är sannerligen unikt med sådan missskötsel, trots (eller kanske på grund av) KTHs priviligierade position. 

lördag 25 juli 2015

Frank Wilczek: Ugly Answer to Ugly Question

In his new book A Beautiful Question: Finding Nature's Deep Design, Frank Wilczek (Nobel Prize in Physics 2004) starts out stating the questions (or paradoxes) which motivated the development of modern physics:

In the quantum world of atoms and light, Nature treats us to a show of strange and seemingly impossible feats. Two of these feats seemed, when discovered, particularly impossible:
  • Light comes in lumps. This is demonstrated in the photoelectric effect, as we’ll discuss momentarily. It came as a shock to physicists. After Maxwell’s electromagnetic theory was confirmed in Hertz’s experiments (and later many others), physicists had thought they understood what light is. Namely, light is electromagnetic waves. But electromagnetic waves are continuous.
  • Atoms have parts, but are perfectly rigid. Electrons were first clearly identified in 1897, by J. J. Thomson. The most basic facts about atoms were elucidated over the following fifteen years or so. In particular: atoms consist of tiny nuclei containing almost all of their mass and all of their positive electric charge, surrounded by enough negatively charged electrons to make a neutral whole. Atoms come in different sizes, depending on the chemical element, but they’re generally in the ballpark of $10^{-8}$ centimeters, a unit of length called an angstrom. Atomic nuclei, however, are a hundred thousand times smaller. The paradox: How can such a structure be stable? Why don’t the electrons simply succumb to the attractive force from the nucleus, and dive in.
  • These paradoxical facts led Einstein and Bohr, respectively, to propose some outrageous, half-right hypotheses that served as footholds on the steep ascent to modern quantum theory. 
  • After epic struggles, played out over more than a decade of effort and debate, an answer emerged. It has held up to this day, and its roots have grown so deep that it seems unlikely ever to topple.
Wilczek then proceeds to prepare us to accept the answers offered by the modern physics of quantum mechanics as the result of epic struggles:
  • The framework known as quantum theory, or quantum mechanics, was mostly in place by the late 1930s. 
  • Quantum theory is not a specific hypothesis, but a web of closely intertwined ideas. I do not mean to suggest quantum theory is vague—it is not. 
  • With rare and usually temporary exceptions, when faced with any concrete physical problem, all competent practitioners of quantum mechanics will agree about what it means to address that problem using quantum theory. 
  • But few, if any, would be able to say precisely what assumptions they have made to get there. Coming to terms with quantum theory is a process, through which the work will teach you how to do it.
We learn that quantum mechanics is not built on specific hypotheses or assumptions, but nevertheless is not vague, and instead rather is a process monitored by competent practitioners. In any case, Wilczek proceeds to give us a glimpse of the basic hypothesis:
  • In quantum theory’s description of the world, the fundamental objects are ....wave functions.
  • Any valid physical question about a physical system can be answered by consulting its wave function.
  • But the relation between question and answer is not straightforward. Both the way that wave functions answer questions and the answers they give have surprising—not to say weird—features.
OK, so we are now enlightened by understanding that the answers that come out are weird. Wilczek continues:
  • I will focus on the specific sorts of wave functions we need to describe the hydrogen atom: 
  • We are interested, then, in the wave function that describes a single electron bound by electric forces to a tiny, much heavier proton.
  • Before discussing the electron’s wave function, we’ll do well to describe its probability cloud. The probability cloud is closely related to the wave function. The probability cloud is easier to understand than the wave function, and its physical meaning is more obvious, but it is less fundamental. (Those oracular statements will be fleshed out momentarily).
  • Quantum mechanics does not give simple equations for probability clouds. Rather, probability clouds are calculated from wave functions.
  • The wave function of a single particle, like its probability cloud, assigns an amplitude to all possible positions of the particle. In other words, it assigns a number to every point in space. 
  • To pose questions, we must perform specific experiments that probe the wave function in different ways.
  • You get probabilities, not definite answers.
  • You don’t get access to the wave function itself, but only a peek at processed versions of it.
  • Answering different questions may require processing the wave function in different ways.
  • Each of those three points raises big issues.
Wilczek then tackles these issues by posing new questions, or lacking question by retreating to an admirable attitude of humility in a lesson of wisdom
  • The first raises the issue of determinism. Is calculating probabilities really the best we can do?
  • The second raises the issue of many worlds. What does the full wavefunction describe, when we’re not peeking? Does it represent a gigantic expansion of reality, or is it just a mind tool, no more real than a dream?
  • The third raises the issue of complementarity....It is a lesson in humility that quantum theory forces to our attention. To probe is to interact, and to interact is potentially to disturb.
  • Complementarity is both a feature of physical reality and a lesson in wisdom.
We see that Wilczek sells the usual broth of strange and seemingly impossible feats, weird features, and outrageous half-right hypotheses, all raising big issues. Wilczek sums up by the following quote of Walt Whitman under the headline COMPLEMENTARITY AS WISDOM:

             Do I contradict myself?
             Very well, then, I contradict myself,
              I am large, I contain multitudes.

But physics is not poetry, and contradictory poetry does not justify contradictory physics. Contradictory mathematical physics cannot be true real physics, not even meaningful poetry. To get big by contradiction is a trade of politics, which is ugly and not beautiful.

Nevertheless, Wilczek started his Nobel lecture as follows:
  • In theoretical physics, paradoxes are good. That’s paradoxical, since a paradox appears to be a contradiction, and contradictions imply serious error. But Nature cannot realize contradictions. When our physical theories lead to paradox we must find a way out. Paradoxes focus our attention, and we think harder.
We understand that to Wilczek/modern physicists, contradictions are good rather than catastrophical and the more paradox the better, since it makes physicists focus attention to think harder.  Beautiful. For more excuses, see What Is Quantum Theory. Wilczek here retells the story of the Father (or Dictator) of Quantum Mechanics, Niels Bohr:
  • How wonderful that we have met with a paradox. Now we have some hope of making progress.
The paradox presented itself in 1925, but what happened to the hope of progress? Is paradoxical physics the physics of our time? Does light come in lumps? Why are atoms stable? Despite paradoxes, no real progress for 90 years!!??

PS1 Here is the question killing the probability interpretation of the wave function: Since the wave function for the ground state of Hydrogen is non-zero even far away from the kernel, does it mean that there is a non-zero chance of experimentally detecting a Hydrogen ground state electron far away from the kernel it is associated with? Or the other way around, since the wave function is maximal at zero distance from the kernel, does it mean that one will mostly find the electron hiding inside the kernel?

PS2 Beauty is an expression of order and deep design, not of disorder and lack of design. An atomistic world ruled by chance can be beautiful only to a professional statistician obsessed by computing mean values.

PS3 Not Even Wrong presents the book as follows: Frank Wilczek’s new book, A Beautiful Question, is now out and if you’re at all interested in issues about beauty and the deep structure of reality, you should find a copy and spend some time with it. As he explains at the very beginning:
  • This book is a long meditation on a single question:
  • Does the world embody beautiful ideas?
To me (and I think to Wilczek), the answer to the question has always been an unambiguous “Yes”. The more difficult question is “what does such a claim about beauty and the world mean?” and that’s the central concern of the book.

PS4 Wilczek expresses a tendency shared by many modern physicists of pretending to know all of chemistry "in principle", simply by writing down a Schrödinger equation on a piece of paper, however without actually being able to predict anything specific because solutions of the equation cannot by computed: 
  • Wave functions that fully describe the physical state of several electrons occupy spaces of very high dimension. The wave function for two electrons lives in a six-dimensional space, the wave function for three electrons lives in a nine-dimensional space, and so forth. The equations for these wave functions rapidly become quite challenging to solve, even approximately, and even using the most powerful computers. This is why chemistry remains a thriving experimental enterprise, even though in principle we know the equations that govern it, and that should enable us to calculate the results of experiments in chemistry without having to perform them.
In this illusion game, the uncomputability of the Schrödinger's many-dimensional equation relieves the physicist from the real task of explaining the actual physics of chemistry, while the physicist can still safely take the role of being in charge of principal theoretical chemistry underlying a "thriving experimental enterprise", which "in principle" is superfluous. Beautiful? 

måndag 13 juli 2015

Johan Rockström: CO2 Global Warming May Prevent New Ice Age

Johan Rockström, Executive Director of Stockholm Resilience Centre and leading Swedish CO2 global warming alarmist, admits that emission of CO2 may prevent new ice age (1.24 into news program):
  • Paradoxically this appears to be a positive effect of global warming.
This adds another paradox to the already long list of paradoxes of CO2 global warming.