torsdag 25 juni 2015

Modern Physics: Meaningless Sacrifice of Causality, Rationality and Reality?

Hermann von Helmholtz in Conservation of Force (1862-63): Reason we call that faculty innate in us of discovering laws and applying them with thought...there is a kind, I might almost say, of artistic satisfaction,when we are able to survey the enormous wealth of Nature as a regular-ordered whole--a cosmos, an image of the logical thought of our mind.

Modern physics in the form of relativity theory and quantum mechanics was born from a perceived impossibility of solving the following "problems" using methods of classical deterministic continuum physics:
  1. Second law of thermodynamics (irreversibility in formally reversible systems).
  2. Blackbody radiation (including avoidance of an ultraviolet catastrophe).
  3. Existence of a unique aether medium for propagation of electromagnetic waves. 
Boltzmann "solved" 1. by introducing statistical physics, thus giving up classical determinism or causality.

Planck "solved" 2. introducing a smallest quantum of energy, thus giving up the classical continuum of rational mechanics.

Einstein "solved" 3. by freeing electromagnetics from an aether, thus giving up classical coordinates of space and time describing reality. 

In each case the sacrifice of pillars classical physics was monumental and the grandness of the sacrifice was taken as a sign that it was inevitable and thus justified: No physicist would be willing the give up so much, unless it was absolutely necessary, as expressed by Planck excusing his introducing of the quantum:
  • ...the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be...
But if one day it shows that 1-3 in fact can be handled using a mild extension of classical deterministic continuum physics, then the monumental sacrifices would be unnecessary and then without rationale.

And yes, it may be that such a mild extension is possible in the form of finite precision computation exposed on The World as Computation.

This connects to Helmholtz' approach to 1. with heat as partly "incalculable" or "disordered" energy as energy with limited capability of being transformed to other forms of ("calculable") energy. This brings us back to the peak of classical physics represented by the mechanism of Helmholtz:
  • Natural phenomena should be traced back to the movements of material objects which possess inalterable motive forces that are dependent only on spatial relations.
  • Science, the goal of which is the comprehension of nature, must begin with the presupposition of its comprehensibility  and proceed in accordance with this assumption until, perhaps, it is forced by irrefutable facts to recognise limits beyond it may not go.
It thus appears to be possible to handle 1. and 2. by classical mechanism modified by finite precision computation. Further, 3. may be handled as suggested by the British physicist Ebenezer Cunningham (1881-1977) by viewing an aether is an immaterial space-time coordinate systems with the observed non-existence of a unique aether medium simply as an expression of the possibility of choosing many immaterial aethers/coordinate systems.

It thus may be that the monumental sacrifices made by modern physicists in order to cope with 1-3, are not necessary, and as such represent human stupidity, rather than heroic victory of the power of the human mind as official truth of modern physics propagated by modern physicists. 

tisdag 23 juni 2015

QM on Shaky Ground, Still after 90 Years

Encyclopedia of Mathematical Physics (2006) states in Introductory Article: Quantum Mechanics:
  • QM in its present formulation is a refined and and successful instrument for the description of the non relativistic phenomena at the Planck scale, but its internal inconsistency is still standing on shaky ground.
  • In this section we describe some of the conceptual problems which plague present day QM...
How is it possible that today 90 years after the formulation of Schrödinger's equation as the foundation of QM, this foundation is still inconsistent and shaky, plagued by conceptual problems. What have physicists been doing all these years?

Solway Conference 1927

torsdag 18 juni 2015

New Theory of Flight Accepted for Publication in Journal of Mathematical Fluid Mechanics

The ground-breaking article New Theory of Flight is now accepted for publication in Journal of Mathematical Fluid Mechanics. The paralyzing spells of Prandtl, father of modern fluid mechanics, and Kutta and Zhukovsky, fathers of modern aerodynamics, are now finally broken after more than 100 years of misleading unphysical mathematics. A post-modern era of (computational mathematical) fluid mechanics and aerodynamics is now approaching...

söndag 14 juni 2015

Spencer Struggles with The Greenhouse Effect and Dragons

Roy Spencer continues his long struggle to convince the world that the Greenhouse Effect as the scientific foundation of CO2 global warming hysteria, is real physics:
  • I’ve had a request to (once again) go through an explanation of the (poorly-named) Greenhouse Effect (GHE). Hopefully there is something which follows that will help you understand this complex subject.
Here is Roy's explanation:
  • The atmosphere DOES absorb IR energy. The IR absorption coefficients at various wavelengths, temperature, and pressures have been measured for water vapor, CO2, etc., in laboratories and published for decades.
  • This absorption means the atmosphere also EMITS IR energy, both upward and downward. And it is that DOWNWARD flow of IR energy (sometimes called “back radiation”) which is necessary for net warming of the surface from the greenhouse effect.
Then Roy reveals the reason behind his irresistible urge to educate the world about the greenhouse effect:
  • (Technical diversion: This is where the Sky Dragon Slayers get tripped up. They claim the colder atmosphere cannot emit IR downward toward a warmer surface below, when in fact all the 2nd Law of Thermodynamics would require is that the NET flow of energy in all forms be from higher temperature to lower temperature. This is still true in my discussion.)
Roy's heavy weapon intended to kill those nasty Sky Dragon Slayers is:
  • You can measure the greenhouse effect yourself with a handheld IR thermometer pointed at the sky, which measures the temperature change caused by a change in downwelling IR radiation. In a clear sky, the indicated temperature pointing straight up (“seeing” higher altitudes) will be colder than if pointed at an angle (measuring lower altitudes). This is direct evidence of the greenhouse effect…changes in downwelling IR change the temperature of a surface (the microbolometer in the handheld IR thermometer). That is the greenhouse effect.
Then Roy shows that he is a humble and open-minded serious scientist: 
  • If I’ve make a mistake in the above, I’ll fix it. I realize some might not like the way I’ve phrased certain things. But I’ve been working in this field over 20 years, and the above is the best I can do in 1-2 hours time....you will find it is a complex subject, indeed.
And yes Roy,  you make a mistake by uncritically accepting a reading of a hand-held IR-thermometer, which being a thermometer measures temperature, as evidence of the reality of downward IR. You can read about your mistake under the category "pyrgeometer" including the following key posts:
And so Roy, what is your reaction to the evidence I present?

PS Roy appears to filter my comment to his post with a link to the above. Of course, it is Roy's responsibility to guarantee that his readers and users/buyers (not to speak of manufacturers such as  Kipp&Zonen) of hand-held IR-thermometers, are not reached by disturbing information: Nobody wants to get told that the reading of a thermometer is temperature, since that is so evident to anyone with slightest education in science. In particular, Roy does not want to get told that he has been cheated by Kipp&Zonen in believing that the thermometer he bought measures Downwelling Longwave Radiation (DLR) and not temperature , and accordingly will no respond to my question. Under the choice of saying something (and revealing ignorance), and saying nothing (only indicating ignorance), Roy chooses to say nothing. But nothing is nothing.


lördag 13 juni 2015

The Copenhagen Interpretation of Quantum Mechanics??

If you ask a physicist today about the foundations of modern physics (the theory of relativity and quantum mechanics), you will get most likely get the answer that all basic questions were answered long ago and neither questions nor answers need to be repeated. In short, "science is settled", and the question now is simply how to advance physics further into the unknowns of dark matter, dark energy, string theory and multiversa.

In particular, the answer for quantum mechanics is the Copenhagen Interpretation coined by Heisenberg in the 1950s as an expression of the influence of the Danish physicist Niels Bohr during the formative years of modern physics following the introduction by Max Planck in 1900 of the smallest quantum of action $h$. 

One of the few who still worries about the foundations of quantum mechanics is Lubos Motl, who in a sequence of posts on The Reference Frame states his commitment to the Copenhagen Interpretation based on the following postulates:
  1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
  2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
  3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
  4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
  5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
  6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)  
Let us now analyze these postulates from scientific point of view. We find:
  1. The idea that the wave function represents the subjective knowledge of a system, makes quantum mechanics into a personal experience, which cannot be science.
  2. The idea that nature "essentially is probabilistic" is an ad hoc assumption, which can never be experimentally tested and thus does not belong to science.
  3. Impossibility of knowledge contradicts scientific principle: Why does certain knowledge make other knowledge impossible?
  4. Wave-particle duality as contradictory reality, does no make sense.
  5. Divison of physics into "classical" and "non-classical" is without reason. Physics is physics.
  6. Without division between "classical" and "non-classical", the idea that "non-classical" will approximate "classical", lacks rationale.  
I leave to the reader to evaluate the scientific value and rationality of these postulates supposedly expressing the contribution to humanity and the science of physics from what is called "modern physics". 

The Creation of Quantum Mechanics: The True Story by J Hendry Part 1

The Creation of Quantum Mechanics and the Bohr-Pauli Dialog by John Hendry is presented as
  • a genuine "history" as opposed to a mere technical report or popular or semi-popular account.
  • My aims in making this attempt have been to satisfy the needs of historians of science and, more especially, to promote a serious interest in the history of science among physicists and physics students.
Hendry states in the Introduction:
  • On one hand the quantum theory has continued in all its formulations to show a remarkable predictive power in respect of experimental observations. In this respect it must rank as an extraordinarily successful physical theory, and as one that will not easily be displaced.
  • On the other hand, however, dissatisfaction with the conceptual foundations of the theory has also apparently endured. 
  • Many working physicists are seemingly content to accept what Einstein referred to as the "gentle pillow" of the Copenhagen interpretation without asking any further questions, and this has long been accepted as an orthodox position.
  • But if we restrict our attention to physicists (or indeed philosophers) of the first rank, then we see immediately that such an orthodoxy is illusory. It was created in the late 1920s when many of the leading quantum physicists, among them Bohr, Born, Heisenberg, Pauli, Dirac, Jordan and von Neumann, sunk their more philosophical differences in an effort to repel the challenge of the semi-classical interpretations and get on with the job of developing quantum electrodynamics. 
  • But those differences remained. Copenhagenism was and is a generic term covering a whole range of related interpretations. Even when these interpretations are taken together, they cannot be considered as an entirely dominant orthodoxy. Among their early opponents some physicists might arguably be dismissed as narrow-sighted conservatives. But such outright dismissal is very difficult to uphold in Einstein's case, and still more so in those of Schrödinger and de Broglie, neither of whose preferred interpretations could reasonably be labelled classical. 
  • More recently attention has shifted from the physical interpretation of quantum mechanics towards the logical and mathematical consistency of quantum field theory, but the issues remain closely connected and opposition to Copenhagenism remains strong. 
  • However, and here lies the crux of the matter, the opponents seem to be no nearer to providing a valid alternative than were their predecessors of the late 1920s. 
  • Beyond the limited compromise of Copenhagenism there is still no such thing as a consistent and generally acceptable interpretation of quantum mechanics, and the evidence of the last fifty years points unerringly to the conclusion that there will not be one until either the structure of our physical conceptions, or our expectations of physical theory, or the quantum theory itself should undergo radical changes more far-reaching than any yet seen.
  • Faced with this dilemma it is tempting to react as did Peter Debye to the problem of electrons in the nucleus, a problem that arose in the immediate wake of quantum mechanics, by treating it as something best ignored, "like the new taxes". 
  • And many physicists have indeed taken this course, either ignoring the interpretative problem altogether (paying the taxes without question) or proceeding stubbornly to seek fundamentally classical interpretations that are demonstrably not there (stalling the taxman). 
  • But whereas such attitudes may be expedient in the short term they are ultimately inconsistent with the very spirit of the scientific enterprise.  
  • The interpretative problem of quantum theory is several orders more fundamental than that of nuclear electrons, and has proved immensely more resistant to attempts at a solution. 
  • But a theory with innate inconsistencies, whatever its present predictive success, cannot be expected to serve for ever. 
  • If the problem, like the tax, does not bear thinking about, then that is the strongest indication we can possibly have that it needs thinking about. 
  • And while it may not be so easily solved we can at least try to understand how such an extreme situation arose in the first place. 
  • One aim of this study, then, is to approach the history of the theory of quantum mechanics as a means of exploring its philosophy. 
What Hendry effectively says is that the foundations of quantum mechanics as physical theory was an inconsistent mess at start hundred years ago and has so remained until now.  How is it then possible that this inconsistent mess "has continued in all its formulations to show a remarkable predictive power in respect of experimental observations"? 

Well, the answer is that since quantum mechanics as a multi-dimensional inconsistent mess is uncomputable, it is impossible to make predictions from theory alone. This means that whatever observation is made, there is a version of quantum mechanical messy theory that can be made to conform with the observation. This is the reason why there is no observation in conflict with any quantum mechanical theory, even though the theory is inconsistent, which of course is used as evidence that the inconsistent messy theory is perfect and consistent and always in perfect consistent  agreement with observation.

In Part 2 I will summarize Hendry's account of the genuine "history" and then ponder Hendry's appeal: quantum theory itself should undergo radical changes more far-reaching than any yet seen.     

fredag 12 juni 2015

Tragedy of Modern Physics: Born's Statistical Interpretation of Quantum Mechanics

Max Born in 1926 just after violating principles of classical physics of reality and causality: 

Max Born was awarded the Nobel Prize in physics in 1954 for his statistical interpretation of solutions of Schrödinger's wave equation named wave functions. Schrödinger formulated his equation, which has come to serve as the basic mathematical model of the modern physics of quantum mechanics, in a moment of heavenly inspiration in the Alps in 1926 (together with one of his many girl friends), with the objective of interpreting the modulus squared $\vert\psi\vert^2$ of a wave function $\psi$ as charge distribution. 

But there was a problem with this interpretation: For an atom with $N$ electrons, Schrödinger's wave function depends on $3N$ space coordinates, which allows a direct physical meaning only in the case of Hydrogen with $N=1$. Schrödinger could not get around this obstacle and his equation was instead hi-jacked by Heisenberg and Born supported by Bohr and was then twisted into the so-called Copenhagen Interpretation with the wave function a probability distribution of particle positions viewed to represent wave-particle duality as the incarnation of the new physics. 

Schrödinger could not accept this probabilistic destruction of causality, but was effectively marginalized (together with Einstein and Planck and Lorentz and others) by the Bohr Copenhagen school leading the world into a new modern physics of wave-particle duality and complementarity outside classical rationality.  

It did not help that grandfather Lorentz joined Schrödinger's protest:
  •  I care little for the conception of  $\vert\psi^2\vert$  as a probability...In the case of an H-atom there is for a given energy E, also a non-vanishing probability outside the sphere which electrons of energy E cannot leave.      
The Copenhagen interpretation took the lead and today we can see the result as a tragedy of modern physics dominated by string theory and multiversa beyond any rationality.

Born describes in his Nobel lecture the sacrifice of classical ideals (or crime) which a modern physicist must be willing to commit:         
  • It is necessary to drop completely the physical pictures of Schrödinger which aim at a revitalization of the classical continuum theory, to retain only the formalism and to fill that with new physical content.
To commit a crime requires a motivation and to commit a big crime requires a strong motivation. The first step on this road of modern physics was taken by Planck in 1900:
  • The whole procedure was an act of despair because a theoretical interpretation (of black-body radiation) had to be found at any price, no matter how high that might beI was ready to sacrifice any of my previous convictions about physics...For this reason, on the very first day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.
Einstein followed up in 1905 with his special relativity asking humanity to sacrifice classical concepts of space and time.  In both cases, the grandness of the sacrifice supported credibility. 

In describing his crime Born first gives credit to scientists following the law: 
  • Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored. 
Born then recalls the historic fact that Bohr was stronger, adding an excuse that the crime rather concerns philosophy than physics:  
  • Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position. The matter concerns the borderland between physics and philosophy, and so my physics lecture  will partake of both history and philosophy, for which I must crave your indulgence.
  • The work, for which I have had the honour to be awarded the Nobel Prize for 1954, contains no discovery of a fresh natural phenomenon, but rather the basis for a new mode of thought in regard to natural phenomena.
Next follows an excuse with reference to "intellectual crisis": 
  • The first point is this: the work at the Göttingen school, which I directed at that time (1926-I927), contributed to the solution of an intellectual crisis into which our science had fallen as a result of Planck’s discovery of the quantum of action in 1900.
  • At the beginning of the twenties, every physicist, I think, was convinced that Planck’s quantum hypothesis was correct. According to this theory energy appears in finite quanta of magnitude $h\nu$ in oscillatory processes having a specific frequency $\nu$ (e.g. in light waves). Countless experiments could be explained in this way and always gave the same value of Planck’s constant .
Then Born puts the blame on Heisenberg, his assistant:

  • Heisenberg, who at that time was my assistant, brought this period to a sudden end. He cut the Gordian knot by means of a philosophical principle and replaced guess-work by a mathematical rule. The principle states that concepts and representations that do not correspond to physically observable facts are not to be used in theoretical description. 
  • I was as excited by this result as a sailor would be who, after a long voyage, sees from afar, the longed-for land...I was convinced from the start that we had stumbled on the right path.

Next, the success in the case $N=1$ is taken as evidence that the theory is correct for $N>1$:
  • The first non-trivial and physically important application of quantum mechanics was made shortly afterwards by W. Pauli who calculated the stationary energy values of the hydrogen atom by means of the matrix method and found complete agreement with Bohr’s formulae. From this moment onwards there could no longer be any doubt about the correctness of the theory . 
But some doubts presented themselves:
  • What this formalism really signified was, however, by no means clear. Mathematics, as often happens, was cleverer than interpretative thought. 
In any case, Schrödinger's wave equation was accepted as the right thing, but not Schrödinger's interpretation of $\vert\psi\vert^2$ as charge density:
  • Wave mechanics enjoyed a very great deal more popularity than the Göttingen or Cambridge version of quantum mechanics. It operates with a wave function $\psi$, which in the case of one particle at least, can be pictured in space, and it uses the mathematical methods of partial differential equations which are in current use by physicists. Schrödinger thought that his wave theory made it possible to return to deterministic classical physics. He proposed (and he has recently emphasized his proposal anew’s), to dispense with the particle representation entirely, and instead of speaking of electrons as particles, to consider them as a continuous density distributions. 
And then Born's commits the crime:
  • I immediately took up Schrödinger's method and an idea of Einstein’s gave me the lead. He had tried to make the duality of particle-light quanta or photons and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. 
  • This concept could at once be carried over to the $\psi$-function: it ought to represent the probability density for electrons (or other particles). 
  • It was easy to assert this, but how could it be proved?
Here is Born's justification of the crime:
  • To us in Göttingen Schrödinger's interpretation seemed unacceptable in face of well established experimental facts. At that time it was already possible to count particles by means of scintillations or with a Geiger counter, and to photograph their tracks with the aid of a Wilson cloud chamber. 
with more "proof" from Heisenberg's Uncertainty Principle:
  • However, a paper by Heisenberg containing his celebrated uncertainty relationship, contributed more than the above-mentioned successes to the swift acceptance of the statistical interpretation of the $\psi$-function. 
  • It showed that not only the determinism of classical physics must be abandonded, but also the naive concept of reality which looked upon the particles of atomic physics as if they were very small grains of sand.
But Born still struggled with the skeptics of atoms as dice-games: 
  • How does it come about then, that great scientists such as Einstein, Schrödinger, and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. Two closely knitted points of view are to be distinguished: the question of determinism and the question of reality. 
arguing that everything including classical physics is a dice-game,:
  • The determinism of classical physics turns out to be an illusion, created by overrating mathematico-logical concepts....and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.
But finally the self-doubts take over and Born's Nobel lecture given 28 year after the commitment of the crime, ends with questions:
  • Are we still justified in applying to the electron the concept of particle and therefore the ideas associated with it?
  • Somewhere in our doctrine is hidden a concept, unjustified by experience, which we must elim- inate to open up the road. 
  • To come now to the last point: can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?  
To sum up we see that Born's justification of giving up the basic principles of classical physics, boils down to the following shaky weak arguments:
  • A perceived need to make the duality of particle-light quanta or photons and waves comprehensible. 
  • Because a Geiger counter gives a "click", what caused the "click" must be a "particle".
We understand following Schrödinger as inventor of the basic mathematical model of quantum mechanics, if the particle idea is given up, then there is no need to make wave-particle duality "comprehensible", since then waves are enough. What remains is to reformulate Schrödinger's multidimensional wave equation into a system of three-dimensional wave functions representing charge distribution. This is what I now explore as (Computational) Physical Quantum Mechanics.

But the sad truth today is that nobody cares if the fundamentals of physics make sense or not: Quantum mechanics and relativity, although incompatible, is "settled modern physics" with all questions answered once and for all by now dead and gone physicists, who took the answers along into the grave.   

PS Note that Heisenberg received the Nobel Prize in physics in 1932 and Schrödinger shared the Prize with Dirac in 1933, while Born had to wait 20 years until the coining of the Copenhagen Interpretation by Heisenberg in the early 1950s as the official formulation of quantum mechanics.
Today, only a few hard core extremist like Lubos Motl claim that this is the final word to which nothing can be added. The historical dimension of this view is described by A. Pais in the opening of his Address to the Annual Meeting of the Optical Society in 1982 entitled Max Born and the Statistical Interpretation of Quantum Mechanics as follows:
  • The introduction of probability in the sense of quantum mechanics, probability as an inherent feature of physical law, may well be the most drastic scientific change yet effected in the twentieth century. 
In other words: A Big Lie is more credible than a small one, so if you are going to cheat, make it Big. CO2 global warming alarmism gives an example of this tactic, which is now threatening to throw Western civilization back to Stone Age: This is "settled science" which is so Big that it cannot be  questioned! 

  

onsdag 3 juni 2015

The Copenhagen Interpretation vs Leibniz' Sufficient Reason

The article Inconsistency of the Copenhagen Interpretation in Foundations of Physics, Vol. 21, No. 5, 1991, by  C. I. J. M. Stuart, argues that:
  • The Bohr-Heisenberg scheme, which forms the basis of any current version of the standard or Copenhagen interpretation of quantum mechanics, is shown to be internally inconsistent.
with the following introduction:
  • The predictive success of quantum mechanics has always been accompanied by vigorous debate concerning the theory's physical content as specified by the Copenhagen interpretation, i.e., the Bohr-Heisenberg scheme. 
  • Einstein at first thought the scheme inconsistent, but later concluded that it made quantum mechanics consistent but incomplete.
  • Since then, the question of completeness has persisted in connection with "hidden variable" theories; but Einstein's opinion as to the scheme's consistency has been generally accep- ted and perhaps overshadowed by concern with the completeness issue, though a widely held modern view is that the scheme is incoherent and perhaps incomplete. 
  • The main objective in this paper is to show that incoherence is not the problem but, much more seriously, the scheme is internally inconsistent. 
The article starts out by identifying the following basic postulates of the Copenhagen Interpretation:
  1. The completeness postulate requires that the quantum mechanical wave function gives a complete specification of what can be known concerning quantum states. 
  2. The superposition principle requires that a quantum state represented by a linear superposition of allowable quantum states is itself an allowable quantum state. 
  3. The Heisenberg uncertainty principle requires that observables represented by noncommuting operators cannot simultaneously be measured with equal exactness, the exactness of the one being inversely proportional to the exactness of the other. 
  4. The probability interpretation requires that the wave function does not correspond to a material wave; instead, its amplitude corresponds to a probability amplitude and its absolute square corresponds to a probability density. 
  5. The principle of inseparability requires that, in quantum mechanics, a physical system consists of the object-system under investigation inseparably from the experimental apparatus used to make measurements; and, moreover, the interaction between object and apparatus forms an inseparable part of quantum phenomena. 
  6. Bohr's principle of complementarity requires that complementary experimental arrangements wilt yield complementary quantum phenomena. 
  7. Bohr's correspondence principle requires that quantum mechanics must converge to classical mechanics in the limit where quantum effects can be disregarded.
This is important information, since the Copenhagen Interpretation seldom is described in precise terms, which makes critical evaluation difficult. Let us subject postulates 1-7 to Leibniz' test of sufficient reason:
  1. What is the reason to believe that the wave function gives a complete specification of what can be known of  the physics of atoms?
  2. What is the reason to believe that the physics of atoms is linear? 
  3. What is the reason that position and velocity cannot be measured simultaneously? 
  4. What is the reason to believe that the wave function cannot correspond to a material wave? What is the reason to believe that it instead corresponds to probability amplitude?
  5. What is the reason to believe that a physical system consists of the object-system inseparably connected to experimental apparatus?
  6. What is reason for complementarity?
  7. What is the reason for requiring that quantum mechanics must converge to classical mechanics if quantum mechanics effects can be discarded?
Let us thus seek the sufficient reason for each postulate and see what we can come up with:
  1. No reason found.
  2. No reason found.
  3. With matter as wave the answer is trivial. With matter as particle, no reason is found.
  4. The reason is the spatial multi-dimensionality of the wave function.
  5. No reason that a physical system must be connected to experimental apparatus.
  6. No reason.
  7. No reason to explicitly require something self-evident: quantum mechanics without quantum effects must be classical mechanics.
We conclude that only one reason has been found: the spatial multi-dimensionality of the wave function makes direct physical interpretation impossible, since physics as we know it takes place in three space dimensions. No other reason has been identified. 

After this evaluation showing that the sole reason for the Copenhagen Interpretation is an ad hoc assumption about mathematical formalism, it is natural to ask if there is a quantum mechanics with wave functions depending on a common three-dimensional space variable plus time?  

In a sequence of posts the category "physical quantum mechanis" I seek to give a positive answer to this question.  The reason for this form of quantum mechanics is the same as for classical mechanics, which may well be sufficient.

We have not found any sufficient reason for the Copenhagen Interpretation which fits with Stuart's observation that the Copenhagen Interpretation is internally inconsistent: Of course, there can never be a sufficient reason for the validity of a scientific model which is internally inconsistent. Of course, there can never be a sufficient reason to view a scientific contradiction as a scientific truth. Only in the Copenhagen Interpretation is this possible, but that means that whatever it is,  it is not science.


torsdag 28 maj 2015

Physics as Analog Finite Precision Computation vs Physics as Statistics


I am exploring an approach to physics as "analog finite precision computation" to be be compared with classical physics as "analog infinite precision physics" and modern physics as "physics of dice games" or "statistical physics".

The step from classical to modern physics was forced upon physicists starting in the mid 19th century when it became clear that the 2nd law of thermodynamics could not be found in classical infinite precision physics of irreversible systems. The way to achieve irreversibility was to assume that atoms play dice games with the outcome of a throw of a dice inherently irreversible: To "unthrow" a dice was (correctly) understood to be impossible and thus irreversibility was introduced and the paralysis of reversible classical physics was broken. So far so good.

But the fix came with severe side effects as real physics independent of human observation was replaced by statistical physics representing "human understanding", as if the world goes around just because some physicist  is making observations and claim them to be understandable. Einstein and Schrödinger could never be convinced that atoms play dice, despite major pressure from the physics community.

The unfortunate result of this collapse of rationality of deterministic physics, has led modern physics into wildly speculative physics of strings and multiverse, which nobody can understand.

But there is a milder way of introducing irreversibility into classical reversible physics, and that is to view physics as analog computation with finite precision instead of infinite precision.

This connects directly to a computer operating with finite decimal expansion of real numbers as a necessary restriction of infinite decimal expansion, in order to allow computations to be performed in finite time: In order to make the world go around, and it does go around, and thus not come into a halt, physical processes cannot be realised with infinite precision and thus finite precision computation is a must in a world that goes around. It is thus necessary, but it is also sufficient to introduce irreversibility into classical reversible physics.

Finite precision computation thus solves the main problem which motivated the introduction of statistical physics, but in a much more gentle way and without the severe side effects of full-blown statistics based on dice games.

Finite precision computational physics is represented by the modern computer, while statistical physics would correspond to a "dice computer" throwing a dice in every step of decision, just like the "dice man" created by the pseudonym Luke Rhinehart. The life of the "dice man" turned into misery, which can be compared with (reasonably) successful ordinary (reasonably controlled) life under finite precision, without a dice but with constant pressure to go onto the next day.

So if you want to compare finite precision analog physics to modern statistical physics, make the thought experiment of comparing your usual finite precision computer, which you use to your advantage, to a "dice computer" which would be completely unpredicatable. This is the comparison between an experienced computer wiz often getting reliable results, to a totally inexperienced user pushing the keys randomely and getting garbage.

Or make the comparison of getting married to a person which follows a principle of "finite precision" to a person like the "dice man" who is completely unpredictable. What would you prefer?

Few ideas can change your view in the same way as "physics as analog finite precision computation". Try it!

Physical Quantum Mechanics: Time Dependent Schrödinger Equation

We consider a Schrödinger equation for an atom with $N$ electrons of the normalized form: Find a wave function
  • $\psi (x,t) = \sum_{j=1}^N\psi_j(x,t)$
as a sum of $N$ electronic complex-valued wave functions $\psi_j(x,t)$, depending on a common 3d space coordinate $x$ and time coordinate $t$ with non-overlapping spatial supports $\Omega_1(t)$,...,$\Omega_N(t)$, filling 3d space, satisfying
  • $i\dot\psi (x,t) + H\psi (x,t) = 0$ for all $(x,t)$,       (1)
where the (normalised) Hamiltonian $H$ is given by
  • $H(x) = -\frac{1}{2}\Delta - \frac{N}{\vert x\vert}+\sum_{k\neq j}\int\frac{\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dy$  for $x\in\Omega_j(t)$,
and the electronic wave functions are normalised to unit charge:
  • $\int_{\Omega_j}\vert\psi_j(x,t)\vert^2 =1$ for all $t$ for $j=1,..,N$.
The total wave function $\psi (x,t)$ is thus assumed to be continuously differentiable and the electronic potential of the Hamiltonian acting in $\Omega_j(t)$ is given as the attractive kernel potential together with the repulsive kernel potential resulting from the combined electronic charge distributions $\vert\psi_k\vert^2$ for $k\neq j$.

The Schrödinger equation in the form (1) is a free-boundary problem where the supports $\Omega_j(t)$ of the electronic wave functions may change over time.

We solve (1) by time-stepping the system
  • $\dot u + Hv = 0$, $\dot v - Hu = 0$       (2)
obtained by splitting the complex-valued wave function $\psi = u+iv$ into real-valued real and imaginary parts $u$ and $v$ (and with $\vert\psi\vert^2 =u^2+v^2$.) 

This is a free-boundary electron (or charge) density formulation keeping the individuality of the electrons, which can be viewed as a "smoothed $N$-particle problem" of interacting non-overlapping "electron clouds" under Laplacian smoothing. The model (1) connects to the study in Quantum Contradictions showing a surprisingly good agreement with observations.

In particular, the time-dependent form (2) is now readily computable as a system of wave functions depending on a common 3d space variable and time, to be compared to the standard wave equation in $3N$ space dimensions which is uncomputable.

I am now testing this model for the atoms in the second row of the periodic table, from Helium (N=2) to Neon (N=10), and the results are encouraging: It seems that time dependent N-electron quantum mechanics indeed is computable in this formulation and the model appears to be in reasonable agreement with observations.  This gives promise to exploration of atoms interacting with external fields, which has been hindered by uncomputability with standard multi-d wave functions.

PS The formulation readily extends to electrodynamics with the Laplacian term of the Hamiltonian replaced by

  •  $\frac{1}{2}(i\nabla + A)^2$
and the potential augmented by $\phi$, where $A=A(x,t)$ is a vector potential, $\phi =\phi (x,t)$ is a scalar potential with $E = -\nabla\phi -\dot A$ and $B=\nabla\times A$ given electric and magnetic fields $E=E(x,t)$ and $B=B(x,t)$ depending on space and time.