lördag 21 januari 2017

Deconstruction of CO2 Alarmism Started

Directly after inauguration the White House web site changes to a new Energy Plan, where all of Obama's CO2 alarmism has been completely eliminated:
  • Energy is an essential part of American life and a staple of the world economy. The Trump Administration is committed to energy policies that lower costs for hardworking Americans and maximize the use of American resources, freeing us from dependence on foreign oil.
  • For too long, we’ve been held back by burdensome regulations on our energy industry. President Trump is committed to eliminating harmful and unnecessary policies such as the Climate Action Plan and the Waters of the U.S. rule. Lifting these restrictions will greatly help American workers, increasing wages by more than $30 billion over the next 7 years.
  • Sound energy policy begins with the recognition that we have vast untapped domestic energy reserves right here in America. 
  • The Trump Administration will embrace the shale oil and gas revolution to bring jobs and prosperity to millions of Americans.
Nothing about dangerous CO2! No limits on emission! Trump has listened to science! CO2 alarmism will be defunded and why not then also other forms of fake physics...

This is the first step to the Fall of IPCC and the Paris agreement and liberation of resources for the benefit of humanity, see phys.org.

The defunding of CO2 alarmism will now start, and then why not other forms of fake science?

PS1 Skepticism to CO2 alarmism expressed by Klimatrealisterna is now getting published in media in Norway, while in Sweden it is fully censored.  I have recently accepted an invitation to become a member of the scientific committee of this organisation (not yet visible on the web site).

PS2 Read Roy Spencer's analysis of the Trump Dump:
  • As Bjorn Lomborg has recently estimated, efforts to “fight” global warming under the U.N.’s Paris Agreement could cost the world $100 Trillion in lost wealth by the end of this century. 
  • That, I guarantee you, will lead to (preventable) deaths, due to poverty and all problems stemming from poverty.
  • And for what gain? An unmeasurable decrease in further warming of maybe 0.1 deg. C at best (and that’s assuming climate sensitivity is high and that we are in for several deg. C of future warming — which I don’t). As someone who knows how temperatures trends are measured on the ground (I’ll bet none of the thermometer climate data “experts” passed NWS weather observer certification exams like I did) and by satellite (I’m the co-inventor), I can say that this level of future temperature reduction is unmeasurable by any system we have.
Bottomline: With plenty of energy, poverty can be eliminated. Unstopped CO2 alarmism will massively increase poverty with no gain whatsoever. Trump is the first state leader to understand that the Emperor of CO2 Alarmism is naked, and other leaders will now open their eyes to see the same thing...and skeptics may soon say mission complete...

The Origin of Fake Physics

Peter Woit on gives on Not Even Wrong a list of fake physics most of which can be traced back to the fake physics character of Schrödinger's linear multi-dimensional equation, as exposed in recent posts.

Woit's list of fake physics thus includes different fantasies of multiversa all originating from the multi-dimensional form of Schrödinger's equation giving each electron its own separate 3d space/universe to dwell in.

But the linear multi-d Schrödinger equation is a postulate of modern physics picked from out of the blue as a ready-made and as such like a religious dogma beyond human understanding and rationality.

Why modern physics has been driven into such an unscientific approach remains to be understood and exposed, and discussed...

The standard view is presented by David Gross as follows:
  • Quantum mechanics emerged in 1900, when Planck first quantized the energy of radiating oscillators.
  • Quantum mechanics is the most successful of all the frameworks that we have discovered to describe physical reality. It works, it makes sense, and it is hard to modify. 
  • Quantum mechanics does make sense, although the transition, a hundred years ago, from classical to quantum reality was not easy. 
  •  The freedom one has to choose among different, incompatible, frameworks does not influence reality—one gets the same answers for the same questions, no matter which framework one uses. 
  • That is why one can simply “shut up and calculate.” Most of us do that most of te time. 
  • By now...we have a completely coherent and consistent formulation of quantum mechanics that corresponds to what we actually do in predicting and describing experiments and observations in the real world. 
  • For most of us there are no problems.
  • Nonetheless, there are dissenting views. 
So, the message is that quantum mechanics works if you simply shut up and calculate and don't ask if it makes sense, as physicists are being taught to do, but here are dissenting views...

Note that the standard idea ventilated by Gross is that quantum mechanics somehow emerged from Planck's desperate trick of "quantisation" of blackbody radiation 1900 when taking on the mission of explaining the physics of radiation while avoiding the "ultra-violet catastrophe" believed to torpedo classical wave mechanics. Planck never believed that his trick had a physical meaning and in fact the trick is not needed because an explanation can be given within classical wave mechanics in the form of computational blackbody radiation with the ultraviolet catastrophe not showing up.

This is what Anthony Leggett, Nobel Laureate and speaker at the 90 Years of Quantum Mechanics Conference, Jan 23-26, 2017, says (in 1987):
  • If one wishes to provoke a group of normally phlegmatic physicists into a state of high animation—indeed, in some cases strong emotion—there are few tactics better guaranteed to succeed than to introduce into the conversation the topic of the foundations of quantum mechanics, and more specifically the quantum measurement problem.
  • I do not myself feel that any of the so-called solutions of the quantum measurement paradox currently on offer is in any way satisfactory.
  • I am personally convinced that the problem of making a consistent and philosophically acceptable 'join' between the quantum formalism which has been so spectacularly successful at the atomic and subatomic level and the 'realistic' classical concepts we employ in everyday life can have no solution within our current conceptual framework; 
  • We are still, after three hundred years, only at the beginning of a long journey along a path whose twists and turns promise to reveal vistas which at present are beyond our wildest imagination. 
  • Personally, I see this as not a pessimistic, but a highly optimistic, conclusion. In intellectual endeavour, if nowhere else, it is surely better to travel hopefully than to arrive, and I would like to think that the generation of students now embarking on a career in physics, and their children and their children's children, will grapple with questions at least as intriguing and fundamental as those which fascinate us today—questions which, in all probability, their twentieth-century predecessors did not even have the language to pose.
The need of a revision, now 30 years later,  of the very foundations of quantum mechanics is even more clear, 90 years after conception. The starting point must be the wave mechanics of Schrödinger without particles, probabilities, multiversa, measurement paradox, particle-wave duality, complementarity and quantum jumps with atom microscopics described by the same continuum mathematics as the macroscopic world.

PS Is quantum computing fake physics or possible physics? Nobody knows since no quantum computer has yet been constructed. But the hype/hope is inflated: perhaps by the end of the year...

fredag 20 januari 2017

Shaky Basis of Quantum Mechanics

Schrödinger's equation! Where did we get that equation from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrodinger.  (Richard P. Feynman)

In the final analysis, the quantum mechanical wave equation will be obtained by a postulate, whose justification is not that it has been deduced entirely from information already known experimentally (Eisberg and Resnick in Quantum Physics)

Schrödinger's equation as the basic mathematical model of quantum mechanics is obtained as follows:

Start with classical mechanics with a Hamiltonian of the following form for a system of $N$ interacting point particles of unit mass with positions $x_n(t)$ and momenta $p_n=\frac{dx_n}{dt}$ varying with time $t$ for $n=1,...N$:
  • $H(x_1,...,x_N)=\frac{1}{2}\sum_{n=1}^Np_n^2+V(x_1,....,x_N)$     
where $V$ is a potential depending on the particle positions $x_n$, with the corresponding equations of motion
  • $\frac{dp_n}{dt}=\frac{\partial V}{\partial x_n}$ for $n=1,...,N$.           (1)
Proceed by formally replacing momentum $p_n$ by the differential operator $i\nabla_n$ where $\nabla_n$ is the gradient operator acting with respect to $x_n$ now viewed as the coordinates of three-dimensional space (and $i$ is the imaginary unit), to get the Hamiltonian 
  • $H(x_1,...,x_N)=-\frac{1}{2}\sum_{n=1}^N\Delta_n +V(x_1,...,x_N)$
supposed to be acting on a wave function $\psi (x_1,...,x_N)$ depending on $N$ 3d coordinates $x_1,...,x_N$, where $\Delta_n$ is the Laplacian with respect to coordinate $x_n$.  Then postulate Schrödinger's equation with a vague reference to (1) as a linear multi-d equation of the form:
  • $i\frac{\partial \psi}{\partial t}=H\psi$.         (2)
Schrödinger's equation thus results from inflating single points to full 3d spaces in a purely formal twist of classical mechanics by brutally changing the meaning of $x_n$ from point to full 3d space and then twisting (1) as well. The inflation gives a wave function which depends on $3N$ space coordinates and as such has no physicality and is way beyond computability.

The inflation corresponds to a shift from actual position, which may be of interest, to possible position (which can be anywhere), which has no interest. 

The inflation from point to full 3d space has become the trade mark of modern physics as expressed in Schrödinger's multi-d linear equation, with endless speculation without conclusion about the possible physics of the inflation and the meaning of (2). 

The formality and lack of physicality of the inflation of course should have sent Schrödinger's multi-d linear equation (2) to the waste-bin from start, but it didn't happen with the argument that even if the physics of the equation was beyond rationale, predictions from the equation always (yes, always!!) agree with observation. The lack of scientific logic was thus acknowledged from start, but it was taken for granted that anyway the equation describes physics very accurately. If a prediction from computation with Schrödinger's equation does not compare well with observation, there must be something wrong with the computation or comparison, never with the equation itself...

But solutions of Schrödinger's multi-d equation cannot be computed in any generality and thus claims of general validity has no real ground. It is simply a postulate/axiom and as such true by assumption as a tautology which can only be true.

The main attempts to give the inflation of classical mechanics into Schrödinger's multi-d linear equation a meaning, are:
  • Copenhagen Interpretation CI (probabilistic)
  • Many World Interpretation MWI (infinitely many parallel universa in certain contact) 
  • Pilot-Wave (Bohm) 
with no one explanation gathering clear acceptance.   In particular,  Schrödinger did not like these interpretations of his equation and dreamed of a different version in 3d with physical "anschaulich" meaning, but did not find it...

In the CI the possibilities become an actualities by observation, while in MWI all possibilities are viewed as actualities and in Bohmian mechanics the pilot wave represents the possibilities with a particle somehow carried by the wave representing actuality...all very strange...        

onsdag 18 januari 2017

Many Worlds Interpretation vs Double Slit Experiment

When I ask David Deutsch what his basic motivation is to believe that the Many Worlds Interpretation MWI of the multi-d linear Schrödinger equation describes real physics, I get the response that it is in particular the single electron double slit experiment, which he claims is difficult to explain otherwise.

But is this so difficult to explain assuming that electrons are always waves and never particles? I don't think so. Here is my argument:

In the single electron double slit experiment a screen displays an interference pattern created by a signal passing through a double slit, even with the input so weak that the interference pattern is created dot by dot as if being hit by a stream of single electron particles.

This is presented as a mystery, by arguing that an electron particle must chose one of the slits to pass through, and doing so cannot create an interference pattern because that can only arise if the single electron is a wave freely passing through both slits. So the experiment cannot be explained which gives evidence that quantum mechanics is a mystery, and since it is a mystery anything is possible, like MWI.

But there is no mystery if following Schrödinger we understand that electrons are always waves and never particles, and that the fact that the effect on the screen of an incoming wave on may be a dot somewhere on the screen triggered by local perturbations. A dot as effect does not require the cause to be dot-like.

It is thus possible to understand the single electron double slit experiment under the assumption that electrons are always wave-like and always pass through both slits and thus can create an interference pattern, in accordance with the original objective of Schrödinger to describe electrons as waves, and then physical waves and not probability waves as in the Copenhagen Interpretation as another form of MWI.

The trouble with quantum mechanics is the multi-d linear Schrödinger equation which describes probability waves or many worlds waves, which are not physical waves. The challenge is to formulate a Schrödinger equation which describes physical waves, that is to reach the objective of Schrödinger, which may possibly be done with something like realQM...

Ironically, Schrödinger's equation for just one electron is a physical wave equation, and so if anything can be explained by that equation it is the single electron double slit experiment and its mystery then evaporates...

PS The fact that putting a detector at one of the slits destroys the interference pattern, is also understandable with the electron as wave, since a detector may affect a wave and thus may destroy the subtle interference behind the pattern.

tisdag 17 januari 2017

David Deutsch on Quantum Reality

David Deutsch is a proponent of Everett's Many Worlds Interpretation MWI of quantum mechanics under a strong conviction that (from Many Worlds? Everett, Quantum Theory and Reality, Oxford Press 2010):
  • Science can only be explanation: asserting what is there in reality.
  • The only purpose of formalism, predictions, and interpretation is to express explanatory theories about what is there in reality, not merely predictions about human perceptions.
  • Restricting science to the latter would be arbitrary and intolerably parochial.
These convictions forces Deutsch into claiming that the multiverse of MWI is reality, which many physicists find hard to believe, including me. 

But I share the view of Deutsch that science is explanation of what is there in reality (in opposition to the Copenhagen Interpretation disregarding reality), and this is the starting point of realQM.

Concerning the development and practice of quantum mechanics Deutsch says:
  • It is assumed that in order to discover the true quantum-dynamical equations of the world, you have to enact a certain ritual. 
  • First you have to invent a theory that you know to be false, using a traditional formalism and laws that were refuted a century ago. 
  • Then you subject this theory to a formal process known as quantization (which for these purposes includes renormalization). 
  • And that’s supposed to be your quantum theory: a classical ghost in a tacked-on quantum shell
  • In other words, the true explanation of the world is supposed to be obtained by the mechanical transformation of a false theory, without any new explanation being added. 
  • This is almost magical thinking. 
  • How far could Newtonian physics have been developed if everyone had taken for granted that there had to be a ghost of Kepler in every Newtonian theory—that the only valid solutions of Newtonian equations were those based on conic sections, because Kepler’s Laws had those. And because the early successes of Newtonian theory had them too? 
Yes, quantum mechanics (based on Schrödinger's linear multi-d equation)  is ritual, formality and magical thinking, and that is not what science is supposed to be.

The logic about Schrödinger's linear multi-d equation then is:
  1. Interpretations must be made to give the equation a meaning. 
  2. All interpretations are basically equivalent.
  3. One interpretation is MWI.
  4. MWI is absurd non-physics.
  5. Linear multi-d Schrödinger equation does not describe physics.

måndag 16 januari 2017

Is Quantum Computing Possible?

  • .....may or may not be mystery as to what the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it. And therefore, some of the younger students ... you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. It has not yet become obvious to me that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm note sure there's no real problem. 
  • So that's why I like to investigate things. So I know that quantum mechanics seem to involve probability--and I therefore want to talk about simulating probability. (Feynman asking himself about a possibility of quantum computing in 1982)
The idea of quantum computing originates from a 1982 speculation by Feynman followed up by Deutsch on the possibility of designing a quantum computer supposedly making use of the quantum states of subatomic particles to process and store information. The hope was that quantum computing would allow certain computations, such as factoring a large natural number into prime factors, which are impossible on a classical digital computer.

A quantum computer would be able to crack encryption based on prime factorisation and thus upset the banking system and the world. In the hands of terrorists it would be a dangerous weapon...and so do we have to be afraid of quantum computing?

Not yet in any case! Quantum computing is still a speculation and nothing like any real quantum computer cracking encryption has been constructed up to date, 35 years later. But the hopes are still high...although so far the top result is factorisation of 15 into 3 x 5...(...in 2012, the factorization of 21 was achieved, setting the record for the largest number factored with Shor's algorithm...)

But what is the reason behind the hopes? The origin is the special form of Schrödinger's equation as the basic mathematical model of the atomic world viewed as a quantum world fundamentally different from the macroscopic world of our lives and the classical computer, in terms of a wave function
  • $\psi (x_1,...,x_N,t)$ 
depending on $N$ three-dimensional spatial coordinates $x_1$,...,$x_N$ (and time $t$) for a system of $N$ quantum particles such as an atom with $N$ electrons. Such a wave function thus depends on $3N$ spatial variables of $N$ different versions of $R^3$ as three-dimensional Euclidean space.

The multi-dimensional wave function $\psi (x_1,...,x_N,t)$ is to be compared with a classical field variable like density $\rho (x,t)$ depending on a single 3d spatial variable $x\in R^3$. The wave function $\psi (x_1,...,x_N,t)$ depends on $N$ different copies of $R^3$, while for $\rho (x,t)$ there is only one copy, and that is the copy we are living in.

In the Many Worlds Interpretation MWI of Schrödinger's equation the $N$ different copies of $R^3$ are given existence as parallel universes or multiversa, while our experience still must be restricted to just one of them, with the other as distant shadows.

The wave function $\psi (x_1,...,x_N,t)$ thus has an immense richness through its contact with multiversa, and the idea of quantum computing is to somehow use this immense richness by sending a computational task to multiversa for processing and then bringing back the result to our single universe for inspection.

It would be like sending a piece of information to an immense cloud for complex computational processing and then bringing it back for inspection. But for this to work the cloud must exist in some form and be accessible.

Quantum computing is thus closely related to MWI and the reality of a quantum computer would seem to depend on a reality of multiversa. The alternative to MWI and multiversa is the probabilistic Copenhagen Interpretation CI, but that does not make things more clear or hopeful.

But what is the reason behind MWI and multiversa? The only reason is the multi-dimensional aspect of Schrödinger's equation, but Schrödinger's equation is a man-made ad hoc variation of the equations of motion of classical mechanics obtained by a purely formal procedure of representing momentum $p$ by a multi-dimensional gradient differential operator as $p=i\nabla$ thus formally replacing $p^2$ by the action on $\psi$ by a multi-dimensional Laplacian $-\Delta =-\sum_j\Delta_j$ with $\Delta_j$ the Laplacian with respect to $x_j$, thus acting with respect to all the $x_j$ for $j=1,...,N$.

But by formally replacing $p$ by $i\nabla$ is just a formality without physical reason, and it is from this formality that MWI and multiversa arise and then also the hopes of quantum computing.  Is there then reason to believe that the multi-dimensional $-\Delta\psi$ has a physical meaning, or does it rather represent some form of Kabbalism or scripture interpretation?

My view is that multiversa and quantum computing based on a multi-dimensional Schrödinger equation based on a formality, is far-fetched irrational dreaming, that Feynman's feeling of a real problem sensed something important,  and this is my reason for exploration of realQM based on a new version of Schrödinger's equation in physical three-dimensional space.

PS1 One may argue that if MWI is absurd, which many think, then CI is also absurd, which many think, since both are interpretations of one an the same multi-dimensional Schrödinger equation, and the conclusion would then be that if all interpretations are absurd, then so is what is being interpreted, right? Even more reason for realQM and less hope for quantum computing...

PS2 MWI was formulated by Hugh Everett III in his 1956 thesis with Wheeler. Many years later, Everett laughingly recounted to Misner, in a tape-recorded conversation at a cocktail party in May 1977, that he came up with his many-worlds idea in 1954 "after a slosh or two of sherry", when he, Misner, and Aage Petersen (Bohr’s assistant) were thinking up "ridiculous things about the implications of quantum mechanics". (see Many Worlds? Everett, Quantum Theory and Reality, Oxford University Press)

PS3 To get a glimpse of the mind-boggling complexity of $3N$-dimensional space, think of the big leaps form 1d to 2d and from 2d to 3d, and then imagine the leap to the 6d of the two electrons of Helium with $N=2$ as the simplest of all atoms beyond Hydrogen with $N=1$. In this perspective a single Helium atom as quantum computer could be imagined to have the computational power of a laptop. Yes, many dimensions and many worlds are mind-boggling, and as such maybe just phantasy.

lördag 14 januari 2017

The Quantum Manifesto Contradiction

The Quantum Manifesto calls upon Member States and the European Commission to launch a €1 billion Flagship-scale Initiative in Quantum Technology, preparing for a start in 2018 within the European H2020 research and innovation framework programme.

The scientific basis of the Manifesto is: 
  • With quantum theory now fully established, we are required to look at the world in a fundamentally new way: objects can be in different states at the same time (superposition) and can be deeply connected without any direct physical interaction (entanglement).
The idea is that superposition and entanglement will open capabilities beyond imagination:
  • This initiative aims to place Europe at the forefront of the second quantum revolution now unfolding worldwide, bringing transformative advances to science, industry and society. It will create new commercial opportunities addressing global challenges, provide strategic capabilities for security and seed as yet unimagined capabilities for the future. As is now happening around the world, developing Europe’s capabilities in quantum technologies will create a new knowledge-based industrial ecosystem, leading to long-term economic, scientific and societal benefits. It will result in a more sustainable, more productive, more entrepreneurial and more secure European Union.
  • Quantum computers are expected to be able to solve, in a few minutes, problems that are unsolvable by the supercomputers of today and tomorrow.
But from where comes the idea that the quantum world is a world of superposition and entanglement? Is it based on observation? No, it is not, because the quantum world is not open to such inspection.  

Instead it comes from theory in the form of a mathematical model named Schrödinger's equation, which is linear and thus allows superposition, and which includes Coulombic forces of attraction and repulsion as forms of instant (spooky) action at distance thus expressing entanglement. 

But Schrödinger's equation is an ad hoc man-made theoretical mathematical model resulting from a purely formal twist of classical mechanics, for which a  deeper scientific rationale is lacking.  Even worse, Schrödinger's equation for an atom with $N$ electrons involves $3N$ space dimensions, which makes computational solution impossible even with $N$ very small.  Accordingly, the Manifesto does not allocate a single penny for solution of Schrödinger's equation, which is nowhere mentioned in the Manifesto. Note that the quantum simulators of the grand plan shown above are not digital solvers of Schrödinger's equation, but Q
  • can be viewed as analogue versions of quantum computers, specially dedicated to reproducing the behaviour of materials at very low temperatures, where quantum phenomena arise and give rise to extraordinary properties. Their main advantage over all-purpose quantum computers is that quantum simulators do not require complete control of each individual component, and thus are simpler to build. 
  • Several platforms for quantum simulators are under development, including ultracold atoms in optical la ices, trapped ions, arrays of superconducting qubits or of quantum dots and photons. In fact, the rst prototypes have already been able to perform simulations beyond what is possible with current supercomputers, although only for some particular problems.
The Quantum Manifesto is thus based on a mathematical model in the form of a multi-dimensional Schrödinger equation suggesting superposition and entanglement, from which the inventive physicist is able to imagine yet unimagined capabilities, while the model itself  is considered to be useless for real exploration of possibilities, because not even a quantum computer can be imagined to solve the equation.  This is yet another expression of quantum contradiction.

Recall that the objective of RealQM is to find a new version of Schrödinger's equation which is computable and can be used for endless digital exploration of the analog quantum world.

See also Quantum Europe May 2017.

onsdag 4 januari 2017

Update of realQM and The Trouble of Quantum Mechanics

I have made an update of realQM as start for the New Year! More updates will follow...

The update contains more computational results (and citations) and includes corrections of some misprints.

The recent book by Bricmont Making Sense of Quantum Mechanics reviews the confusion concerning the meaning of quantum mechanics, which is still after 100 years deeply troubling the prime achievement of modern physics. As only salvation Bricmont brings out the pilot-wave of Bohm from the wardrobe of dismissed theories, seemingly forgetting that it once was put there for good reasons. The net result of the book is thus that quantum mechanics in its present shape does not make sense...which gives me motivation to pursue realQM...and maybe someone else sharing the understanding that science must make sense...see earlier post on Bricmont's book ...

Yes, the trouble of making sense of quantum mechanics is of concern to physicists today, as expressed in the article The Trouble with Quantum Mechanics in the January 2017 issue of The New York Review of Books by Steven Weinberg, sending the following message to the world of science ultimately based on quantum mechanics:
  • The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. Today, despite the great successes of quantum mechanics, arguments continue about its meaning, and its future. 
  • I’m not as sure as I once was about the future of quantum mechanics. It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. 
  • What then must be done about the shortcomings of quantum mechanics? One reasonable response is contained in the legendary advice to inquiring students: “Shut up and calculate!” There is no argument about how to use quantum mechanics, only how to describe what it means, so perhaps the problem is merely one of words. 
  • On the other hand, the problems of understanding measurement in the present form of quantum mechanics may be warning us that the theory needs modification. 
  • The goal in inventing a new theory is to make this happen not by giving measurement any special status in the laws of physics, but as part of what in the post-quantum theory would be the ordinary processes of physics.
  • Unfortunately, these ideas about modifications of quantum mechanics are not only speculative but also vague, and we have no idea how big we should expect the corrections to quantum mechanics to be. Regarding not only this issue, but more generally the future of quantum mechanics, I have to echo Viola in Twelfth Night: “O time, thou must untangle this, not I.” 
Weinberg thus gives little hope that fixing the trouble with quantum mechanics will be possible by human intervention, and so the very origin of the trouble, the multi-dimensional linear Schrödinger equation invented by Schrödinger, must be questioned and then questioned seriously (as was done by Schrödinger propelling him away from the paradigm of quantum mechanics), and not as now simply be accepted as a God-given fact beyond question. This is the starting point of realQM.

Of course Lubos Motl, as an ardent believer in the Copenhagen Interpretation, whatever it may be, does not understand the crackpot troubles/worries of Weinberg.

As an expression of the interest in quantum mechanics still today, you may want to browse the upcoming Conference on 90 Years of Quantum Mechanics presented as:
  • This conference celebrates this magnificent journey that started 90 years ago. Quantum physics mechanics has during this period developed in leaps and bounds and this conference will be devoted to the progress of quantum mechanics since then. It aims to show how universal quantum mechanics is penetrating all of basic physics. Another aim of the conference is to highlight how quantum mechanics is at the heart of most modern science applications and technology.  ago
Note the "leaps and bounds" which may be the troubles Weinberg is referring to...

måndag 19 december 2016

New Quantum Mechanics 21: Micro as Macro

The new quantum mechanics as realQM explored in this sequence of posts offers a model for the microscopic physics of atoms which is of the same form as the classical continuum mechanical models of macroscopic physics such as Maxwell's equations for electro-magnetics, Navier's equations for solid mechanics and Navier-Stokes equations for fluid mechanics in terms of deterministic field variables depending on a common 3d space coordinate and time.

realQM thus describes an atom with $N$ electrons realQM as a nonlinear system of partial differential equations in $N$ electronic wave functions depending on a common 3d space coordinate and time.

On the other hand, the standard model of quantum mechanics, referred to as stdQM, is Schrödinger's equation as a linear partial differential equation for a probabilistic wave function in $3N$ spatial coordinates and time for an atom with $N$ electrons.  

With realQM the mathematical models for macroscopic and microscopic physics thus have the same form and the understanding of physics can then take the same form. Microphysics can then be understood to the same extent as macrophysics.

On the other hand, the understanding of microphysics according to stdQM is viewed to be fundamentally different from that of macroscopic physics, which effectively means that stdQM is not understood at all, as acknowledged by all prominent physicists.

As an example of the confusion on difference, consider what is commonly viewed to be a basic property of stdQM, namely that there is limit to the accuracy that both position and velocity can be determined on atomic scales, as expressed in Heisenberg's Uncertainty Principle (HUP).

This feature of stdQM is compared with the situation in macroscopic physics, where the claim is that both position and velocity can be determined to arbitrary precision, thus making the case that microphysics and microphysics are fundamentally different.

But the position of a macroscopic body cannot be precisely determined by one point coordinate, since  a macroscopic body is extended in space and thus occupies many points in space.  No one single point determines the position of and extended body. There is thus also a Macroscopic Uncertainty Principle (MUP).

The argument is then that if the macroscopic body is a pointlike particle,  then both its position and velocity can have precise values and thus there is no MUP. But a pointlike body is not a macroscopic body and so the argument lacks logic.

The idea supported by stdQM that the microscopic world is so fundamentally different from the macroscopic world that it can never be understood, thus may well lack logic. If so that could open to understanding of microscopic physics for human beings with experience from macroscopic physics.

If you think that there is little need of making sense of stdQM, recall Feynman's testimony:
  • We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I’m an old enough man that I haven’t got to the point that this stuff is obvious to me. Okay, I still get nervous with it ... You know how it always is: every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. I cannot define the real problem, therefore I suspect that there is no real problem, but I’m not sure there’s no real problem. (Int. J. Theoret. Phys. 21, 471 (1982).) 
It is total confusion, if it is totally unclear if there is a problem or no problem and it is totally clear that nobody understands stdQM....

Recall that stdQM is based on a linear multi-dimensional Schrödinger equation, which is simply picked from the sky using black magic ad hoc formalism, which could be anything, and is then taken as a revelation about real physics when interpreted by reversing the black magics. 

This is like scribbling down a sign/equation at random without intentional meaning, and then giving the sign/equation an interpretation as if it had an original meaning, which may well be meaningless, instead of expressing a meaning in a sign/equation to discover consequences and deeper meaning.   

fredag 16 december 2016

New Quantum Mechanics 20: Shell Structure

Further computational exploration of realQM supports the following electronic shell structure of an atom:

Electrons are partitioned into an increasing sequence of main spherical shells $S_1$, $S_2$,..,$S_M$ with each main shell $S_m$ subdivided into two half-spherical shells each of which for $m>2$ is divided into two angular directions into $m\times m$ electron domains thus with a total of $2m^2$ electrons in each full shell $S_m$.  The case $m=2$ is special with the main shell divided radially into two subshells which are each divided into half-spherical subshells each of which is finally divided azimuthally, into $2\times 2$ electron domains for $S_2$ subshell, thus with a total of $2m^2$ electrons in each main shell $S_m$ when fully filled, for $m=1,...,M$, see figs below.

This gives the familiar sequence 2, 8, 18, 32,.. as the number of electrons in each main shell.

4 subshell of S_2
8 shell as variant of full S_2 shell
 9=3x3 halfshell of S_3

The electron structure can thus be described as follows with parenthesis around main shells and radial subshell partition within parenthesis:
  • (2)+(4+4)
  • (2)+(4+4)+(2)
  • ...
  • (2)+(4+4)+(4+4) 
  • (2)+(4+4)+(8)+(2)
  • ....
  • (2)+(4+4)+(18)+(2)
  • ...
  • (2)+(4+4)+(18)+(8)
Below we show computed ground state energies assuming full spherical symmetry with a radial resolution of 1000 mesh points, where the electrons in each subshell are homogenised azimuthally, with the electron subshell structure indicated and table values in parenthesis. Notice that the 8 main shell structure is repeated so that in particular Argon with 18 electrons has the form 2+(4+4)+(4+4):

Lithium (2)+1: -7.55 (-7.48)                  1st ionisation:      (0.2)
Beryllium (2)+(2): -15.14 (-14.57)           1st ionisation: 0.5 (0.35)
Boron (2)+(2+1): -25.3 (-24.53)               1st ionisation: 0.2 (0.3)
Carbon (2)+(2+2): -38.2  (-37.7)               1st ionisation 0.5 (0.4)
Nitrogen (2)+(3+2):  -55.3 (-54.4)            1st ionisation  0.5  (0.5)
Oxygen (2)+(3+3): -75.5 (-74.8)               1st ionisation  0.5  (0.5)
Fluorine (2)+(3+4):  -99.9   (-99.5)            1st ionisation  0.5      (0.65)
Neon (2)+(4+4):   -132.4     (-128.5  )        1st ionisation 0.6        (0.8)
Sodium (2)+(4+4)+(1): -165 (-162)
Magnesium (2)+(4+4)+(2): -202  (-200)
Aluminium (2)+(4+4)+(2+1): -244 (-243)
Silicon (2)+(4+4)+(2+2): -291 (-290)
Phosphorus (2)+(4+4)+(3+2): -340 (-340)
Sulphur (2)+(4+4)+(4+2): -397 (-399)
Chlorine (2)+(4+4)+(3+4): -457 (-461)
Argon: (2)+(4+4)+(4+4): -523 (-526)
Calcium: (2)+(4+4)+(8)+(2): -670 (-680)
Titanium: (2)+(4+4)+(10)+(2): -848 (-853)
Chromium: (2)+(4+4)+(12)+(2): -1039 (-1050)
Iron: (2)+(4+4)+(14)+(2): -1260 (-1272)
Nickel: (2)+(4+4)+(16)+(2): -1516 (-1520)
Zinc: (2)+(4+4)+(18)+(2): -1773 (-1795)
Germanium: (2)+(4+4)+(18)+(2+2): -2089 (-2097)
Selenium: (2)+(4+4)+(18)+(4+2):- 2416 (-2428)
Krypton: (2)+(4+4)+(18)+(4+4): -2766 (-2788)
Xenon: (2)+(4+4)+(18)+(18)+(4+4): -7355  (-7438)
Radon: (2)+(4+4)+(18)+(32)+(18)+(4+4): -22800 (-23560)

We see good agreement even with the crude approximation of azimuthal homogenisation used in the computations.

To see the effect of the subshell structure we compare Neon: (2)+(4+4) with Neon: (2)+(8) without the (4+4) subshell structure, which has a ground state energy of -153, which is much smaller than the observed -128.5.  We conclude that somehow the (4+4) subdivision of the second is preferred before a subdivision without subshells. The difference between (8) and (4+4) is the homogeneous Neumann condition acting between subshells, tending to increase the width of the shell and thus increase the energy.

The deeper reason for this preference remains to describe, but the intuition suggests that it relates to the shape or size of the domain occupied by an electron.  With subshells electron domains are obtained by subdivision in both radial and azimuthal direction, while without subshells there is only azimuthal/angular subdivision of each shell.

We observe that ionisation energies, which are of similar size in different shells, become increasingly small as compared to ground state energies, and thus are delicate to compute as the difference between the ground state energies of atom and ion.

Here are sample outputs for Boron and Magnesium as functions of distance $r$ from the kernel along the horizontal axis :

We observe that the red curve depicting shell charge $\psi^2(r)r^2dr$ per shell radius increment $dr$, is roughly constant in radius $r$, as a possible emergent design principle. More precisely, $\psi (r)\sim \sqrt{Z}/r$ mathches with $d_m\sim m^2/Z$ and $r_m\sim m^3/Z$ with $d_m$ the width of shell $S_m$ and thus the width of the subshells of $S_m$ scaling with $m/Z$, and thus the width of electrons in $S_m$ scaling with $m/Z$.

We thus have $\sum_mm^2\sim M^3\sim Z$ and with $d_m\sim m^2/Z$ the atomic radius $\sum_md_m\sim M^3/Z\sim 1$ is basically the same for all atoms, in accordance with observation.

Further, the kernel potential energy and thus the total energy in $S_m$ scales with $Z^2/m$ and the total energy by summation over shells scales with $\log(M)Z^2\sim \log(Z)Z^2$, in close correspondence with $Z^{\frac{1}{3}}Z^2$ by density functional theory.

Recall that the electron configuration of stdQM is based on the eigen-functions for Schrödinger's equation for the Hydrogen atom with one electron, while as we have seen that of realQM rather relates to spatial partitioning. Of course, eigen-functions express some form of partitioning, and so there is a connection, but the basic problem may concern partitioning of many electrons rather than eigen-functions for one electron.