måndag 17 juni 2013

Welcome Back Reality: Many-Minds Quantum Mechanics

The new book Farewell to Reality by Jim Baggott gets a positive reception on Not Even Wrong (and accordingly a negative by Lubos). The main message of the book is that modern physics (SUSY, GUTS, Superstring/M-theory, the multiverse) is no longer connected to reality in the sense that experimental support is no longer possible and therefore is not considered to even be needed.

But science without connection to reality is pseudo-science, and so how can it be that physics classically considered to be the model of all sciences, in modern times seems to have evolved into pseudo-science? Let's take a look back and see if we can find an answer:

My view is that the departure from reality started in the 1920s with the introduction of the multi-dimensional wave function as solution to a linear scalar Schrödinger equation, with 3N space dimensions for an atom with N electrons. Such a wave function does not describe real physics, since reality has only 3 space dimensions and the only way out insisting on the truth of the linear Schrödinger equation as given by God,  was to give the wave function a statistical interpretation. But that meant a non-physical and non-real interpretation, since there is no reason to believe that real physics can operate like an insurance company filled with experts doing statistics, in Einstein's words expressed as "God does not play dice".  The statistical interpretation was so disgusting to Schrödinger that he gave up further exploration of the quantum mechanics he had invented. 

Schrödinger believed that the wave function had a physical meaning as a description of the electron distribution around a positive kernel of an atom. A non-linear variant of the Schrödinger equation in the form of a system of N equations in 3 space dimensions for an N-electron atom was early on suggested by Hartree as a method to compute approximate solutions of the multi-dimensional Schrödinger, an equation which cannot be solved, and the corresponding wave function can be given a physical meaning as required by Schrödinger. I have explored this idea a little bit in the form of Many-Minds Quantum Mechanics (MMQM) as an analog of Many-Minds Relativity.

MMQM seems to deliver a ground state of Helium corresponding to the observed minimal energy E = - 2.904,  with the 2 electrons of Helium distributed basically as two half-spherical shells (blue and green patches) filling a full shell around the kernel (red) as illustrated in the left picture. This configuration is to be compared with the spherically symmetric distributions of Parahelium 1s1s (hydrogenic orbital) in the middle with E = -2.75 and Ortohelium 1s2s with even bigger energy to the right:

Classical quantum mechanics based on a multi-dimenisonal wave function satisfying the linear Schrödinger equation (QM) presents Parahelium as the ground state of Helium with the two electrons sharing a common spherically symmetric orbit in accordance with the Pauli Exclusion principle (PEP).  But the energy E = -2.75 of Parahelium is greater than the observed E = -2.904 and so Parahelium cannot be the ground state.

QM with PEP thus does not describe even Helium correctly, a fact which is hidden in text books, while the non-spherical distribution of MMQM appears to give the correct energy.

MMQM does not require any PEP and suggests a different explanation of the electronic shell structure of an atom with the numbers of 2, 8, 8, 18, 18... of electrons in each shell arising as 2 x n x n, with n=1,  2, 2, 3, 3, and the factor 2 reflecting the structure of the innermost shell as that of Helium, and n x n the two-dimensional aspect of a shell.

The Farewell to Reality from modern physics was thus initiated with the introduction of the multi-dimensional wave function of the linear Schrödinger equation of QM in the 1920s, and the distance to Reality has only increased since then.  Once the connection the Reality is given up there is no limit to how far you can go with your favorite theory.

QM is cut in stone as the linear multidimensional Schrödinger equation with wave function solution being either symmetric or antisymmetric and satisfying PEP, but QM in this form lacks real physical interpretation.

The exploration of non-linear Schrödinger equations in 3 space dimensions with obvious possibilities of physical interpretation, has been pursued only as a way to compute approximate solutions to the multi-dimensional linear Schrödinger equation, but may merit attention also as true models of physical reality.   

23 kommentarer:

  1. Like you, I am a "realist", and would insist QM is not a theory of physical reality. Most importantly, in my mind, you mention the electron distribution within the atom, which Dr. Robert G. Brown also discussed recently, at Bishop Hill. I will say here the same thing I said there, on what I consider a crucial point about assumption vs. reality in the matter of atomic electrons:

    "Prove that atomic electrons (electrons inside the 'atom') even exist, as the electrons we know outside of the atom, Dr. Brown. Once you've assured yourself that they don't (and won a Nobel prize for what others have known for a long time now--read Dewey Larson's 'The Case Against the Nuclear Atom'), then you will appreciate how hard it is to get climate scientists to accept that CO2 has nothing to do with global warming. The structure of the atomic electron cloud and the CO2 greenhouse effect are the same thing: They are both wrong physics, but 'settled science'."

  2. What exactly is the problem with a many-body wavefunction?

    The usual interpretation is that the wavefunction is not a physical object, but a mathematical one. The wavefunction gives different physical observables, with physical meaning, when operated on. In a similar way that we use the vector potential in electrodynamics.

  3. Statistics is not real physics and the many dimensions of the wave function asks for statistics while the 3d vector pot does not.

  4. What do you mean with real physics?

    It sure has predictive power of real experimental outcomes in the form of observables.

    What else can you know about these systems?

  5. Oh sorry. I had one more question.

    Are you saying that the vector potential is real? And I was actually thinking about the 4-dimensional potential to be honest. I should not have called it vector potential, four-potential is a more appropriate name. Just being a bit sloppy.

  6. If you really want to test the validity of your theory you shouldn't calculate something trivial, like atom ground states.

    As a first step you should calculate something where conventional methods, like Hartree Fock and DFT performs poorly, like bandgaps in semiconductors.

    Do you have any plans of such calculations?

  7. Do you have a reference that QM predicts a groundstate energy of E0 = -2.75Eh

    Since the empirical value is -2.90Eh, my guess is that the calculation you have seen uses some approximation like low order perturbation.

    Using more sophisticated methods there is no problem in getting a converged result that predicts -2.90Eh.

  8. Yes, in Bransden, "Physics of Atoms and Molecules" I found that a ground state energy of He is -2.75 when doing a calculation with first order perturbation.

    In fact, in that book it is further stated that the groundstate of He is one of the most accurate theoretical numbers which has been calculated using quantum mechanics.

    It gives some references and among other states a theoretical value of

    E0 = -2.90372427703411959813

    That number is accurate to about one part in 10^19.

    So your suggestion that quantum mechanics isn't able to describe the groundstate of He correctly just isn't true.

  9. Why is it nec to use perturbations if QM is so perfect? The supposed ground state with two spherically sym electrons on top of each other has too big energy, and so what does the correct ground state look like?

  10. According to quantum mechanics the correct groundstate is 1s² necessarily a singlet state (that is anti-parallel spins). The energy for the lowest energy state as measured is extremely well correlated with theoretical calculations as stated in the comment above. So what's the problem?

    Further, there is no triplet (parallel spins) in 1s².

    First excited state is 1s2s triplet.

    Second excited state is 1s2s singlet.

  11. The 1s^2 state does not have minimal energy and thus is not the ground state.

  12. I think you need to provide a good source showing that it is not the ground state.

    Here is a typical diagram for the helium energy states

    Energy states for para- (left) and ortho-(right) helium

    The 1s² is by far the lowest level.

  13. Here is a good source: Hutchinson, Baker and Marsiglio: The Spectral Decomposition of the Helium atom two-electron configuration in terms of Hydrogenic orbitals, arXiv, Nov 22, 2012.

  14. Ok, point taken.

    But what does it change?

    The article further focuses on an antisymmetric singlet state.

    It is still basic quantum mechanics, correctly describing the He-atom with spin statistics.

    The article seems really interesting by the way, thanks!

  15. My basic criticism is that the multiD wave function is way too rich to be meaningful as an object of scientific study and that the real challenge is to find less rich models (systems of non-linear wave equations in 3 space dim) of Hartree-Kohn type which are computable and thus potentially meaningful. The multiD wave equation is an uncomputable monster which should not be allowed to enter into physics.

  16. Ok, but there is already a direct bridge between a many body wavefunction and an easier function that gives us observables through the Hohenberg-Kohn theorems. Unfortunate is the functional link between them unknown so approximations must be made. But in principle they are equivalent.

    This equivalent form is very often used.

    I still don't understand what there is to be upset about.

  17. The statistical interpretation of the multiD wave function represents pseudo-science and that is upsetting. Once you resort to pseudo-science you have given your scientific soul away like Dr Faustus and you can only continue on a road which leads no-where as illustrated by string theory.

  18. Pseudoscience?

    It stems from a set of postulates, motivated by empirical observations, that further makes quantitative predictions that can be tested against experiments. It's is fully falsifiable.

    I do want you to explain one observed phenomenon. Please explain entanglement.

  19. Is entanglement really a real phenomenon or just an imagined phenomenon suggested by multiD wave functions?

  20. Have you looked deeper into the experimental field of quantum optics?

  21. Entanglement in quantum optics seems to be more of a dream than reality.

  22. I wonder if this observation may have a relationship with how Helium behaves in the superfluid state. I included my own perspective in “The superfluid state: a chain of tightly coupled atoms”
    This also takes the perspective that the electrons are spherically distributed.