söndag 19 januari 2014

Tegmark's Unphysical Mathematical Universe

Max Tegmark is now touring to sell his latest book Our Mathematical Universe with the following opening:
  • This book is my quest to explore the ultimate nature of reality, from the microcosm to our universe and beyond. 
Here are some main quotes from the book:
  • When I think about the Copenhagen interpretation I just can't get this Hamlet quote out of my mind: "There is something rotten in the state of Denmark".
  • The wave function never collapses. Ever.
  • The fundamental reason that quantum mechanics appears random even though the wave function evolves deterministically, is that the Schrödinger equation can evolve a wave function with a single you into one with clones of you in parallel universes.
  • So how does it feel to get cloned? It feels random!
Tegmark says that the randomness of quantum mechanics is an illusion resulting from a deterministic multiverse containing the ensemble of all possible versions or clones of yourself or the universe we happen to live. The ensemble of all possible universa thus is made into some kind of reality in Tegmark's multiverse. But this is against principles of both physics and statistics. 

There is a simpler way out of the "rotten state of the Copenhagen interpretation", namely to eliminate as the basis of quantum mechanics the linear multidimensional Schrödinger equation and its solutions as multidimensional wave functions without physical meaning requiring a probabilistic interpretation,  and replace the linear multidimensional Schrödinger with a system of nonlinear wave equations in three space dimensions with solutions having a physical meaning without any need to impose randomness.

The insistence to view atomistic physics to be based on a linear multidimensional wave equation (in 3N space dimensions for an atom with N electrons) without direct physical meaning, is a fundamental mystery of modern physics. Why insist on linearity? Why insist on 3 independent space dimensions for each particle without any common space to share? Why start out with an equation without physical interpretation which forces a probabilistic interpretation, as if physics is a giant insurance company?

Ockham's principle says that you should not ad hoc assume anything which makes things more complicated than necessary. Nothing dictates that quantum mechanics must be based on a unphysical linear wave equation in multi dimensions. At least what I can see.

The simpler way avoiding these unsurmountable unnecessary ("rotten") complications, is to go back to the original idea of Schrödinger, who together with Einstein never accepted a probabilistic interpretation of quantum mechanics. One possibility in this direction is explored in Many-Minds Quantum Mechanics. Here the world is one, but there are many perspectives on the world. Have a look from your perspective!

PS My question to Max what makes him believe in a linear multidimensional wave equation asking for  the Copenhagen interpretation, which Max says is rotten, did not get any answer. Instead of answering my question, Max asked me a question. I have met this tactic in discussions with both climate scientists and physicists, which may be quite effective in science. But it would be ridiculus for politician when asked a question by a journalist to turn the situation around and instead subject the journalist to interrogation, instead of answering the question posed. But here I am the journalist and my question remains to be answered. 

23 kommentarer:

  1. Claes, I think you are mixing up to different discussions here. I agree that there is something rotten about talking about a multidimensional schrödinger equation as a fundament of physics but never solving it. Instead most people go about solving some variant of many-minds, like density functional theory and so on.

    However, the double slit experiment can be performed with only one electron which does not require MDSE. How do you explain the outcome?

  2. How do you know that you are dealing with just one electron? What is an electron?

  3. I don't know the answers to the questions you just posed, but I guess they could be thrown back at you any time. Anyhow, how do you explain the double slit experiment with the substance we call/believe to be "electrons" ?

  4. In any case I don't think we need that level of profundity to make the distinction between a multi-universe and a multi-dimensional schrödinger equation. I'm sure you can appreciate that distinction.

  5. Hej Claes: it sounds like you're making the controversial claim that that the many-minds interpretation elegantly solves the quantum measurement problem. Which version of the many-minds interpretation are you advocating? That of Don Page?

  6. Max: I am not making any claim, in this context. Instead I ask you what makes you start from a linear multidimensional wave equation which you describe yourself as somehow "rotten". It seems to me that you are led into multiverse from the probabilistic interpretation quantum mechanics? Is that correct?

  7. Anders: The double slit exp is explained by wave mech, but does not need probablistics, or?

  8. The double slit exp is explained by wave mech, but does not need probablistics, or?

    How do you want to explain the observation that measurement of which slit was used reduces the apparatus into two single slits with no interference, while during no measurement the interference is there?

  9. Of course measurement may interfere with the phenomenon being measured, but I don't see you need probabilistics to understand that. Probabilistics is introduced when you do not understand, and so does not help understanding.

  10. Well, to express myself more clearly.

    This effect persist even when the intensity of the incident beam is adjusted so that only one electron (at least the overwhelmingly majority of them) resides in the apparatus in one instance. Before you doubt this, please read up on the literature on designing thermionic and field emission electron sources for microscopes.

    So the question still stands.

  11. If the double-slit needs statistics is at the very heart of the discussion. I though you had a solution to that with many-minds. It appears as if the detector doesn't pick up an electron "wave" but rather particles at certain distinct positions. Bohr solved this by interpreting the square of the wave function as a probability function. How do you interpret the wave-function?

  12. I still miss a compelling reason to introduce statistics which is the same as to give in to irrational unexplicable pseudo-science. If there is something about the double-slit experiment that deterministic wave mechanics cannot explain, let it be with that and continue to seek an explanation without statistics. What is the interest of making an extreme experiment with just one electron at a time, which is very tricky, and then from this extreme situation draw far-reaching extreme conclusions about everything which is not extreme? I don't think this is necessary nor constructive, since it ruins physics into meaningless multiversa.

  13. If you give up the linear multid wave equation as an ad hoc assumption picke from the sky, then there will be no multid wave function to give a physical meaning.
    Better is to take the Hartree approach with a set of 3d wave functions, one for each electron, sharing a common 3d space, and interacting by Coulomb forces with the 3d wave function for an electron representing the "presence" of the electron. This is quantum mechanics as deterministic wave mechanics without imposed statistics.

  14. Better is to take the Hartree approach with a set of 3d wave functions


    The Hartree approach performs poorly compared to methods that incorporate more than just a mean field Coulomb interaction.

    From the summary of a "random" (first that "popped up") paper comparing different computational methods with the Hartree method included. PRB 47, 2244 (1993) (Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium)
    We have compared the energy, the electron density,
    and the correlation function of the singlet and triplet
    helium calculated in the
    ground state of quantum-dot helium calculated in the
    Hartree and HF approximation with the exact quanti-
    ties. As expected, the results of the Hartree approxima-
    tion show strong deviations due to the unphysical self-
    which enters this approximation and which is of
    the same order of magnitude as the interaction energy
    between both electrons.

  15. Jag har inte sagt att standard Hartree är lösningen på alla problem. Det jag säger är att statistik inte är fysik och att tvinga elektroner att spela roulette är korkat, eftersom det skapar många fler problem än det löser.

  16. Jag har inte sagt att standard Hartree är lösningen på alla problem.

    Well, to be honest, it is rarely the solution to any problem at all. Due to it's unphysical deviation (that is greater than more refined methods) from a more correct description of electron interaction. Only in the case where your computational resources are extremely limited it could be justified I guess (in practice that was many years ago).

    Regarding the statistics. As it is used in practice, quantum mechanics is a theory that makes quantitative predictions based on expectation values, that themselves can be compared with expectation values collected in repeated experiments. If it makes you uneasy to think of quantum mechanics as a theory, think of quantum mechanics as a model then instead.

    You seem to be focusing on the wrong issues regarding quantum mechanics and modern physics, the most interesting applications in my opinion is connected to the study of materials and nano-scale engineering. Do yourself a favour and look into these fields instead of string-theory and other minority fields of physics. The bulk of interesting modern physics isn't in those kind of exotic subjects but in condensed matter.

  17. The post was stimulated by Tegmark's view that "there is something rotten with the Copenhagen interpretation" and what is rotten is statistics and it is rotten because statistics is not physics, and to base physics on a rotten foundation is what opens to the multiversa and the like. What is needed is a fresh healthy solid foundation and not a rotten swamp.

  18. I think you need to correlate your view on what physics is.

    Physics is the collection of models and theories that are used to describe and make predictions about certain kinds of observations of nature. Discarding statistical descriptions from this set is borderline moronic, at best ;)

  19. Tegmark says that the Copenhagen interpretation is rotten and I agree, and if so physics is in bad shape, regardless of all excuses that can be invented to turn the rottenness into virtue.

  20. Det jag säger är att statistik inte är fysik och att tvinga elektroner att spela roulette är korkat, eftersom det skapar många fler problem än det löser.

    Har du gjort någon kartläggning och analys som stöder det här påståendet? Eller är det enbart retorik?

  21. Fråga Tegmark varför han säger att Copenhagen Interpretation (statistisk tolkning) är rutten. Också Einstein och Schrödinger ansåg detta. Där har Du en form av kartläggning och analys, men det finns många många fler som tycker att CI är rutten.
    Vad tycker Du?

  22. I all välmening, du verkar blanda ihop ett par fundamentala begrepp.

    Köpenhamnstolkningen är inte det samma som en statistisk tolkning, även om den är indeterministisk. De flesta kvantmekaniska tolkningarna är indeterministiska (Bohmska tolkningen är ett undantag. Finns kanske fler?). Köpenhamnstolkningens signum är väl kollapsen av vågfunktionen som sker vid en mätning inom denna tolkning. Utan att ha läst den aktuella boken av Tegmark är jag ganska säker på att det är problemen med denna kollaps som är 'rotten'.

  23. Exakt vad som är ruttet kanske tillhör avdelning hårklyverier?