Wednesday, November 05, 2014

The paradigm shift you didn’t notice

Inertia creeps.

Today, for the first time in human history a scientist has written this sentence – or so would be my summary of most science headlines I read these days. Not only do the media buy rotten fish, they actually try to resell them. The irony is though that the developments which really change the way we think and live happen so gradually you wouldn’t ever learn about them in these screaming headlines.

HIV infection for example still hasn’t been cured, but decades of hard work turned it from a fatal disease into a treatable one. You read about this in longwinded essays in the back pages where nobody looks, but not on the cover page and not in your news feed. The real change didn’t come about by this one baby who smiles on the photo and who was allegedly cured, as the boldface said, but by the hundreds of trials and papers and conferences in the background.

These slow changes also happen in physics. Quantum measurement is a decoherence process rather than collapse. This doesn’t break the ground but slowly moves it. It’s an interpretational shift that has spread through the community. Similarly, it is now generally accepted that most infinities in quantum field theory do not signal a breakdown of the theory but can be dealt with by suitable calculational methods.

For me the most remarkable shift that has taken place in physics in the last decades is the technical development and, with it, acceptance of renormalization group flow and effective field theories. If this sounds over your head, bear with me for I’m not going into the details, I just want to tell you why it matters.

You have certainly heard that some quantum field theories are sick and don’t make sense – they are said to be non-renormalizable. In such a theory the previously mentioned infinities cannot be removed, or they can only be removed on the expense of introducing infinitely many free parameters which makes the theory useless. Half a century ago a theory with this disease was declared dead and went where theories go to die, into the history aisle.

Then it became increasingly clear that such non-renormalizable theories can be low-energy approximations to other theories that are healthy and renormalizable. The infinities are artifacts of the approximation and appear if one applies the approximation outside its regime of validity.

These approximations at low energies are said to be “effective” theories and they typically contain particles or degrees of freedom that are not fundamental, but instead “emergent”, which is to say they are good descriptions as long as you don’t probe them with too high energy. The theory that is good also at high energies is said to be the “UV completion” of the effective theory. (If you ever want to fake a physics PhD just say “in the IR” instead of “at low energy” and “UV” instead of “high energy”.)

A typical example for an effective theory is the nuclear force between neutrons and protons. These are not fundamental particles – we know that they are made of quarks and gluons. But for nuclear physics, at energies too small to test the quark substructure, one can treat the neutrons and protons as particles in their own right. The interaction between them is then effectively mediated by a pion, a particle that is itself composed of two quarks.

Fermi’s theory of beta-decay is a historically very important case because it brought out the origin of non-renormalizability. We know today that the weak interaction is mediated by massive gauge-bosons, the W’s and the Z. But at energies so low that one cannot probe the production and subsequent decay of these gauge bosons, the weak interaction can be effectively described without them. When a neutron undergoes beta decay, it turns into a proton and emits an electron and electron-anti-neutrino. If you do not take into account that this happens because one of the quark constituents emits a W-boson, then you are left with a four-fermion interaction with a coupling constant that depends on the mass of the W-boson. This theory is not renormalizable. Its UV completion is the standard model.

Upper image: One of the neutron's quark constituents interacts via a gauge boson with an
electron. Bottom image: If you neglect the quark substructure and the boson-exchange, you get a four-fermion interaction with a coupling that depends on the mass of the boson and which is non-renormalizable.

So now we live and work with the awareness that any quantum field theories is only one in a space of theories that can morph into each other, and the expression of the theory changes with the energy scale at which we probe the physics. A non-renormalizable theory is perfectly fine in its regime of validity. And thus today these theories are not declared dead any longer, they are declared incomplete. A theory might have other shortcomings than being non-renormalizable, for example because it contains dimensionless constants much larger than (or smaller than) one. Such a theory is called unnatural. In this case too you would now not simply discard the theory but look for its UV completion.

It is often said that physicists do not know how to quantize gravity. This isn’t true though. Gravity can be quantized just like the other interactions; the result is known as “perturbatively quantized gravity”. The problem is that the theory one gets this way is non-renormalizable, which is why it isn’t referred to as quantum gravity proper. The theory of quantum gravity that we do not know is the UV-completion of this non-renormalizable perturbative quantization. (It cannot be non-renormalizable in the same way as Fermi’s theory because gravity is a long-range interaction. We know that gravitons, if they have masses at all, have tiny masses.)

But our improved understanding of how quantum field theories at different energies belong together has done more than increasing our acceptance of theory with problems. The effective field theory framework is the tool that binds together, at least theoretically, the different disciplines in physics and in the sciences. No longer are elementary particle physics and nuclear physics and atomic physics and molecular physics different, disconnected layers of reality. Even though we cannot (yet) derive most of the relations between the models used in these disciplines, we know that they are connected through the effective field theory framework. And at high energies many physicists believe it all goes back to just one “theory of everything”. Don’t expect a big headline announcing its appearance though. The ground moves slowly.


    Pellucid essay!

    "We know that gravitons, if they have masses at all, have tiny masses" Discard undetectable dark matter. Gravitation grows stronger with distance re Tully-Fisher. But galaxy clusters? Milgrom acceleration arises from testable vacuum trace chirality toward hadrons (fermion quarks). Relativistic electrons are chiral. Velocity is POV not fundamental.

    The greatest obstacle to understanding reality is not ignorance but the illusion of knowledge. Reality is not a peer vote. Assume (Aristotle) and model (economics), but look (Galileo, Popper) at risky contradictions, not only at safe confirmations.

  2. In AWT the matter and space are emergent continuum of underlying material inhomogeneous space-time phase. The problem is, the physicists have no idea, what topology they're actually trying to describe. They're trying to integrate the fractal structure similar to Alexander horned sphere - which is fuzzy in addition. We can describe this hyperdimensional structure only with approximate, effective and phenomenological models with using of low-dimensional theories, like the quantum mechanics and general relativity.

    The quantum field theory community now behaves like the alchemists with respect to search for Philosopher stone. We could distinguish two main groups there in essence. These smarter and more pragmatic ones tried to cover the actual scope and complexity of this task for not to lose the perspective of their jobs prematurely in the eyes of sponsors. These more stupid ones simply had no idea, that their quest has no chance for success with existing tools and paradigms and they did promote it from pure naivety.

    Now, the only question remains, into which group our Bee belongs...?

  3. Next Exit: I have moved your comments into the next exit because they contain links to your page. You seem to be new here, so please go and read our comment rules. I do not tolerate links for the sake of self-promotion. We all know how SEO works and this blog will not indirectly approve of your work, which I do not know, by letting links to your homepage stand here. Best,


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  5. "And at high energies many physicists believe it all goes back to just one “theory of everything”. Don’t expect a big headline announcing its appearance though. The ground moves slowly."

    I've simply offered the holy grail should you be interested to pursue it further. We all have a lot to learn, it would seem.

  6. Zephir,

    Are you asking us to choose between turtles all the way up and all the way down or turtles moving in a row?

    I am not sure what your point intends us to imply as to your remaining question. But the art in itself was good and the problems they hint at. Where do you think you or me would fit in for that question?

    I am naive to imagine alchemy and astrology an early form of science progress vague before crystallization and philosophically something the next generation of thinkers find to look down upon. Can we not turn lead into gold yet the energy gain is the deeper question?

    I do not think very much of ideas of renormalization, certainly in the realm of vague incomplete theory and a face saving concept for our quanta as a measure of ignorance of a possible, even magical sense of focusing a "holy grail" theory of everything. And I find even when things like cures are known the pace is excruciatingly slow. Ebola much like HIV the current example. No funding all projects are orphans, no return on investment, no promoted need. Nothing but getting in bed with the monkeys in the primal jungle of inquiry.

    So as in the horny landscape art, the vague speculation became rather focused yesterday, or my orientation walking by old buildings in some phantom sense like fung shui but deeper: Mass and Memory, reconsidered for old and new thought experiments as physics. (Look, I am ahead of the game in any case by knowing just how lost I am - think about that Zephir).

    Each building contained memories including my own as a passer by in other times. A bridge rebuilt with the same material but a little more mangled to retrieve. A brick layer who recalled one speck or dint somewhere deep within of his tens of thousands of lain bricks- what he had for dinner that day... also part of the bigger picture.

    But is such a thought not a reasonable speculation in this constant debate as to what we mean by gauge theory, Weyl or Otherwise?

  7. My hope, as an independent researcher, is to bring together facets of a changing world so that we may pass through the doorways of discovery with the least amount of turbulence.

    Growing pains can be awful, but once we are through that phase, a breath of fresh air and opportunity for real and lasting understanding can take hold across the planet.

    A Paradigm is a set of assumptions, concepts, values, and practices that constitutes a way of viewing reality for the community that shares them. Not everyone shares them where mainstream physics is concerned.

    I would agree that a paradigm shift of unlikely proportions is upon us, and I whole heartedly disagree that "the ground moves slowly."

    What I'm finding is that there are a group of people moving and advancing our understanding at such a rapid pace, it's unprecedented how quickly things are happening now.

    Most of us don’t even know the transition has been made, or that the corner has been turned. I believe that it has.

    It is up to us as individuals in all our fields of endeavor to break free of the chains of education, and to use our intelligence to create a better understanding of our Universe.

    Geometry rules our Universe not math.

    While mathematics is the language of science it remains a language that lacks a well defined physical model on which to test it and further its many and varied solutions to quantum mechanics. it is this lack of any rigid, enforceable geometry [grammar] that has allowed the flourishing of numerous statistical and probabilistic solutions to the physical problems in turn impending our scientific advancement of quantum processes.

    Tetryonics offers the world a gift, but so many 'experts' in the field won't even spend 3 minutes with the material before passing judgement, and we all wonder why process is so painstakingly slow. It's heartbreaking in all actuality. Do we want answers, or not?

    Humanity has shifted, and all I'm doing is trying to share knowledge. Tetryonics has nothing to sell, only wisdom to share. The lips of wisdom are now closed, except to the ears of Understanding.

  8. @Exit Next: 356 words? Nobel Laureate Henry Taube: "Explain it with a swizzle stick and a cocktail napkin, or you cannot explain it."

    Creutz-Taube ion: Taube-designed, Creutz-discovered when the Cary ran past 1600 cm^(-1) during lunch.

    34 words. 9.6% of your maunder, and it has a citation: DOI: 10.1021/ja01042a072

  9. Alice,

    The last to go are (post mitotic)neurons.
    The last to notice are neurons.
    The last to notice what?
    That the rest of you (your mitotic cells) is the ship of Theseus.
    For what?
    The neurological paradigm shift

    Brainy Bob

  10. Very nice writing, I completely agree. An important thing now is to spread the message of these modern findings, bring them "down to earth" and replace the many (old) misconceptions out there. You are doing an excellent job with this BLOG and I hope you keep doing so.

  11. In principle, I do not disagree with you, especially since I know how much you care about open fundamental question.

    I think one should, however, be careful with the statement that saying "that physicists do not know how to quantize gravity" wasn't true. Such a statement can easily lead to big misunderstanding, since it seems to imply the opposite: that physicist do know how to quantise gravity, which completely ignores, that there is another, still open question, which is IF to quantise gravity is the right thing to do at all. And I have the feeling that the ignorance of this question is very far spread among physicists.

    The situation is different for gravity than it has been with Fermi's theory. Though Fermi's theory was known to not be renormalisable, it could be tested experimentally against other - particularly classical - theories, and could be shown to work well in the appropriate limit.

    This is not the case, yet, for gravity, where the believe that - whatever quantum theory it might be the limit of - perturbatively quantised gravity is right, comes solely from the analogy of the gravitational field with other classical fields. An analogy that might very well turn out to be misguiding, since the philosophical ideas behind GR as well as its mathematical structure feature notable differences to other fields.

    Hence, I prefer to continue saying that physicists do not know how to deal with gravity in the quantum regime, since this at least does not conceal the fact that there are a lot of open questions.

  12. Very nice article. I do think, however, that the particular case of effective field theories being good theories in their own right was well reported in the media. Mainly because Wilson won the Nobel prize for the renormalization group and low-energy effective field theories. Of course, new insights and applications have been obtained, but the idea is the same. Also, I know everyone is going to sigh when I write this, but I can't resist and complain that "Quantum measurement is a decoherence process rather than collapse." is a might need some nuance. This answer is put forward often and I think it is detrimental to discussion especially for newcomers to the field. Unless you are a believer in many-worlds, the fact that a reduced density matrix in a pointer basis is obtained is not an explanation why we perceive there is a single measurement outcome.

    Anyway, love your blog! Keep up the great work!

  13. Hum Bug: Note that I carefully did not say that decoherence solves the measurement problem...

  14. Guess it all depends on what you mean by measurement.. If by quantum measurement you mean some process in which you do not have a single outcome then, you can say "Quantum measurement is a decoherence process rather than collapse.", but it is a bit confusing to call it measurement. I don't know what you want to say with that sentence unless it's something like: Systems rapidly lose their coherence in some preferred basis the more macroscopic it becomes, which is a process in time and not instantaneous. This is something which does not seem like "measurement", however. In any case, forgive my nitpicking. I understand what you wanted to say.

  15. @ Uncle Al - I couldn't agree with you more about explaining quantum mechanics on the back of a napkin. I can do just that and even have room to spare. The thing to realize here is that Geometry is king, Math is okay, and English sucks in comparison to the descriptive qualities that the geometric relations provide. We can highlight key components of any system with images and instantly recognize what pages and pages of math never could. Many books would then be necessary to translate the insights into a step by step explanation of things in sentence form.

    Here are 30 words to change the world.

    "Energy is Equilateral, with a plus and a negative side and has equal but orthogonal Electric and Magnetic-field components, joining into larger Equilateral EM fields, resulting in 'square' numbered geometries."

    Obviously a little image would better suffice, but I'm not sure where I could upload and link it without my comments being removed. I'd encourage you to seek out the Tetryonic solution that unifies Planck with Einstein. I can describe the flaw in excruciating detail using English word combinations, but the images themselves reveal the underlying error better than words ever will.

    A closer examination of the geometries we are describing highlights a long-standing error is the mathematical formulation of QM energy formulae, namely the mistaken interchanging of Planck's quanta [v] for Einstein’s frequency [f] in relation to energy.

    It in fact, takes 2 charged Bosons [hv] to create a neutral Photon [hf] mathematically equating the two, as has been the case historically, is the same as saying 2=1.

    hv does not equal hf and this must be corrected in every text book moving forward if science is to progress. Rather [2hv=hf] highlighting that modern physics has yet to distinguish between even and odd numbers of energy quanta.

  16. Exit Next

    Not bad for a 19th century theory.

    2 and 1 and zero and -1 are very special numbers. The problem is that we have not confused 1 and 0 this wise and every future formulas will have to consider this.

    2=0 if we divide by zero is strictly the sum of parts of a geometric structure in odd and even dimensions.

    Now tell me, what is the fourth root of minus one? Don't bother to look it up for textbooks give different answers. All is not such geometry.

  17. @ L. Edgar Otto - Irrational numbers pop up everywhere, and have been a constant frustration and source of many theses for mathematicians investigating where they come from and what their source is. In this particular case the square root of Negative One is that of a very real charged energy geometry. Despite it being a Negative charge geometry, it still possesses a real [non-negative] linear momentum.

    It is simply the orientation of M-dipole fields that determines the ‘charge’ of any energy moment quanta. Magnetic monopoles do not exist and the search for them is absurd. The root of a negative charge is equal in magnitude and identical to that of a positive linear momenta. In fact it is the opposite side of the same quantum energy geometry.

    Geometrically revealing that the square root of a negative charge geometry has a real [non-negative] integer linear momentum value identical to its Lorentz transformed Positive value. The square root of -1 can never be a negative. Thus revealing one of the inherent weakness of using math without the foundational ‘grammar’ of geometry in physics.

    A lot of the irrational numbers stem from the square root of 3 over 2 or the height of an equilateral geometry. Sin 60 and Cos 60 crop up because our mathematics has a hard time rationally or correctly explaining what geometry alone can show you. The math will just go on and on for the square root of 3 on 2, and for sin 60. But when you draw the altitude of an equilateral triangle, or the angle within an equilateral triangle, it's fixed. It doesn't go on and on. It is what it is, and that's why geometry is superior than the mathematics when learning quantum mechanics and QED.

    In fact, all science as we move further and further on will employ geometry to set up an intuitive understanding that mathematics has failed to provide.

    All the math you want, all accurate, nothing wrong with the math. The problem with math is it's hard for people to visualize and then to understand as they are learning it. It's harder to grade people on it, so far as their understanding of what's been going. And when it comes to extrapolating from the math, there are no rigid guideline as to what can and what cannot be done. All things are equally possible. And that's led to our past 50 or 60 years of many wild theories and possibilities such as string theory, M theory, Black Holes. They are all extrapolations of the math where it's not precluded until you use the Equilateral Geometry of Tetryonics. In which case, a lot of things suddenly become precluded and we then have a rigid framework to build our mathematics even further.

    All of the source of mysteries and problems in mathematics within physics come back to equilateral geometries of energy.

  18. Exit Next

    The height of an equilateral triangle if we put in the values pi and e does not quite give an exact value- it is on the order of about .002 difference which is not easy to see by simple drawing. There is more than one way to inscribe squares in a various triangles.

    We can take six equal lengths and intersect them different ways to get different (say diamond jack of two or three sets of them for a crystal or in flat 3 space a large six sided hexagon like figure that contains more area than an equilateral hexagon by about the same .002 error.

    You only think you agree with Uncle AI - but I am nobody to discourage you or anyone interested in such inquiry. An equilateral triangle results from three trisections of any triangle in the center- now follow down that and ask yourself how such a simple observation escaped us even since the time of Euclid.

  19. Yeah, I like this post; this is why I like SUSY, it potentially explains a good deal about the transition between effective theories. Recently I read about how Galoy's error-correcting code based on 24-bit strings is related to Leech's packing lattice for 24-dimensional hypersheres, the inspiration for Conway's three sporadic groups; is it possible that all error-correcting codes correspond to groups? I can't help but wonder . . .

    The only way paradigm shifts in science elicit major headlines is if they lead to a new, more proficient, weapon of mass extinction . . . sad to say . . .

    California dreaming . . .

  20. Wes

    Good comment. I think we have a too restricted application of the group idea. Would SUSY be as clear as to what say Five Dimensions mean if it can be shown there is also a correspondence of such Lattices, only they begin in the next order of structures based on 240 dimensional hyperstrings so to speak?

    Note also that 240 eight dimensional hyperspheres surround a central one as far as the packing goes.

  21. Somehow in a bad year it is encouraging to read someone who knows physics as well as you do. Perhaps there is some hope for the human race.

  22. The Graviton is not a Messenger is the title of my next article.
    Considering it as a messenger is the source of the UV catastrophe. Picture it as quantized energy state of space-time in this way GR is seamlessly integrated.

  23. There is a beautifull application of the effective QFT approach to Regge quantum gravity, see
    arxiv:1407.1394, 1407.1124 and 1402.4672. When the edge lengths of a spacetime triangulation are
    much larger than the Planck length and if the number of triangles is large, then the effective theory is the perturbative QFT for GR and matter with a cutoff which is determined by the minimal length in the triangulation. The correspondig momentum cutoff K satisfies
    10 TeV < K << E_P = 10^{18} Gev. The first bound comes from the LHC experiments, and it reflects
    the fact that we have not seen quantum gravity effects in LHC.



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