4 ms·

Interest and hope is fine. I was responding to the parent poster's stated revulsion for these theories -- and not just any of them but all of them, as though th

by ajkjk 5y ago

Interest and hope is fine. I was responding to the parent poster's stated revulsion for these theories -- and not just any of them but all of them, as though they have a blanket distrust in any unproven theory in physics, uncorrelated with the experimental evidence for it. > fundamental axioms are proven incorrect It's not that fundamental axioms are disproven so much as simplifying assumptions are invalidated. The standard model models the particles we understand well, and has obvious extension points for new physics (like new Lagrangian terms / new gauge fields). Nobody thinks that it models all of physics as written; it clearly doesn't account for lots of things.

chasil 5y ago
Is a massless neutrino an axiom of the standard model, or is this somehow a simplifying assumption?
- ajkjk 5y ago
  It's an assumption. You can skim the details here: https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Neutrino_masses https://en.wikipedia.org/wiki/Mathematical_formulation_of_th... The standard model in its normal form assumes neutrinos to be massless (and that right-handed neutrinos don't exist). Neutrino oscillation implies that they have mass (because to oscillate, they must have an 'internal clock', meaning that they experience proper time, thus are not massless). In light of the fact that they are not massless, some sort of additional term needs to be added to the standard model, but experiment has not provided a way to distinguish between (or invalidate) the candidate theories... yet. The standard model has two parts -- a general schema for theory building (Lagrangians with terms corresponding to each symmetry field and each coupling between fields, plus symmetry breaking and the Higgs mechanism for conferring mass to (some of) the gauge bosons) -- and a particular set of choices within this schema, which is the specific Lagrangian + choices of constants that predict essentially all of the physics we've seen in particle colliders. As far as I know, massive Neutrinos can be solved 'within' the SM schema, although additional Lagrangian terms are required. What's unclear is whether dark matter, gravity, fermionic masses, etc can be resolved within the same framework. But massive neutrinos don't _necessarily_ challenge it (although if the existing theories are ruled out, they might start to). Everyone is pretty much on board that the exact choice of Lagrangian terms can't completely describe reality, and needing to add terms doesn't mean invalidating the theory.
  - denton-scratch 5y ago
    I will have to find out what "Lagrangian" means. It seems to be important in SM.
    - ajkjk 5y ago
      Unfortunately it is very hard to find a lucid explanation of the idea .. anywhere.. that isn't a bunch of 'just so' explanations. The 'short version' is that a Lagrangian is a device for book-keeping the interactions in a physical theory. It consists of terms like aBa, where 'a' is some physical quantity, and (Ba) is the 'cost' to change it. B in general is an operator that can depend on all of the other physical quantities around, possibly including derivatives. So you end up with something like: L = aBa + cDc + eFe + gHg + ... Derivatives of this function with respect to a given variable -- for instance, a particular value `a` or `c` -- tell you the 'physical law' for that field. The simplest example in classical mechanics is L = 1/2mv^2 - V(x), and the derivative rule is dL/dx - d/dt dL/dv = - V_x - m dv/dt = (F - ma) = 0. In general including a term like ... + cD(a)c +... causes the c field to couple to the a field, which is how interactions between different fields (represented by the lower-case variables a, c, etc here) are encoded in field theory. I haven't found out a cogent explanation of why the terms have the form aBa, though, or why this is the 'simplest' way to express the concepts that it encodes, but it seems to be. But it works well in part because of it expresses physical laws in terms of scalar functions (instead of a vector-equality like F=ma, which becomes a complicated differential equation in practice), which somehow means it is more naturally encoding the underlying symmetries of the system (because, I guess, one equation is simpler than three).
      - denton-scratch 5y ago
        I'm grateful for your attempt at explaining! I've read it twice, and I'll read it again. Your explanation relies on calculus; at school, I grokked differentiation, but I got a huge mental block on integration. My maths teacher was very good, he wrote famous maths textbooks, but he had no insight into my difficulties. He couldn't teach me, because he was too clever. That's why I never tackled graduate-level maths. I resent that old maths teacher; he meant well, but being super-clever wasn't his job. His job was to teach me.
denton-scratch 5y ago
True. I do have a revulsion; not like a vomit reflex, just that I don't like them. It's not a "blanket distrust" - rather, it's that cosmologists are proposing three distinct ideas, each with very strong implications, none supported by more than what amounts to circumstantial evidence. I just have an instinct that those three ideas might not be as distinct as they look.
- ajkjk 5y ago
  My point in, uh, scolding you for that take is that the circumstantial evidence is _massive_ for each of them, and I ... have a feeling... that you do not appreciate that fact. (well! not for dark energy, but also nobody would disagree with you that dark energy isn't much of a theory. It's the other two that are well-founded in detailed experimental evidence). For my part I don't think the evidence for dark matter is any more 'circumstantial' than the evidence for massive neutrinos or the Higgs. Both are well indicated in extensive data .. by their byproducts and effects on other matter. But neither has been 'seen directly'; indeed it's not even clear what it would mean to see them directly, given that they apparently don't interact via the forces we can directly detect.
  - denton-scratch 5y ago
    > feeling... that you do not appreciate that fact. Actually, I do; at least, I think that galaxies rotations are peculiar, but can be explained by the addition of unobserved matter. And I think inflation is a plausible candidate explation for the smoothness of the CMB. And I note the evidence that the universe's expansion appears to be accellerating, but I wonder is that is an observational error (rewally, I don't know - nobody I know is a physicist, or even interested in cosmology). So I'm an armchair cosmologist; same as I used to be an amateur astronomer. We serve a purpose: amateur astronomers are usually the first to spot new comets, because they have a wide perspective. I'd consume more material about cosmology, but it's generally either dumbed-down mass-media crap, or something about Lagrangians. I'm not a maths graduate, I did Philosophy. None of that invalidates my viewpoint.
    - 5y ago

by ajkjk 5y ago

chasil 5y ago

Is a massless neutrino an axiom of the standard model, or is this somehow a simplifying assumption?

ajkjk 5y ago
It's an assumption. You can skim the details here: https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Neutrino_masses https://en.wikipedia.org/wiki/Mathematical_formulation_of_th... The standard model in its normal form assumes neutrinos to be massless (and that right-handed neutrinos don't exist). Neutrino oscillation implies that they have mass (because to oscillate, they must have an 'internal clock', meaning that they experience proper time, thus are not massless). In light of the fact that they are not massless, some sort of additional term needs to be added to the standard model, but experiment has not provided a way to distinguish between (or invalidate) the candidate theories... yet. The standard model has two parts -- a general schema for theory building (Lagrangians with terms corresponding to each symmetry field and each coupling between fields, plus symmetry breaking and the Higgs mechanism for conferring mass to (some of) the gauge bosons) -- and a particular set of choices within this schema, which is the specific Lagrangian + choices of constants that predict essentially all of the physics we've seen in particle colliders. As far as I know, massive Neutrinos can be solved 'within' the SM schema, although additional Lagrangian terms are required. What's unclear is whether dark matter, gravity, fermionic masses, etc can be resolved within the same framework. But massive neutrinos don't _necessarily_ challenge it (although if the existing theories are ruled out, they might start to). Everyone is pretty much on board that the exact choice of Lagrangian terms can't completely describe reality, and needing to add terms doesn't mean invalidating the theory.
- denton-scratch 5y ago
  I will have to find out what "Lagrangian" means. It seems to be important in SM.
  - ajkjk 5y ago
    Unfortunately it is very hard to find a lucid explanation of the idea .. anywhere.. that isn't a bunch of 'just so' explanations. The 'short version' is that a Lagrangian is a device for book-keeping the interactions in a physical theory. It consists of terms like aBa, where 'a' is some physical quantity, and (Ba) is the 'cost' to change it. B in general is an operator that can depend on all of the other physical quantities around, possibly including derivatives. So you end up with something like: L = aBa + cDc + eFe + gHg + ... Derivatives of this function with respect to a given variable -- for instance, a particular value `a` or `c` -- tell you the 'physical law' for that field. The simplest example in classical mechanics is L = 1/2mv^2 - V(x), and the derivative rule is dL/dx - d/dt dL/dv = - V_x - m dv/dt = (F - ma) = 0. In general including a term like ... + cD(a)c +... causes the c field to couple to the a field, which is how interactions between different fields (represented by the lower-case variables a, c, etc here) are encoded in field theory. I haven't found out a cogent explanation of why the terms have the form aBa, though, or why this is the 'simplest' way to express the concepts that it encodes, but it seems to be. But it works well in part because of it expresses physical laws in terms of scalar functions (instead of a vector-equality like F=ma, which becomes a complicated differential equation in practice), which somehow means it is more naturally encoding the underlying symmetries of the system (because, I guess, one equation is simpler than three).
    - denton-scratch 5y ago
      I'm grateful for your attempt at explaining! I've read it twice, and I'll read it again. Your explanation relies on calculus; at school, I grokked differentiation, but I got a huge mental block on integration. My maths teacher was very good, he wrote famous maths textbooks, but he had no insight into my difficulties. He couldn't teach me, because he was too clever. That's why I never tackled graduate-level maths. I resent that old maths teacher; he meant well, but being super-clever wasn't his job. His job was to teach me.

denton-scratch 5y ago

True. I do have a revulsion; not like a vomit reflex, just that I don't like them. It's not a "blanket distrust" - rather, it's that cosmologists are proposing three distinct ideas, each with very strong implications, none supported by more than what amounts to circumstantial evidence. I just have an instinct that those three ideas might not be as distinct as they look.

ajkjk 5y ago
My point in, uh, scolding you for that take is that the circumstantial evidence is _massive_ for each of them, and I ... have a feeling... that you do not appreciate that fact. (well! not for dark energy, but also nobody would disagree with you that dark energy isn't much of a theory. It's the other two that are well-founded in detailed experimental evidence). For my part I don't think the evidence for dark matter is any more 'circumstantial' than the evidence for massive neutrinos or the Higgs. Both are well indicated in extensive data .. by their byproducts and effects on other matter. But neither has been 'seen directly'; indeed it's not even clear what it would mean to see them directly, given that they apparently don't interact via the forces we can directly detect.
- denton-scratch 5y ago
  > feeling... that you do not appreciate that fact. Actually, I do; at least, I think that galaxies rotations are peculiar, but can be explained by the addition of unobserved matter. And I think inflation is a plausible candidate explation for the smoothness of the CMB. And I note the evidence that the universe's expansion appears to be accellerating, but I wonder is that is an observational error (rewally, I don't know - nobody I know is a physicist, or even interested in cosmology). So I'm an armchair cosmologist; same as I used to be an amateur astronomer. We serve a purpose: amateur astronomers are usually the first to spot new comets, because they have a wide perspective. I'd consume more material about cosmology, but it's generally either dumbed-down mass-media crap, or something about Lagrangians. I'm not a maths graduate, I did Philosophy. None of that invalidates my viewpoint.
  - 5y ago