4 ms·

He addresses this in the comments. The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments. Rou

He addresses this in the comments. The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments. Roughly put: - A particle is a "minimum stretching" of a field. - The "stiffness" corresponds to the energy-per-stretch-amount of the field (analogous to the stiffness of a spring). - So the particle's mass = (minimum stretch "distance") * stiffness ~ stiffness The author's point is that you don't need to invoke virtual particles or any quantum weirdness to make this work. All you need is the notion of stiffness, and the mass of the associated particle and the limited range of the force both drop out of the math for the same reasons.

pdonis 2y ago
> The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments. Then why not just call it "mass"? That's what it is. How is the notion of "stiffness" any better than the notion of "mass"? The author never explains this that I can see.
- kridsdale1 2y ago
  Undergrad-only level physics person here: I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. Mass as a term is particle-centric. It seems these minimum-stretching could also be thought of as a “wrinkle”. It’s a permanent deformation of the field itself that we give the name to, and thus “instantiate” the particle. Eye opening.
  - pdonis 2y ago
    > I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. "Stiffness" to me isn't a field term or a particle term; it's a condensed matter term. In other words, it's a name for a property of substances that is not fundamental; it's emergent from other underlying physics, which for convenience we don't always want to delve into in detail, so we package it all up into an emergent number and call it "stiffness". On this view, "stiffness" is a worse term than "mass", which does have a fundamental meaning (see below). > Mass as a term is particle-centric. Not to a quantum field theorist. :-) "Mass" is a field term in that context; you will see explicit references to "massless fields" and "massive fields" all over the literature.
    - scotty79 2y ago
      Do you also object quarks and gluons having "color" charge? Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
      - pdonis 2y ago
        > Do you also object quarks and gluons having "color" charge? No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects. This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors. > it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.
        scotty79 2y ago
        > An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors. They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory. > there is no such thing as what this author calls a "floppy" object It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons. What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality". There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
- timewizard 2y ago
  In the unit analysis it appears as if it's just kinematic viscosity.
  - pdonis 2y ago
    Kinematic viscosity, though, is an emergent property just as stiffness is. See my response to kridsdale1 upthread. In the unit analysis that is most natural to quantum field theory, it's mass.
yccs27 2y ago
This is it. Typically in a QFT lecture, you'd include a "mass term" (in the article: stiffness term) in your field equations, and later show that it indeed gives mass to the excitations of this field (i.e. particles). So you temporarily have two definitions of "mass" and later show that they agree. For this discussion it makes sense call the "mass" of a field "stiffness" instead, since it's not known a priori that it corresponds to particle mass.
- rnhmjoj 2y ago
  I think mathematically "stiffness" is well-defined, but the interpretation varies substantially depending on the context. For example, in chemistry or plasma physics, one writes down Poisson's equation for a collection of positive and negatives charges in thermal equilibrium and linearise the Boltzmann factors. The result is called the Debye–Hückel equation and is identical to the one shown in the "with math" section. Here the "stiffness" is interpreted as the effect of nearby charges "screening" a perturbing "bare" charge of the opposite sign. If you solve the equation you find the that effective electric field produced by the bare charge is like that of the usual point charge but with a factor exp(-r/λ). So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length. see this illustration [1]. Interestingly, if you look at EM waves propagating in this kind of system, you find some satifying the dispersion relation ω² = k²c² + ω_p² [2]. With the usual interpretation E=ℏω, p=ℏk you get E² = (pc)² + (mc²)², so in a sense the screening is resulting in "photons" gaining a mass. [1]: https://en.wikipedia.org/wiki/File:Debye_screening.svg https://en.wikipedia.org/wiki/File:Debye_screening.svg [2]: https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#O_wave https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#...

pdonis 2y ago

> The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments. Then why not just call it "mass"? That's what it is. How is the notion of "stiffness" any better than the notion of "mass"? The author never explains this that I can see.

kridsdale1 2y ago
Undergrad-only level physics person here: I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. Mass as a term is particle-centric. It seems these minimum-stretching could also be thought of as a “wrinkle”. It’s a permanent deformation of the field itself that we give the name to, and thus “instantiate” the particle. Eye opening.
- pdonis 2y ago
  > I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. "Stiffness" to me isn't a field term or a particle term; it's a condensed matter term. In other words, it's a name for a property of substances that is not fundamental; it's emergent from other underlying physics, which for convenience we don't always want to delve into in detail, so we package it all up into an emergent number and call it "stiffness". On this view, "stiffness" is a worse term than "mass", which does have a fundamental meaning (see below). > Mass as a term is particle-centric. Not to a quantum field theorist. :-) "Mass" is a field term in that context; you will see explicit references to "massless fields" and "massive fields" all over the literature.
  - scotty79 2y ago
    Do you also object quarks and gluons having "color" charge? Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
    - pdonis 2y ago
      > Do you also object quarks and gluons having "color" charge? No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects. This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors. > it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.
      - scotty79 2y ago
        > An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors. They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory. > there is no such thing as what this author calls a "floppy" object It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons. What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality". There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
timewizard 2y ago
In the unit analysis it appears as if it's just kinematic viscosity.
- pdonis 2y ago
  Kinematic viscosity, though, is an emergent property just as stiffness is. See my response to kridsdale1 upthread. In the unit analysis that is most natural to quantum field theory, it's mass.

yccs27 2y ago

This is it. Typically in a QFT lecture, you'd include a "mass term" (in the article: stiffness term) in your field equations, and later show that it indeed gives mass to the excitations of this field (i.e. particles). So you temporarily have two definitions of "mass" and later show that they agree. For this discussion it makes sense call the "mass" of a field "stiffness" instead, since it's not known a priori that it corresponds to particle mass.

rnhmjoj 2y ago
I think mathematically "stiffness" is well-defined, but the interpretation varies substantially depending on the context. For example, in chemistry or plasma physics, one writes down Poisson's equation for a collection of positive and negatives charges in thermal equilibrium and linearise the Boltzmann factors. The result is called the Debye–Hückel equation and is identical to the one shown in the "with math" section. Here the "stiffness" is interpreted as the effect of nearby charges "screening" a perturbing "bare" charge of the opposite sign. If you solve the equation you find the that effective electric field produced by the bare charge is like that of the usual point charge but with a factor exp(-r/λ). So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length. see this illustration [1]. Interestingly, if you look at EM waves propagating in this kind of system, you find some satifying the dispersion relation ω² = k²c² + ω_p² [2]. With the usual interpretation E=ℏω, p=ℏk you get E² = (pc)² + (mc²)², so in a sense the screening is resulting in "photons" gaining a mass. [1]: https://en.wikipedia.org/wiki/File:Debye_screening.svg https://en.wikipedia.org/wiki/File:Debye_screening.svg [2]: https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#O_wave https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#...