3 ms·

For the layman, what exactly is going to theoretically "explode" if spacetime is continuous?

naasking 3y ago
The article discusses this question actually, about the apparent incompatibility between classical and quantum systems. Basically, there's a fundamental inconsistency where you can detect a particle's position gravitationally as it passes through a slit in the double slit experiment, which destroys the quantum properties of "passing through both slits" that leads to interference patterns.
- H8crilA 3y ago
  Oh no I get that, but two comments above inciampati was suggesting that we will end up in a situation where some variable will have to have an infinite value. Like, famously, with the ultraviolet crisis: https://en.wikipedia.org/wiki/Ultraviolet_catastrophe https://en.wikipedia.org/wiki/Ultraviolet_catastrophe Detecting (something about) the particle through gravity would at best remove the interference, not create an \infty somewhere in the model, implying that the model is self inconsistent.
  - naasking 3y ago
    > Oh no I get that, but two comments above inciampati was suggesting that we will end up in a situation where some variable will have to have an infinite value The black hole information paradox from that article presumably fits. The conclusion from GR is that no information can escape, which is ultimately incompatible with QM, and that conclusion ultimately depends on the infinite density of the singularity. I think the more charitable reading is that we'll find situations where either no sensible calculation can be done, or the sensible calculations we do churn out nonsense. Divergence in the UV catastrophe was an example of that, and Baez covered more here: Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
    - GoblinSlayer 3y ago
      Problems 1-3 there are caused by point particles, not by space. They mention ultraviolet catastrophe was caused by continuous space, but it was caused by non-quantum radiation, so there's no classical electrodynamics with discreet space, instead there's quantum electrodynamics with continuous space.
      - naasking 3y ago
        I'm not sure what "problems 1-3" are referring to here, but all of these problems fundamentally trace their roots to issues with the foundational assumption of continuity.
        GoblinSlayer 3y ago
        Per numbered titles: 1 Newtonian gravity 2 Quantum mechanics of charged particles 3 Classical electrodynamics of point particles They explicitly mention they use point particles. Problem in 1 Newtonian gravity is especially egregious example. They model planets(!) as material points and see how they come infinitely close to each other. The author does mention these problems are pure math unrelated to reality.
NoMoreNicksLeft 3y ago
Zeno would win. And though he is thousands of years dead at this point, I'll be damned if I'm going to let that happen.

The article discusses this question actually, about the apparent incompatibility between classical and quantum systems. Basically, there's a fundamental inconsistency where you can detect a particle's position gravitationally as it passes through a slit in the double slit experiment, which destroys the quantum properties of "passing through both slits" that leads to interference patterns.

H8crilA 3y ago
Oh no I get that, but two comments above inciampati was suggesting that we will end up in a situation where some variable will have to have an infinite value. Like, famously, with the ultraviolet crisis: https://en.wikipedia.org/wiki/Ultraviolet_catastrophe https://en.wikipedia.org/wiki/Ultraviolet_catastrophe Detecting (something about) the particle through gravity would at best remove the interference, not create an \infty somewhere in the model, implying that the model is self inconsistent.
- naasking 3y ago
  > Oh no I get that, but two comments above inciampati was suggesting that we will end up in a situation where some variable will have to have an infinite value The black hole information paradox from that article presumably fits. The conclusion from GR is that no information can escape, which is ultimately incompatible with QM, and that conclusion ultimately depends on the infinite density of the singularity. I think the more charitable reading is that we'll find situations where either no sensible calculation can be done, or the sensible calculations we do churn out nonsense. Divergence in the UV catastrophe was an example of that, and Baez covered more here: Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
  - GoblinSlayer 3y ago
    Problems 1-3 there are caused by point particles, not by space. They mention ultraviolet catastrophe was caused by continuous space, but it was caused by non-quantum radiation, so there's no classical electrodynamics with discreet space, instead there's quantum electrodynamics with continuous space.
    - naasking 3y ago
      I'm not sure what "problems 1-3" are referring to here, but all of these problems fundamentally trace their roots to issues with the foundational assumption of continuity.
      - GoblinSlayer 3y ago
        Per numbered titles: 1 Newtonian gravity 2 Quantum mechanics of charged particles 3 Classical electrodynamics of point particles They explicitly mention they use point particles. Problem in 1 Newtonian gravity is especially egregious example. They model planets(!) as material points and see how they come infinitely close to each other. The author does mention these problems are pure math unrelated to reality.

NoMoreNicksLeft 3y ago

Zeno would win. And though he is thousands of years dead at this point, I'll be damned if I'm going to let that happen.