3 ms·

I've seen a clever way to derive QM out of GR equations by making a single assumption: ds2exp(Cexp(-iwt)) = c2*dt2 - dx2 - dy2 - dz2. This extra exp() factor mo

I've seen a clever way to derive QM out of GR equations by making a single assumption: ds2exp(Cexp(-iwt)) = c2*dt2 - dx2 - dy2 - dz2. This extra exp() factor modulates the ds2 slightly, and when mixed with GR equations, it makes the time-dependent Schrodinger equation. Whether this math corresponds to any physics is a question, but if this idea is right, then the psi-function isn't some abstract "probabilities cloud", but rather a standing wave on top of the spacetime field governed by the GR equations.

ganzuul 6y ago
AFAIK a standing wave requires the interference of two waves going in opposite direction, as in a resonant cavity. How does that work in a boundless space? Do we need some kind of time symmetry for this to work?
- vertbhrtn 6y ago
  The relativistic effects create this standing wave, i.e. the particle distorts the spacetime as it's moving and the relativistic "glitch" mixed with the modulated ds2 creates the standing wave. IIRC, the idea was to apply the Lorentz moving frame transformation to the ds2 x exp() interval to derive some bits of QM. To derive the non time-dependent SE, some bits of GR were needed and to derive the time-dependent SE, more GR was needed.
  - ganzuul 6y ago
    Is this glitch the same as what causes an accelerating charged particle to emit photons?
    - vertbhrtn 6y ago
      I have no idea. The "glitch" I meant is the Lorentz coordinates transform.
mhh__ 6y ago
The Schrodinger equation is non-relativistic so your program seems flawed.
- vertbhrtn 6y ago
  SE is just a diff equation that approximates physics well. It's non relativistic in the same sense as the textbook wave equation is non relativistic. The "true SE" is likely way more complex, includes some bizarre math, but is compatible with GR and all relativistic effects.
  - mhh__ 6y ago
    The relativistic equation is called the Dirac equation, with QFT governing the radiation etc. The schrodinger equation is just not lorentz covariant

ganzuul 6y ago

AFAIK a standing wave requires the interference of two waves going in opposite direction, as in a resonant cavity. How does that work in a boundless space? Do we need some kind of time symmetry for this to work?

vertbhrtn 6y ago
The relativistic effects create this standing wave, i.e. the particle distorts the spacetime as it's moving and the relativistic "glitch" mixed with the modulated ds2 creates the standing wave. IIRC, the idea was to apply the Lorentz moving frame transformation to the ds2 x exp() interval to derive some bits of QM. To derive the non time-dependent SE, some bits of GR were needed and to derive the time-dependent SE, more GR was needed.
- ganzuul 6y ago
  Is this glitch the same as what causes an accelerating charged particle to emit photons?
  - vertbhrtn 6y ago
    I have no idea. The "glitch" I meant is the Lorentz coordinates transform.

mhh__ 6y ago

The Schrodinger equation is non-relativistic so your program seems flawed.

vertbhrtn 6y ago
SE is just a diff equation that approximates physics well. It's non relativistic in the same sense as the textbook wave equation is non relativistic. The "true SE" is likely way more complex, includes some bizarre math, but is compatible with GR and all relativistic effects.
- mhh__ 6y ago
  The relativistic equation is called the Dirac equation, with QFT governing the radiation etc. The schrodinger equation is just not lorentz covariant