Nonlinear Quantum gravity / Schroedinger Equation

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SUMMARY

The discussion centers on the fundamental nature of the linear Schrödinger Equation in quantum mechanics and the implications of its potential nonlinearity. Participants highlight that if the Schrödinger Equation were nonlinear, it would challenge existing interpretations of quantum mechanics, such as Copenhagen, Many-Worlds, and Bohmian interpretations, which would no longer be observationally equivalent. Historical experiments from the 1990s, following Weinberg's insights, suggest that the likelihood of quantum mechanics being nonlinear is minimal. However, the possibility of underlying nonlinear dynamics influencing quantum mechanics remains a topic of interest.

PREREQUISITES
  • Understanding of the Schrödinger Equation in quantum mechanics
  • Familiarity with quantum interpretations: Copenhagen, Many-Worlds, and Bohmian
  • Knowledge of linear versus nonlinear dynamics in physics
  • Awareness of historical experiments in quantum mechanics from the 1990s
NEXT STEPS
  • Explore the implications of nonlinear quantum mechanics on existing interpretations
  • Research the historical experiments conducted in the 1990s regarding quantum nonlinearity
  • Investigate the Bohmian interpretation of quantum mechanics in detail
  • Learn about the mathematical foundations of linear and nonlinear quantum theories
USEFUL FOR

Physicists, quantum mechanics researchers, and students interested in the foundational aspects of quantum theory and the implications of potential nonlinear dynamics.

Fyzix
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Is there any good arguments or reasons for why it seems the general consensus is that the linear Schroedinger equations is fundamental?

I know that if it turns out either of these are nonlinear it would falsify certain readings of QM so it would be interesting if there is indeed no real good reasons why the Schroedinger Equation can't be nonlinear?
 
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In principle, linearity of quantum theory could be only an approximation.
In nonlinear quantum theory, different interpretations (Copengahen, many world, Bohmian, ...) would not be observationally equivalent.
In fact, I have argued elsewhere that only Bohmian interpretation would be self-consistent:
http://xxx.lanl.gov/abs/0707.2319
 
Hey thanks man, really interesting.

I did some more digging and found that experiments conducted in the 1990's after Weinberg published his thoughts on this matter pretty much made the chance of quantum mechanics being nonlinear very slight.

However, even if the Schroedinger Equation is perfectly linear couldn't there be nonlinear dynamics beneath quantum mechanics which inreturn could explain QM?
 

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