I've been looking over quantum gravity threads here for a year or so. One thing keeps puzzling me. It appears to me that difficulty coming up with a viable quantum gravity theory is melding the continuous nature of the general relativity equations with the discrete (i.e. quantized) nature of quantum mechanics.(adsbygoogle = window.adsbygoogle || []).push({});

Nature is clearly both continuous and discrete at the same time.

Besides string theory, it appears to me that the other approaches try to build a gravity model using discrete pieces, spin foam networks and such in LQG, various n-dimensional simplex networks in CDT, etc.

What is the merit of this approach? Why start with quanta and try to build a continuous model rather than starting with a continuous model and then try to build quanta from it? Is there some theoretical benefit that one gains?

It seems that some of the models for quantum mechanics rely on resonance or quantum harmonic oscillators to model quantized energy levels, couldn't this same approach work for a model of quantum gravity? Is there anything that argues against the idea of some continuous substrate with the quanta coming out via resonances?

String theory seems to partially argue from the opposite direction. That one can start with inherently fuzzy notions and get quanta due to different vibrational harmonics and resonances. But string theory also seems to start with discrete particles. There are strings for every particle rather than one giant string, connected network of strings or interconnected mesh of strings.

Has anyone tried to model quantum gravity using interconnected strings (i.e. a multi-dimensional mesh or network)? Or does this end up looking like LQG or CDT as soon as you connect the string together anyway?

Finally, is there anything besides a desire for theoretical purity, that indicates that gravity is quantized in any way? Any observation or phenomena? Is there any reason that would preclude gravity from being a continuous phenomena assuming we could find a model that didn't exhibit the singularities one gets from too much matter in too little space?

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# Starting from Discrete or Continuous?

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