New theories edit
Theories like causal dynamical triangulation (CDT) and spin networks look like the right direction to quantum gravity.
CDT takes logical approaches:
- spacetime is quantized at small scales and appears as smooth, curved spacetime at large scales,
- that timelines must agree and casualty is preserved - not just describing, but possibly explaining, the very nature of space and time itself,
- interesting is it's automatic fractal nature.
- perfectly simple (minimum number of essential assumptions) and extremely appealing.
Not string theory or the like - which make ludicrous assumptions that particles "are" strings or membranes or whatever and then require extremely complex modifications to spacetime just for consistency (Calabi–Yau manifolds? Really?).
- The worst part of string theory is right from the very beginning, is the assertion particles "are" strings etc. How can we ever know that experimentally? We can sit down speculating/guessing/modelling what particles "really are" (only to change again and again anyway in the future) a much as we like:
- "let's pretend everything, even the "fabric" of space and time, is vibrating strings or springs or trampolines or twirling tops or spinning wheels or pendulums or twiddling knots/links or... then there are a number of fundamental normal modes/rotational frequencies/tensions of these ... and everything in the universe is derived from these fundamental things..."
- It's weak - just making stuff up just for the sake of explaining physical phenomena, and yet the maths is ludicrously excessively complicated just so it works... CDT is not like that.
- Should the unification of forces really be related by the number (10, 11, 26...) of spacetime dimensions??...
- Yes, it may combine GR and QFT and has passed internal consistency, but proponents seem too confident that it "is" the only approach, that "only all of the good ideas" come from string theory...
- What happens when new forces are found - shall we hope they still fit into the theory, or insert more dimensions, or what?
- Without question - the SHO, classical or quantum, or any form of linear normal mode oscillations, are the most inanely dull physical systems to ever solve for.. Yes - SHOs are important systems for perturbation theory methods, and oscillatory systems are ubiquitous and can be modeled by linear oscillations... but even the idea of something oscillating linearly is extraordinarily boring and tiresome. This idea is used in string theory. (Non-linear chaotic oscillations are much more interesting).
Formulations and spaces edit
Quantum theory: Has the path integral formulation using Lagrangians had its day? Phase space formulation in QM and replacement of wavefunctions by Wigner functions offers new insight - no need to take sides with position/momentum representations as they're on equal footing.
Relativity: Space and time are always deeply mysterious, in classical mechanics and general relativity. GR itself apparently has a number of flaws (but then which physical theory is truly perfect?), one of them is that "events" are points in spacetime. Do points really exist in nature? How can we even physically define a point in spacetime? In superspace (and other spaces I haven't encountered) points themselves are replaced by spaces, no points actually exist. According to the ADM formulation of GR, space itself is 3d and curved, and time-dependent (dynamic).
Fractals, chaos, non-linearity, everywhere edit
Rather than changing the integer number of spacetime dimensions, and postulating wave or field or evolution equations of integer order, newer methods of
- (stochastic) fractal/multifractal geometry filling continua of dimensions between 0 and 3 or 4, and
- using geometric algebra and fractional calculus (or even fractional differential forms or fractional geometric calculus?), for example fractional quantum mechanics,
look like the right way forward. "Particles/waves/fields" may be replaced by fractal structures which propagate self-similarly through spacetime.
Given how ubiquitous fractals are everywhere (literally everywhere, one way or another), a better notion of space and time may be dynamic and curved fractal spaces. Replacing the description of "particles/strings (etc)" described by wave-like or field-like probability amplitudes, by a fractal-geometric probability amplitude propagating through curved dynamical space, seems very appealing. Interpreting the constituents of matter always transforms, first "particles" (classical mechanics), then wave-particle duality (quantum mechanics), then fields (quantum field theory).
A non-linear, but simple, theory based on fractal geometry... should connect GR and QFT with SUSY?... Not yet sure how exactly to do that mathematically and make everything work though...