Partanen-Tulkki’s theory, known as unified gravity, is a novel approach aiming to reconcile gravity with quantum mechanics by describing gravity as a gauge theory—similar to how the Standard Model treats the electromagnetic, weak, and strong forces.
Main ideas
- Space-Time Dimension Field: This novel field acts as a bridge, mediating gravitational interactions as gauge interactions. Particles with energy interact gravitationally through this field, just as charged particles interact electromagnetically via photons.
- Internal Symmetry Action: The four U(1) symmetries are compact internal gauge symmetries acting on components of the space-time dimension field, which encodes gravitational degrees of freedom. These transformations are like phase rotations in quantum fields (e.g., electromagnetism’s U(1)), meaning they rotate internal components without changing spacetime points or coordinates.
Achievements
- Flat Spacetime Formulation: Gravity is described without requiring curved spacetime geometry. Yet, by choosing an appropriate gauge, the theory can reproduce the teleparallel equivalent of general relativity (TEGR), which is consistent with all current gravitational observations, including gravitational waves and black hole imaging4.
- It reproduces results to teleparallel gravity
- Four U(1) Symmetries enable gravity to be described with the same mathematical machinery as other fundamental forces The theory is built on four U(1) symmetry transformations acting internally on components of the space-time dimension field. These internal symmetries are analogous to those in the Standard Model but differ from the infinite-dimensional spacetime symmetries of general relativity. This subtle re-interpretation enables gravity to be described with the same mathematical machinery as other fundamental forces.
Testability and vision promotion
- Bridging Quantum Mechanics and Gravity: Unified gravity places gravity on equal footing with the other fundamental forces within the quantum field theory framework, potentially solving long-standing conflicts between general relativity and quantum mechanics.
- A Step Toward the Theory of Everything: While not yet a complete Theory of Everything, unified gravity is a concrete, mathematically consistent step toward that goal, inviting further research and experimental scrutiny.
- Testable and Predictive: Unlike many speculative quantum gravity theories, this approach is grounded in established quantum principles and does not require extra dimensions or unknown particles. It aligns with current experimental data and offers new avenues for exploring phenomena like black hole sngularities and the Big Bang.
Citations:
It's not new that gravity is a gauge theory-its gauge group is the group of diffeomorphisms, which is a noncompact group. That property is the reason why the techniques that work for the quantization of gauge theories with compact gauge groups don't work for gravity. So the problem is to show how a gauge theory with such a gauge group can emerge as the classical limit of another structure-and what that structure could be.
Partanen and Tulkki do address the issue that the problem is the property that the gauge group of classical gravity is noncompact-but they don't show how it emerges in the classical limit of their formulation. So they're describing a particular gauge theory, with a compact gauge group-but they must prove that this gauge theory does describe gravity.
Essentially they're taking a particular compact subgroup of the group of diffeomorphisms and claiming that this subgroup controls the quantum properties. But they must prove this statement-they're postulating it.
One problem of their approach is that it eliminates classical spacetime singularities-whereas one would expect that quantum effects resolve them. Because they write down a classical Lagrangian that is invariant under a compact gauge group and then show, as might be expected, that this Lagrangian doesn't have any of the problems that quantum fields coupled to gravity have. But their gravity doesn't have anything to do with gravity, it's a gauge theory of four U(1) gauge fields. Such fields can't describe known properties of classical gravity.
If the gauge group of the coordinates is U(1)^4, there's just no way they can get global Lorentz invariance in the flat spacetime limit-contrary to their assertion. SO(3,1), which is a noncompact group (but acts globally in the flat spacetime limit), isn't a subgroup of U(1)^4... Any subgroup of a compact group is, also, compact.
Of course it's possible to define tensors that transform covariantly under U(1)^4-but they don't transform covariantly under general coordinate transformations! So they must show how the putative U(1)^4 group of the quantum theory becomes the group of diffeomorphisms in the classical limit. Which seems impossible in their construction, since they write the classical Lagrangian that's invariant only under U(1)^4 transformations of the coordinates. So they can't recover any of the predictions of general relativity, by construction (nor of special relativity, indeed). They've broken explicitly global Lorentz invariance and have obscured this.
The only thing that matters in their approach is their hypothesis that the coordinates are invariant under U(1)^4 local transformations. From that it's possible to show that what they do can't have anything to do with classical gravity-which they admit, in fact-nor with global Lorentz invariance (which they obfuscate).
It's easy, unfortunately, to do very complicated calculations that lead nowhere...
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