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There is no (widely accepted) theory that describes the structure of spacetime down to the quantum scale. You mention loop quantum gravity, but as far as I know the removal of singularities has been addressed only in the simplified form of loop quantum cosmology. However as far back as the 60s there have been suggestions that quantum effects would cause the ...

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The majority of the sources that LIGO (and other gravitational wave detectors) are aiming for are astrophysical (e.g. neutron stars, black holes, supernovae, pulsars). The expected cosmological gravitational radiation from standard inflationary models (see this recent article from P. Steinhardt) would be very weak in the LIGO band (10-1000 Hz). There are a ...

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1. Hawking-Bekenstein entropy of a black hole is given by $S_{\text{BH}} = \frac{kAc^3}{4\hbar G}$ where $A$ is the area of the event horizon. Assuming a non-rotating black hole, there holds $r_s=\frac{2GM}{c^2}$ for the Schwartzschild radius, and therefore $A=4\pi r_s^2=\frac{16\pi G^2M^2}{c^4}$, which results in $$S_{BH}=\frac{4kGM^2}{\hbar c}$$ For ...

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Gravity can be seen as a gauge theory of the Lorentz group (which acts on the tangent space). These was pointed out by Kibble and Sciama during the 50s and 60s. As John said before, it's better seen in terms of differential forms. Another reference you might find interesting is the Lecture notes on Chern-Simons gravity by Jorge Zanelli (available in ...

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John Rennie's answer is good already, but I want to add a single point: These fluctuations are very very short. In quantum mechanics you've got Heisenbergs uncertainty principle, which is often stated as $$\Delta x \cdot \Delta p \le \frac \hbar 2$$ and which means, that for any quantum object (think of an electron or a positron created in such a vacuum ...

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I think the key conceptual hurdle is that the vacuum state is not nothing. Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is ...

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The planck length is not necessarily an absolute limit to how small thing can be sub divided. The planck length is theoretical and it is empirically defined by dimensional analysis. At this length scale our knowledge of physics makes no sense. The planck length $\ell_P$ is defined as: $\ell_\text{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616\;199 (97) \times ... 1 Let's start by setting the scene. We've got a hyperdense (understatement) singularity containing everything at$t = 0$. This is the beginning of time. Right now, we have no reason to assume that anything existed before then. Asking what happened before the Big-Bang ( depending on which model you use ) is not something that one can ask since we assume nothing ... 0 The Higgs is responsible for Mass, Gravity is different. The Graviton if it even exists would be nearly impossible to detect directly. Gravity is incredibley weak, the Detector would have to be huge. I'm talking the scale of Solar System and maybe even a entire Galaxy. I read somewhere that a Detector the Size of Jupiter close to Neutron star would ... 0 I'll also throw in a few words about the issue. As TwoBs points out, the problem is the comparative weakness of gravity, which makes quantum effects only relevant under extreme conditions: Essentially black holes and the big bang. The problem with the former is that we cannot peek beyond the horizon, so it might be more fruitful to try to tackle the issue by ... 3 A quantum theory of gravity does make definite predictions. One such an example, which is the same for any theory of quantum gravity that reproduce GR at low energy, is the famous correction to the newton$1/r$potential:$\$ V(r)=\frac{M_{star}}{M_{Planck}r}\left(1-\frac{M_{star}}{M_{Planck}^2 r}-\frac{127}{30\pi^2}\frac{1}{M_{Planck}^2 r^2}+\ldots\right). ...

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I would say that there is not too much experimental evidence for a quantum theory of gravity yet, the reasons why such a theory is desirable are mainly of conceptual/theoretical nature. I will give a (likely to be incomplete) list of motivations for studying quantum gravity. Unification of all four fundamental interactions: The Standard Model of particle ...

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