There are several theoretical approach of vary degrees of success.
However, to test you want it to also describe theories we know, but the energy scales are so different how do we test them?
Eg. Particle colliders are still limited to the energy range of the standard model.
Cosmology seems perhaps more promising. So perhaps we need to look at quantum cosmology before we look for a theory of quantum gravity.
Gravitational wave detection from the early universe.
If we could make precise measurements of all over the universe, this could allow us to gain insight back to the big bang and early universe.
We could look for a dispersion relation of light in a vacuum.
For many people theoretical predictions will never been satisfying for promoting one theory over another, we really need some real experimental evidence.
There is not yet a single theory of quantum gravity. Throughout the years several approaches has been built in order to address the problem of quantizing gravity. In particular two current trends correspond to string theory and loop quantum gravity (LQG). The developments, theoretical or experimental, that may prove or disprove the different theories about quantum gravity depend strongly on 'philosophical convictions'. That is, there is no ultimate 'smoking gun' that will rule out all but one theory. The reason behind this is that most of the current approaches rely on different assumptions and, although they address the problem of quantizing gravity, their predictions may be different and may not overlap with one another. Thus, it is a matter of choice to determine which of such predictions will be considered as a proof of the validity of a theory of quantum gravity. Data coming form experiments like BICEP may give some information about the so-called linearized quantum gravity. The data provided by the experiment serves as a motivation to seek for an underlying quantum theory of gravity. However, the results from this experiment may only offer information about a piece of the problem and may not serve as sufficient evidence to prove or disprove the current approaches. It has been suggested that an important step towards an experimental proof of a theory of quantum gravity is to observe a primordial black-hole in evaporation. This will at least give some data that can be compared to certain approaches to quantum gravity. One of the main requirements on a quantum theory of gravity is that it reduces to the standard general relativity in an appropriate limit. This at least serves a way of ruling out certain theories since the description offered by general relativity agrees very well with the data obtained from experiments. In summary, the 'smoking gun' for a quantum theory of gravity is absent. There may be several future proposals that may suggest that one theory is better than the other, but this wont be sufficient to rule out other approaches. If all the approaches could provide the same observational predictions, then it will be an easy task to rule out some theories according to observations. In the current state of the field, this remains an open question without a general consensus.
The question was slightly reformulated: What developments would really bring you to drop a certain approach to quantum gravity.
As an example it was pointed out that any sign of Lorentz violating effect would drastically change the landscape of quantum gravity research but that so far it is surprising that no such effect has been found.
It was asked at which point should we drop SUSY as a credible explanation?
Any theory that would a posteriori reduce the number of (standard model) parameters would gain huge credibility. Likewise for explaining dark energy or dark matter.
Strings – smoking gun is extra dimensions/black holes
Is there any theory that can’t wiggle out of experimental evidence?
String theory – compare what it predicted in 1998 to what we see since then…
What would rule a theory out? If it doesn’t have the right low energy limit.
Any experiment which show violation of quantum mechanics would kill most theories
What about violation of Lorentz invariance?
Is there a smoking gun signature for a bounce?
Good evidence if one can accommodate standard model type matter and predict a small positive cosmological constant
Possible metastability of the current vacuum – what happens after. Since it’s related to vacuum, also related to \lambda
In the case of string theory, it doesn’t seem that any experimental data could really convince us that the theory is true - or that it is not true. This is because string theory seems to accommodate every possible experimental result via the string landscape. It’s difficult to rule out a theory that is so flexible. Also, at this point string theory only describes perturbative quantum gravity; it can’t tell us anything about the black holes at the center of galaxies, for example.
Other approaches, such as loop quantum gravity, try to give a non-perturbative description of quantum gravity, which is harder to do but is more conceptually interesting. It could be that several of the existing approaches to quantum gravity will each contribute to a different part of the final theory, or a different regime of validity. Regarding loop quantum gravity, the question of whether we can obtain general relativity from it in the semiclassical limit still remains open. If this is achieved, it might convince some people that this theory is more worth working on.
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