Phenomenological Quantum Gravity

[This is the promised brief write-up of my talk at the Loops '07 in Morelia, slides can be found here, some more info about the conference here and here.

When I submitted the title for this talk, I actually expected a reply saying "Look. This is THE international conference on Quantum Gravity. We already have ten people speaking about phenomonelogy - could you be a bit more precise here?". But instead, I found myself joking I am the phenomenology of the conference. Therefore, I added a somewhat extended motivation to my talk which I found blog-suitable, so here it is.]

The standard model (SM) of particle physics [1] is an extremely precise theory and has demonstrated its predictive power over the last decades. But it has also left us with several unsolved problems, question that can not be answered - that can not even be addressed within the SM. There are the mysterious whys: why three families, three generations, three interactions, three spatial dimensions? Why these interactions, why these masses, and these couplings? There are the cosmological puzzles, there is dark matter and dark energy. And then there is the holy grail of quantum gravity (see also: my top ten unsolved physics problems).

There are two ways to attack these problems. The one is a top-down approach. Stating with a promising fundamental theory one tries to reach common ground and to connect to the standard model from a reductionist approach. The difficulty with this approach is that not only one needs that 'promising candidate for the fundamental theory', but most often one also has to come up with a whole new mathematical framework to deal with it. Most of the talks on the conference [2] were top down approaches. The other way is to start from what we know and extend the SM in a constructivist approach. Examples for that might be to take the SM Lagrangian and just add all kinds of higher order operators, thereby potentially giving up symmetries we know and like. The difficulty with this approach is to figure out what to do with all these potential extensions, and how to extract sensible knowledge about the fundamental theory from it.

I like it simple. Indeed, the most difficult thing about my work is how to pronounce 'phenomenology' (and I've practiced several years to manage that). So I picture myself somewhere in the middle. People have called that 'effective models' or 'test theories'. Others have called it 'cute' or 'nonsense'. I like to call it 'top-down inspired bottom-up approaches'. That is to say, I take some specific features that promising candidates for fundamental theories have, add them to the standard model and examine the phenomenology. Typical examples are e.g. just asking what the presence of extra dimensions lead to. Or the presence of a minimal length. Or a preferred reference frame. You might also examine what consequences it would have if the holographic principle or entropy bounds would hold. Or whether stochastic fluctuations of the background geometry would have observable consequences.

These approaches do not claim to be a fundamental theory of their own. Instead, they are simplified scenarios, suitable to examine certain features as to whether their realization would be compatible with reality. These models have their limitations, they are only approximations to a full theory. But to me, in a certain sense physics is the art of approximation. It is the art of figuring out what can be neglected, it is the art of building models, and the art of simplification.

"Science may be described as the art of systematic over-simplification."

~Karl Popper

But.

One can imagine more beyond the standard model than just QG! So, if we are talking about phenomenology of quantum gravity we'll have to ask what we actually mean with that. To me, quantum gravity is the question how we can reconcile the apparent disagreements between classical General Relativity (GR) and QFT. And I say 'apparent' because nature knows how quantum objects fall, so there has to be a solution to that problem [3]. To be honest though, we don't even know that gravity is quantized at all.

I carefully state we don't 'know' because we've no observational evidence for gravity to be quantized whatsoever. (The fact that we don't understand how a quantized field can be coupled to an unquantized gravitational field doesn't mean it's impossible.) Indeed one can be sceptical about whether it's observable at all. This is reflected very aptly in the below quotation from Freeman Dyson, which I think is deliberately provocative and basically says my whole field of work doesn't exist:

"According to my hypothesis, the gravitational field described by Einstein's theory of general relativity is a purely classical field without any quantum behavior [...] If this hypothesis is true, we have two separate worlds, the classical world of gravitation and the quantum world of atoms, described by separate theories. The two theories are mathematically different and cannot be applied simultaneously. But no inconsistency can arise from using both theories, because any differences between their predictions are physically undetectable."

~Freeman Dyson [Source]

Well. Needless to say, I do think there there is phenomenology of QG that is in principle observable, even though we might not yet be able to observe it. And I do think that observing it will lead us a way to QG.

However, there are various scenarios that could be realized at Planckian energies. Gravity could be quantized within one or the other approach. Also, higher order terms in classical gravity could become important. Or, there could be semi-classical effects coming into the game. Now one tries to take some insights from these approaches, leading to the above mentioned phenomenological models. Already here one most often has a redundancy. That is, various scenarios can lead to the same effect. E.g. modified dispersion relations, or the Planck scale being a fundamental limit to our resolution are effects that show up in more than one approach. In addition, there's a second step in which these models are then used to make predictions. Again, various models, even though different, could yield the same predictions. That's what I like to call the 'inverse problem': how can we learn something about the underlying theory of quantum gravity from potential signatures?

In the figure below I stress 'new and old' phenomenology because a sensible model shouldn't only be useful to make new predictions, it should also reproduce all that stuff we know and like. I have a really hard time to take seriously a model that doesn't reproduce the standard model and GR in suitable limits.



Now here are some approaches in this category of 'top down inspired buttom up approaches' that I find very interesting (for some literature, see e.g. this list):

• Extra dimensional extensions of the standard model, which can lower the Planck scale to values soon accessible at the LHC
• Deformations of Special Relativity (observer independent ?!? )
• Effects of a generalized uncertainty principle or a minimal length scale rspt.
• Breaking of Lorentz invariance
• Decoherence effects from space-time fluctuations
• Imprints of early an early quantum phase in the CMB/neutrino/graviton background

(And possibly we can maybe soon add macroscopic non-locality to that list, an interesting scenario that Fotini, Lee and Chanda are presently looking into.)

However, whenever one works within such a model one has to be aware of its limitations. E.g. the models with large extra dimensions are in my opinion such a case in which has been done what sensibly could be done. And now we'll have to turn on the LHC and see. After the original ideas had been outlined, many people began to build more and more specific models with a lot of extra features. It's not that I don't find that interesting, but it's somewhat besides the point. To me it's like building a house and worrying about the color of the curtains before the first brick has been laid.

Now, all of the approaches I've mentioned above are attempts to get definitive signatures of QG, but so far none of these predictions on its own would be really conclusive. Take e.g. a possible modification of the GZK cutoff - could have been 'new' physics, but not clear which, or maybe just some ununderstood 'old' physics, like the showers not being created by protons from outside our galaxy as generally assumed?

So, my suggestion to make progress in this regard is to construct models that are suitable to investigate observables in varios different areas. In such a way, we could be able to combine predictions and make them more conclusive. Think about the situation with GR at the beginning of the last century: It predicted a perihelion precession of Mercury, but there were other explanations like an additional planet, a quadrupole moment of the sun, or maybe a modification of Newtonian gravity. It took another observable - in this case light deflection by the sun - that was predicted within the same framework, and confirmed GR was the correct description of nature [4]. And please note, a factor 2 mattered here [5].

I personally am very optimistic about the future progress in quantum gravity - and that not only because it's hard to beat Dyson's pessimism. I think it doesn't matter where we start from, may it be a top-down, a buttom-up approach or somewhere in the middle. I also think it doesn't matter which direction each of us starts into. The history of science tells us that there often are various different ways to arrive at the same conclusion. A particularly nice example is how Schrödinger's wave formulation and Heisenberg's matrix approach turned eventually out to be part of the same theory.

I think as long as we listen to what our theories tell us, if we take into account what nature has to say, are willing to redirect our research according to this - and if we don't get lost in distractions along the way, then I think we have good chances to find a way to quantum gravity. And this finally solves the mystery of the quotation on the last slide of my talk:

'The problem is all inside your head' she said to me
The answer is easy if you take it logically
I’d like to help you in your struggle to be free
There must be fifty ways to [quantum gravity]

~Paul Simon, 50 Ways to leave your lover

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[1] In my notation the SM includes General Relativity.
[2] The exception being the very recommendable talk on Effective Quantum Gravity by John F. Donoghue.
[3] Though 3 years living in the US have tought me there's actually no such thing as a 'problem' - it's called a challenge. One just has to like them, eh?
[4] Admittedly, what the measurement actually said was not as straight forward as one would have wished. I leave it to my husband to elaborate on this interesting part of the history of science.
[5] The resulting deviation can be reproduced in the Newtonian approach up to a factor 1/2.

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TAGS: PHYSICS, QUANTUM GRAVITY, PHENOMENOLOGY