Gravity in Quantum Mechanics

COMMENTARY | INSIGHT

Gravity in quantum mechanics Giovanni Amelino-Camelia Gravity and quantum mechanics tend to stay out of each other’s way, but this might change as we devise new experiments to test the applicability of quantum theory to macroscopic systems and larger length scales.

he remarkable accomplishments of Among the numerous approaches1 on phenomena of a mainly relativistic twentieth-century physics revolve used to define the interface between and gravitational nature that are studied Taround the success of two theoretical relativity and quantum mechanics, I find with experimental sensitivities for which paradigms. On the one hand, we have it easiest to focus on the one centred one might expect tiny effects originating phenomena described by quantum on modified uncertainty relations and/ from the interface between gravity and mechanics and involving interactions or modified commutator relations. A quantum mechanics. Some of the most that are governed by the standard model well-studied scenario3,4 assumes that the interesting opportunities for such tests of particle physics. On the other hand, uncertainty relations for measuring the concern the description of the propagation we have (general) relativity and its position coordinates xj and momenta pk of particles over astrophysical distances. description of gravitational phenomena. are produced by non-commutativity of the Relativity makes firm predictions for These two very different theories manage relevant observables of the form: these laws of propagation — assuming, to share quarters by keeping clear of however, that spacetime coordinates are 1 2 2 each other . Gravity is negligible in [xj, pk] = iδjkh(1 + α p ) (1) unaffected by uncertainty principles. the typical applications of quantum But new uncertainty principles, such mechanics, which involve microscopic where δjk is 1 only when j = k (0 otherwise) as the one encoded through equation particles and relatively short distances. and α is a length-scale characteristic (2), would affect the structure of the Analogously, quantum mechanical of the modification to be determined signal in photons and neutrinos seen by effects are usually inconsequential experimentally. The standard Heisenberg telescopes monitoring distant explosions in when we study macroscopic bodies and commutator is recovered in the limiting astrophysical bodies. large distance scales, where gravity is case where the effects ofα can be neglected. Such imprints are now being sought in charge. In addition, there may also be new with the Fermi (see Fig. 1), HESS and Still, we do not expect gravity to be uncertainty principles and non-trivial MAGIC telescopes for photons, and truly absent at microscopic scales or that commutators involving pairs of position with IceCube for neutrinos. There is a quantum mechanics should somehow coordinates of the form5,6: determined effort to find evidence of switch off at macroscopic distances: it is spacetime fuzziness effects. The data m just that the effects they produce in those [xj, xk] = iΘjk + iΦjkxm (2) analysis would be very simple if we could regimes are very small and we have not yet assume that the astrophysical source m managed to develop the technologies and where the matrices Θjk and Фjk would emits a burst of high-energy photons devise the experiments capable of seeing have to be characterized by small length and neutrinos all in exact simultaneity: such small effects. But this frustratingly scales, small enough to explain why if such a short-duration burst propagates leaves us without a clue about how quantum mechanics was so far successful in a classical spacetime, then all particles these very different theories manage to ignoring them. in the burst must reach our telescope cooperate when they both must be taken For measurements involving large (nearly) simultaneously. One of the m into account. distance scales, the term Фjk in equation (2) possible implications of the modified The early Universe is the prototypical could be important in two very different uncertainty relations is that the signal example of where we expect both theories ways. There will be situations that we would propagate with some fuzziness to produce large effects1,2. However, with usually describe only in terms of relativity and the particles would not reach our no direct experimental access to the and gravitational effects and in these cases telescope simultaneously — the arrival conditions in the early Universe we have to the analysis of the spacetime properties times might therefore exhibit some sort of look elsewhere, and our best chances are will be affected by the new properties statistical spread. in regimes where one of the two theories of spacetime coordinates governed by However, we know that the duration of m dominates the description of the dynamics Фjk. And there will be situations that particle bursts from astrophysical sources and yet the smaller effects of the other we usually describe using quantum is not ideally small: in the best cases the theory might come within the reach of theory alone — here the analysis of the bursts last a few seconds. This decreases some high-sensitivity experiments. More quantum uncertainties might receive small the sensitivity of the studies, but we are simply put, we should then be looking corrections of quantum-gravitational origin learning how to compensate for these m either for (i) modifications of gravity by governed by Фjk. aspects of the emission mechanisms. quantum mechanics or, conversely, for The first of these two possibilities has The results so far have been negative, (ii) modifications of quantum mechanics already been studied intensely, particularly but the expected pace of improvement by gravity. over the past decade2. These efforts focused in sensitivities for the next decade or so

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provides hope that a discovery might be just around the next corner. Much less has been done for the Ursa Major second possibility, the case of phenomena primarily governed by standard quantum Leo mechanics, but affected by small corrections originating from the interface between gravity and quantum mechanics. Nevertheless, over the past couple of years GRB 130427A there have been some studies that I believe might set the stage for quick progress in this line of research. In this respect I feel it is very significant that techniques are being developed for testing some of the most striking features of quantum mechanics — such as entanglement — in experiments involving the exchange of particles over truly macroscopic distances, including the COLLABORATION LAT NASA/DOE/FERMI possibility of exchanging particles between Figure 1 | Searching the skies for the tiny effects that originate from the interface between gravity and a ground laboratory and a satellite7 (see also quantum mechanics. Gamma-ray bursts are short-lived and very bright. The highest-energy light ever the Review by Shadbolt et al. in this issue8). detected from such an event (GRB130427A) was observed in 2013. The image in the left panel taken by On the theory side, we will have to catch NASA’s Fermi Gamma-ray telescope shows how the northern galactic hemisphere of the gamma-ray sky up with these experimental opportunities looked just before the GRB130427A burst depicted in the right panel. and we have just recently started to make progress9,10 in understanding how the non-commutativity of coordinates exploited in the search of manifestations of I used here. More realistic theoretical (equation (2)) could affect entanglement the interface between gravity and quantum descriptions of macroscopic bodies could and other striking aspects of quantum mechanics. provide guidance for these experiments. theory. For instance, we expect that the It is useful to contemplate an idealized I, for one, am not at all frustrated by the presence of further contributions to the description12,14,15 of a macroscopic body fact that theory might have to catch up with uncertainties that grow with distance composed of N identical particles in experiments. For a long time — a time that would produce a loss of coherence in the terms of its centre-of-mass coordinates might be eventually viewed as the dark ages 1 N n 1 N n quantum states that becomes increasingly Xj =-N ∑n=1 xj and Pj =-N ∑n=1 pj where of quantum-gravity research — it seemed n n significant over large distances. This x j and p j denote the coordinates and that the study of the interface between coherence loss would lead to a gradual loss momentum of the nth particle. In the gravity and quantum mechanics should of entanglement. So with an entangled state current formulation of quantum mechanics, be a unique case of ‘pure-theory science’. shared between Earth and a distant satellite, the validity of standard commutators It was not expected that experiments m n we could find an otherwise unexpected for the constituent particles [x j, x k] = 0 would ever reach the level of the theory. m n loss of coherence — possibly signalling a and [x j, pk] = iδnmδjkh implies that also But things are now changing, and it would quantum-gravity effect. [Xj, Xk] = 0 and [Xj, Pk] = iδjkh, meaning be extremely exciting if experiments It would be very interesting to look that the same commutation relations apply took the lead in some areas of quantum for such an effect, even though the to the centre-of-mass degree of freedom gravity research. ❐ theoretical efforts aimed at modelling such of the macroscopic body. This striking phenomena cannot give us much guidance property of standard quantum mechanics Giovanni Amelino-Camelia is in the Physics yet. We understand qualitatively the turns out to be fragile, and as soon as any Department, Sapienza University of Rome, m mechanism that should produce the loss of the parameters α, Θjk, Фjk in equations Rome 00185, Italy. of coherence, but we are still looking for a (1) and (2) become non-negligible, the e-mail: [email protected] satisfactory phenomenological description correspondence between the quantum for guiding these long-distance quantum- properties of the microscopic particles and References theory tests. those of the macroscopic body is lost12,14,15. 1. Carlip, S. Rep. Prog. Phys. 64, 885–942 (2001). Another promising direction is the This should encourage accurate tests 2. Amelino-Camelia, G. Living Rev. Rel. 16, 5 (2013). 3. Kempf, A. et al. Phys. Rev. D 52, 1108–1118 (1995). development of experimental techniques of quantum mechanics with macroscopic 4. Ali, A. F. et al. Phys. Lett. B 678, 497–499 (2009). for testing the applicability of quantum bodies, especially if we can manage to take 5. Doplicher, S. et al. Phys. Lett. B 331, 39–44 (1994). theory to macroscopic systems. In differential measurements that compare 6. Majid, S. & Ruegg, H. Phys. Lett. B 334, 348–354 (1994). 7. Rideout, D. et al. Class. Quant. Grav. 29, 224011 (2012). particular, it is now possible to observe the quantum properties of a macroscopic 8. Shadbolt, P., Mathews, J. C. F., Laing, A. & O’Brien, J. L. the quantum behaviour of the observables body to those of one of its constituents. But Nature Phys. 10, 278–286 (2014). of truly macroscopic mechanical here too theory needs to advance to a level 9. Adhikari, S. et al. Phys. Rev. A 79, 042109 (2009). 11,12 10. Ghorashi, S. A. A. & Bagheri Harouni, M. Phys. Lett. A oscillators (see also the Review by where it can feed back to experiments: the 377, 952–956 (2013). 13 Arndt and Hornberger in this issue ). sort of descriptions of macroscopic bodies 11. Chen, Y. J. Phys. B 46, 104001 (2013). If the gravitational corrections to the for which the relevant quantum-gravity 12. Pikovski, I. et al. Nature Phys. 8, 393–397 (2012). quantum mechanics of macroscopic scenarios have been so far analysed do 13. Arndt, M. & Hornberger, K. Nature Phys. 10, 271–277 (2014). 14. Quesne, C. & Tkachuk, V. M. Phys. Rev. A bodies are very different from those not go much further than the idealized 81, 012106 (2010). for microscopic particles, this could be description of a macroscopic body that 15. Amelino-Camelia, G. Phys. Rev. Lett. 111, 101301 (2013).

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