Time dilation affecting quantum superpositions

Can gravity affect quantum systems? Quantum theory and gravity seem to apply to very different physical regimes. It is often argued that gravity is irrelevant on very small scales, where typical quantum phenomena are observed. But as has been shown in numerous experiments, gravity can indeed influence a quantum wave function of the smallest particles. Newtonian gravity from Earth can induce a quantum phase-shift for a particle that is in a superposition between two different heights. This was first demonstrated with Neutrons in the famous COW (Colella-Overhauser-Werner) experiment in 1975 [1].

The gravitational field causes time dilation: clocks closer to 

Earth run slower than clocks further away. For a quantum 

superposition of a single clock at two heights, the clock 

states and its position become entangled.

What about Einstein’s gravity? If the Newtonian potential can influence a quantum wave function, what can one expect from post-Newtonian effects stemming from general relativity? It turns out that novel phenomena arise, with no classical analogue. Classically, two clocks placed at different heights will experience different proper times, and thus will be time dilated with respect to each other. But in quantum theory, an additional effect arises: If a single clock is brought into superposition of two heights, its internal degrees of freedom (or clock states) get entangled with its position [2]. The acquired “which-way information” affects the quantum coherence of the position.

In a recent publication [3], we showed that the effect of time dilation on quantum systems is very general and affects the quantum coherence of any composite quantum system. Time dilation is universal: it affects any system regardless of its structure or composition. Clocks are affected by time dilation as much as the heart beat or the half-life of a decaying particle. In fact, all composite quantum systems are affected, as they usually have a finite temperature or energy spread: there is usually some internal dynamics present within the system. If such a composite system is brought into superposition between different heights above Earth, as in the above example with a clock, time dilation will correlate all internal dynamics with the height of the system. And this causes decoherence of the center-of-mass if a sufficient difference in proper times is accumulated along the superposed paths. Quantum coherence is lost because of the relative time delay of the internal dynamics of the system, which becomes position-dependent due to gravitational time dilation. There is no “external” environment, only the presence of time dilation causes the system’s center-of-mass to decohere due to the dynamics of its own composition. The effect follows from two very basic concepts of quantum theory and relativity: time dilation and quantum superpositions. 

A complex molecule in superposition in a gravitational 

field. Because of time dilation, the frequencies of the 

individual atoms depend on the height of the molecule. 

This causes decoherence of quantum superpositions 

of the center-of-mass of the molecule.

Even though time dilation is very weak on Earth, the effect can already be relevant on mesoscopic scales: If a micro-scale object at room temperature is put into a micrometer superposition, then time dilation will cause decoherence on the order of milliseconds. This is because many internal degrees of freedom contribute to the effect. Each individually is affected by time dilation only a tiny bit, but for a larger composite system, the effect can become significant. For quantum systems, it is of course very challenging to prepare such large superpositions, and other decoherence effects will also be of importance. But there is a parameter range at superfluid Helium temperatures, where experiments with very large molecules or microspheres could in principle observe the predicted phenomena in the future. Importantly, the effect is universal and any internal dynamics will contribute to decoherence. Thus one can think of other possible experiments, utilizing any internal dynamics. Many basic concepts that enter the effect are also discussed in our pedagogical note [4].

Finally, what do we actually learn from this study? In our work, we do not treat the gravitational field quantum mechanically, thus there is no direct connection to “quantum gravity”. Yet, we study how quantum mechanical test systems behave on a background space-time, as opposed to classical test particles, and new effects arise. We found a new decoherence mechanism, but the most important aspect of the work is that the interplay between quantum theory and gravity has novel phenomena to offer. Our work shows one example, but this research direction is still widely unexplored: Many more possible effects and experiments on the interplay between these two great theories are waiting to be discovered!

[1] R. Colella, A. W. Overhauser, S. A. Werner. “Observation of Gravitationally Induced Quantum Interference”, Phys. Rev. Lett. 34, 1472 (1975).

[2] M. Zych, F. Costa, I. Pikovski, Č. Brukner. “Quantum interferometric visibility as a witness of general relativistic proper time”, Nature Communications 2,505 (2011).

[3] I. Pikovski, M. Zych, F. Costa, Č. Brukner, “Universal decoherence due to gravitational time dilation”, Nature Physics 11,668-672 (2015).

[4] I. Pikovski, M. Zych, F. Costa, Č. Brukner, “Time Dilation in Quantum Systems and Decoherence: Questions and Answers”, arXiv:1508.03296 [quant-ph] (2015).