Quantum Complementarity Meets Gravitational Redshift
(From left to right) Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner
Authors: Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner
Affiliations: Faculty of Physics, University of Vienna, Austria
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The unification of quantum mechanics and Einstein's general relativity is one of the most exciting and still open questions in modern physics. In general relativity, space and time are combined into a unified underlying geometry, which explains the gravitational attraction of massive bodies. Typical predictions of this theory become clearly evident on a cosmic scale of stars and galaxies. Quantum mechanics, on the other hand, was developed to describe phenomena at small scales, such as single particles and atoms. Both theories have been confirmed by many experiments independently. However, it is still very hard to test the interplay between quantum mechanics and general relativity. When considering very small systems, gravity is typically too weak to be of any significance. The most precise experiments so far have only been able to probe the non-relativistic, Newtonian limit of gravity in conjunction with quantum mechanics. Conversely, quantum effects are generally not visible in large objects.
According to general relativity, time flows differently at different positions due to the distortion of space-time by a nearby massive object. A single clock being in a superposition of two locations allows probing quantum interference effects in combination with general relativity. [Image credits: Quantum Optics, Quantum Nanophysics, Quantum Information; University of Vienna]
There is, however, a possibility to measure predictions of Einstein’s theory of general relativity without using extremely massive probe particles: one of the counterintuitive predictions of Einstein's general relativity is that gravity distorts the flow of time. The theory predicts that clocks tick slower near a massive body and tick faster the further they are away from the mass. The earth’s gravitational field produces a sufficient distortion of space-time such that the different flow of time at different altitudes can be measured with very precise clocks. This has been confirmed experimentally with classical clocks and the results were in full agreement with Einstein’s theory.
Two initially synchronized clocks placed at different gravitational potentials will eventually show different times. According to general relativity a clock near a massive body ticks slower than the clock further away from the mass. This effect is known as gravitational time dilation or gravitational redshift.
Scientists at the University of Vienna now proposed that the effect described above, which is also commonly known as the “gravitational redshift”, can also be used to probe the overlap of general relativity with quantum mechanics. In the scheme published in October in Nature Communications, the classical version of the experiment is modified such that it becomes necessary to take quantum mechanics into account. The idea is to exploit the extraordinary possibility that a single particle can be without a well-defined position, or as phrased in quantum mechanical terms: it can be in a “superposition” of two different locations. This allows single particles to produce typical wave-like detection patterns, i.e. interference.
Superpositions of particles are, however, very fragile: if the position of the particle is measured, or even if it can in principle be known, the superposition is lost. In other words, it is not possible to know the position of the particle and to simultaneously observe interference. Such a connection between information and interference is an example of quantum complementarity - a principle originally proposed by Niels Bohr. Because of the above-mentioned fragility, it is very challenging to observe and to maintain superpositions of particles. Even a very weak interaction of the particle with its surrounding leads to the demise of quantum interference. But even though the loss of superpositions is a nuisance in many quantum experiments, the newly proposed experimental scheme to probe general relativity in conjunction with quantum mechanics actually builds upon this complementarity principle.
The novel idea developed in the group of Prof. Č. Brukner is to use a single clock (which can be any particle with evolving internal degrees of freedom, such as spin) that is brought in a superposition of two locations – one closer and one further away from the surface of the Earth. Afterwards, the two parts of the superposition are brought back together, and it is observed whether or not an interference pattern is produced. According to general relativity, the clock ticks at a different rate depending on its location. But since the time measured by the clock reveals the information on where the clock was located, the interference and the wave-nature of the clock should be lost. The amount of the loss of quantum mechanical interference becomes a measure of the general relativistic redshift. To describe this effect, both general relativity and quantum mechanics are required. Such an interplay between the two theories has never been probed in experiments yet. It is therefore the first proposal for an experiment that allows testing the genuine general relativistic notion of time in conjunction with quantum complementarity.
A single clock is brought in a quantum superposition of two locations: closer and further away from the surface of the Earth. Because of the gravitational redshift, the time shown by the clock reveals the information on the clock’s location. Thus, according to the quantum complementarity principle, interference and the quantum wave-nature of the clock will be lost.
In the setup described above, the loss of quantum interference becomes a tool to measure the general relativistic time dilation. It is not even necessary to read out the clock itself: The sheer existence of the clock is sufficient to destroy the interference. But since quantum interference effects are very fragile, it is important to verify that their demise is really caused by the distortion of the flow of time. This can be done by performing the same experiment in two different ways: one where the clock is running, as described above, and one where the clock is “switched off”. In the latter case the quantum interference should become visible, as opposed to the former case.
A further application of the proposed experiment is that it can also test new physical theories. For example, in the context of theories that aim at combining general relativity and quantum mechanics into a single framework, it has been proposed that every particle carries a clock with itself, which measures time along its path. Such a possibility can be probed by the proposed experiment, without the need to directly measure such a hypothetical internal clock: if quantum interference is lost even in the case when the clock which is controlled by the experimentalist (for example, the aforementioned precession of the particle’s spin) is switched off, one can infer that there is an intrinsic mechanism which can keep track of time by itself. On the other hand, if interference is observed, the existence of an internal clock can be ruled out.
Another interesting possibility is that the quantum interference persists even with the experimentally controlled clock turned on. This would mean that quantum mechanics or general relativity breaks down when phenomena inherent to both theories become relevant. Such a scale has never been accessible for experimental tests so far.
To experimentally observe the predicted interplay of quantum interference and the gravitational redshift, three parameters are of importance: The height difference of the two locations at which the particle is held in a superposition, the time that the particle is kept in the superposition and the ticking rate of the clock. The larger any of those values, the easier it is to observe the effect. Currently, the most promising systems for such an experiment are single atoms. They can be brought into superpositions in atomic fountains and their internal states can be used as atomic clocks. There are also other systems that can be used to successfully perform the experiment: neutrons, electrons and even large molecules. There has been rapid experimental progress in the precision of clocks and in the size of the superpositions that can be created and maintained in the laboratory. It is therefore possible that within the next few years the proposed experiment with quantum clocks can be realized.
Both quantum mechanics and general relativity seem to be universal theories, though we still don’t know how to properly combine them in a universal framework. New phenomena are expected at some scale at the interplay between the two theories. Only experimentally probing this interplay may give a hint as to how to proceed in constructing a unifying description of nature.
 Magdalena Zych, Fabio Costa, Igor Pikovski & Časlav Brukner. "Quantum interferometric visibility as a witness of general relativistic proper time". Nature Communications, 2:505 doi: 10.1038/ncomms1498 (2011). Full Article: PDF, HTML.