Folks have been asking about the new *Nature Physics* article by Pikovski et al., “Universal decoherence due to gravitational time dilation” . Here are some comments:

- I think their calculation is probably correct for the model they are considering. One could imagine that they were placing their object in a superposition of two different locations in an electric (rather than gravitational field), and in this case we really would expect the internal degrees of freedom to evolve in two distinct ways. Any observer who was “part of the superposition” wouldn’t be able to tell locally whether their clock was ticking fast or slow, but it can be determined by bringing both clocks back together and comparing them.
- It’s possible the center of mass (COM) gets shifted a bit, but you can avoid this complication by just assuming that the superposition separation is much bigger than the size of the object , and that the curvature of the gravitational field is very small compared to both.
- Their model is a little weird, as hinted at by their observation that they get “Gaussian decoherence”, , rather than exponential, . The reason is that their evolution isn’t Markovian, as it is for any environment (like scattered or emitted photons) composed of small parts that interact for a bit of time and then leave. Rather, the COM is becoming more and more entangled with each of the internal degrees of freedom as time goes on.
- Because they don’t emit any radiation, their “environment” (the internal DOF) is finite dimensional, and so you will eventually get recoherence. This isn’t a problem for Avagadro’s number of particles.
- This only decoheres superpositions in the direction of the gravitational gradient, so it’s not particularly relevant for why things look classical above any given scale. More precisely, if this were actually an important effect in understanding the quantum-classical transition, we’d expect things to be substantially “more quantum” in horizontal directions than vertical ones.
- This effect is miniscule. Taking a quick look at Table 3.1 of Schlosshauer’s book, I estimate that the CMB (already an extremely small weak source of decoherence compared to other sources) is roughly 16 orders of magnitude stronger than the effect discussed by Pikovski et al. This is confirmed by Fig. 2, which shows that you’d need a gigantic superposition to observe this effect: a micron-sized object superposed over a mm for multiple minutes! This is many orders of magnitude beyond even the very ambitious MAQRO experiment. I expect many, many novel sources of decoherence to appear between the levels we can currently suppress and this time-dilation effect.
^{a }

In summary: the basic calculation is fine, but this doesn’t tell us anything new about the quantum-classical transition.

See the good discussion by Sabine Hossenfelder, and my previous post on why we care about the decoherence of the COM.

**Edit 2016-3-23**: See also this and especially this by Gooding and Unruh.^{b }

### Footnotes

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**Edit 2016-3-10**: Carlesso & Bassi agree that this isn’t an important decoherence sources for any superpositions that could be constructed any time soon.↵- Abstract: ‘We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer (Gooding and Unruh in Phys Rev D 90:044071, 2014). The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell’s position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed “universal” decoherence mechanism attributed to gravitational time dilation (Pikovski et al in Nat Phys, 2015). We note that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in (Pikovski et al in Nat Phys, 2015) vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect.’↵

In this paper, does the mixedness of the final COM state come from the fact that initially the constituents were in a mixed (thermal) state? Otherwise the process is completely unitary, right?

The internal degrees of freedom (IDOM) do have an initial temperature, but the mechanism described in this paper is capable of decohering the COM even for T=0. This can happen since the COM and the IDOM become correlated, i.e., the overall state evolves to |COM_1>|IDOF_1> + |COM_2>|IDOF_2>. This can be unintuitive if one is used to thinking of decoherence as a process that happens to an object as a whole, but really it’s just the irreversible build up of correlations between any two quantum degrees of freedom. An object can perfectly well decohere it’s own COM.