Thursday, June 18, 2015

No, Gravity hasn’t killed Schrödinger’s cat

There is a paper making the rounds which was just published in Nature Physics, but has been on the arXiv since two years:
    Universal decoherence due to gravitational time dilation
    Igor Pikovski, Magdalena Zych, Fabio Costa, Caslav Brukner
    arXiv:1311.1095 [quant-ph]
According to an article in New Scientist the authors have shown that gravitationally induced decoherence solves the Schrödinger’s cat problem, ie explains why we never observe cats that are both dead and alive. Had they achieved this, that would be remarkable indeed because the problem has been solved half a century ago. New Scientist also quotes the first author as saying that the effect discussed in the paper induces a “kind of observer.”

New Scientist further tries to make a connection to quantum gravity, even though everyone involved told the journalist it’s got nothing to do with quantum gravity whatsoever. There is also a Nature News article, which is more careful for what the connection to quantum gravity, or absence thereof, is concerned, but still wants you to believe the authors have shown that “completely isolated objects” can “collapse into one state” which would contradict quantum mechanics. If that could happen it would be essentially the same as the information loss problem in black hole evaporation.

So what did they actually do in the paper?

It’s a straight-forward calculation which shows that if you have a composite system in thermal equilibrium and you push it into a gravitational field, then the degrees of freedom of the center of mass (com) get entangled with the remaining degrees of freedom (those of the system’s particles relative to the center of mass). The reason for this is that the energies of the particles become dependent on their position in the gravitational field by the standard redshift effect. This means that if the system’s particles had quantum properties, then these quantum properties mix together with the com position, basically.

Now, decoherence normally works as follows. If you have a system (the cat) that is in a quantum state, and you get it in contact with some environment (a heat bath, the cosmic microwave background, any type of measurement apparatus, etc), then the cat becomes entangled with the environment. Since you don’t know the details of the environment however, you have to remove (“trace out”) its information to see what the cat is doing, which leaves you with a system that has now a classic probabilistic distribution. One says the system has “decohered” because it has lost its quantum properties (or at least some of them, those that are affected by the interaction with the environment).

Three things important to notice about this environmentally induced decoherence. First, the effect happens extremely quickly for macroscopic objects even for the most feeble of interactions with the environment. This is why we never see cats that are both dead and alive, and also why building a functioning quantum computer is so damned hard. Second, while decoherence provides a reason we don’t see quantum superpositions, it doesn’t solve the measurement problem in the sense that it just results in a probability distribution of possible outcomes. It does not result in any one particular outcome. Third, nothing of that requires an actually conscious observer; that’s an entirely superfluous complication of a quite well understood process.

Back to the new paper then. The authors do not deal with environmentally induced decoherence but with an internal decoherence. There is no environment, there is only a linear gravitational potential; it’s a static external field that doesn’t carry any degrees of freedom. What they show is that if you trace out the particle’s degrees of freedom relative to the com, then the com decoheres. The com motion, essentially, becomes classical. It can no longer be in a superposition once decohered. They calculate the time it takes for this to happen, which depends on the number of particles of the system and its extension.

Why is this effect relevant? Well, if you are trying to measure interference it is relevant because this relies on the center of mass moving on two different paths – one going through the left slit, the other through the right one. So the decoherence of the center of mass puts a limit on what you can measure in such interference experiments. Alas, the effect is exceedingly tiny, smaller even than the decoherence induced by the cosmic microwave background. In the paper they estimate the time it takes for 1023 particles to decohere is about 10-3 seconds. But the number of particles in composite systems that can presently be made to interfere is more like 102 or maybe 103. For these systems, the decoherence time is roughly 107 seconds - that’s about a year. If that was the only decoherence effect for quantum systems, experimentalists would be happy!

Besides this, the center of mass isn’t the only quantum property of a system, because there are many ways you can bring a system in superpositions that doesn’t affect the com at all. Any rotation around the com for example would do. In fact there are many more degrees of freedom in the system that remain quantum than that decohere by the effect discussed in the paper. The system itself doesn’t decohere at all, it’s really just this particular degree of freedom that does. The Nature News feature states that
“But even if physicists could completely isolate a large object in a quantum superposition, according to researchers at the University of Vienna, it would still collapse into one state — on Earth's surface, at least.”
This is just wrong. The object could still have many different states, as long as they share the same center of mass variable. A pure state left in isolation will remain in a pure state.

I think the argument in the paper is basically correct, though I am somewhat confused about the assumption that the thermal distribution doesn’t change if the system is pushed into a gravitational field. One would expect that in this case the temperature also depends on the gradient.

So in summary, it is a nice paper that points out an effect of macroscopic quantum systems in gravitational fields that had not previously been studied. This may become relevant for interferometry of large composite objects at some point. But it is an exceedingly weak effect, and I for sure am very skeptical that it can be measured any time in the soon future. This effect doesn’t teach us anything about Schrödinger’s cat or the measurement problem that we didn’t know already, and it for sure has nothing to do with quantum gravity.

Science journalists work in funny ways. Even though I am quoted in the New Scientist article, the journalist didn’t bother sending me a link. Instead I got the link from Igor Pikovski, one of the authors of the paper, who wrote to me to apologize for the garble that he was quoted with. He would like to pass on the following clarification:
“To clarify a few quotes used in the article: The effect we describe is not related to quantum gravity in any way, but it is an effect where both, quantum theory and gravitational time dilation, are relevant. It is thus an effect based on the interplay between the two. But it follows from physics as we know it.

In the context of decoherence, the 'observer' are just other degrees of freedom to which the system becomes correlated, but has of course nothing to do with any conscious being. In the scenario that we consider, the center of mass becomes correlated with all the internal constituents. This takes place due to time dilation, which correlates any dynamics to the position in the gravitational field and results in decoherence of the center of mass of the composite system.

For current experiments this effect is very weak. Once superposition experiments can be done with very large and complex systems, this effect may become more relevant. In the end, the simple prediction is that it only depends on how much proper time difference is acquired by the interfering amplitudes of the system. If it's exactly zero, no decoherence takes place, as for example in a perfectly horizontal setup or in space (neglecting special relativistic time dilation). The latter was used as an example in the article. But of course there are other means to make sure the proper time difference is minimized. How hard or easy that will be depends on the experimental techniques. Maybe an easier route to experimentally probe this effect is to probe the underlying Hamiltonian. This could be done by placing clocks in superposition, which we discussed in a paper in 2011. The important point is that these predictions follow from physics as we know, without any modification to quantum theory or relativity. It is thus 'regular' decoherence that follows from gravitational time dilation.”


  1. skeptic ---> skeptical, like "critic" is a person who is critical. (The spelling "sceptic"/"sceptical" also exists, with the same pronunciation, but c or k are both fine here.)

  2. "New Scientist further tries to make a connection to quantum gravity, even though everyone involved told the journalist it’s got nothing to do with quantum gravity whatsoever."

    As you said yourself: "Just because it's something with quantum and something with gravity doesn't mean it's quantum gravity."

  3. Bee, "In fact there are many more degrees of freedom in the system that remain classical than that decohere by the effect discussed in the paper." -- did you mean "In fact there are many more degrees of freedom in the system that remain quantum than that decohere by the effect discussed in the paper."?

  4. Arun,

    Thanks! Yes, that's what I meant. I have corrected this.

  5. Thanks a lot Sabine for clarifying the significance of this paper. I was quite excited seeing this in Nature Physics (which is not the usual place for fancy new theories on quantum decoherence) as it is mark of scientific seriousness. But of course what journalists are making of it is not always controlled by the authors. Your explanations are very welcome!

  6. Molecules retain structure via decoherence. One chiral camphor molecule floats in a vacuum cavity resonant with the impedance of free space. Is it a superposition of both hands, does it racemize?

    1970s' debate concluded "no," but never looked. Bicyclic camphor need only "break" one bond to flip. That image also contains tricyclic twistane, requiring two bonds to break. Pentacyclic D_3-trishomocubane, second image stereogram, is classically unbreakable. The only way to know is to look.

  7. Isn't this similar to Penrose theory of effect of gravity on collapse of wave function? I understand, Penrose's theory has been also criticized for extreme weakness of gravity.

  8. The Copenhagen interpretation, that Schrödinger address, is nonsense as it has free will as axiom. Without free will no superposition.

  9. For some years now, I have found the coverage of physics in NS pretty terrible. This impression was confirmed last year, when they agreed to publish an article describing our discovery of Einstein's attempt at a steady-state model of the cosmos.
    For some reason, the editor kept changing the thrust of the piece to a completely irrelevant story about the cosmological constant - in the end, I had to pull the article.

  10. Dear Sabine,

    since you brought it up, I would like to offer some clarification regarding temperature in a gravitaitonal field, which is an interesting topic in itself. The first thing to notice is that the density matrix of the internal degrees of freedom doesn't change as the particle is pushed in the gravitational field, because the particle is isolated and not in thermal equilibrium with an external environment. If the probability to find the particle in its internal ground state is p0, this will not change as the particle is moved around, as this would require an exchange of energy with some external degrees of freedom. In this sense the internal temperature, as defined by a local observer sitting with the particle, doesn't change. A lobaoratory observer at a fixed gravitational potential, however, assigns different energy levels to the internal states, because of redshift, thus will also assign a different temperature. In other words, the occupation numbers of the internal degrees of freedom are independent of the observer, while energies and temperature are not.
    This situation is in a sense complementary to what is known as the Tolman effect (or Ehrenfest-Tolman). This effect concerns systems at different positions in a gravitational field in thermal equilibrium with each other (a typical example is a column of gas). In this case, the temperature as measured by the laboratory observer is the same for all systems, whereas the local temperature of each system depends on its position in the field.
    Both situations can be easily understood in terms of gravitational redshift and correspond to two limiting scenarios: isolated systems in our case and systems in thermal equilibrium for the Tolman effect. The notion of local vs laboratory temperature, and the relation with the Tolman effect, is discussed in the supplementary material attached to the Nature Physics article:


  11. My interest (and knowledge) about this stuff is a bit amateurish, but I have a question or two.

    I understand that there could be two general ways to actually manipulate the particles in question in this kind of experiment:
    (a) Create a beam of particles and do some kind of interferometry
    (b) Trap some particles in an optical tweezer or similar

    My question is, in case (a) the beam follows a geodesic - so there is in a sense no gravitational effect within the proper reference frame of a particle. Would this eliminate (or greatly reduce) the effect reported in the paper?

  12. I'm sorry about the delayed comment/question... I only recently started reading your blog and have come to various past posts by internet search. I am particularly interested in this post, and I apologize if this seems like a dumb question. Let's assume you somehow thermally isolate a Schrodinger Cat experiment, which is inside a large box. Wouldn't the superposition of the radioisotope (or whatever) quickly decohere INSIDE the box due to interactions with the cat, etc., thus reducing the superposition to a mixed state? Or would "isolation" keep the whole lab in a superposition? And if so, why would my later observation of the cat decohere the superposition when the cat couldn't? Thank you.

    1. Dear Andrew,
      I find this question quite crucial indeed, it touches the core of the Schrödinger Cat "paradox". In my opinion, which is not to be considered as authority, here is how to express the situation you are describing in term of quantum mechanics.
      Let's call all that is in the box system A, and all the rest outside the box system B. Initially, we can assume that system A is in a pure state, i.e. we have complete knowledge about it (difficult with a cat :) but doable with a few atoms).
      Now, a mixed state of system A can always be expressed as the partial trace over system B of a pure, entangled state of A+B. The partial trace means that we have no access to information contained in B, which is typically what we mean when B is an "environment".
      So, if A and B can interact, they will most likely become entangled (correlations will develop between them), but since we cannot measure all variables of the environment, we have to take a partial trace over B's eigenstates to obtain the state of A, which turns out to be a mixed state if A and B are entangled.
      If you run the argument in reverse (which I am not completely certain you can do), then A can only end up in a mixed state if it got entangled with B. Therefore, with a totally isolating box enabling no interaction, I think that A would remain in a pure state, i.e. a coherent superposition and not a mixture.
      Happy to hear if I made a mistake in my reasoning!


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