“The quantum state cannot be interpreted statistically”

The Nature.com summary is here, the new paper is here (pdf), abstract:

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.

I have no ability to judge this, but it seems serious people are taking it seriously.  Hat tip goes to Kevin Drum.


"I have no ability to judge this, but it seems serious people are taking it seriously."

That made me laugh. Certainly very interesting though, thanks for sharing.

I always thought that this just followed from the violation of Bell's Inequality... wouldn't interpreting a quantum state statistically require the presence of a hidden variable?

I have read elsewhere that the difference is this:
Bell's theorem applies to quantum states that are entangled, whereas with this result, unentangled states (quantum states that are unconnected across space and time) are able to communicate with each other, unless the wave function is not a real object.

Like Tyler, however, I have no ability to judge this.

Oops, didn't proofread... that should be "unless the wave function *is* a real object".

Naturally, communicating information between unentangled states would be a whole lot more mind-boggling than the now-experimentally-confirmed communication between entangled stages, which Einstein et al. freaked out about and considered an absurd impossibility at the time.

It would be amusing if the current authors, like Einstein, turned out to be too conservative about how freaky the universe is, and their "it's gotta be this way because the alternative is nonsense" conclusion turns out to be just as wrong as Einstein's.

Disclaimer: I might not know what I'm talking about.

Another proofreading fail: make that "entangled states", not "stages". Sigh...

Remember the 'faster than light' particles, later 'debunked'?

Maybe it's a real thing: http://www.nature.com/news/neutrino-experiment-replicates-faster-than-light-finding-1.9393

No one has claimed the experiment has been debunked. They need to go through all their systematic errors, not just the one in that paper. Mainly the timing between the accelerator and the detectors is the main suspect.

That new experiment reduced a lot the number of places where they could have made a mistake. But they still could have made a mistake, and it will be better when another team do another experiment on another pair of devices measuring the same thing.

I liked Steve Hsu's write up about Many Worlds interpretation that complements this:

I made it through physics grad school thinking of particles as "localized wave packets."

It is not news. Ok, their methods are new, but their conclusion can be found at the introduction to quantum physics on any book. Quantum particles interfere in a way that isn't compatible with just adding the probability of finding the particles on each place.

When you are talking about "physically distinct states of reality," you are talking about a philosophical question, not a scientific one. They are probably just saying something like one model better fits experimental results and/or is more logically clear and consistent than another model. That just means that it is a better model. Even if they have conclusively shown that one model is far superior to another, it doesn't tell us anything about "reality." When you are talking about things at a quantum scale, you only have access to experiments and scientific models. You don't have access to anything that can let you know about "reality."

Are you talking about economics, physics, or both?

It's the same thing, pretty much. Physicists sometimes don't realize that their models are just that -- models. However, their results are much more impressively interesting and useful than those of economists, so you can't blame them if they get carried away a bit.

Economists like to flatter themselves this way. Math != economics, however, as you can tell whenever you ask an economist for a prediction, or when one is foolish enough to make one.

Most people get carried away thinking that there's anything except models.

Quantum physics more useful than economics? Doubtful.

I know, the invention of the transistor didn't have much utility.

Quantum physics produced the transistor? Don't think so.

You're right! Quantum Physics didn't actually produce the transistor. People produced the transistor, using their knowledge of Quantum Physics.

More like people produced the transistor using their knowledge of classical physics. There's nothing quantum about transistor theory.

Bell's theorem only states that no local hidden variable theory cannot reproduce the predictions of QM. Non-local hidden variable theories (such as Bohm's) are still fine. This paper is claiming something else, that no theory that denies the reality of the wavefunction can reproduce the predictions of QM. Since the Copenhagen interpretation doesn't consider the wavefunction to be a real, physical object, it would be invalidated if this paper is correct.

"Since the Copenhagen interpretation doesn’t consider the wavefunction to be a real, physical object, it would be invalidated if this paper is correct."

I thought rather that Copenhagen was agnostic on the wavefunction's physicality?

Whereas many physicists have generally interpreted the wavefunction as a statistical tool that reflects our ignorance of the particles being measured, the authors of the latest paper argue that, instead, it is physically real.

I thought this would happen sooner or later; it's about time the Copenhagen interpretation died. The last gasp of classical physics -- it turns out Shrodinger's cat is actually both dead and alive.

Some info here btw:


I was going to say what Amasa Amos said.

I was going to say what Noah just said.

I was going to...never mind.

It always seemed to me that the Copenhagen interpretation is agnostic about "what is really going on" and that there is no disproving it, therefore. One could argue that it doesn't go far enough, but that is the appeal of it, in a way..

The interpration that Schrodinger's cat is both alive and dead, or that a particular particle traverses both this path AND that path, is not new or particularly at odds with Copenhagen. It's just a huge leap of intuition to admit that the cat is both alive and dead, but with a probability attached to both states such that all states add up to one. .

Yeah, I think it really depends who's talking. Bohr seems to argue the wavefunction is just a theoretical construct and is not an actual physical phenomenon itself, others are more agnostic.

I've never liked Copenhagen because to me it smacks of clinging to classical physics, almost like saying the particle is truly classical but we just can't know its properties until it is measured and collapse the waveform.

... Doh, shoulda kept reading the thread.

A good read, by the way:


The paper is just not careful in distinguishing between the mathematical representation of a physical system, i.e. a vector in Hilbert space, and the physical system itself. So you get very strange statements like "Some physicists hold that quantum systems do not have physical properties." What? I know what they are getting at... well, to avoid a long treatise, I think the content of this paper is pretty much tautology when you are more careful with language.

RE: @efp:"I think the content of this paper is pretty much tautology when you are more careful with language."


I believe the "everything is entangled" version of this result is probably correct. There have been problems with using the wavefunction as a probability distribution since the Dirac equation, so that is not particularly new except that it has been now been shown in a non-relativistic system.

The probability interpretation (Born Rule) has never been proven and appears to only apply in particular limits of the theory.

Besides, all this 4D stuff is bound to be wrong as the real theory is probably on a 2D holographic screen where we interpret parameters or running coupling scales as extra dimensions of time and space. Everything is entangled in a theory like that because our 4D concept of spacetime distance is just a low energy construct. [wink]

My take (as as someone who got a PhD in quantum measurement and control)
The paper starts by distinguishing what the results of a probabilistic theory are from a deterministic theory using a simple two atom (or qubit) experiment. So far so good. Then they show that a four atom experiment does not obey this simple rule. The step they are missing is to show that the same probabilistic/deterministic distinction holds for a four atom experiment as for a two atom one.

This is a standard frequentist mistake in regular probability theory and is well addressed inside the Copenhagen interpretation by a quantum version of De Finetti's theorem, similar to the classical De Finetti theorem. This theorem shows how one treats multiple copies of an experiment (or preparation) with probability.

I would be amazingly surprised if this result actually caused anyone who had thought about the subject to change their interpretation of quantum mechanics.

Quantum theory gives me a headache.

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