Quantum entanglement and instantaneous communication: exploring our own assumptions

A recent article by the brilliant Scott Aaronson gave a (as usual, for Aaronson) calm, rational and insightful discussion of the potential for quantum computing and information. I got the link from my friend Julian Klappenbach, who was then inspired to muse on the potential for instantaneous communication based on quantum entanglement:

Is it possible to send superluminal messages using quantum entanglement? There’s a good body of work that says: “no”. But like most rules, these were made to be side-stepped.

Birgit Dopfer’s experiment – From Wikipedia

Although such communication is prohibited in the [no communication theorem], some argue that superluminal communication could be achieved via quantum entanglement using other methods that don’t rely on cloning a quantum system. One suggested method would use an ensemble of entangled particles to transmit information, similar to a type of quantum eraser experiments.

Birgit Dopfer, a student of Anton Zeilinger’s, has performed an experiment which seems to make possible superluminal communication through an unexpected collective behavior of two beams of entangled photons, one of which passes through a double-slit, utilising the creation of a distance interference pattern as bit 0 and the lack of a distance interference pattern as bit 1 (or vice versa), without any other classical channel. Since it is a collective and probabilistic phenomenon, no quantum information about the single particles is cloned and, accordingly, the no cloning theorem remains inviolate.

Physicist John G. Cramer at the University of Washington is attempting to replicate Dopfer’s experiment and demonstrate whether or not it can produce superluminal communication.

I’m always glad that people are working on mind-bending science. In this case, there’s an important point being left out: what does “instantaneous” mean?

The thing that makes people get all brain-melty about quantum entanglement is that it says, basically, two particles are described by a single wavefunction. Supposedly in QM, “making an observation” results in “collapsing the wavefunction”. So when you make an observation on what we shallowly think of as “one of the pair”, that’s actually an observation on the combined wavefunction, which causes the whole thing to collapse all at once: instantaneously, regardless of the spatial extent of the wavefunction. But right now, there’s no theory that integrates QM with relativity. So, on the mega-scale, we have relativity telling us all kinds of weird things about the nature of timelines with respect to different reference frames (i.e. how different observers observe time differently), but in QM the conception of TIME is actually classical. So in QM, now is just now; there’s no other math describing how it could be anything else. Thus, when you observe one particle and “collapse the wave function”, that happens “now”, which (in the absence of any further elaboration, in QM) means it happens simultaneously regardless of distance.

But the thing is, the lack of integration of QM with what we know from relativity about mega-scale behavior of time and simultaneity is a gap in our understanding. It means that we actually don’t have the theoretical tools to make real scientific predictions about what would happen with entanglement over very long distances. In the absence of real scientific tools, we’re left with “simultaneous” which leads to “instantaneous”. But everyone is so obsessed with quantum weirdness these days that they’ve forgotten that relativity tells us that there is no such thing as an absolute chronological reference frame. Once you look at it like that, it becomes clear that instantaneous communication is impossible not because of some limitation on communication, but simply because relativity has already established that there is no way of defining what it would mean for two things to happen at the same time. In other words, we might want to think that we built a machine for instantaneous communication over long distances, but different observers in different reference frames would see different chronological relationships between the two sides of the communication device.

I just double-checked my understanding here by looking at the “time dilation” article on wikipedia, which refers to the “twin paradox” article. Also try “relativity of simultaneity”. Consider the simplest case, with no acceleration (so, inertial reference frames only; keeping us in the domain of Special Relativity). Two spaceships are zooming past each other in opposite directions, at constant speed. They both have accurate clocks which they will use to try to figure out whether their quantum entanglement communication is instantaneous or not. Also, I’m sitting still (i.e. each ship sees me moving at half the velocity of the other one; there is no such thing as “absolutely at rest”, there are only different relative inertial reference frames) right at the point where they will pass each other.

When they pass, we all look at each other and see that our clocks all read zero (we planned it like that). At that moment, I take the collection of entangled particles and give half of them to one ship and half of them to the other ship. So now the ships are ready to start their communications. 

In each ship, when they look at the other ship, they see the clock running slowly. So, say that when the ship 1 clock reads 1 year, they send the “instantaneous” signal to ship 2. But what does that mean? Does that mean that Ship 2 receives the signal when their clock reads 1 year? From the reference frame of Ship 1, the clock on Ship 2 reads 1 year much later, because of time dilation. So Ship 1 has a clock that reads 1 year, and they send the “instantaneous” quantum message, and Ship 2 receives it when *their* clock reads 1 year. But ship 1 already took a look at Ship 2’s clock and saw that it was running at (say) half speed. That means that Ship 1 knows that the time when Ship 2’s clock reads 1 year, is actually 2 years out. So Ship 1 sends their signal, and then they would expect Ship 2 to receive it when Ship 2’s clock reads 1 year, which is actually when Ship 1’s clock reads 2 years. So that certainly doesn’t feel instantaneous to the people on Ship 1 who sent the message; it’s pretty useless, in fact.

Even worse, let’s say hypothetically that what we expect to happen is that Ship 1 sends a signal when Ship 1’s clock reads 1 year, and then they expect Ship 2 to receive it “instantaneously”, which means as far as Ship 1 is concerned, they expect Ship 2 to receive it when Ship 2’s clock reads whatever Ship 1 thinks it should be reading “right now”. Namely, 1/2 year. So now say Ship 2 receives the signal when their clock reads 1/2 year, and sends a return signal. Then, by the same logic, they expect Ship 1 to receive the return signal when Ship 1’s clock reads 1/4 year! And if you set each clock to “ping” mode, basically you get a convergent infinite series all the way back to zero. 

We may or may not have a problem with the idea of information moving back in time, but that’s not what’s at issue here. The issue is that it’s clear that this also fails to be a useful “instantaneous” communication device.

Again, the problem is that the very nature of space-time itself is that there is NO SUCH THING as objective simultaneity over long distances. And in the absence of an integrated theory of relativistic quantum mechanics, we simply don’t know what we ought to expect to happen with the entangled wavefunction over space-travel-relevant distances.

Of course, it’s still an interesting question, even though we don’t know what’s “supposed” to happen, because we can postulate various possible options and consider what each one leads to. Having just gone through this just now, I’d say that I think the most likely option is the first one I described, at least for situations of special relativity. That means that it effectively works as if each entangled particle has its own internal clock, and that’s how they know when “the same time” is. That means that Ship 1 sends a message when their clock (and their particle’s imaginary internal clocks) reads 1 year, and Ship 2 receives it when their clock reads 1 year. What this means is that although the external observer (“me”, the way I set this up) sees the communication as instantaneous, each ship actually sees the communication taking a long time from their reference frames. So basically, this leads to a result where it never leads to anything other than an amusing curiosity where (just as with the experiments already being done) we can externally observe simultaneity, but it doesn’t do us any good when we try to get involved in it for communication purposes.

If we take this one step further, and try to figure out what happens in a more practical situation involving General Relativity, things get even weirder and less satisfying. Also I think the “particles internal clocks” heuristic breaks down.

Imagine we have home, which is an inertial reference frame (more or less), and then we build a very fast ship to colonize a distant planet. We synchronize our clocks and then the ship takes off on a round trip. When the ship gets back, their clocks only measure the passage of 1 year, but our clocks measure the passage of (say) 100 years. So say we know it takes them 1/2 year of their subjective time to reach the destination, but it takes 50 years of our subjective time. If we wait 50 years for them to reach the destination, and we send a signal, then if you use the “particles internal clocks” heuristic, then the ship doesn’t receive the signal until 99 years after the mission is over! That’s not very useful. On the other hand, using the same heuristic, if the ship sends a signal when they land at the destination, it will be received when the home clocks read 6 months, which is pretty exciting. It would be a really great “one small step for man, one giant leap for mankind” moment, but it would also be an absolutely one-way communication channel. If we tried to reply, they wouldn’t receive it for a very long time.

I actually suspect that the “internal clock” heuristic would break down under general relativity (i.e. the non-intertial-reference frame scenario described here) and something else would happen, but I have no idea what it would be. In any case, the point holds that space-time itself does not contain any way of defining what “instantaneous” means over long distances.

My point here is not that I think I can solve the problem of whether or not quantum entanglement allows “instantaneous” communication. My point here is merely that the word “instantaneous” doesn’t mean what ordinary usage thinks it means, on relativistic scales, and in fact there is no single correct way of interpreting that word, in the situations that we actually care about.  Therefore, if we want to get anywhere in the discussion of “instantaneous communication”, we have to start by being scientifically precise about what we are considering.  Relativity gives us the tools to be precise about space-time relationships over long distances; but the way it ends up working out is kind of unsatisfactory for the simple sci-fi “ainsible” idea we were hoping for, because there isn’t any possible definition of “instantaneous” that works out that way.

Note: The “particles internal clocks” heuristic shouldn’t be taken literally, because that would be a local hidden variables theory, which was already disproven (although, to be fair, the whole thing seems to rest on a wide range of assumptions which are so subtle that I certainly don’t understand them all.)

Postscript: some of you might be wondering why I’m blogging about this, when I’m supposed to be a psychologist researching the neuroscience of meditation.  The short answer is that one of the main things that has caught my attention in the course of my graduate education up to now, is the problem of the psychology of scientists themselves. In particular, when scientists are and are not aware of the assumptions they are making. In this case since I am a recovering Caltech physicist I knew enough to recognize some important assumptions that seemed to mainly go unacknowledged, and wanted to write them out.