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Background
I recently read that a group had managed to overcome both the communication loophole and the detection loophole for Bell's theorem.

In reading the article, I started to think about another issue which I had not realized upon first learning about quantum entanglement. I am aware that entanglement does not necessarily mean one can communicate faster than the speed of light in vacuum1. I am also aware2 that entanglement shows the wave function need not be local.

What I thought about after reading the article was that regardless of these issues, one could never physically separate two particles faster than the speed of light. So even if we did manage to use entanglement as a near-instantaneous communication method, we would not necessarily violate relativity because the entangled particles cannot be separated faster than $c$.

Question
I assume someone has already thought of this but I am curious if I am thinking about this correctly3.

  • Have I misunderstood a fundamental aspect of entanglement?
  • Am I focusing on a trivial, non-issue and missing the bigger picture?
  • Or am I understanding at least part of the issue correctly?

Footnotes

  1. Well, actually two different quantum professors told me two different things: one said it was possible to use entanglement for communication the other said it was not possible.
  2. Aware at a mathematical level, not really an intuitive level...
  3. I used the soft-question tag because I doubt my formulation of this question is rigorous. However, my lack of knowledge/experience with the deeper parts of quantum like entanglement make it very difficult to constrain a question as well as I would like.
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    $\begingroup$ One can't use entanglement alone as a communication method, at all. It always takes a second classical path to exchange information about the entangled states. It's that path that limits the speed at which information can be exchanged, not the separation velocity of the parts of the entangled state. $\endgroup$ – CuriousOne Oct 29 '15 at 1:07
  • $\begingroup$ @CuriousOne - So the fact that one cannot separate the particles faster than $c$ is irrelevant? Darn it... $\endgroup$ – honeste_vivere Oct 29 '15 at 1:09
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    $\begingroup$ I wouldn't say it's irrelevant, it's just not what stops us from communicating trough entanglement IMHO. The curious thing about entanglement is that it stems from a second, completely orthogonal structural element of reality that is independent of the Lorentz structure of spacetime. To me the real question is about the single principle that lies behind both. $\endgroup$ – CuriousOne Oct 29 '15 at 1:26
  • $\begingroup$ This isn't really what the soft-question tag is for. $\endgroup$ – Emilio Pisanty Oct 29 '15 at 13:25
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I thought entanglement involved sharing a similar (or the same?) wave function.

Nothing could be farther from the truth. I could entangle the polarization of a photon with the position of an electron. Or entangle the energy of an electron with the direction of propagation of a photon.

Its really just superposition. A state with an electron on the left and a photon with a vertical polarization is a fine state. So is a state with the electron on the right and the photon having a horizontal polarization. And since both those states are fine, so is a complex superposition. And that particular superposition is an entanglement of the two options.

And here is the key. You could get something similar to entanglement by just flipping a coin and if it is heads making the state with an electron on the left and a photon with a vertical polarization. And if it is tails making a state with an electron on the right and a photon with a horizontal polarization. But that isn't true entanglement, because a true entanglement really is that superposition so it allows you to measure a circular polarization and you'll get your position in a superposition rather than than just getting the left or right you made.

So an entanglement is similar to just making one option or another. But it is different, it has the full superposition of the two possibilities. And this means interactions have access to both.

And there is another key here. A non entangled state could be written as $\left|\text{left}\right\rangle_e\otimes\left|\updownarrow \right\rangle_\gamma$ and it makes sense to say the electron has a state (of being on the left) and the photon has a state (of vertical polarization). And a non entangled state could be written as $\left|\text{right}\right\rangle_e\otimes\left|\leftrightarrow \right\rangle_\gamma$ and it makes sense to say the electron has a state (of being on the right) and the photon has a state (of horizontal polarization). But for the entangled state $$\frac{1}{\sqrt 2}\left|\text{left}\right\rangle_e\otimes\left|\updownarrow \right\rangle_\gamma+\frac{1}{\sqrt 2}\left|\text{right}\right\rangle_e\otimes\left|\leftrightarrow \right\rangle_\gamma $$ it doesn't make sense to say the electron has a state or that the photon has a state. Instead the system has a state and that's all we can really say.

In effect, any action on one is no different than an action on the other as if they were the same exact particle at the same location, right?

This is 100% wrong. From the example above you can see that a massive charged electron with spin 1/2 can have its position be entangled with the polarization of a massless uncharged spin 1 particle. That's as different as things can be. The point is that it is similar to just making $\left|\text{left}\right\rangle_e\otimes\left|\updownarrow \right\rangle_\gamma$ or making $\left|\text{right}\right\rangle_e\otimes\left|\leftrightarrow \right\rangle_\gamma$. Similar in that you might get one option or you might get the other and this isn't going to send information from one to the other. If you measure the polarization of your photon and find it is vertical then you could know which pair exists now, but you didn't control which you got, you just learned which you got.

But it isn't as simple as just making one or the other, since you might measure something other than horizontal/vertical polarization. So the entire joint state exists.

What you really have is a joint state that can split into different possibilities depending on how you interact with it. And the fact that it is nonlocal means that an interaction in one region can split the entire state into parts.

But this is because it is a joint state and the individual particles don't have their own states to break into parts. Normally things break into parts but in an entangled system the joint system has to be what breaks into parts.

the entangled particles cannot be separated faster than c.

Now this is a problem too. Firstly, entanglement can be swapped so the particles could become entangled through a swapping of entanglement and the newly entangled particles could be ones that have never ever seen each other. Secondly, a particle might not have a well defined position. If one particle is in superposition of states with very different positions then what does it mean to talk about how far in space it is from something else?

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  • $\begingroup$ Ah, so you can entangle two particles that have "never" been in close proximity to one another? Okay, that makes the topic even more confusing (though your answer is much better explained than most articles I found). $\endgroup$ – honeste_vivere Oct 29 '15 at 17:49
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The reason your argument is wrong is that one could imagine something like the following:

We create an entangled pair of electrons, say in state $UU-DD=(U+D)(U-D)+(U-D)(U+D)$. You put one in your pocket (unobserved), I put one in my pocket (unobserved) and we travel to distant places, arriving at noon on January 1, 2016. At that moment, you decide to send me a message, which you do by choosing a measurement to perform on your electron. You can either do a U/D measurement or a U+D/U-D measurement. The outcome of your measurement then determines the state of my electron (instantly).

You might think that you could use this to send me an instant message. The message is composed at noon on 1/1/2016 and received instantly. The fact that we spent several years traveling before you sent your message is irrelevant to the fact that the message is instant.

Now in fact that's wrong---you cannot actually use this method to convey any information, for reasons that are well understood. But the point is that without those reasons, your argument does not suffice.

To put this another way: Suppose I want to broadcast a TV show to your house. It takes me five years to build a transmitter. I then broadcast the show and it arrives at your house half a second later. That's communication, and it's communication that takes only half a second, quite independent of how long it took me to build the transmitter.

Separating the entangled particles is like building the transmitter. It doesn't count toward calculating the speed of any communication that might subsequently take place.

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  • $\begingroup$ So even if one set up a binary code (spin up/down states) of two entangled sets of particles sharing the same code, one could still not use that to chat? This is even more confusing than the idea of entanglement to me... $\endgroup$ – honeste_vivere Oct 29 '15 at 11:43
  • $\begingroup$ However, I am confused by the TV/transmitter analogy. I thought entanglement involved sharing a similar (or the same?) wave function. Thus, entanglement experiments show that the wave function need not be local. So far as I can tell, that is saying that action on the wave function of one particle is independent of the space-time distance to the other particle, correct? In effect, any action on one is no different than an action on the other as if they were the same exact particle at the same location, right? $\endgroup$ – honeste_vivere Oct 29 '15 at 11:49
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But, what if you could create a galactic network of faster-than-light transmitter/receiver hubs using Quantum Entanglement?

Say you have four pairs of quantum particles and you separate them in 8 "jam jar" nodes. There are four local broadband digital devices which can be connected to two nodes at a time and work at the normal speed of light.

AB CD EF GH

W X Y Z

Node A remains on Earth connected to W. Node B is moved to Mars with Node C. Both are connected to X. Node D is moved to Europa along with node E. Both are connected to local broadband Y. F and G are moved to Pluto and connected Z. H remains on Earth and is connected to W. Therefore although it has taken years for these to be installed once working you have instant communication. Now, such units would allow for instant remote controlling of robotic devices on planets, etc. This would revolutionise robotics devices for exploring somewhere like Mars. Placed onboard spaceships they would allow for similar instant communication to Earth.

If something like this were possible it could also explain why Seti has not heard from ET. ET would find radio communication impractical beyond local wifi. ET instead would seek to seed much of the galaxy with such nodes. Perhaps we should look out for monoliths? (Que..Thus Spake Zarathustra......)

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You asked three questions. My answers focus on those questions without attempting to introduce the notation of quantum states. As described below, I show in a Wikiversity article that the behavior of entangled particles can be modeled with virtually no quantum mechanics, except that the concept of the "photon" is required.

Have I misunderstood a fundamental aspect of entanglement?

Nothing that you wrote suggests that you misunderstand. Keep in mind that nobody "understands" Bell's theorem. At some level it's a mystery to everyone.

Am I focusing on a trivial, non-issue and missing the bigger picture?

Let's look at bigger picture ideas:

  1. There is no known way to use quantum entanglement to allow signals to travel faster than light. You seemed to understand that.

  2. Bell's theorem has been called a disproof of something called a "local hidden variable theory". Even Bell admitted that his proof was not airtight. Having said that, it is safe to say that there are no serious cadidates for such a hidden variable theory. (A hidden variable theory assumes that the outcomes of future measurements are somehow "known" to the particle before the measurement is made)

  3. I think what you are missing are mathematical details. That requires quantum mechanics and a knowledge of how to write quantum states as described in the other answers.

You wrote one statement that suggests a lack of understanding:

So even if we did manage to use entanglement as a near-instantaneous communication method, we would not necessarily violate relativity because the entangled particles cannot be separated faster than c.

I don't understand the question. What does it mean to say that entangle particles cannot be separated faster than c?

I don't know if it referencing one's own website is allowed, but I wrote an explanation on Wikiversity at:

http://en.wikiversity.org/wiki/Bell%27s_theorem

This argument does not require a mastery of quantum mechanics, yet it proves a simple version of Bell's inequality and also calculates the behavior of two entangle photons (using known properties of light passing through polarizing filters). At a slightly less mathematical level, I also wrote this paper for Philosophical Quarterly many years ago:

http://www.wright.edu/~guy.vandegrift/shortCV/Papers/bell.pdf

For me, the bottom line to Bell's theorem is that:

  1. Particles "seem" to do the impossible.

  2. This "impossible" behavior is not only predicted by quantum theory, it has been confirmed beyond reasonable doubt (most agree that the "loopholes" in the experiment will someday be removed).

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