Faster-Than-Light II: Information?

To follow up on the faster than light post here, let’s ask another question:

If you can make a way of transferring information that doesn’t involve matter, is that information limited by the speed of light?

First off, let’s go over what information is, and then we’ll talk about how transferring information without matter is even possible. Information is anything that’s organized in a meaningful manner. Take a look at the following three sentences:

  1. This sentence contains some information.
  2. Tihs scnnteee cainntos smoe imnfriatoon.
  3. Not a imfro nimsoe mnoisn ctrnsnet sihto.

Each of the three sentences contains the same number of bits, the same exact letters, but they are arranged differently. The first sentence is arranged in a meaningful manner, and is easily readable. The second sentence is still legible by many due to a trick of human perception, but the arrangement of letters is far from optimal to convey the intended information. The third sentence, which contains the same letters in a completely random order, contains no meaningful information.

Why is the first sentence meaningful, but the third one isn’t? It’s because we know how to decode the letters in the first sentence, and turn it into useful information, as opposed to the third one. That’s how Morse code worked with a telegraph; a simple set of dot and dashes could be used to reconstruct an entire language.

Computers work off of a very similar (binary) language, using 0s and 1s instead of dots and dashes to encode their language. DNA has a similar alphabet, based on a 2-bit language (ACGT) instead of a 1-bit language. The alphabet used isn’t important, but what is important is that there is meaningful information that can be used to accomplish something encoded in that language.

If someone knows your language, you can transmit your information to them. You can use mechanical signals (such as a telegraph), electronic signals (such as a copper wire), or electromagnetic (i.e., light) signals, such as the antenna above, to transmit information. If you use a mechanical or electronic signal, the information transmitted always travels slower than light. If you use an electromagnetic signal, the information travels at the speed of light.

But quantum mechanics does weird things, and one of the weirdest is a phenomenon known as quantum entanglement. What this means is that two particles can have their quantum states interrelated; if you measure the state of one, you know the state of the other, but until you measure one, they’re both undetermined. This is like a double Schrodinger’s Cat paradox, except when you open the box, you find out whether your cat is dead or alive, and instantly know whether the entangled cat that you haven’t looked at is dead or alive, too. Here’s the kicker: you don’t find out whether the entangled cat is dead or alive at any given speed. You find out instantly.

In reality, this experiment doesn’t work with cats and whether they’re dead or alive, but with entangled photons and their spins (whether their spins are +1 or -1). You know the sum of their spins, but you don’t know the individual spins until you measure them. Experiments have separated the photons by miles before measuring one, and then instantly knew the spin of the other one, even though it was miles away.

So, what does this mean? Is information being passed instantly, or faster than the speed of light? Maybe; I’m not entirely sure. Because you’re learning something about the spin of a particle faster than the speed of light, and the particle starts acting like a particle of definite spin (either +1 or -1) rather than an indeterminate wave-like state, and it starts doing that instantly. But is that a transfer of useful information? I’m not sure. If it is, then it is certainly happening at superluminal speeds (at least 30,000 times faster than the speed of light). I wonder what she has to say about this:

If I send you the entangled photon and then I measure mine and you measure yours, we’ll never both see +1 or both see -1, we’ll always have opposite answers. And yet, there’s no way that the two photons can communicate with each other to tell one another what their spins are.

What can this be used for? Possibly for quantum cryptography. If I send you an entangled photon, and I use the measurement of my photon to figure out what yours is, I can use mine as an encryption key. Only you, who knows what my photon is doing because of the entanglement, will be able to decrypt it. And you’ll know the decryption key before you even get the encrypted message, because you get it instantly. Is this an instantaneous transfer of information? I think it is — do you?

Comments

  1. #1 benhead
    February 11, 2008

    Can you explain for us how the ability to transmit information faster than light can lead to causality issues? I know that it’s supposed to lead to effects preceeding causes in some reference frames (or something), but don’t recall the details.

  2. #2 ethan
    February 11, 2008

    Ben(head),
    Let’s say I send you one of the entangled photons (or two, or 10, or 128, or however many bits I need in the encryption key). Then I observe my photons, making the encryption key, and send the encrypted message to you at the speed of light. You’ll know the decryption key *instantly*, and yet you’ll only see me making the observation of the photons at the speed of light. So to you, you get the information before I make the observation in your reference frame. Weird enough?

    Ethan

  3. #3 benhead
    February 11, 2008

    Right, but I can compute how long it takes light to reach me from your position, and know that you “actually” made the observation first (or at the same time). It only gets weird if we’re in relative motion, right?

    Even then, simultaneity problems are common enough in special relativity. The way scientists talk about superluminal transmission (of arbitrary information, rather than just correlations) being “impossible”, I expected some arrangement to lead to you sending a message (possibly via one or more accomplices) to your own past or something.

  4. #4 OKThen
    entanglement of 3 or more particles
    September 26, 2012

    I don’t understand it all; but it seems that quantum entanglement ideas are being seriously stressed.
    http://www.newscientist.com/article/mg21528834.700-new-maths-triggers-a-call-to-iron-out-quantum-world.html
    I’m trying to understand the Constraints on Chronologies paper by Alfred Shapere and Frank Wilczek http://arxiv.org/pdf/1208.3841v1.pdf

    But it’s rough slogging. Very difficult for me to understand.

    But it seems very important for cosmology since in a sense, with the big bang, the whole universe is entangled. And those wilcek and Shapere’s insights into entangle ment involving 3, 4 and more bodies seems relavant.

    Any thoughts on this paper’s meaning in particular relative to cosmology.
    2

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