Introduction to the Information Velocity

What is Information?

In a mathematical sense, information is knowledge of events in the physical world. In the context of the speed limit imposed by relativity, information is what connects a cause and its effect (or effects). Imagine two people (lets call them Dan and Michael) standing on two different hills. Dan either raises his right arm or his left. Based on this event, Michael either goes back into the lab or goes home and has a beer¹. In this case, Dan's hand-raising is the cause and Michael's choice is the effect.

Communication of Information

Whenever we communicate information, we need to have a "carrier" of the information, a medium that allows the transfer of information. Sound is the carrier of information when two people talk to each other. Electrical current flowing through a wire is used to communicate information over telephone wires. Light is used to communicate information over fiber optic communication networks.

The workings of an optical fiber. Most information transmitted over telephones or the internet is encoded on light pulses and sent through optical fibers. For a description of how fiber optics work, visit HowStuffWorks.com.

But having a "carrier" doesn't mean that you are communicating information. For example, having the ability to utter a sound doesn't mean that humans can communicate with each other. First, we need to agree upon an alphabet that we will use for communicating information. We then use that alphabet to build up words, etc. In this example, sound is the carrier of the information, but we can't use this carrier until we agree about the alphabet.

The act of human speech has two processes. First, we think in our mind what we want to say. Next, our brain controls our mouth and vocal cords to produce the proper letters of the alphabet (the sounds we associate with A,B,C, etc.) For the person receiving the information, the ears turn the sound waves into electrical signals, which the brain processes into understandable letters of the alphabet.

Thus, the ability to create sounds with our mouth is really only one necessary resource for communicating information. The real part of communication is agreeing on the alphabet and encoding our thoughts using this alphabet.

The Information Velocity

The idea of the speed of information can be understood with this analogy. If Dan and Michael are standing on opposite sides of a field, it will take some length of time for sound, and the information encoded on it, to travel across the field. For most cases, no one has considered the idea that the sound might travel across the field faster than the information. But the fact of the matter is that the carrier of the information - the sound wave - can travel at a different speed than the information itself. This is because the nature of the sound can change as it propagates, like when you talk through a cardboard tube.

An optical fiber. Photo courtesy Corning.

The same is true with light, and this is the focus of our research. We have devised an experiment where the carrier of information (a pulse of light) appears to be traveling faster than the speed of light in vacuum. Some people believe that information encoded on light has to travel at this same speed. If so, this could be a violation of the special theory of relativity, and there are all sorts of weird paradoxes that would be possible if that were true.

The question we are trying to answer is the following: If Michael is located at one location (say, Duke), and Dan is located at another (say, a nice beach in the Bahamas), how long does it take for a single bit (short for "binary digit", either 0 or 1) of information¹ to travel from Michael to Dan. We can then arrive at the speed of this information transmission process by dividing the distance between us by the time it took to send the information. Surprisingly, the speed of this information transmission process can be very different from the typical speeds that are used to characterize the propagating of the optical pulse (in this case, we compare it to the so-called group velocity, which describes the speed of the peak of the pulse).

The Experiment

Specifically, we created a medium for which pulses propagated with a group velocity greater than the speed of light in vacuum. Over the last 100 years or so, some scientists have said that such an observation contradicts the special theory of relativity. Yet, when we encoded information on the pulse (i.e, making and transmitting a waveform that we decided a priori represents a 1 or a 0), we found that the information travels at slightly less than the speed of light in vacuum. This means that Einstein's special theory of relativity seems to be correct (because it states that the information velocity is less than or equal to the speed of light in vacuum), even though the speed of the peak of the pulse travels faster than the speed of light in vacuum.

Footnotes and References

1. Those familiar with information theory will recall that the likelihood of an event affects the amount of information associated with it. Events that were essentially expected carry less information. Taken to the extreme limit, the occurrence of an event that was guaranteed to occur yields no information.
2. Limiting ourselves to a binary alphabet may seem very restrictive, but this is exactly how modern communication systems function. There are only two letters or symbols in the alphabet - a 1 and a 0. Any letter of the English alphabet can represented by several 1's and 0's via an established standard like ASCII. For example, the letter "M" is represented by the binary series "01001101". Thus, to send a single letter of the English alphabet, 8 1's and 0's can be transmitted.