Question: What does it mean by information in physics? From the answers of a previously asked question I could know that something can travel at a speed greater than the speed of light with respect to a frame of reference if it doesn't transfer any information to the frame of reference. So, is it that actually the theory of relativity puts a bound on the speed on which information can travel through space and not on the speed of something? In what form does the so called information travel through space?

Chris Mansell answered on 23 Jun 2013:

This article nicely explains why information cannot travel faster than the speed of light:

http://www.univie.ac.at/qfp/publications3/pdffiles/1997-07.pdf .

I’d like to say a bit more about what inforamtion is though. It is a property that we know how to calculate. It is sometimes called Shannon information. Imagine some possible events that could happen. Let the letter “i” denote the counting numbers. We can use the counting numbers to refer to the events. So, we have event 1, event 2, event 3 and so on. Let us say we know the probabilities with which the events occur. That is, we know that event i occurs with probability p_i. (So, event 1 occurs with probability p_1, event 2 occurs with probability p_2, and so on.) By looking at which events actually occur we gain information. The average amount of information we gain each time we see an event is the sum over i of p_i log (p_i). In other words, the average amount of information we gain is p_1 log (p_1) + p_2 log (p_2) + p_3 log (p_3) + … . (Here, log (x) means take the logarithm of x. You may have to look up what a logarithm is if you haven’t covered it in maths yet.)

To give an example, we can imagine that the events we are watching are blue flashes or red flashes that your friend you lives opposite your house is sending you. If your friend always sends blue flashes and only blue flashes (because he doesn’t own a red torch), then you can say that a blue flash happens with probability equal to one and a red flash happens with probability zero. So when you see your friend across the road shining his torch, the average amount of information he is giving you is 0 log (0) + 1 log (1). Evaluating this sum tells you that the average amount of information he is sending you with his torch “messages” is zero bits of information (i.e. no information). This should make sense. Your friend always sends blue flashes, so it’s not very surprising or informative when he sends you yet another blue flash.

Even though I have given an extreme example, where the probabilities are one and zero and the average information is zero bits, the formula is valid for more general situations.

I hope this has helped somewhat. This is my best understanding but the others may have another way of looking at it.