|Computer memory (this one is RAM): An example of information being equivalent to an amount of mass.|
As a physicist I immediately think that any system in the world is a physical one i.e. is constructed of matter in space time. So when we talk about changing a system we have to realize that this change has to be some physical change or interaction with other physical systems. If a sequence of 1's and 0's changes the color of a computer screen it must do so by some physical mechanism. It doesn't happen by magic.
Let's suppose that there is a program called colorchange.exe and when activated the screen changes color. The program accesses a sequence of binary code stored in the memory, this code when read causes the computer to change the color of the screen. We know that the screen is made up of LEDs (small light bulbs basically) and we know that light bulbs need to be part of a circuit with a current (flow of electrons). The screen is part of the whole circuitry of the computer and the initial current is provided by the charger. So when colorchange.exe is executed it must cause a change in the current flow of electrons in the circuit to cause the screen to change color. So when it accesses the stored binary code (information) in the memory this code must somehow flow through the circuit to cause a change in the outputs of the circuit. In order for this to happen the stored binary code must be fundamentally a collection of charge (electrons). That is what it is. A '1' in the code is a number of electrons and a '0' is no electrons. So the information to change the color of a screen is really stored as collections of electrons and no electrons.
To cause a change in the screen one must convert work and so the electrons stored as the code when accessed convert their energy to move another piece of the circuit and so on. There is a simple formula for this:
(The formula states that an amount of work W equals a summation of coulomb force of electrons between two points on a line over many line elements).
According to this formula and other basic principles of physics information in a computer converts an electrons energy. Information IS the sum of the electrons energy. This view is again confirmed when we delete information. When you empty your recycle bin the electrons stored in memory compartments gets ejected by the computer and turned to heat in the air. This is partly why your fan is there, when data gets deleted this data IS energy and hence the electrons energy must be converted to another type without energy loss, the type of energy converted to is heat which is the vibration of molecules, to avoid over heating the fan constantly blows cooler air from the outside and inside the computer.
A question we can ask is: is the information lost? For example, a picture of your friend on your computer is stored as information. this information is in an ordered form i.e. ordered to be read by the machine.When you permanently delete it, the information is converted to heat which according to statistical mechanics will spread throughout the air... scattered and dissembled. The information is not lost but converted from an ordered form to a disordered form. This complies with the conservation of energy... energy is not lost but only converted and when energy goes from ordered to disordered in a direction of time then this is just entropy. Entropy is the measure of energy disorder.
I like to use examples to try and explain things and to try and test my current view of a question. My current view is that information essentially is energy. Let's look at something else and try and test that viewpoint. Okay, so I am now looking next to my laptop and see a post-it note with some writing on it 'email university', and 'don't forget med insur'. When I read this post-it I am retrieving information about what I must do in the near future. I am gaining information but unlike the computer the words don't flow to my brain through some circuit, they stay there. I can walk away and they will be there and I will still have the information in my head. What the hell is going on!? Again, let's look at this physically. Like the binary code, writing is a code for a machine.. that machine is our brains. So when the writing code is read by our brains our brain as a physical system will change (the cells in the hippocampus or something change, I am ignorant of the specific mechanism), this change must be a transfer of energy. The reading of the post-it occurs something like this: light from my lamp becomes incident on the post-it, the ink absorbs some wavelengths and reflects dark blue the post-it reflects yellow, these rays become incident on photo-receptor cells in my eye which get converted to electrical current which is sent to my brain and processed by many lobes to form a picture, my brain recognizes language and interprets it and executes it. So the transference of information was REALLY the transference of different energies of light which got converted to electrical currents.
The writing on the post-it is in the form of ink atoms spread on the post-it, when light becomes incident on it the ink atoms absorb some photon energy and reflect some back etc. I could look at the post-it everyday and get the same information again in the same manner, like the computer could access stored code for a program every time the program is executed; the stored electrons could be replaced in the same way when the stored information is accessed over an over again... a bit like re-filling it in the same way. So the mechanisms are not that different, they all involve some symbols (which mean something in some system) stored physically as energy and these symbols can only be accessed and read by transferring energy or doing work.
If you think about a few more examples e.g. talking to people (through sound waves) and texting (stored electrons and then beamed by EM radiation) and loads more you soon realize that for a system to access and process information, the language of the symbols must be energy or matter stored in an ordered fashion somewhere. To read these symbols energy must be transferred from that somewhere to the systems processing unit.
I think this idea may breakdown when we look at quantum systems. If I wanted to know where an electron is i'll send a photon to it and this photon will reflect back etc. i can work out where the electron is by some process like this. However the uncertainty principle see ' http://newphysicistphi.blogspot.co.uk/2012/09/physicists-question-heisenbergs.html ' dictates that when I know precisely where an electron is I lose information about its momentum.. almost infinitely more information is lost than gained. Is it lost? Was the information there in the first place? Such mindfucking-ness occurs when we talk about information in relation to quantum systems. Don't even get me started on the Hawking information paradox.
This question is an interesting one and it is at the edge of theoretical physics, mathematics and computing. The true mathematical answers have yet to be uncovered, will there be another Kurt Godel like 'Lol we cannot show diss to be true cos derp'? Who knows. Stay alive to find out or take part in its discovery.