# Mass and Information Bits

1. Aug 4, 2013

### jkg0

I've been thinking somewhat about how to link mass to a number of information bits.

Consider the universe as a self-referential representation of information. Each particle in the universe may be defined relative to each other particle in the universe as some number of bits of information. In this view of the universe mass is a quantity of information relative to each other mass in the universe. If this is true, could a minimum quantum of mass be defined from other physical constants?

Let us make some simple computations.

We know from Leó Szilárd that the amount of energy storable per bit as a function of temperature is:

$E_{bit}=kTln2$

where k is Boltzmann’s constant and T is the temperature of the storage medium.

We combine this with Einstein’s equation for the conversion of mass to energy:

$(mc^{2})/kTln2=n_{bits}$

We also know from the microwave background radiation that the average temperature of the universe is 2.73K. Assuming the entire universe is storing the information we call mass, we can transformation from mass to bits:

$(mc^{2})/(k2.73[K]ln2)=n_{bits}$

From this we can compute the minimum quantum of mass, that is the amount of mass represented by one bit:

$m=k2.73ln2/c^{2} = (1.3806488 \times 10^{-23} [m^{2} kg s^{-2} K^{-1}]2.73[K])/(2.99792458\times10^{8} [m^{2}/s^{2} ])= 1.2572601889804714 \times 10^{-31} kg$

Does anyone know of any papers that might be useful in this line of reasoning?

2. Aug 5, 2013

### jfizzix

The big question here could be said to be, "Is mass quantized (like charge)?"

With the masses of the fundamental particles as they are, this cannot be the case unless the quantum of mass is much smaller than the one calculated here which is roughly a tenth the mass of an electron (not exactly 1/10).

For books on information theory, I recommend Nielsen and Chuang
https://www.amazon.com/Quantum-Computation-Information-Anniversary-Edition/dp/1107002176
for quantum information theory/quantum computing, and Cover and Thomas
https://www.amazon.com/Elements-Information-Edition-Telecommunications-Processing/dp/0471241954
for classical information theory, They are both good books, though I found the classical one easier to get through.

Hope this helps:)

Last edited by a moderator: May 6, 2017