# Does an ordered abacus have a higher mass (no matter how small) than a random one?

In 2019, physicist Melvin Vopson of the University of Portsmouth proposed that information is equivalent to mass and energy, existing as a separate state of matter, a conjecture known as the mass-energy-information equivalence principle. This would mean that every bit of information has a finite and quantifiable mass.

So, if I invest energy in creating an ordered pattern on an abacus, it will have a different mass than a random one. Now the marbles making up the pattern stays the same. But obviously their positions wrt one another are different. The gravitational potential, however small, is different.

Is this plausible? Does an ordered abacus weigh more? Could we, in principle, weigh two identical abacusses and determine by weight which is more ordered?

• To me, for the abacus to carry information it has to be associated with an external encoding. Who is to say what the position of the beads mean? You can encode any information you want in any pattern given some set of rules. So assuming the encoding is separate, I don't think the mass can be related to the pattern of the beads. Jun 15 at 9:01
• @rghome Well, you could know if the pattern is random or not by weighing them (in principle). A random pattern (shake the abacus) is different from ordered. Jun 15 at 9:14
• You can invest energy in creating an ordered pattern, and if this energy stays in the abacus (e.g. as increased internal energy), then it increases its mass according to Einstein's formula $\Delta m = \Delta E/c^2$. But there is no reason to think this energy has to remain in or near the abacus. In the usual case it will dissipate into environment. Jun 15 at 9:19
• @JánLalinský Only if it returns to randomness. Which probably is the case. Jun 15 at 9:26
• The idea that information is equivalent to mass or energy is not part of established physics knowledge, and has obvious problems - what is the solid way to determine the amount of information in particular arrangement of the abacus? It seems to be a subjective concept, while mass is not. Jun 15 at 9:36

The answer to your question is "almost certainly not", for 3 reasons:

(1) First, and probably most importantly, the paper you reference is highly speculative. We don't really understand the connection, if any, between information and energy, and if there is a relation it may well be more complicated than "more information = more energy".

(2) Secondly, the information contained in the arrangement of a few dozen beads is utterly dwarfed by the information contained in the arrangement of the $$10^{25}$$ or so atoms making up the beads.

(3) Lastly, even if the first two items were somehow overcome, the ordered arrangement of beads has less information than a random arrangement. This may seem counter-intuitive at first, but it becomes more obvious if you think about how much information is required to describe the beads. For an ordered arrangement you might be able to specify a simple rule (like "all the beads pushed as far to the left as possible"). For a truly random arrangement you would need, in general, to describe the position of each bead separately.

Similarly, in computer science a random string cannot be compressed, whereas ordered strings (like text) can generally be compressed, and the more ordered they are the more they can be compressed.

• I don't mean the entropic information. Obviously for a gas, containing no useful information, there is a higher entropy. But if the gas particles are distributed in a meaningful pattern, like the picture of a house, the entropy is less but the picture meaningful. You might say the gas particles dont know this, but the gas particles have a relation they didnt have before. You could arrange them in a circular pattern too, or whatever form. Jun 15 at 16:15
• Did you look at Vopson's paper? He uses entropic information. Indeed, it's hard to think of any precise or quantifiable definition of information for which an ordered sequence carries more information than a random one. I know that the "intuitive" idea of information is the other way around, but our intuition is a poor guide to reality. If we want to do physics we need precise definitions. Jun 15 at 22:12
• I was just writing a new question on this when your message arrived! I wanted to ask if a random collection of masses has the same energy as an ordered collection. On the same distance scale. Do you have thoughts on this? :) Jun 15 at 22:17
• I find Vopson's arguments unconvincing, and I doubt that information has mass. That's also the current opinion in mainstream physics. But ultimately it will be up to experiment to determine this, and I hope someone does the experiment. Jun 15 at 22:24
• One bit weighs 10exp-38kg... Could we ever measure this? With a large information content maybe? Jun 15 at 22:34

So, if I invest energy in creating an ordered pattern on an abacus, it will have a different mass than a random one.

No The energy invested will be used as work to change the potential energy of each bead by changing its height wrt to the bottom of the abacus ($$m_{bead}gh$$). None of this energy is being transformed into mass. You can argue (since gravity decreases with height) that the weight of an abacus with all its beads against the top will weigh ($$W = m_{beads}g(h)$$ ) slightly less than an abacus with its beads against the bottom and use this to state that in general the weight of an abacus will be a function of positions of the beads but it won't be a function of "order"

• Oops, sorry! I forgot to state that no external gravity is involved. The question is purely meant to investigate if the random state, by shking it randomly, has a higher mass than an ordered, lesser entropy (higher Gibbs energy) one. It would be a tiiiiiny difference, but you could decide which one is random by weighing. At least, if that's possible (in principle obviously) is the question. Still, +1! Jun 15 at 19:04
• I'm assuming the beads are held in place by friction against the wire. In the absence of gravity, work still needs to be done to move the beads. Instead of Work = $F_{gravity}h$ it's now Work = $F_{friction}h$. But all the energy goes to this work and any heat generated by frictional motion. If your arguments about entropy were true than all systems would gain mass over time since entropy increases over time and we know this is not the case. Jun 15 at 19:27
• Yes, I understand your reasoning. But I think I didn't make myself clear. Suppose you have two identical abbaci (is that correct, abbaci?). Without friction or heat evolving. One of them has it's beads randomly scattered, the other has a nice pattern in the beads (say they form a circle, or whatever). The theory says that this non-random pattern, containing information, has a tiny higher weight. Jun 15 at 19:35
• I think I understand. Each abacus required a different amount of energy to reach it's state (one random one ordered) because each abacus had different total bead movement. You are attempting to equate this difference in energy as a difference in mass and I am attempting to equate this difference in energy as a difference in work to reach each state. Jun 16 at 2:12