Predicted 'information catastrophe' may be caused by fifth state of matter
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The second is, umm, ridiculous on the face of it to put it mildly, namely, that information literally has mass all by itself, and that a storage medium full of coherent data weighs more than the same media in an erased state. This is from Vopson's paper: https://aip.scitation.org/doi/full/10.1063/1.5123794
He further extends this to propose that dark matter is information mass. I can't even...
The obvious problem here is that "erased state" means nothing. From the standpoint of information, there is no difference between an "erased" and "non-erased" storage medium. Both contain exactly the same amount of information. If there is an information component to mass, it is already implicit in the mass of baryonic matter. It cannot be added to or taken away. It can only be transformed from one information state to another, and thus any such implicit mass would be preserved.
I would think erased data would have higher entropy, assuming it's relative to the interpreter which would contextualize the meaning of erased or valid data. "Erased" would mean the action of raising the entropy on some arrangement of matter.
Even the concept of baryonic entropy contributing a mass component is rather ludicrous. This is akin to the idea that either the Higgs field, and/or the quark and gluon energy within a hadron respond to the specific arrangements of the hadrons to which they impart mass. I.e., that the mass of the particles changes in some proportion relative to their physical relationships to one another in spacetime. That's a rather extraordinary claim that is nowhere in the math.
From your example of storage medium, I think you're missing that someone or something has to do the erasing in said storage medium (by definition, there is an interpreter interpreting the information in that example). So "erase" would be defined by the interpreter, however by any definition it would involve destroying information, and that would require work.
But the radical claim of this paper, and the one I am addressing, is that information, in and of itself, contributes a mass component to a storage media regardless of the media involved. That's a completely different proposition.
All baryonic matter has an information component. But the theorems concerning information stipulate that information is never destroyed. Entropy does not destroy it either. This paper violates the central theorem of information science. That is why "erased" here is meaningless. Entropy state is irrelevant.
Further, it violates the conservation of mass-energy. The work required to "erase" a given medium is the same as the work required to record information on it. Yet this paper claims the one process adds mass, and the other removes it. The whole thing is just nonsense.