https://pubs.aip.org/aip/sci/article/2022/9/091111/2849001/A...
Unfortunately, your argument here is implausible. There have been tens of thousands of experiments demonstrating mass to energy conversion. It is the basic principle behind nuclear energy production. Mass energy equivalence is necessary to maintain conservation laws and has been proven by empirical observation. The total mass/energy in the system will not change, however the two can be exchanged for each other.
> Information having energy is well known since Boltzmann
Information having mass/energy has not been proven. There have been no experiments to support this argument. It is merely a theory.
> ..as entropy is measured in J/K
Entropy is not a conserved quantity since it will increase within a closed system. The Joules/Kelvin unit comes from statistical mechanics where temperature is defined as a change in entropy per increase in total energy. The entropy used in information theory is different, although related. Entropy in information theory is measured in bits.
To be more concrete, bmacho equation, E = mc^2 + q*6*10^23 J/e holds for every experiment, every theory (standard model, GR). It states that energy is equivalent to mass and charge.
It's an active area of research because of this because it may point to a way to reconcile the incompatibilities between QM and Relativity to get a Grand Unified Theory. I believe Loop Quantum Gravity ends up with effects around this mass-energy-information/entropy equivalence idea as an emergent property of how it's trying to reconcile QM and Relativity.
How intuitive is the mass-energy equivalence? Before Einstein's era, people might have said that such an idea clashes with the intuition that is a completely separate thing from energy.
Physicists are always looking for equivalences and conserved quantities. They are the basis for modern physics. It's how we discovered that 3 of the 4 known forces were all based on the same equivalent principle. You find a conserved quantity that unifies the two forces.
Possibly one of the greatest feats of this was Maxwell when he unified electrical and magnetic forces by discovering an equivalence between the two that allowed energy to be conserved. This helped us to discover the underlying principles of light itself and describe it as an electromagnetic wave.
Information conservation could prove to unify gravity with the remaining forces. Or not! Or it could break them all apart again. That's just what scientific inquiry is all about.
Intuition hasn't been a good guide for physics since newton. It's not clear to me that anything physical is separate from the information that describes it though.
A lot of "Ifs" though.
And if you ascribed meaning to random data it would gain weight...
Possibly.
> And if you ascribed meaning to random data it would gain weight...
You would have to create a dictionary with that meaning which would be more information that would add that theorized weight. This is a common problem in compression.
For instance, if you have the state "H" and want to add a meaning to it "High Temperature" you need to create a third piece of information "H" -> "High Temperature"
You are not changing the information in "H" or "High Temperature" you are merely creating a third piece of information which is the lambda.
Take for instance the word "Red." To a computer this means: 52, 65, 64
The there is a mapping to letters call an ASCII table or UTF-8 encoding. Then there is a mapping from character data to a bitmap containing the letters projection on a screen. Then there is a mapping in your brain that associates that sequence of letters to a neural structure that encodes your memory of the color red. That mapping was created by a teacher that showed you the color red next to those letters.
But in the end, the numbers 52, 65, 64 haven't gained any information. They could still mean anything based on which system interacts with them. An RGB color picker will interpret it as a nice teal color. Without knowing what system to use to interpret their meaning, they are meaningless aside from the numbers themselves. You need the key to find the difference which is information itself.