Information has mass

Polymath257 said:

Except that it cannot have an arbitrary physical representation. There has to be a detectable difference between however 0 is stored and however 1 is stored. Whether it be the direction of a magnetic field, the spin of some electron, the state of some transistor, there has to be some way to discern between 0 and 1, and usually to transfer that difference to another location.

That puts the CS idea of information into a more general context, which is the way that physical states can carry information, transfer it, store it and erase it. And *that* puts us into thermodynamics because there is a strong analogy between information in the CS sense and entropy in thermodynamics. At base, the equations are very, very similar.



This gets to the notions of reversibility and irreversibility. In essence, entropy represents our *lack* of information about the microscopic details of a physical state. The fact that entropy always increases in a closed system corresponds to the idea that we are always losing that detailed information as time goes on. This is why some reactions can only happen one direction in time: even though the basic equations are symmetric in time, the information less is one-way.

And this isn't an issue in classical physics. But, in quantum mechanics, there is a requirement that things evolve in what is known as a 'unitary' manner. And unitarity, it is known, preserves information. For most physical situations, this is fine because it is a difference between a low level viewpoint and a high level viewpoint.The information is still there.

But, at black holes, there is an irreversible loss of information when something passes the event horizon. And *that* is one of the big reasons it is difficult to unify gravity and quantum mechanics. It isn't simply a lack of low level information: even that low level information has disappeared past the event horizon. It is the corresponding violation of unitarity that is the problem.

Again, this comes from the thermodynamics of the situation. In essence, it turns out that heat is released whenever information is erased. The amount of heat generated is directly proportional to the number of bits erased and corresponds to an entropy per bit of information. If this did not happen, we would be able to construct a perpetual motion machine using stored and erased information (using an analog of Maxwell's demon).

Technically, a bit of information corresponds to a certain amount of entropy. The amount of heat is the product of that entropy and the temperature. So, to erase a bit at a cold temperature emits less energy that erasing the same bit at a higher temperature.

it is then the equivalence between energy and mass that leads to the claim that information has mass. This isn't quite true since, as I noted above, the information corresponds to entropy, not energy. The amount of energy (and hence, mass) depends on the temperature.

Hopefully this helped a bit. Or two.

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Heyo said:

And another one:

This one got me thinking ...
Information increases when space increases (because there are more possible states where the matter can be).
If we live in a closed universe (which will collapse back on itself) space would decrease and so would entropy?
But decreasing space also heats things up, so no increase in entropy.
Then again, the universe was hotter in the past. So was there really less entropy?

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Information has mass. Information increases when space increases. Does that mean that the universe gains mass with expansion. Could that mass counteract the expansion?

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I need to think about that and maybe get some formulas and crunch some numbers.

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