I Is Information Conserved in the Universe?

[windy miller]

It's said that information is never destroyed ( I know there is some controversy here regarding black hole information loss but let's put that aside for the moment). But what about created? I information a conserved quantity for the universe as a whole? Is there a consensus on this issue? It seems that information increases naturally in the universe, think of sunspot forming on the sun , this is information for those wishing to protect the power grid from flares. So that would mean information is not conserved. But I appreciate my understanding of the subject is limited so if there's anyone that can enlighten me, would be very grateful.

 

[bapowell]

Every time you flip a coin you are creating information: 1 bit, to be exact.

 

[newjerseyrunner]

Every time you flip a coin you are creating information: 1 bit, to be exact.

I disagree, or at least find this incomplete. When you flip a coin, you change information, but you didn't create it. The same 1 bit of information existed before you flipped the coin because it had a previous state. I would use the analogy of when you create a coin, you create information and flipping it is just changing state.

 

[bapowell]

So how much information do you create upon minting the coin? Sounds like you're talking about "potential" information or some such idea. Can't I flip a coin arbitrarily many times into the future? Is the number of times I can flip the coin in some way limited by the nature of the minting process?

 

[Bandersnatch]

From my limited knowledge on the subject, and with the caveat that I'm merely trying to dress a quantum-mechanical idea into old Newtonian clothes, I believe the term 'information' as used in this context has got a specific meaning - it's the ability to predict past and future evolution of a system from complete knowledge of its current state. The information is conserved if we can, in principle, draw an unbroken and unique chain of cause and effect between current state and any other state.

So the example in the OP doesn't fit the idea of 'new information', since you can look at the system with those sun spots, and be in principle able to say why they're there: what interactions and particles and fields conspired yesterday to create them today. It's all the same, conserved info.

That's why black holes throw a wrench into this line of thinking - since all infalling stuff gets reduced to just 3 parameters, with no way of probing the interior of the event horizon, you are forever unable to say if the past of some black hole consisted of 10 regular elephants falling into it, or just one elephant, 10 times as big, and made of antimatter.
Thus the information is not conserved in this case, as you cannot derive from the perfect knowledge of the state of the black hole and its Hawking radiation a large fraction of the properties of stuff that fell into it.

In this sense Big Bang is not any sort of new information, as whatever came before uniquely determined what came after.

 

[Chalnoth]

It's said that information is never destroyed ( I know there is some controversy here regarding black hole information loss but let's put that aside for the moment). But what about created? I information a conserved quantity for the universe as a whole? Is there a consensus on this issue? It seems that information increases naturally in the universe, think of sunspot forming on the sun , this is information for those wishing to protect the power grid from flares. So that would mean information is not conserved. But I appreciate my understanding of the subject is limited so if there's anyone that can enlighten me, would be very grateful.

It's a little difficult to say precisely, because there isn't anyone unambiguous definition of "information".

In the sense that black holes do not destroy information, however, that information is neither created nor destroyed.

Fundamentally, this comes down to the question of whether or not the laws of physics are unitary. If the laws of physics are unitary, then if you had the complete wavefunction of the entire universe at a given time, then given enough computer power you could calculate the complete wavefunction of the universe at any other point in time (past or future).

This isn't the whole of the story, though. There are other definitions of information. For example, we might want to talk about useful information. In some sense, entropy that is below the maximum represents useful information. This kind of information is decidedly not conserved. As entropy increases, useful information necessarily decreases. We can still produce information in one system, but only by reducing even more information in another system. Note that the information isn't so much "destroyed" as it is scrambled: the information still exists in some sense, but it's been randomized so much that it's a practical impossibility to read the information back.