Information Conservation in Logic Gates and Computer Components

[Ontophobe]

There are irreversible logic gates, are there not? Gates who's outputs don't preserve information about their inputs, no? Or take for example computer parts that crunch numbers. If you know the answer to a calculation is 12 but that's all you know, then you can't figure out whether the calculation was 5+7, or 10+2, or 6x2, or 98,425-98,413, or the square root of 144, etc. So how can there be a conservation law with regard to information?

 

[anorlunda]

Information is not the same thing as knowledge.

Consider an electron. It has two possible spin states, up and down. Two states is one bit of information. Information measures the quantity of possibilities, not our knowledge or lack of knowledge of which state the electron is in right now.

A hard disc may have the capability of storing 100 GB of information. That number does not change if the disc holds files, or if it is wiped clean, either way it is a 100 GB disc. (quantity) of information is not the same as knowledge.

Now, physics says that an electron can not evolve into something which more than two or less than two spin states. That information is conserved.

A more general way to say this is that the sum of all probabilities in all systems must add up to exactly one.

In classical mechanics we call this Liouville's Theorem, in quantum mechanics it is called unitarity. Regardless of the words, they both mean that the sum of all probabilities remains one.

Think of the logic gate in your question. If it has two binary inputs, that is two bits of information. Even if we had an irreversible gate where we can't figure out what the inputs were, there are still two bits of information in the inputs. Once again, knowledge is not the same as information.

It is in that sense that we say that information is conserved.

 

[Ontophobe]

So, floppy discs and thumb drives can be empty or full, but their storage capacity remains the same. We therefore might say that the universe's storage capacity is a fixed quantity. There is a fixed number of bits in the entire universe. Floppy discs and thumb drives can be destroyed, but subatomic particles can't, so if there are a fixed number of, say, electrons in the world, then the total amount of info that can be stored on the universe's electrons is fixed. And the same is true of all quantum entities: they can't be destroyed and they always retain the same number of possible spin states, so they always "have" the same number of bits of information "in" them. So when things fall into black holes, they're gone forever, but particles of Hawking radiation take their place so the number of spin states in the universe stays the same. One electron falls into the black hole, a corresponding two-spin-state particle takes its place in the world. Do I have it right?

 

[anorlunda]

So, floppy discs and thumb drives can be empty or full, but their storage capacity remains the same. We therefore might say that the universe's storage capacity is a fixed quantity. There is a fixed number of bits in the entire universe. Floppy discs and thumb drives can be destroyed, but subatomic particles can't, so if there are a fixed number of, say, electrons in the world, then the total amount of info that can be stored on the universe's electrons is fixed. And the same is true of all quantum entities: they can't be destroyed and they always retain the same number of possible spin states, so they always "have" the same number of bits of information "in" them. So when things fall into black holes, they're gone forever, but particles of Hawking radiation take their place so the number of spin states in the universe stays the same. One electron falls into the black hole, a corresponding two-spin-state particle takes its place in the world. Do I have it right?

You got it a bit right, but maybe not the details.

Quantum objects can decay into other kinds of objects, but certain things are conserved in the process. All time evolutions in quantum mechanics conserve information.

The black hole is a very difficult and controversial case. Our best theorists use advanced arguments about conservation of information with a black hole. I think most of them agree that information must be conserved with a black hole , but they can't explain how.

But this thread is marked B, so no advanced theories here.

It occurrs to me that our language makes it harder to understand. The phrase "specific information" means about the same thing as knowledge. But quantity of information and quantity of knowledge do not mean the same thing. So when we just use the word information, what does that really mean? The meaning of ordinary words aren't precise enough in this case.

 

[Ontophobe]

Keeping it basic, is "information" really the best word here? Scientists are notoriously bad at naming things. "Information" certainly does invoke concepts like knowledge and minds, and it makes laypeople like me ask questions that don't actually make sense, like "What sense does it make to speak of information in situations where there's nobody around to know any of it?" Of course, that's a silly question, but it seems reasonable to laypeople #DunningKruger. So if you could choose another word for it that might bypass these misconceptions, what would it be?

 

[anorlunda]

I would have to iinvent new word for precisely what I mean. My choice would be shannon.

But scientists and engineers are stuck using imprecise natural language, just like everyone else.