Is the Theory of Conservation of Information Faulty?

[bkelly13]

Homework Statement

This is not a homework assignment.

Relevant Equations

a^2 + b^2 = c^2, the distance between two particles. Just to meet in the requirement of an equation.

I am searching for a definition of “information” in the concept of physics and the theory that information is conserved. Rather than a general question, here are a couple of specific questions about information. Not limiting, just two possible examples of information.

• The magnetic state of some amount of matter is information. An example is a specific magnetic area on a computer hard drive for a particular bit of information. The information is the orientation of that magnetic field. When examined by the drive hardware, it is interpreted as either a one or a zero.
• The location of particles in some amount of matter. Pick an atom in a crystal of something. Lets say it is held in position on my desk. For convenience, call it atom 100. Adjacent to that atom is atom 101. The distance from atom 100 to atom 101 is, using a standard Cartesian coordinate system, X, Y, and Z Plank distances.

Are these two concepts examples of “information?”

 

[berkeman]

Homework Statement:: This is not a homework assignment.
Relevant Equations:: a^2 + b^2 = c^2, the distance between two particles. Just to meet in the requirement of an equation.

I am searching for a definition of “information” in the concept of physics and the theory that information is conserved.

What learning resources have you found so far in that searching? You do know how to use the Google search engine, correct? Please post links to what you have found so far in your searching, and ask *specific* questions about that reading. Thanks.

 

[haruspex]

Are you familiar with the concepts of macrostates and microstates?

 

[bkelly13]

I am familiar with the prefixes macro and micro. I have used Google and Bing and searched for phrases such as conservation of information, similar to conservation of energy. The broader question of conservation of information is not well defined to a non-physics major. The goal of the question is to present a couple of specific questions. How many sites I have visited is really not important.
Will someone please answer the questions? Are those two situations valid examples of "information" within the basic topic?

 

[phinds]

How many sites I have visited is really not important.

Which is probably why no one asked you for that information.

I realize you are here to get a question answered but what you need to realize is that this is not a Q&A forum where you just ask and we just answer. We try to lead you to an understanding and often that means WE need to ask questions that you need to answer. You should answer post #2

Please post links to what you have found so far in your searching, and ask *specific* questions about that reading

 

[hutchphd]

A more succinct answer is "yes". These situations contain information. So what ?

 

[bkelly13]

Post 2 asks for links to what I have found. Here are some links to pages suggested by Google, a phrase that seems relevant, and my questions / comments.

https://theoccasionalinformationist...n of momentum,to determine every other moment.

Quote: Just as conservation of momentum implies that the universe can just keep on moving, without any unmoved mover behind the scenes, conservation of information implies that each moment contains precisely the right amount of information to determine every other moment.

My question: does this imply that the precise position of any particle of matter is “information?” I suspect so, but ask for an answer from someone more knowledgeable than I.

https://www.mdpi.com/1099-4300/23/6/779

There is a long abstract that deals with the question. I cannot extract the information I search. Here are a few quoted sentences

“One needs to be cautious when dealing with information since it is defined differently in different fields such as physical sciences, biological sciences, communications, philosophy, and daily life. Generalization of a particular meaning into other fields results in incompatibilities and causes confusion. Therefore, clear distinction with precise language and mathematics is needed to avoid misunderstandings.”

The following explanations delve into electronics and binary data. Yes, that is information, but I am pretty sure that such information is not “conserved” and is not the topic of my interest.

Is the position of an atom considered “information?”

Here is a Quora question: https://www.quora.com/What-is-the-law-of-conservation-of-information

One reply takes the position that conservation of energy may be violated in regards to a black hole. There are some theories, Stephen Hawking I think, that say that information might be in the event horizon, or it might be recovered through the process of black hole evaporation.

But nothing there provides any concrete example of “information.”

The questions I asked are the results of a long time involving several searches and attempts to understand the concept. This time I decided to ask a few narrowly defined specific questions.

Within the concepts of physics and the question of conservation of information, are my two examples valid examples of “information?”

Regarding post 6: It states the simple answer is Yes. Ok. Thank you.

So what? Now I am thinking about conservation of information.

One principle of quantum mechanics, to my understanding, is that the precise position and velocity of a particle cannot be known. Position is information that does exist. If it cannot be known, even in theory, maybe specifically in theory, then the information is not conserved, it is lost. Hence a contradiction between two laws of physics.
Does that mean the simple answer of Yes is not completely valid? Or is too lacking to be considered the grounds for my supposed contradiction?

 

[haruspex]

the precise position and velocity of a particle cannot be known

More accurately, the more precisely you know the position, the less precisely you know the momentum.
But I don't think this is the right way to think about it. It's not what some observer knows that matters. Note that because you don’t know the momentum exactly, you become less certain of the position over time.
It's more that over time there is an increasing number of possible states, so the information required to specify the state increases.

 

[PeroK]

One principle of quantum mechanics, to my understanding, is that the precise position and velocity of a particle cannot be known. Position is information that does exist. If it cannot be known, even in theory, maybe specifically in theory, then the information is not conserved, it is lost.

In classical physics, a particle is described by specifying its position at every point in time. In QM, the particle does not have a well-defined position. Instead, it is described by a state. The state contains all the information about the particle. This information includes a probability distribution for the result of a measurement of the particle's position.

The information about the particle's position at each point in time does not exist. It's not a question of this information being "lost". It was never there in the first place.

Or is too lacking to be considered the grounds for my supposed contradiction?

What contradiction are you thinking about?

 

[PeroK]

More accurately, the more precisely you know the position, the less precisely you know the momentum.
But I don't think this is the right way to think about it. It's not what some observer knows that matters. Note that because you don’t know the momentum exactly, you become less certain of the position over time.
It's more that over time there is an increasing number of possible states, so the information required to specify the state increases.

I'm not convinced this is true. The point about unitary evolution (of the quantum state) is that the state of a system at some future time is entirely determined by the initial state and the time evolution operator (which is determined by the Hamiltonian for the system).

 

[hutchphd]

Does that mean the simple answer of Yes is not completely valid? Or is too lacking to be considered the grounds for my supposed contradiction?

Thanks for the clarification. I like the question.
For my money, this is one of the indicators that Quantum Mechanics is much more reasonable than its predecessors. It provides, in principle at least, a means to specify the information content in a proscribed subsystem The amount of information available is constrained. Whether it exists on some cosmic scale is beyond my pay grade.

 

[bkelly13]

From here: https://scienceexchange.caltech.edu...the German physicist,about its speed and vice
Is the quote:
Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927, the uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy; the more we nail down the particle's position, the less we know about its speed and vice versa.
I believe it is mostly true but leads to an incorrect presumption. The key is: “… with perfect accuracy;” Perfect accuracy seems to be an unobtainable goal. Can we capture that position of a proton, for example make it two protons in a helium nuclear, to the accuracy that the measurements of each proton will show them side by side? Can we measure the position to within a Plank length?

I disagree with PeroK’s statement: The information about the particle's position at each point in time does not exist. It's not a question of this information being "lost". It was never there in the first place.

Every bit of matter that exists, exists somewhere. If it is a particle, well, that part is easy. If at the time of measurement, it takes a wave format, then the crest, valley, position, and velocity of the wave are somewhere.

(Side note: I am aware of the concepts and claims that particles can pop in and out of existence. But as there has never been any example of anything in the macro world popping out of existence and back in, that is not of statistical relevance for this discussion.)

In any case, we cannot determine the position exactly. The position did or does exist. Therefore some information is lost.

But another question is buried within the concept of, from the scienceexchange quote: “… we cannot know both ….” Who is this “we?” Does that statement proclaim that we humans cannot determine that. Or is the “we” in a general sense in that the exact position cannot be determined or known by “anything.” Particle A cannot know exactly where its neighboring particle B currently resides. Particle A will respond to or be influenced by the approximate position of particle B, but is indifferent to the “exact” position of particle B. And what is “perfect accuracy?”

Trying to simplify: Any given particle has a position, down to the Plank lengths in, say, Cartesian coordinates. But, that position is not knowable and is therefore lost. This leads to a conclusion that the theory of conservation of information is faulty.

 

[Couchyam]

Have you heard of the Von Neumann entropy?

 

[haruspex]

I'm not convinced this is true. The point about unitary evolution (of the quantum state) is that the state of a system at some future time is entirely determined by the initial state and the time evolution operator (which is determined by the Hamiltonian for the system).

As I noted in the next paragraph, I think there is a confusion here between the information in the system (microstate combination) and the information possessed by the observer. My remark you responded to concerned the former, while unitary evolution concerns the latter.

 

[PeroK]

From here: https://scienceexchange.caltech.edu/topics/quantum-science-explained/uncertainty-principle#:~:text=Formulated by the German physicist,about its speed and vice
Is the quote:
Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927, the uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy; the more we nail down the particle's position, the less we know about its speed and vice versa.

That's not a valid source to learn QM. It's states a popular-science interpretation of the HUP.

I believe it is mostly true but leads to an incorrect presumption. The key is: “… with perfect accuracy;” Perfect accuracy seems to be an unobtainable goal.

This is wrong. Physics isn't about analysing the words that are used in a pop-science article. Physics is about the mathematical models.

Can we capture that position of a proton, for example make it two protons in a helium nuclear, to the accuracy that the measurements of each proton will show them side by side? Can we measure the position to within a Plank length?

There are two issues here. The first is that a proton is not an elementary particle: it's a well-defined state of three quarks. The second is that the quarks cannot be separated for their position to be measured.

Your main problem is trying to describe subatomic particles in classical terms (not in QM terms). You end up with questions that don't make sense, because they assume implicitly that the subatomic world is just a smaller version of the macroscopic world. The above article you referenced makes the same mistake, when it imagines shrinking a tortoise down to the size of an electron. An electron is fundamentally different from a tortoise. It's not just a matter of size.

I disagree with PeroK’s statement: The information about the particle's position at each point in time does not exist. It's not a question of this information being "lost". It was never there in the first place.

It's your prerogative to disagree with what you learn on this site. But, that's what QM says. There's no point in trying to learn about physics and then "diagree" with what you learn.

Every bit of matter that exists, exists somewhere.

This is wrong. PF is not the place to promote your own personal theories.

If it is a particle, well, that part is easy. If at the time of measurement, it takes a wave format, then the crest, valley, position, and velocity of the wave are somewhere.

This is wrong/nonsense.

In any case, we cannot determine the position exactly. The position did or does exist. Therefore some information is lost.

This is wrong.

Trying to simplify: Any given particle has a position, down to the Plank lengths in, say, Cartesian coordinates. But, that position is not knowable and is therefore lost. This leads to a conclusion that the theory of conservation of information is faulty.

On the contrary, the conslusion is that you don't understand the theory. Physics isn't wrong everytime a new student fails to understand the basics.