# Proof of Conservation of Information

• gabeeisenstei
In summary: So, for a given model, it is a theorem.In summary, the conversation revolves around the concept of conservation of information and its application in different scenarios. The idea of entropy is introduced as "hidden information" and the recoverability of this information is discussed. The use of momentum and trajectory as encoding of relevant information is also mentioned. The conversation questions the validity of conservation of information and seeks proof for its preservation.
gabeeisenstei
I'm having trouble with the idea of conservation of information.

I watched Susskind introduce the concept of entropy as "hidden information", using an example of drops of water filling a bathtub: a message encoded in the sequence of drops is lost for practical purposes, but in principle is recoverable at the micro-level. I don't understand this recoverability "in principle".

Let's simplify with an ideal box, into which particles are shot through a window (which is subsequently closed). Can we use momentum and the tracing of a trajectory as the encoding of relevant information? Another piece of information might simply be the time intervals between identical particles shot into identical boxes with identical momentum.

In the first case, let the velocities be the same, and the difference be the angle at which the particle goes through the window (or where it first strikes the far wall of the box). It seems to me that there are at least two different initial angles that will, after some number of bounces around the box, settle into the same trajectories. At that point the information as to their initial angles would seem to be lost.

In the second case, it seems clear that pairs of particles entering the box separated by different time intervals will attain the same trajectories if one interval is a multiple of the other, in terms of the time needed to travel across the box.

What am I missing? Is my box too ideal, not absorbing any of the particle's momentum? Is it wrong even to say that a single particle bounces around in the box, since a photon striking a mirror should actually be described as exciting an electron which then emits a different photon? Or would you apply the uncertainty principle to deny the hypothesis of identical particles with identical momentum? (But then the uncertainty principle would serve to destroy information, not preserve it?)
Where is the proof that information is never lost?

***

I wrote the above before viewing previous threads about conservation of information. I see that many people here don't believe in it or don't think it is well defined. I was assuming that it is widely acknowledged, given the prominence of the "information paradox" generated by black holes. If people like Hawking didn't assume conservation of information (at least outside of black holes), there would be no paradox. Surely he thinks there is a proof?

Where is the proof that information is never lost?
Whether the "information" (distinction in initial conditions) is preserved depends on the model of the evolution. There are models that preserve it, and models that violate it.

## 1. What is the concept of "Proof of Conservation of Information"?

The concept of "Proof of Conservation of Information" is a scientific principle that states that information cannot be created or destroyed, but can only be transformed or transferred from one form to another. This principle is based on the law of conservation of mass and energy, which states that matter and energy cannot be created or destroyed, only transformed.

## 2. How does "Proof of Conservation of Information" relate to the field of science?

"Proof of Conservation of Information" is a fundamental principle in many fields of science, including physics, chemistry, biology, and information theory. It is used to explain and predict the behavior of systems and processes, and is essential for understanding the laws of nature and the workings of the universe.

## 3. What evidence supports the concept of "Proof of Conservation of Information"?

There is a vast amount of evidence that supports the concept of "Proof of Conservation of Information." This evidence includes numerous experiments and observations, such as the conservation of energy in chemical reactions, the conservation of mass in nuclear reactions, and the conservation of genetic information in biological processes.

## 4. What are the implications of "Proof of Conservation of Information" for technology?

The principle of "Proof of Conservation of Information" has significant implications for technology. It allows us to design and develop systems and processes that are efficient and sustainable, as well as to understand and mitigate potential negative impacts on the environment. It also forms the basis for many technological advancements, such as renewable energy sources and information storage and transfer.

## 5. Are there any exceptions to the concept of "Proof of Conservation of Information"?

While the principle of "Proof of Conservation of Information" is generally accepted in science, there are a few exceptions. One example is the phenomenon of virtual particles in quantum mechanics, where particles can seemingly appear out of nowhere and then disappear. However, these exceptions still follow the overall principle, as the energy and information are ultimately conserved in the system.

• Mechanics
Replies
11
Views
1K
• Mechanics
Replies
7
Views
2K
• Cosmology
Replies
13
Views
268
• Mechanics
Replies
1
Views
1K
• Cosmology
Replies
1
Views
1K
• Mechanics
Replies
16
Views
6K
• Quantum Physics
Replies
11
Views
1K
• Quantum Interpretations and Foundations
Replies
25
Views
2K
• Mechanics
Replies
1
Views
2K
• Quantum Physics
Replies
28
Views
3K