There are 3 sub questions below:
1. Suggest your own answer:
This paper seems to suggest that both laws are not operating in the same set. http://link.springer.com/article/10.1007/s10701-007-9159-z ArXiv link: http://arxiv.org/ftp/cond-mat/papers/0703/0703235.pdf
If possible, please don't bring in the black hole information paradox, as the paradox is an exercise of the application of the fundamental issue of this question. Unless the example is illuminating with specific assumptions clearly laid out. For example:
2. Do you agree with this?
This paper suggests that:
http://arxiv.org/pdf/1009.5111v3.pdf
We postulate that all kinds of information, in general, about a physical system fall
into two categories. Let’s call them Π1 and Π2 (Π is the first letter of the Greek word that stands for information). The Π1 class contains the most fundamental information that defines a particle, such as the mass, the electric and magnetic charge and the angular momentum of it. The much larger Π2 category includes information about how particles mingle with each other and the properties that rise from their combinations. A book, for example, contains a vast amount of Π1-info about the aforementioned conserved quantities, of the elementary particles it consists of, and an even larger amount of Π2-info about how these particles unite to form different nucleons, atoms and molecules including also the way all these combine to form letters and words that mean something.
So Unitarity is preserving Π1 information and the second law is destroying Π2 information.
3. Please clarify if information is lost when going from the pure to mixed state. If so, why do we believe in unitarity?
http://arxiv.org/pdf/1009.5111v3.pdf, http://arxiv.org/ftp/cond-mat/papers/0703/0703235.pdf
Great question,
Answering your question in §2 , yes, Pappas's paper is a great contribution.
You can relate the 2 kinds of information to what happens during a quantum coherence/decoherence process : when decoherence happens (during the timelike evolution of a system's wave function) the second type of info is lost.
The unitary info however, far more fundamental and representing attributes inherent to the wave function variables undergoing evolution (such as decoherence from their earlier environment and/or establishment of new coherence with a new environment) , abides throughout the process.
I'll toss in an idea that I've already mentioned in other forums and plan to write a paper on: What is a bit? I would say this: It is the conversion of a 50/50 quantum probability choice (e.g. the classic double slit) into a specific event detection. If you play that out fully, it's equivalent to saying the full set of such bits in the universe is the "address" of that universe in a Deutsch-style multiverse, and that entropy is in one sense the loss of quantum uncertainty in favor of classical certainty. Apart from the curious special case of quantum information erasure, the idea that the collection of all bits in the universe define its "Deutsch address" (I just made that up) in the multiverse also pretty much guarantees that no information can be lost. We are in effect dangling at a very specific twig-end on a very, very large multiverse tree, and all those bits are the branching address of that twig.
So according to you Terry, quantum information is lost in the end due to erasure.
Nope, my intent was pretty much the exact opposite of that. Information erasure is a local phenomenon that is possible only when the scope of distribution of the information stays small, local, closed, and experimentally controllable . Once a bit -- a classical observation of a possible path really -- gets tangled up with the. thermodynamic complexity of classical phenomena, it becomes so difficult to "untangle" all the points that it has touched that for all practical purposes it becomes irreversible. Shoot, the entire universe is *in principle* always reversible and thus erasable, but the intertwining of all those events will never allow it. If erasure happens at the end, it will be through some other mechanism. Our end from our inside-the-universe perspective will be "bit fatigue," the exhaustion of all to the interesting quantum possibilities of the early universe, and the locking down of all histories through the massive intertwining of the possible paths. You can interpret as sort of the be-all and end-all of symmetry breaking, if you accept an unobserved quantum state as a more symmetric form of the object (I do).
I'm thinking in terms of do the information in our mind (or brain) survive our death?
If Pappas's contribution is the right way to see the world, then the information in our mind can be the Π2 information that gets destroyed with death.
However, according to Terry the information in our mind should survive our deaths. Since we obviously interact with the world so much. Is that right?
Xin, just to be clear: I used to think that the idea of our information surviving our death via information preservation at the level of physics was just bogus, even though Feynman argues that all information is indeed preserved (I need to look that up). However, ever since coming up with the definition of a bit as a choice between two equal-probability quantum paths -- a definition that I think is both practical and mathematically precise -- I've had to change my position to what you just said: The information that defines who we are -- including of course our minds and thoughts, which are physical processes -- cannot be lost. Such a loss would jump between branches of the Deutsch multiverse, without any clear explanation for why such a jump should (or even could) occur. Worse, if you instead postulate true erasure of that information, you would go backwards on the tree, and that would violate the increase in classical entropy in a rather profound way. Entropy *is* the accumulation of all the classical information that defines how our universe has unfolded from quantum indeterminacy. The massive collection of very-fine-grained information threads that collectively defined our entropic state are it is the "Deutsch address" (David Deutsch I'm sure has no idea I'm using his name this way, BTW) that defines our current tree location.,
Now, with all that said, please also be aware of this side of it: Good luck at extracting that information, because except in special cases where certain threads dominate the outcomes (we call those special cases "history"), it's going to be *really* hard.
There is an obvious answer to the question if you stick to the mathematical models of classical and quantum interaction.
The second law says: information is either lost OR at best remains constant. In the special case of perfectly known unitary evolution (also in classical conservative e.g. Hamiltonian systems), the information remains constant.
When you see a state at time t, you have to guess where it was a second ago. If you know exactly the unitary evolution operator, you can compute that. If you do not know it, then you have to guess, with uncertainty, and information is lost. If the system you are interested in has interacted, even in a perfectly known unitary way, with another system about which you do not have complete knowledge, then again you must guess how that other system has affected the state, and information is lost. There is an interpretation of the second law as such information "dispersal": not actual loss, but effective loss unless you measure the whole universe.
In that sense: yes, according to our models, the information stored as electrical signals in our brain are present somewhere even when we die. The problem is, physically our brain cells interact with the whole universe. As long as we live, there seems to be a control mechanism that prevents information to get lost by arbitrary interactions. Once we die, there is no such control anymore and basically you would have to measure every tiny electrical interaction that happens around the person, and compute back what it means about the information stored initially. For instance: if bacteria nr.2345678 eating your brain cell moves a µm/s faster at time t=1.98765, then maybe the charge there was positive and not negative. As it would be a colossal task already to retrieve brain information in vivo, it is currently beyond reach to imagine retrieving all that information once it is dispersed throughout everything with which our brain physically interacts.
Conclusion: information from our brain is indeed always present, but filtering it out of the state of the world is unrealistic.
All this is valid in classical and quantum physics alike; even in a quantum measurement (non-unitary evolution), information can only be lost about the initial state.
Then information conservation does provide a theoretical possibility (at least not theoretical impossibility) from physics for the cases of rebirth, or (partial or whole) information transfer from a dead person to another person (usually) born after the previous person had died.
In particular cases of xenoglossy is intriguing.
http://www.iisis.net/index.php?page=semkiw-reincarnation-xenoglossy-ian-stevenson-definitions
I have been interested in rebirth research for a while and I think it's high time Physics provide some response to this. I think a fair response would be:
Information is preserved in Physics, the increase in entropy just counts lost as information that are meaningful for us and we are able to keep track. Thus, besides not knowing how the mechanism of information transfer between lives work (recall quantum jump), there is no theoretical objection to transfer of information from one life to another. In fact, even if the information is not transferred to a new body after death, it is still out there in the universe, somewhere.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
However, quantum memory (as a possible physical equivalent of entropy) can be quite a physical quantity.
See e-print viXra:1712.0614
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