What do physicists mean by "information"?

[koganbot]

What do physicists mean by information?

Every now and then I'll read a book by a scientist trying to explain a field or subfield or subproblem to laypeople like me (by Randall, Susskind, Greene, to name a few of the recent). I almost always like these books, but Sean Carroll's From Eternity To Here is the first that's really clicked for me. I wouldn't remotely claim to understand it. But I got enough while reading to follow what it was doing as it went circling and chasing a few basic questions. Fundamentally: our universe, or our part of it, seems to start with low entropy, the entropy increasing over time. (Other possibilities are explored.) Without this low-entropy start, time wouldn't have the direction it has. Why did we start with low entropy?

This actually encompasses a whole bunch of questions and contentions. I read the book several months ago, in spare time, needing all three library renewals and finishing on the last day, not thinking concentratedly enough to master one part before moving onto the next. I couldn't have mastered the parts anyway. At one point I copied down the following passage, writing underneath, "If I want to test whether I've understood the book so far, I could look at this passage and ask myself to explain it: to fill in the background, to describe how his argument got here. I don't think I can right now." I understand it even less a few months removed:

In that sense, the irreversibility that crops up when wave functions collapse appears to be directly analogous to the irreversibility of ordinary thermodynamics. The underlying laws are perfectly reversible, but in the messy real world we throw away a lot of information, and as a result we find apparently irreversible behavior on macroscopic scales. When we observe our cat's location, and our own state becomes entangled with hers, in order to reverse the process we would need to know the precise state of the outside world with which we are also entangled, but we've thrown that information away. It's exactly analogous to what happens when a spoonful of milk mixes into a cup of coffee; in principle we could reverse the process if we had kept track of the position and momentum of every single molecule in the mixture, but in practice we keep track of only the macroscopic variables, so irreversibility is lost.
--Sean Carroll, From Eternity To Here, p. 255

My question about information is this: We use the word "information" for a whole lot of fairly different stuff, but I think of it as including, e.g., "The test tomorrow is at 1:00 PM." But when a physicist like Leonard Susskind is talking about "conservation of information," I don't think he means that something like "The test tomorrow is at 1:00 PM" is preserved — e.g., would survive planets being absorbed into black holes and the black holes dissipating. But when he uses the phrase "conservation of information" he does indeed mean that all information is conserved after planets are absorbed and black holes dissipate; so I'm surmising that the sort(s) of information he's talking about differ from the type of info that would include "The test tomorrow is at 1:00 PM." But maybe the latter is included.* If so, how would that work?

*I read The Black Hole War and of course have forgotten most of what I read.

Comments

[arbitrary-greay.livejournal.com]

Hell if I know if this is correct, but based on that excerpt, the information in "The test tomorrow is at 1:00 PM," as dubdobdee says, is primarily in marking time.

"1:00PM" refers to a specific point in the earth's rotation on its axis.
"tomorrow" refers to the rotational cycle after the one we are currently in.

Information thrown away here includes the location of the test, (what part of the earth is facing the sun at 1:00PM) the point in the earth's orbit around the sun, (The time of year) and possibly the possibly the locations of our solar system in the galaxy and the location of the galaxy in the universe. (relative to the "big bang starting point) Without this information, we cannot reconstruct the location of the earth and sun any exact moment and therefore the exact time at which it happened, and therefore the passage of time is irreversible. I think.
Given that Carroll manages to limit his milk-in-coffee example to within the cup, possibly time in this test-at-one example could be constrained to earth-and-the-sun.

[koganbot]

My poor memory tells me that Carroll is on the side of information being preserved, but that he doesn't think the controversy has been resolved yet. But my question might be whether he's using "information" differently in this example from how he'd use it in saying "information is conserved."

"Reversibility" (maybe here and here?) is probably crucial to the idea of conservation of information, though I of course don't know. But the reversibility in the coffee cup would mean that, in principle, if we know the location of and momentum of all particles in the cup after the milk has thoroughly mixed into the coffee, we could know exactly where the milk droplets landed when they entered the coffee and tendrils of milk began to snake out from the original droplets. (Hmmm. Carroll uses the phrase "keep track of." Why would we have to do that? Knowing the current locations and momenta should be sufficient.) "Reversibility" means that reconstructing the past and predicting the future are identical operations (so, in effect, we're also predicting the past and reconstructing the future). But looking macroscopically, what we see doesn't seem to conserve the information, since the mixed together milk and coffee could be compatible with a whole number of different landing spots for the milk when it was poured into the cup. Whereas, we know that, from whichever landing spot we started, we'll get the sort of mix we actually got. That's why time seems irreversible.

As I ponder this, I'm thinking maybe I'm wrong in believing they (Carroll, Susskind, et al.) wouldn't include "The test tomorrow is at 1:00 PM" as being preserved. That raises a number of questions and problems in my mind (if intelligent beings are gone, how could the concept "1:00 PM" be preserved? wouldn't you have to introduce a real, physical entity into the black-hole-dispersed future, that entity being capable not only of reconstructing the past, but of comprehending "1:00 PM" as part of the reconstruction? if not, what right do you have to say that information is preserved?), but I don't know enough to even know if the questions I'm posing are relevant or would make any sense to the discussion.

[arbitrary-greay.livejournal.com]

Keep track of: This is because movements of particles require work, which are not path-independent. "from whichever landing spot we started, we'll get the sort of mix we actually got" is simplifying the situation into a path-independent one by throwing away the specifics of energy exerted to move each particle in its particular path, but without knowing those exact energies, we cannot reverse?

The concept of "1:00 PM" as a matter of a 24-hours-in-a-day, 12-hour-half-day-cycle might not be information preserved, but as I guessed before, 1:00 PM as signified by some point of the earth's rotation on its axis might be. The terms and jargon used to characterize these states ("so many degrees away from the GMT line is facing so many degrees away from the sun is 1:00 PM at this location") aren't what are preserved, but the state itself is. Our descriptors do not fundamentally change the state of the object, otherwise 1:00PM would be different from 下午一點鐘. So "The test tomorrow is at 1:00 PM" as language is not what they're including under "information."

[koganbot]

I probably ought to try and read and understand this Wikip entry. I have time to do the former, but the latter will have to wait:

http://en.wikipedia.org/wiki/Physical_information

But as I said to Anonymous below, I don't in principle see why, if locations of planets can be reconstructed after a planet and its sun are gone, the location and disposition of synapses and neurons of inhabitants of planets can't be reconstructed as well, and languages, and how people interpret sentences in that language, even the ones that communicate false beliefs and lies, and contain ambiguities.

I don't see how "size" and "speed" and "location" are any less conceptual than "1:00 PM" is. So conversely, I suppose, I don't see how "1:00 PM" is any less physical. Seems to me if you can get one of them, you can get them all. (But as I also said to Anonymous below, my question isn't about what seems right to me, but about what physicists believe, and how they use the term "information.")

[(Anonymous)]

I'm not a physicist but I suspect what they're referring to as information might be simply independent of entropy. A sun or planet would take considerably more entropy to destroy than a memory, a language or a book. Though perhaps a black hole wouldn't even let that information escape it.

A film on blu-ray disc usually requires large amounts of disc space to capture the quality of the grain of the film, the noise. Something that contains almost no useful information (it could literally be replaced by some new "generic" grain and nobody would be able to tell the difference). But this grain is also extremely information-dense thanks to the nature of the physical processes by which it is generated (it can take up even more space than the picture itself) despite being high in entropy.

If you burned a book information would be both preserved (in principle, since each atom's history could be reconstructed if you knew precisely the energies involved in the burning and the precise locations of the atoms) and destroyed (in practice, since nobody could have that information; entropy has definitely increased).

[(Anonymous)]

I think the problem is that the information of a phrase like "test tomorrow at 1:00 pm" isn't contained in the sentence itself, which is just a series of arbitrary squiggles that correspond to sounds arbitrarily assigned to words. So the meaning isn't inherent to the sentence or the words (which refer to concepts but aren't the concepts themselves), it has to be generated/interpreted/comphrehended by the brain reading it.

[koganbot]

The question for me here isn't what I believe — I don't know what to believe — but what physicists believe (not that they necessarily all believe the same thing). So the question would be: do physicists count all of what we (or I) think of as "information" in the information that ought to be conserved if the principle of "conservation of information" is correct, or do they only count some of that as (the relevant sort of) information? I don't in principle see why, if locations of planets can be reconstructed after a planet and its sun are gone, the location and disposition of synapses and neurons of inhabitants of planets can't be reconstructed as well, and languages, and how people interpret sentences in that language, even the ones that communicate false beliefs and lies, and contain ambiguities.

[arbitrary-greay.livejournal.com]

Hmmm, best I can guess is to think in programming terms: at the high-level language stage, variables are given names, and when searching for a piece of data stored in a variable, you call its name, which therefore is dependent on its descriptor. Searching the wrong descriptor will give you the wrong variable, and thus the wrong data.

However, at lower levels, compiler and binary languages, the descriptor is only used as a reference to a location. The data in that location does not change regardless of what descriptor is used to simply "remember" where that location is. I'm guess that "information" is referring to the data, (the state of being) not the name given to the location.

"size," "speed," "location," and "1:00 PM" are variable names in the sense that they are terms in the english language referring to size, speed, location, and time, and thus aren't preserved information. Size, speed, location, and time as the actual states of being are not variable names, and thus are preserved, no matter what language we use to refer to them. If a box has an edge of 13cm, whether I call it "height," "width," or "length" does not change that the edge is 13cm. 13cm is preserved, whatever term I call it is not. (Although I need a physicist to confirm this.)
And, of course, "13cm" itself is a variable name. The distance of that edge still doesn't change whether I use metric, customary, latin numbers, or base 10, and in turn, the choice of metric/customary/latin/base 10 to describe that distance have no effect on the reconstruction of that edge.

I do see your point. Yes, a specific term should be able to be reconstructed through the reconstruction of history and the evolution of a language, so yes, "The test tomorrow is at 1:00 PM" can be information preserved as objects of language. But only where they are objects in and of themselves, the things being referred to, and not as a reference to a test occurring at a certain time and location.

[koganbot]

Why must they be "objects in and of themselves"? That is not a clear concept anyway. "Object" is a concept. The earth is an "object" in contrast to the space around it; but earth doesn't make such a comparison, but rather people make the comparison, by contrasting earth with non-earth. Earth, and its atmosphere, and the space beyond that, don't draw distinctions. We draw distinctions.

But regardless, if earth and planets count as objects, so should neurons and synapses. Hence "The test tomorrow is at 1:00 PM" ought to be as eligible for conservation as the actual location of the earth — even if it turns out the test gets postponed till 2:45, so that students can witness the arrival of the unicorn at 1:00 PM.

[arbitrary-greay.livejournal.com]

But the reconstruction of neurons and synapses constructs the words and relations between them in "The test tomorrow is at 1:00 PM," not the location of the earth. The reconstruction of "The test tomorrow is at 1:00 PM" is not necessary to the reconstruction of the location of the earth, which would happen independent of any particular evolution of neurons and synapses. That's what I personally mean when I differentiate being "objects in and of themselves" and being a reference to something else, and why a phrase as a linguistic construct is preserved, but not the phrase as a description of something.

Like in programming: the name given to a variable is itself stored as a series of 1s and 0s (or at the physical level, two different phases of silicon) somewhere on a chip. That is conserved. But when we consider it as a pointer to where some other data is, that data is conserved, and not the pointer.