What is Information? Simplest Answer

[Padraic]

They (physicists) say that information can't be lost and I heard Susskind saying that he thought information of objects going into a black hole was stored in the outside of the black hole while the material was sucked in. I thought information was almost like a fossil, where an imprint of an event is left on lots of other things, however that can be destroyed so I must have that wrong. What is information (in the simplest terms you can think of)?

 

[aimforclarity]

Great Question! I've been puzzling over this myself.
I think we are talking about physical information, as in one spin can contain 1 bit of information. it is either up or down. (or is it two since it also has direction?). When we measure it, to know it is there, must we be receiving information from it, so that that scrambles the information that is in it? eg when we measure the spin along the X or the Y direction when it starts off in the Z.

Wiki has a nice article that probably won't answer your question with satisfaction (http://en.wikipedia.org/wiki/Physical_information):

Information itself may be loosely defined as "that which can distinguish one thing from another"

 

[Padraic]

Yeah I tried to understand it but I couldn't completely.

So would physical information be something that occurs simply at the quantum level? I got the impression from the Hawking Susskind black hole debate that it had to do with reversibility, so since things happening at our level are part of reversibility why wouldn't everything be included?

If it did include things happening at our level it seems like a lot of it would get destroyed but I guess if you're good enough you can still figure it out. It also sounded like physical information has to do with messages being sent off.

 

[atyy]

In the context of black holes, information loss is defined as a pure state evolving into a mixed state.
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/DensityMatrix.htm

This is also known as non-unitary evolution. The information loss can be related to an increase in entropy.
http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/info_loss.html

 

[Naty1]

Padraic: there is no simple explanation of information that is very useful. At least I have never found one. Maybe someone will surprise!

One thing we can say: In general, information as the answer to some question should reduce your uncertainty about which among possible answers is correct.

A source of a message should have HIGH uncertainty, otherwise you'll know what the message contains before it is sent...we say it has high entropy, yet we want a received message to have LOW uncertainty...so we can understand it!

yet a stream of bits like 1,1,1,1,1,1,1,1,1,1,1,1,1...doesn't tell you much...you know what the next bit will be...
The above ideas pertain most directly to communications 'information'. From an engineering [applications] perspective, that much is pretty well understood.


Let's say I want to gather some "information" about local particles: Accelerated detectors will register different particle counts than an inertial detector! This is called the Unruh
Effect. So how many local particles and the energies (temperature) I observe is not so simple.

Let's switch and talk about manipulating 'information' (bits) in a computer:
only erasure costs energy...that means it increases entropy...so when entropy increases information decreases. This is called Lanudaur's Principle.

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

So at the end of the universe as entropy is at a maximum...information will be at a minimum.
Reversible processes behave one way, irreversible another.

As another perspective: someone posted this elsewhere and I liked it:

So the rule for objectivity is not that everyone lives in the same reality, it is that no two observers' realities can be inconsistent with each other. This also means that "complete" information does not imply a unique description of the reality, it merely implies access to all the information that is locally available to that observer in principle. The locality of the information is what preserves causality…”

The above means different observers see different things based on different available information but they should not be inconsistent.This also applies in cosmology.

Finally, you might want to look at 'entanglement', an idea of quantum mechanics.

 

[Naty1]

Wow...here is something crazy:

Toshiyuki Nakagaki, a professor at Future University Hakodate, northern Japan, cultivates the slime in petri dishes and has discovered how the brainless organism is capable of finding its way out of a maze...

The findings highlight how slime mould possesses information processing abilities shared by humans which are more sophisticated than the most advanced computers, according to Professor Nakagaki...

http://www.telegraph.co.uk/news/wor...ime-able-to-navigate-its-way-out-of-maze.html

 

[Naty1]

And another perspective:

And it is the wave function that lies at the heart of puzzles about the nonlocal effects of quantum mechanics. But what is it, exactly? Investigators of the foundations of physics are now vigorously debating that question. Is the wave function a concrete physical object, or is it something like a law of motion or an internal property of particles or a relation among spatial points? Or is it merely our current information about the particles? Or what?

from Post #1 here:
https://www.physicsforums.com/showthread.php?t=562437

 

[Padraic]

Sorry it took me so long to get back to you guys.

In the context of black holes, information loss is defined as a pure state evolving into a mixed state.
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/DensityMatrix.htm

This is also known as non-unitary evolution. The information loss can be related to an increase in entropy.
http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/info_loss.html

How is a mixed state a real thing and not just something we don't know? If something is 50% probable this way and 50% probable that way isn't it really just one or the other but we don't know which one?

Padraic: there is no simple explanation of information that is very useful. At least I have never found one. Maybe someone will surprise!

One thing we can say: In general, information as the answer to some question should reduce your uncertainty about which among possible answers is correct.

A source of a message should have HIGH uncertainty, otherwise you'll know what the message contains before it is sent...we say it has high entropy, yet we want a received message to have LOW uncertainty...so we can understand it!

yet a stream of bits like 1,1,1,1,1,1,1,1,1,1,1,1,1...doesn't tell you much...you know what the next bit will be...
The above ideas pertain most directly to communications 'information'. From an engineering [applications] perspective, that much is pretty well understood.


Let's say I want to gather some "information" about local particles: Accelerated detectors will register different particle counts than an inertial detector! This is called the Unruh
Effect. So how many local particles and the energies (temperature) I observe is not so simple.

Let's switch and talk about manipulating 'information' (bits) in a computer:
only erasure costs energy...that means it increases entropy...so when entropy increases information decreases. This is called Lanudaur's Principle.

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

So at the end of the universe as entropy is at a maximum...information will be at a minimum.
Reversible processes behave one way, irreversible another.

As another perspective: someone posted this elsewhere and I liked it:



The above means different observers see different things based on different available information but they should not be inconsistent.This also applies in cosmology.

Finally, you might want to look at 'entanglement', an idea of quantum mechanics.

I'm pretty familiar with entanglement so if you can explain it from that it might help. I still don't see why something like what you are discussing can't be destroyed. I still don't get what is being stored in the outer part of a black hole while it's mass falls in.

And another perspective:


from Post #1 here:
https://www.physicsforums.com/showthread.php?t=562437

That sounds like a whole nother can of worms but it sounds incredible. I've started reading it.

 

[Naty1]

I'll tackle one small piece:

I still don't get what is being stored in the outer part of a black hole while it's mass falls in.

join the crowd...there are some explanations, but are they correct?...

you can check in wikipedia I'm sure...

ok, here is one good place:


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

The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon.

So information appears to be related to enclosed surface area NOT volume! What a crazy
situation. Information in a black hole is FINITE>>>>

Leonard Susskind in his book THE BLACK HOLE WAR (his controversy with Stephen Hawking)
has some really interesting insights on information and horizons...like the horizon of a black
hole is "stringy"...it can be described in terms of quantum strings...and so hiodden information is proportional to the total LENGTH of a string!...and Hawking radiation can be viewed as string bits breaking loose from just outside the horizon...due to quantum fluctuations...a perspective akin to virtual particles causing the Hawking radiation.

Also: consider acceleration...that also causes a horizon to form...which leads to a temperature (called the Unruh effect)...that means different particles are observed under
acceleration...this is the same as sitting stationary outside a black hole horizon...
so just what information is available locally?? not as obvious as once thought. A stationary and accelerating observer passing each other locally read different temperatures!

 

[phinds]

How is a mixed state a real thing and not just something we don't know? If something is 50% probable this way and 50% probable that way isn't it really just one or the other but we don't know which one?

No, most emphatically not. Quantum indeterminacy is NOT a measurement problem it is reality.

The most graphic demonstration of this, to me, is the concept of an electron going through a slit (see the "double slit" problem) and hitting a phosphor screen. At any specified tiny amount of time prior to it striking the phosphor, we have NO idea where it is except that there's a low probability that it is anywhere near the place where it strikes the screen. In classical physics, which seems to be how you are looking at things, this is nonsensical. Welcome to the quantum world.

 

[Ken G]

so just what information is available locally?? not as obvious as once thought. A stationary and accelerating observer passing each other locally read different temperatures!

It was my quote above about information available locally, and I confess I can't give a precise meaning to what that is (maybe that is a crucial question of current research). But I think Unruh radiation doesn't break the importance of thinking in terms of the locality of information, because for an accelerating observer to read a different temperature requires some time for the observation, and so they cannot remain in the same reference frame as the observer reading a different temperature. Thus they cannot have access to the same "local" information, because reference frames are also local, so changing reference frames requires changing the available information. In special relativity, a reference frame is viewed as global, but Unruh radiation requires general relativity, and there reference frames (AFAIK) should be regarded as local, and should also be regarded as having access to local information.

So there might be a direction connection between information and reference frames-- the information that any observer could call "complete" is connected with the reference frame of that observer, and some "global union" of complete information would then require uniting the information of all the reference frames, like putting together a jigsaw puzzle. There would be significant redundancy there, but it would not be completely redundant, so I think understanding the redundancies and independences of the information available in different reference frames might be a good way to connect information in relativity with information in quantum mechanics. I feel that physics must always be about information, so unifying theories of physics can be framed as ways of unifying the various treatments of information.

 

[Ken G]

How is a mixed state a real thing and not just something we don't know? If something is 50% probable this way and 50% probable that way isn't it really just one or the other but we don't know which one?

Actually, that question is at the heart of a lot of the distinctions between the various interpretations of quantum mechanics. We should distinguish this from the concept of quantum indeterminacy, which actually applies to pure states (superpositions of states with definite outcomes for some given measurement). Quantum indeterminacy does indeed seem to be part of reality, but mixed-state indeterminacy is harder to say. In the Copenhagen interpretation, for example, a mixed state is interpreted as you say-- it is one or the other we just don't know which. In Everett's many-worlds interpretation, the mixed state is interpreted as a projection onto some measured subsystem of what is in reality a much larger pure state that includes the entire system (including the observer), and the larger state includes all the possible outcomes even if we don't perceive them.

So in the two-slit experiment, for example, if the apparatus does not determine which slit the particle goes through, then the particle is in a superposition of going through both slits. I wouldn't say it actually does go through both slits, merely that it is in a superposition that does not answer the which-slit question. But if the apparatus does determine which slit, even if we are not privy to that information, then we have a mixed state of going through each slit, and in the Copenhagen approach, we can say the particle actually did go through one or the other. So the information about the particle has changed, and that is irreversible, whether or not we know that information.

As to whether or not a mixed state "is the real thing", you need to take a stance on some flavor of realism. To Bohr, a state is never a "real thing", it is always a description in the mind of the physicist who is trying to understand the real thing. But the same holds for information and entropy-- they are live in the mind of the physicist doing some analysis, and their connection to reality appears only in how they work for some goal. They are the ways we talk about reality, which is not the same as the reality itself, but nevertheless are effective in theories like thermodynamics so connect perfectly well with the concepts of information and entropy.

 

[Naty1]

Ken G:

... because reference frames are also local, so changing reference frames requires changing the available information.

that seems to be the situation.

In special relativity, a reference frame is viewed as global, but Unruh radiation requires general relativity, and there reference frames (AFAIK) should be regarded as local, and should also be regarded as having access to local information.

yes, the only thing I'd mention that frames are also local in SR.

So there might be a direction connection between information and reference frames-...-

quite possibly; I don't recall the details but the appearance of a horizon is behind the Unruh effect... like Hawking radiation just outside a black hole horizon...And as Leonard Susskind points out ,changing the encompassing horizon changes the "location" of the information to a new horizon...say a bigger one...so not only may information be two dimension, it is not so local as one might think. Apparently, evey 'bit' of information in our universe is stored on the enclosing boundary(horizon)...Maybe the cosmic censorship hypothesis is also linked to all this "information"...

 

[DNMock]

Wouldn't a simple description of information be like this:

"Information is anything that can be used to help find the cause to an effect"?

ex.
effect: a neutrino hits a detector
cause: a star went supernova
information: any form of data that could possibly be collected from the neutrino that would be needed to help find out the who, what, when, where, or why of the effect (in this case a supernova).

In the listed example information could be how fast was the neutrino going, what direction was it going, when did it hit the detector, how energetic was the particle, all of which could be used in some way to find the who, what, when, where, and why of the source.

Why, as far as I am aware, that Hawking radiation loses information is because the particle that is created is not capable of giving all the information of the cause of it's existence (the effect).

Back to my neutrino example, you can find out exactly when where how and why it was created from it's information theoretically speaking that is. You can know how long it's existed theoretically, how fast it was going which way it was going, etc. etc. True Hizenberg's Uncertainty Principle won't allow you to know all these things at the same time, but the information is there. You can find any of these things individually from a particle, therefor the information exists.

With the Hawking's radiation since the particle's anti-particle pair was sucked into the black hole if you track the particles information back to the moment of it's original creation you still would not be able to find out the everything about it's creation since it's anti-particle pair technically doesn't exist anymore because it has been condensed down to a singularity where, according to our best available understanding and math, is a place where infinities and all sorts of chaos occurs, the information needed to be able to find out using pure math the cause for the effect of the existence of the particle is lost. Thus information is lost.

TL:DR version:
Laymans version of information that's probably wrong.

 

[Ken G]

Apparently, evey 'bit' of information in our universe is stored on the enclosing boundary(horizon)...Maybe the cosmic censorship hypothesis is also linked to all this "information"...

There might indeed be some deep duality between how we think about what local means in spacetime, and holographic kinds of thinking about information on surfaces or horizons. Or maybe what we think of as local information is actually some kind of change in information or expectation across some surface. I don't have a clear sense of what information really is, other than how we use it in specific situations, but it does seem to have something to do with changing expectations, with winnowing down the possibilities.

 

[drbutler]

Mathematically there are currently two types of information: macroscopic and quantum. My knowledge of quantum Information, accounted (not measured) with units of qbits is currently minimal and I will not address that here. Macroscopic information can be further divided into two sub-classes. First there is an absolute information, defined by Shannon's entropy measure and which involves an implicit comparison of an observed system against a virtual uniformly random background. This is the measure of information used in communication theory, and is of particular importance in showing how to send the most message content in a given bandwidth within a noisy universe. A second macroscopic measure is known variously as relative entropy, relative information, or relative information. An important example of this type of information measure is the Kullback-Liebler divergence, which for some time has been known to provide a basis for unification of diverse statistical methods. The Kullback-Liebler divergence is a measure of the number of bits of information available to make a discrimination in favor of one probabilistic description over another as a correct description of a physical system. This is potentially useful in physics since cause and effect states suggested by an earlier correspondent's note as information are, at their core, different states which can be subject to statistical comparison. The Kullback-Liebler divergence has several interesting properties: it is invariant under a non-singular transformation of random variables, and the lowest order expansion in probability parameter differences is a quadratic form based on the Fisher information matrix; the Fisher information matrix has been used as the basis of some derivations of quantum mechanics.

There have been some suggestions that a truly fundamental physical theory (potentially more fundamental than current quantum theories) might be based on information. Such an approach has the curious potential to make some thermodynamic concepts, which are now understood to be based on the underlying statistics and information constraints, to be regarded as more fundamental than quantum theory.

 

[Ken G]

Such an approach has the curious potential to make some thermodynamic concepts, which are now understood to be based on the underlying statistics and information constraints, to be regarded as more fundamental than quantum theory.

That's an interesting comment. Personally, I feel that the next great theory will need to move closer to an understanding of how we do physics, and farther from the model that physics is about things that have nothing to do with how we think. Recognizing the importance of information might be a step in that direction, if we also recognize our own role in information processing.

 

[Naty1]

For those interested in some different perspectives on information, consider the book
DECODING THE UNIVERSE, by Charles Seife...
from biological reproduction to Heisenberg uncertainty...

 

[aimforclarity]

That's an interesting comment. Personally, I feel that the next great theory will need to move closer to an understanding of how we do physics, and farther from the model that physics is about things that have nothing to do with how we think. Recognizing the importance of information might be a step in that direction, if we also recognize our own role in information processing.

i agree, i think this is the essence of heisengber uncertainty and infromation.

for something to be ontological (that it can exist), it must have effect, and must be also epistomological (knowable), we must be able to know about it, to learn it is there.

we can only deal with things we know are there and exist, that is basically science (in some coarse outline :) )

but to know it is there we have to intearact with it, and the thing with the microscopic world is that any interaction is bidirectional, coupling to the system affects the system and also affects the measurmnet system as well.

mesurment is no different in essence than any system being measured.

to be more concrete, consider how qubits are read out dispersively,
the qubit energy levels get coupled to a SHO resonator (cavity qubit can talk to),
if we put the cavity near the qubit at a smaller frequency,
the interaction shifts the energy levels of the cavity slightly,
the one photon in cavity qubit levels get pushed up and down and by the zero photon exited energy level of the qubit, and so the cavity resonant frequency shifts depending on the state of the qubit.

i think this picture is at the essence of measurement.

 

[Ken G]

Yes, I agree that we learn about things by interacting with them, it was always kind of a cheat to pretend we could "observe" rather than "interact."

 

[jartsa]

They (physicists) say that information can't be lost and I heard Susskind saying that he thought information of objects going into a black hole was stored in the outside of the black hole while the material was sucked in. I thought information was almost like a fossil, where an imprint of an event is left on lots of other things, however that can be destroyed so I must have that wrong. What is information (in the simplest terms you can think of)?

Let us consider a box of molecules. The position and the momentum of the molecules can be measured accurately, which allows us to calculate the positions and the momentums 10 hours earlier, so no information deterioration happened in the box during ten hours.

Other thing is that the measurement caused every molecule to have a new unknown position and momentum. Second measurement would tell us this information, but not the information of the first measurement, that information disappeared from the box, but we can hope that that information exists somewhere outside the box, as the point of measuring is to extract information.

So conservation of information works something like this:

If you want to create new information, then you need to do a measurement. The measurement tells you old information. If you fail to remember the information, then you did not do a measurement, no information was created, and the old information is in its original state.

 

[salvestrom]

Some comments posted here have touched on a question I have. One poster mentioned how physical models often use things that don't necessarily tie directly to reality. The numbers come out right, but the mathematical mechanism doesn't correlate directly to the physical mechanism occurring. One example is how I was emphatically told NO in the quantum forum when I said I was under the impression virtual particles actually exist, just not long enough to be observed. They said it was just part of the maths and ought to be left there.

Is this a problem? Shouldn't the primary goal of science be to understand how a thing atually works, not just on having a strong maths model for predicting the results of how it works?

Another example from this thread was the question of whether a wave function is a physical object. I think it could be - a general disturbance, accentuated by interactions with other disturbances - but I feel there are going to plenty of people who would quite strongly tell me it's just part of the maths.

Another poster above notes that these things aren't even settled within the community, so I guess those on the outside need to wait for the dust to settle.

 

[H2Bro]

Information to my understanding is the requirements to describe a physical system to some arbitrary degree of accuracy. This places as a limit the amount of information that can be contained in a system to the accuracy and non-intrusiveness of our measurement devices.

if we claim the position and velocity of particles of gas in a box actually encode instructions on how to build a table we can't actually extract that information unless we have some method of observing the position and velocity without changing it in the process, and since we do not we cannot truly claim that the box encodes that information.

But I guess this is open to the criticism that a hypothetical encoder/decoder could potentially derive any "information/instructions" out of any physical system if the encoding process were fancy enough. Also some would distinguish between human information i.e. answers to questions and absolute information i.e. objective states.

 

[Ken G]

Shouldn't the primary goal of science be to understand how a thing atually works, not just on having a strong maths model for predicting the results of how it works?

The problem is, it's very hard to tell if there is actually any difference between these possibilities. How could you tell when you have the first instead of the second? Are there any examples from the history of physics that were demonstrably the first rather than the second? I view the first as a kind of temporary mindset we enter primarily for convenience, rather than anything that is actually true.

ETA: but I don't mean to undersell the importance of "convenience"-- mental convenience is very close to what we might call understanding, and I do think understanding is a key goal of scientific inquiry.

 

[Ken G]

Also some would distinguish between human information i.e. answers to questions and absolute information i.e. objective states.

Some might try, but I don't see how they could ever actually pull it off. Information is the answer to a question, it is a mental sorting of possibilities. What is the difference between "human" information and "absolute" information? I can't see a demonstrable difference there, and suspect that any imagined difference there is just a kind of pipe dream.

 

[aimforclarity]

Some might try, but I don't see how they could ever actually pull it off. Information is the answer to a question, it is a mental sorting of possibilities. What is the difference between "human" information and "absolute" information? I can't see a demonstrable difference there, and suspect that any imagined difference there is just a kind of pipe dream.

yes, you are saying that information is a human construct and does not exit beyond us, like the alphabet or the idea of the color green.

this is true, the concept of information is 'artifical' in the sense that as a concept it is not ontological (does not exist), but like all human concepts, i think that it reflect an ontological reality, just like the color green is an abstraction but is a conceptual map to a certain type of response of matter to light. (matter and light being again human concepts referring to corporeal things (real))

 

[ThomasT]

What is information (in the simplest terms you can think of)?

Data.

 

[ThomasT]

... the concept of information is 'artifical' in the sense that as a concept it is not ontological ...

I think that the term "information" refers to anything that can be pointed to and manipulated. So, it's real, in any sense that the term "real" is meaningful.

... the color green is an abstraction ...

The word "green" refers to a particular real em frequency which happens to be within the our sensory, or sensible, spectrum.

 

[aimforclarity]

I think that the term "information" refers to anything that can be pointed to and manipulated. So, it's real, in any sense that the term "real" is meaningful.

im not sure that's any better. just because 200 years ago we could not "point to" or manipulate say cooper pairs or atoms, doesn't mean they don't exist and don't have an effect.

this is a real problem in physics, how do we see and manipualte, people are discovering new ways every so often to see new things and manipulate old things in new ways, which expands their 'dimensionality'.

we usually talk to the atomic energy levels with E fields, but we can just as well use B fields, or potentially gravitions one day.

 

[Ken G]

The usual analogy is a map-- it refers in some way to the territory, but is not the territory. Without the mapmaker, one has only the territory, but no map. I suspect it is the same with "information."

 

[ThomasT]

im not sure that's any better. just because 200 years ago we could not "point to" or manipulate say cooper pairs or atoms, doesn't mean they don't exist and don't have an effect.

You can point to what you mean by cooper pairs or atoms or photons or electrons. All of these terms have real physical referents. Wrt some terms in fundamental physics there are only formal referents. Wrt some terms there are real physical instrumental referents.

But information is just data. That is, information refers to recorded and manipulable, interpretable, instrumental results. Just my two cents.

 

[dm4b]

At the risk of being controversial, I'll just say that until we fully understand consciousness, we will not fully understand what information is, either. I'm thinking of specific potential traits to consciousness that seem to allow the non-local exchange of "information". I'll go ahead and say the "dirty" words - psychic ability.

You can argue all you want there is no valid evidence it is a reality, but that is in no way decidedly true at this point.

Some noted physicsts like Michio Kaku have recently said an open mind is needed based on results from current laboratory testing. Even Carl Sagan, who said he doubted positive test results in the end, still thought it was worthy of investigation:

"At the time of this writing there are three claims in the ESP field which, in my opinion, deserve serious study: (1) that by thought alone humans can effect random number generators in computers; (2) that people under mild sensory deprivation can receive thoughts or images projected at them; (3) that young children sometimes report the details of a previous life, which upon checking turn out to be accurate and which they could not have known about in any other way than reincarnation."

Based on current findings, psychic ability, or information exchange via consciousness, appears to be non-local, and does not seem to favor a preferred direction in time.

If any of this turns out to be decidedly factual, it adds a whole 'nother dimension to the question, "what is information?". Ignoring it won't make it go away either.

 

[Maui]

What is information (in the simplest terms you can think of)?

Neurons humming in a highly specific pattern:

http://www.pbs.org/wgbh/nova/mind/media/elec_chat.html