Information encoding in the Holographic principle

In summary: And there may thus be a "physical basis" for why one dual model is imlpemented over the other by nature.In summary, the holographic principle can be understood as a duality between two mathematical models, which can be used as a problem solving tool in physics. However, there is a possibility that the holographic duality has a deeper meaning in unifying particle physics and cosmological theories. It is also suggested that the complexity of the human brain or other complex systems may not be easily captured by mathematical models, but this does not mean that the information itself is non-mathematical.
  • #1
Suekdccia
272
24
Can whatever type of information be encoded in a boundary in holographic principle?
in a question some years ago regarding holography (https://physics.stackexchange.com/q...theorem-examples-of-the-holographic-principle)

It is said that AdS/CFT is the most common type of holography treated in physics, and although whatever information of a bulk could be encoded in a boundary, is very uncommon to talk about holography outside AdS/CFT correspondence.

Then, if whatever/any information could be encoded there, then could info of anything of whatever dimensions, characteristics, nature, logic/mathematic/non-mathematical/illogic nature (even illogical things)...etc (anything) be encoded in a boundary so the universe inside of it would behave according to this info (as the info encoded in the boundary dictates what will happen in the universe inside that boundary)?

(Asking only of it's possible, I understand that the AdS/CFT point of view is the only way we can talk about holography in a definite way, but I'm only asking if that would be possible)

PS: I had a conversation about this with another user in Physics Stack Exchange:

He told me that "I am not willing to start thinking outside the mathematically well-established background of the theory. It is irresponsible to use the knowledge that we have for a specific thing to extend it to some hypothetical and unestablished basis" and that my question couldn't be answered because AdS/CFT is the only well established type of holography and this was out of that theory.

I agree with him in the part that my question is too hypothetical (and I apologize for that), but I was asking only if it's possible (I mean, if as you say, whatever info could be encoded in the boundary, although is very hypothetical and obviously not well studied, it could be physically possible, isn't it? If yes, then why he says that my question could not be answered?)

<Mentor moved thread to Quantum Physics>
 
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  • #2
The holographic principle can be understood either pure mathmatically, as a duality between two mathematical models, which can be used as a problem solving tool. If you see it this strict way, all possible physics is gone.

Or in more fuzzy way and try to understand if the holographic duality between the mathematical models in physics, has a deeper message to us in how to unify particle physics with cosmological theories.

See old threads https://www.physicsforums.com/threa...inciple-make-predictions.937872/#post-5929983

/Fredrik
 
  • #3
Fra said:
The holographic principle can be understood either pure mathmatically, as a duality between two mathematical models, which can be used as a problem solving tool. If you see it this strict way, all possible physics is gone.

Or in more fuzzy way and try to understand if the holographic duality between the mathematical models in physics, has a deeper message to us in how to unify particle physics with cosmological theories.

See old threads https://www.physicsforums.com/threa...inciple-make-predictions.937872/#post-5929983

/Fredrik

Tack så mycket för ditt svar
So, in holographic principle, you can establish a duality between two mathematical models. However, it is always said that in holographic principle, information about a bulk is encoded in the boundary. Then can non-mathematical information be encoded in the boundary (so in the boundary we would have a non-mathematical model)?

And also, then, could information about a computer or a hypothetical brain capable of thinking anything of whatever dimensions, characteristics, nature, logic/mathematic/non-mathematical/illogic nature (even illogical things)...etc (anything) be encoded in the boundary, so all that it thinks happens in that universe?
 
  • #4
Suekdccia said:
Then can non-mathematical information be encoded in the boundary (so in the boundary we would have a non-mathematical model)?
The question here is what you mean by non-mathematical information?

If you are talking to things that we - so far - does not have good mathematical models for, like the complexity of the human brain. Then that doesn't mean that the information itself is different in any way. Its just too complex for us to encode and compute, even if we did have the model. This is IMO even one of the possible deeper meanings of hologprapy, because the dual ways of representing a theory has different comptutational complexity as well. And there may thus be a "physical basis" for why one dual model is imlpemented over the other by nature.

But just to make another point here, i think holography should not be mixed up or confused with any mysticism or anything such. Even complex systems and living systems are from the point of physics no different - except the order of complexity. Which MEANS, that computers of "information processing agents" of too low complexity, can not easily capture it.

/Fredrik
 
  • #5
Fra said:
The question here is what you mean by non-mathematical information?

If you are talking to things that we - so far - does not have good mathematical models for, like the complexity of the human brain. Then that doesn't mean that the information itself is different in any way. Its just too complex for us to encode and compute, even if we did have the model. This is IMO even one of the possible deeper meanings of hologprapy, because the dual ways of representing a theory has different comptutational complexity as well. And there may thus be a "physical basis" for why one dual model is imlpemented over the other by nature.

But just to make another point here, i think holography should not be mixed up or confused with any mysticism or anything such. Even complex systems and living systems are from the point of physics no different - except the order of complexity. Which MEANS, that computers of "information processing agents" of too low complexity, can not easily capture it.

/Fredrik
Ok, so I understand that information about a computer or a hypothetical brain capable of thinking anything of whatever dimensions, characteristics, nature, logic/mathematic/non-mathematical/illogic nature (even illogical things)...etc (anything) could be encoded in the boundary, so all that it thinks happens in that universe.

But what about information that cannot be described with mathematics (that's why I meant with non-mathematical information)? Could it be encoded in a boundary?

I had a conversation about this with another user in Physics Stack Exchange:

He told me that "I am not willing to start thinking outside the mathematically well-established background of the theory. It is irresponsible to use the knowledge that we have for a specific thing to extend it to some hypothetical and unestablished basis" and that my question couldn't be answered because AdS/CFT is the only well established type of holography and this was out of that theory.

I agree with him in the part that my question is too hypothetical (and I apologize for that), but I was asking only if it's possible (I mean, if as you say, whatever info could be encoded in the boundary, although is very hypothetical and obviously not well studied, it could be physically possible, isn't it? If yes, then why he says that my question could not be answered?)
If that information could be encoded in the boundary (it would be physically possible), then, why did he said that my question could not be answered? Did he mean that although is perfectly possible, since obviously there are no mathematical well studied models that refer to my question, we cannot know how that info would be encoded in the boundary?
 
  • #6
Suekdccia said:
But what about information that cannot be described with mathematics
I have a hard time to imagine what you mean by this. And i suspect most physicists have, so that may explain how your question was received.

One can certainly discuss different competing mathematical measures of "information", but that is one thing, but if we start to talk about information that escapes mathematical characterisation altogether then would suggest the first task to to work on that characterisation. Maybe I am old fashioned, but measures of information in some way or the other has to relate to counting, and distinguishable states. This is where it all starts for me. And already there you have the mathematics.

/Fredrik
 
  • #7
Fra said:
I have a hard time to imagine what you mean by this. And i suspect most physicists have, so that may explain how your question was received.

One can certainly discuss different competing mathematical measures of "information", but that is one thing, but if we start to talk about information that escapes mathematical characterisation altogether then would suggest the first task to to work on that characterisation. Maybe I am old fashioned, but measures of information in some way or the other has to relate to counting, and distinguishable states. This is where it all starts for me. And already there you have the mathematics.

/Fredrik
Well, I read that Max Tegmark said once that there are things that we can imagine that are not describable by maths for example.
In any case, my question is, in the case (even if it's hypothetical) there is information that cannot be described by maths, could that non-mathematical info be encoded in a boundary so what that info describes happens in the universe in the boundary? In the original link from the question that i posted first it is said that whatever information could be encoded in a boundary so i suspect that even non-mathematical info could be encoded there...
 
  • #8
If you ask the physicist side of me, I'd reply with "How could we ever measure information not described by math, if we use math to describe information?" I can't follow your logic, as a physicist.

Now if I leave that side of me, what you're essentially asking is "is it possible that information that we can't interpret be encoded in the boundary?" Which would be a "Sure, why not?" but eventually you're going to need to describe it, and that would be math.

So, let's say it's true you would start with "Well, there is certain things in this boundary that I can't measure with current methods, or with current math..." then where would I go? I'd have to think of what I think the information could be, and how to describe it. The natural language for physics is math, so boom, i'd have to describe it with math.

I think the issue you're going to run into when asking about it the way you're asking is, we're interested in measuring information. If there is something we can't describe, what are the chances it even gets thought of? How can I tell you something exists in this boundary if I can't even show it exists? It's of no use to be thinking about it from this point of view, I'd rather start from what I do know and can describe, and build it up from there. Then if I run into issues, I know where they are. Starting at the "There are non-mathematical releases of information in the boundary" is not the right approach to this problem.
 
  • #9
Fra said:
I have a hard time to imagine what you mean by this. And i suspect most physicists have, so that may explain how your question was received.

One can certainly discuss different competing mathematical measures of "information", but that is one thing, but if we start to talk about information that escapes mathematical characterisation altogether then would suggest the first task to to work on that characterisation. Maybe I am old fashioned, but measures of information in some way or the other has to relate to counting, and distinguishable states. This is where it all starts for me. And already there you have the mathematics.

/Fredrik

Or are you saying that information that would escape mathematical characterisation and that has nothing to do with maths would need to be characterized by it?
but what about information that could not be characterised by maths? or even info that could not be described? could that be encoded in the boundary in holographic principle (so the universe inside would behave according to this info)?
 
  • #10
Suekdccia said:
Or are you saying that information that would escape mathematical characterisation and that has nothing to do with maths would need to be characterized by it?
Yes, that is roughly what i meant.

But its not just "mathematics" itself. Its the physical reality that mathematics describe. Holography is on on hand a way to transform a mathematical problem or computation. But the interesting part is what this may have todo with physics.

Its the abstractions that are interesting. These can be "mathematics" of dynamical systems, it can be interacting computations(ie communication) or it can be interacting physical coding structures.

We should indee seek beyond the surface for deeper understanding, but all above respresentations are sort of isomorphic to each other and has the traits of "mathematics".

Not only the concept of "information" but also "encode" and "behave according to" are really qualitative structured ways to classify and measure things. These ARE all precursors to "mathematics".

So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.

/Fredrik
 
  • #11
Fra said:
Yes, that is roughly what i meant.

But its not just "mathematics" itself. Its the physical reality that mathematics describe. Holography is on on hand a way to transform a mathematical problem or computation. But the interesting part is what this may have todo with physics.

Its the abstractions that are interesting. These can be "mathematics" of dynamical systems, it can be interacting computations(ie communication) or it can be interacting physical coding structures.

We should indee seek beyond the surface for deeper understanding, but all above respresentations are sort of isomorphic to each other and has the traits of "mathematics".

Not only the concept of "information" but also "encode" and "behave according to" are really qualitative structured ways to classify and measure things. These ARE all precursors to "mathematics".

So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.

/Fredrik

Ok, I think I'm beginning to understand everything.

So, for every information that we wanted to encode in the boundary (even if it does not relate to mathematics in any way) it would need to be encoded, and thus characterised with maths, in order to do that (for example Max Tegmark once said that there are things that we imagine that cannot be described with maths. If we wanted to encode the information of those things into the boundary (so the universe inside of it would behave according to that info, i mean, what happens in the universe is due to what that info "tells"), we would need to characterize it with maths (although the information itself is not maths and it cannot be used to describe it, we would need to characterize it with maths to encode it isn't it)?
So, in a few words, even information that is not related with maths or cannot be described by it needs to be characterized by it in order to encode that info in the boundary right?

And a last question: what did you meant with this phrase:
Fra said:
So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.
 
  • #12
Fra said:
Its not anything you can imagine
I'm specially interested in this part
 
  • #13
Fra said:
Yes, that is roughly what i meant.

But its not just "mathematics" itself. Its the physical reality that mathematics describe. Holography is on on hand a way to transform a mathematical problem or computation. But the interesting part is what this may have todo with physics.

Its the abstractions that are interesting. These can be "mathematics" of dynamical systems, it can be interacting computations(ie communication) or it can be interacting physical coding structures.

We should indee seek beyond the surface for deeper understanding, but all above respresentations are sort of isomorphic to each other and has the traits of "mathematics".

Not only the concept of "information" but also "encode" and "behave according to" are really qualitative structured ways to classify and measure things. These ARE all precursors to "mathematics".

So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.

/Fredrik

So, Is it right what I said then?
Suekdccia said:
So, in a few words, even information that is not related with maths or cannot be described by it needs to be characterized by it in order to encode that info in the boundary right?
 
  • #14
Fra said:
Yes, that is roughly what i meant.

But its not just "mathematics" itself. Its the physical reality that mathematics describe. Holography is on on hand a way to transform a mathematical problem or computation. But the interesting part is what this may have todo with physics.

Its the abstractions that are interesting. These can be "mathematics" of dynamical systems, it can be interacting computations(ie communication) or it can be interacting physical coding structures.

We should indee seek beyond the surface for deeper understanding, but all above respresentations are sort of isomorphic to each other and has the traits of "mathematics".

Not only the concept of "information" but also "encode" and "behave according to" are really qualitative structured ways to classify and measure things. These ARE all precursors to "mathematics".

So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.

/Fredrik

And another thing I forgot to ask you.
Assuming that you said that even information that is not related with maths or cannot be described by it needs to be characterized by it in order to encode that info in the boundary (so information about a computer or a hypothetical brain capable of thinking anything of whatever dimensions, characteristics, nature, logic/mathematic/non-mathematical/illogic nature (even illogical things)...etc (anything) could be encoded in the boundary, so all that it thinks happens in that universe), then, why Max Tegmark, in his ultimate multiverse hypothesis (where he defends that every hypothetical universe describable by maths exist: https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) did say that not every imaginable universe would exist in his theory, because there are things that we can imagine that cannot be described by maths (and of course, other types of things like illogical things for example, cannot be described by them.)
But if in holography we could encode them in the boundary, we would need, as you say, to characterise them with maths. How can this be coherent with what Tegmark said?
In addition, it is supposed that Tegmark's hypothesis would include all mathematically possible worlds (and there are a lot of pages that classify holographic universes in that theory). But again, if in holography we can encode things that cannot be described by maths (or even by logic...), then, how can this be coherent? Besides, there are even philosophical theories that defend that all logically possible universes exist. Would holography be put in there? What about holographic universes where non-logical (for example) info was encoded in the boundary?...

And I still seeing with interest this phrase you said last time:
Fra said:
So its i would say about something even deeper than only math. Its not anything you can imagine. It is still about structures and their interrelations in th physical world.
Tack så mycket
 
  • #15
"Something deeper than math that cannot be encoded." What would that be? That notion is imaginable, and easily communicated. But no example can be found. It cannot be communicated, not even as a thought between the hemispheres of one's own brain, because communication requires an encoding into some sort of language made of words, formulas, or nerve impulses.
 

Related to Information encoding in the Holographic principle

What is the Holographic Principle?

The Holographic Principle is a theory that suggests that all of the information in our 3-dimensional universe can be encoded on a 2-dimensional surface, much like a hologram. This principle is based on the idea that the universe is a hologram, meaning that it is a projection of information from a higher-dimensional space.

How is information encoded in the Holographic Principle?

According to the Holographic Principle, information is encoded on the surface of a black hole or on the event horizon. This means that all the information from an object that falls into a black hole is stored on the surface rather than inside the black hole itself.

What are the implications of the Holographic Principle?

The Holographic Principle has many implications for our understanding of the universe. It suggests that the laws of physics in our 3-dimensional world are actually derived from a 2-dimensional surface. It also challenges our understanding of space and time, as well as the concept of locality.

What evidence supports the Holographic Principle?

One major piece of evidence for the Holographic Principle is the Bekenstein-Hawking formula, which relates the surface area of a black hole to its entropy. This formula suggests that the information in a black hole is encoded on its surface. Additionally, recent studies of the cosmic microwave background radiation have found patterns that support the idea of a holographic universe.

How does the Holographic Principle relate to quantum mechanics and general relativity?

The Holographic Principle is an attempt to reconcile the two major theories of physics, quantum mechanics and general relativity. It suggests that these two theories can be unified by understanding the universe as a hologram. However, there is still much debate and ongoing research about how exactly these theories can be reconciled through the Holographic Principle.

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