Minimum Data Set For Atoms

[Max560]

What is the minimum data set required to completely describe an atom at a given instant in time?

I imagine that to be able to fully discribe an atom, you would have to identify its coordinates in the universe, its vector, its speed, etc. You would also need to know the composition of the atom, accounting for all particles, electrical charges, and where all of these things are located relative to each other.

When you account for all the data for a particular atom, at a particular instant in time, exactly how much information would you have? What would be the most efficient way to encode this information?

What is the minimum number of Ones and Zeros requred to completely describe a single atom in a single instant of time?

As I understand it, some people believe that the world as we know it exists because it is held in mind by God.

In order to fully realize the implications of this belief, I want to get a clear Idea of just how much information is actually being held in mind. This would be a large amount of course, but how much are we really talking about?

Once we find an acceptable data set size for a single atom in a single instant, we can extrapolate to all atoms in the universe to get the minimum data set for the Universe at any instant in time.

Then, we might be able to speculate on how much processing would be required to have the entire universe in mind in realtime.

[ImpyTimpy]

Yeah but that's assuming the said God would have a human mind or a binary mind capable of storing 1's and 0's only. I would think if God existed, the mind would be Godly or something, as in beyond human concepts. :P

[c4ts]

First they tell me there's a limited number of elements and now this?

[Uncertainty]

I imagine that to be able to fully discribe an atom, you would have to identify its coordinates in the universe, its vector, its speed, etc. You would also need to know the composition of the atom, accounting for all particles, electrical charges, and where all of these things are located relative to each other.

It's not as simple as that. As far as modern physics knows, you can never know the position of a particle exactly, or its speed.

The most accurate way we have of describing something like that is with waves describing where the particle COULD be. As far as we know, anything could be anywhere in the universe at any time (though the probability of that is very small).

Worse still, it seems that there is no formula that can give even the functions of these waves exactly. The more you want to know about a particle the more complicated the math. Unfortunatly, it seems like no amount of data would be able to decribe any thing exactly.

Don't blame me, blame Heisenburg.

[Agammamon]

Rather than trying to specify the velocity/position of a particle, you could just specify its quantum state/position. In each atom the quantum state of each particle is unique.

Greg Bear, in his novel "Moving Mars", talks about how many bits it takes to completely describe a particle (relating to Bell Continuum theory, ie viewing the universe as a computaional machine and particles as data) but I don't remember the exact number (8 bits or bytes keeps popping into my head).

[aggle_rithm]

Lawrence M. Krauss discussed this in "The Physics of Star Trek". He was talking about whether teleportation was a feasible technology.

Krauss' estimate was one kilobyte of data for each atom. If this were the case, he said, then the information on every atom in a human body would fill so many 10-gigabyte hard drives that a stack of them would extend for 20,000 light years.

[DrChinese]

I understand the idea of the complete description of a particle with mass. Just to make sure that the proper notion is communicated...

Particles do not have those attributes simultaneously. Conceptually, you may resolve the position of a particle to nearly any degree desired, but when you do that the momentum takes on a progressively wider range of values (according to the uncertainty relations). It's not just a question of being able to measure them at the same time... they don't exist.

[Vorticity]

Originally posted by Agammamon
Rather than trying to specify the velocity/position of a particle, you could just specify its quantum state/position. In each atom the quantum state of each particle is unique.
Its actually even more complicated than that.

In order to specify the complete state of an atom, you need the joint wave function for all the particles in the atom. You can't handle them separately, because then you lose information regarding their interaction.
Now, when you talk about the wave function (i.e. "state") of a physical system (such as an atom), it can usually be written as the superposition of an infinite number of special wave functions that do not vary in time. These are called "stationary states". By "superposition", I mean that the complete wave function will be equal to some complex number times stationary state #1 plus some other complex number times stationary state #2 plus... etc. You need all those complex numbers to perfectly specify the atom's "state", and in general there are an infinite number of them.
So: that means that you need to store a countably infinite number of complex coefficients, which of course, would take an infinite amount of memory. It gets worse: Each complex coefficient would, in general, be an irrational number, i.e. one whose decimal expansion goes on forever and does not repeat. So, in fact, each one of the infinite # of complex #'s would itself take an infinite amount of memory to store.
So the answer is: a countably infinite # of bits are required for each atom.

(All of the above assumes we are really recording the complete state of the atom. If we are allowed to make approximations, such as neglecting higher, extremely improbable stationary states, then things can be made a little better, poossibly even finite. But then we lose information.)

[Iconoclast]

Originally posted by Uncertainty
As far as we know, anything could be anywhere in the universe at any time (though the probability of that is very small).
Well, except for car keys.

[Zombified]

Originally posted by DrChinese
Particles do not have those attributes simultaneously. Conceptually, you may resolve the position of a particle to nearly any degree desired, but when you do that the momentum takes on a progressively wider range of values (according to the uncertainty relations). It's not just a question of being able to measure them at the same time... they don't exist. There's a difference between the state of a quantum system, which is the vector of probability amplitudes, and the measurements you can make on it, and you're right: measure position will "mess up" any prior momentum measurement you made.

When you do measure something, the state changes to match what you actually measured, so you can perform measurements and determine completely the state of the atom... but it will not be the state the atom started in, it will be the state corresponding to the outcome of your measurements. The complete state never corresponds to a precisely defined position and momentum simultaneously.

[Max560]

Originally posted by ImpyTimpy
Yeah but that's assuming the said God would have a human mind or a binary mind capable of storing 1's and 0's only. I would think if God existed, the mind would be Godly or something, as in beyond human concepts. :P

I am making no assumptions about how the mind of God would work. I want to know how much information is required to fully describe a given atom at a given point in time.

Saying that we simply couldn't comprehend how complex the mind of God is strikes me as a rather simple dodge of a straightforward question. It's just a variation of the "God works in mysterious ways" non-answer.

When someone claims that a god is responsible for making the universe as we know it exist by merely having it in mind, I want to get an idea of just how much information we are talking about. I only selected binary as an encoding method because binary is a concept that we simple humans can understand.

[Max560]

Originally posted by aggle_rithm
Krauss' estimate was one kilobyte of data for each atom. If this were the case, he said, then the information on every atom in a human body would fill so many 10-gigabyte hard drives that a stack of them would extend for 20,000 light years.

So we have a lower limit of one kilobyte per atom,

So the answer is: a countably infinite # of bits are required for each atom.

and an upper limit of infinity.

Greg Bear, in his novel "Moving Mars", talks about how many bits it takes to completely describe a particle (relating to Bell Continuum theory, ie viewing the universe as a computaional machine and particles as data) but I don't remember the exact number (8 bits or bytes keeps popping into my head).

I haven't read that book for a while. The numbers did seem manageable somehow.

[BobK]

Using 1 Kilobyte to describe 1 atom would mean that each atom will require 8192 bits of information.

In order to fully describe the current state of the universe, a database with a mass equivalant to 8192 universes would be required, if 1 atom is used to represent 1 bit of information.

Maybe that's where the so called missing mass of the universe is?:D

That also does not include software to access and manipulate the information.

[Agammamon]

It doesn't neccessarily follow that the amount of matter needed to simulate the universe would equal or exceed the universe's mass.
You could, for example, use electrons or quarks (or even neutrinos or photons) to store your data. Assuming your one atom is hydrogen, using electrons (1049 to store 1kb) cuts the required your required mass in half. Take into consideration that a largish percentage of visible matter is He or even heavier atoms and the required mass drops even further.

[BobK]

Agamammon,

You are of course correct that if particles could be used instead of atoms the mass required would be less.

I was just trying to point out that knowing the current state of the universe is not likely ever to be acheived.

Also, I don't understand your figure (1049 to store 1kb).

One byte is equivalant to 8 bits therefore 8192 bits in one Kilobyte.

Hydrogen is most common element in universe by mass and also by quantity.

Common elements (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961112a.html)

[Agammamon]

I agree with you about computing the state of this universe (though it could be possible to simulate other/smaller universes at such a fine scale).

The 1048 number I got because I basically mix up bit and byte.

Yes, I know hydrogen is the most common element, but the other elements and dark matter move the average mass of the universe above that of hydrogen.

[Vorticity]

Originally posted by Max560
So we have a lower limit of one kilobyte per atom, and an upper limit of infinity.
If you really mean a complete (i.e. 'containing all the information') description of the state of an atom, then it is definitely infinity. I'm as sure of that as I am of anything.

People might say that you only need a few integer numbers to store the quantum state of an atom (the so-called "quantum numbers" that specify energy, angular momentum, etc...), but these are insufficient. Quantum numbers describe the state of an atom that happens to be sitting in a so-called "stationary state". In general, though an atom might be very close to being in a stationary state, it will actually be in a state that is a superposition of an infinite number of stationary states. The coefficients that determined "how much" of each stationary state the atom "has" will in general be irrational numbers, hence requiring an infinite number of bits to describe precisely.

I don't understand the "one kilobyte" figure. Perhaps that comes from making the approximation that each atom is in a stationary state. But by making this approximation you are losing data about the nature of the atom's true wave function.

[JesFine]

Hmmm... also, as any computer guy on here could tell you, there are many many compression schemes used to deal with huge amounts of data. Presumably God would know the absolute most efficient one ever and would shove all this data into his copy of WinZip Infinity.

Also, we assume that God can violate the Heisenberg Uncertainty Principle at will. Otherwise, I believe the amount of data required would be infinite, and even if you compress Infinity a millionfold, it is still infinite.

Oh also, we assume that god has some way of deducing the value of certain things, otherwise, just the value of pi (or e, or sqrt(2)) would require an infinite amount of data points. So perhaps he can deduce the location/velocity/quantum state of all points in the universe from a single cesium atom he keeps in his billfold.

Seems like there are a lot of hidden hypotheticals in this question.