# How many bits or bytes of information are present in 1 atom

• I
• Wolfenstein3d
In summary, the number of bits that can be encoded into the state of an atom is much smaller than the number of bits that can be read out of the state of an atom.f

#### Wolfenstein3d

My guess is the number is huge,but I don't know what transformations from the hip Iwould use to figure this out.

My guess is the number is huge

Why?

Aren't there different types of atoms?

Use a basic atom like H. I think it's huge relative to a computers memory. Not necessarily huge compared to the info of a larger mass

I think it's huge relative to a computers memory.

Again, why? Either you have some basis for thinking this or you don't. If you do, what is it? If you don't, why are you guessing?

Again, why? Either you have some basis for thinking this or you don't. If you do, what is it? If you don't, why are you guessing?
Because hup defines a lot of detail being packed into matter

Because hup defines a lot of detail being packed into matter

How?

hsdrop
My guess is the number is huge,but I don't know what transformations from the hip Iwould use to figure this out.

The question of how much information is "in" an atom is very interesting, but hard to pin down philosophically. The easier question to answer is how many bits can be written into the state of an atom, and how many bits can be read out of the state of an atom?

So, one way to answer this question is to ask how many bits of information can you communicate by sending an atom?

The quantum state of the hydrogen atom can be expressed in terms of principal quantum numbers (energy, angular momentum, magnetic, spin), and the number of distinct values that this chain of 4 quantum numbers can have is the number of distinct quantum states that can be communicated. The base 2 logarithm of this number would be the number of bits you can encode into the state of the hydrogen atom. Since they are all distinguishable quantum states, one could read out the message at the other end with the appropriate measurements assuming it didn't get disturbed along the way.

Since there's technically an infinite number of values these four numbers can have, it is tempting to say one could encode an infinite amount of information into the state of the atom. However, due to practical limitations, like that the atom has an energy small enough that any disturbance won't just knock the electron away before any measurement can happen, and that our technical abilities are still developing in preparing atoms with specific quantum states when they get so close together at higher energy, the actual number of bits is much more reasonable.

For example, with 110 distinct orbitals from 1s up to 5g, one could encode 6.8 bits of information onto the state of the atom if that was the limit of your capabilities. One can go a good deal higher than this under special circumstances (see https://en.wikipedia.org/wiki/Rydberg_atom), so one could imagine encoding at least one byte into the state of the atom in a way that can be read later.

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Dale, atyy, DennisN and 2 others
I'm asking how much detail is packed into an atom. Like if the hup was smaller by a factor of a million, you would expect the amount of information present in an atom to be higher by a factor of 1 million. Follow?

if the hup was smaller by a factor of a million, you would expect the amount of information present in an atom to be higher by a factor of 1 million.

Why?

You keep making these general assertions without anything to back them up. Where are you getting this understanding from? What QM textbooks have you studied?

Why?

You keep making these general assertions without anything to back them up. Where are you getting this understanding from? What QM textbooks have you studied?

Please keep in mind that not everyone get their info from textbooks or "proper schooling" and asking just "why"over and over again. it does not help if the person asking the question if thay does not really have a good reason other then cerostie. they may not know how to break down the question to a why anser. It also does not help anyone understand anything when someone answering a question with another question please do not take any offence to this it just an outside point of view from the mainstream way of learning physics

i would like to know what a "hup" is wolf if possible

It also does not help anyone understand anything when someone answering a question with another question

The reason I'm doing it is that the question appears to be based on a mistaken understanding, but I don't have enough information to tell where the OP's understanding is mistaken, if it is. That's why I keep asking him to give reasons for the claims he is making. He's not just asking questions, he's making statements, but without explaining why he thinks they're true.

Dale and hsdrop
ok now that makes sense. ty for clarifying but why would you not just point out the misunderstanding and go from there but that's not the topic of the thred right now sooooo
now I'm not shere but i think he is trying to ask how meny bits would it take to record an H atom completely
for me to even try to answer that one it would take me weeks of research or more

i would like to know what a "hup" is wolf if possible
Heisenberg uncertainty principle: http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

Edit:
And when I read the original post I saw it was pretty strangely worded:
I'm asking how much detail is packed into an atom. Like if the hup was smaller by a factor of a million, you would expect the amount of information present in an atom to be higher by a factor of 1 million. Follow? (my bolding)
The uncertainty principle is a relation and a relation can't be a million times smaller. However, Planck's constant $h$ could be, at least for thought experiments...

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hsdrop
Heisenberg uncertainty principle: http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

Edit:
And when I read the original post I saw it was pretty strangely worded:

The uncertainty principle is a relation and a relation can't be a million times smaller. However, Planck's constant $h$ could be, at least for thought experiments...
Right. I basically mean that hup puts an upper limit about how detailed the universe is.. In a way its like the size of pixels on a screen. From a pixel density on a computer screen you can infer the amount of data needed to encode the image displayed. There cannot be infinite detain in a given system, bc infinite detail would form a black whole due to endless energy density.right?

I basically mean that hup puts an upper limit about how detailed the universe is.. In a way its like the size of pixels on a screen.

That's not how the HUP works in standard QM or in standard QFT. There are speculations about spacetime being made of discrete "pixels" at the Planck scale, but those are just speculations.

There cannot be infinite detain in a given system, bc infinite detail would form a black whole due to endless energy density.right?

No. I don't know where you are getting this from.

That's not how the HUP works in standard QM or in standard QFT. There are speculations about spacetime being made of discrete "pixels" at the Planck scale, but those are just speculations.

No. I don't know where you are getting this from.

People definitively answered a question i had on stack saying that the HUP is the precise reason there is not infinite information or infinite detail present in any sort of matter or energy. If you had infinite detail you would be able to say things like “the electron actually DOES HAVE both a definite position and definite momentum at the same time.”
It doesnt, because hup puts limits on how much information there is in a system/particle. You can't get more detail than the hup allows. Thats probably the most important corollary of the hup. Infinite detail isn't only counter intuitive, (unless you believe in the free will), its also paradoxical. How can you have infinite information without infinite energy or mass. You cant.

To your second part- I read some science mag article saying the reason you can't store infinite data on a hard drive or it would collapse into a black hole. For the same reason i have stated. You can't have information without energy. If some people have a concept of information that violates this then they shouldn't be calling it information. Information can affect the universe. Things that have 0 energy and zero mass cannot effect the universe. Storing information takes energy or mass equivalent. And I am not talking about programming molecule spins. I am referring to the amount of resolution that exists in the uni wrt the HUP. Again, Peter, isn't this well established? Because both this forum and stack are the places that have guided my intuitions.

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People definitively answered a question i had on stack saying that the HUP is the precise reason there is not infinite information or infinite detail present in any sort of matter or energy.

Did they give any references to textbooks or peer-reviewed papers? Can you give a link to the discussion?

i wouldve assumed you knew this PeterAdonis

I know a quantum particle doesn't have an exact position and an exact momentum at the same time, yes. I have not seen anything in a QM textbook or peer-reviewed paper about the claims you are making about the HUP and information.

Also read this in an article

What article? Can you provide a link?

the reason you can't store infinite data on a hard drive or it would collapse into a black hole

This is silly. The reason you can't store infinite data on a hard drive is that it stores data in finite size cells and it has only a finite number of them. But this limitation is imposed by our limited technology, not by the laws of physics.

Storing information takes energy or mass equivalent.

This is true. However, I don't think it means what you think it means.

There is a physical result called the "Bekenstein bound" which says that only a finite amount of information can be stored in a finite volume, and uses characteristics of black holes to make the argument for what that finite amount is. It's possible that you are reading garbled versions of this.

Again, how do u not know this?

Know what? Know the vague, confused things you are claiming, taken from sources you have provided no links to, and paraphrased by you so I don't even know that what you think the sources said is what they actually said?

I have asked you repeatedly to provide references for where you are getting your understanding from, because the things you are saying do not seem like things that I know from textbooks and peer-reviewed papers and my understanding of them. It's possible that you are misunderstanding or mis-stating actual true pieces of physics that you've read. It's also possible that you are reading pop science sources that are misrepresenting the science. Unless you give some actual references, I have no way to tell. Either provide some references or this thread will be closed.

Did they give any references to textbooks or peer-reviewed papers? Can you give a link to the discussion?

I know a quantum particle doesn't have an exact position and an exact momentum at the same time, yes. I have not seen anything in a QM textbook or peer-reviewed paper about the claims you are making about the HUP and information.

What article? Can you provide a link?

This is silly. The reason you can't store infinite data on a hard drive is that it stores data in finite size cells and it has only a finite number of them. But this limitation is imposed by our limited technology, not by the laws of physics.

This is true. However, I don't think it means what you think it means.

There is a physical result called the "Bekenstein bound" which says that only a finite amount of information can be stored in a finite volume, and uses characteristics of black holes to make the argument for what that finite amount is. It's possible that you are reading garbled versions of this.

Know what? Know the vague, confused things you are claiming, taken from sources you have provided no links to, and paraphrased by you so I don't even know that what you think the sources said is what they actually said?

I have asked you repeatedly to provide references for where you are getting your understanding from, because the things you are saying do not seem like things that I know from textbooks and peer-reviewed papers and my understanding of them. It's possible that you are misunderstanding or mis-stating actual true pieces of physics that you've read. It's also possible that you are reading pop science sources that are misrepresenting the science. Unless you give some actual references, I have no way to tell. Either provide some references or this thread will be closed.

I cleaned up my post just now and reinforced the points I am making please read through it.
Ill look for the articles i read which reinforced my preformed understandings.
Also i didnt see you disagree with anything i said other then semantic(s/ally) so I want to clarify; infinite detail in a confined space would cause the creation of a black whole because of concentrated mass or energy density. You sounded kind of dragging your feet about conceding that but i know you understand that.
Also the hard drive is under a similar constraint to raw information. The density of info on the hard drive is limited by the ability of transistors to function, and raw information is limited by tbe HUP.
I don't think we are in a major disagreement Peter, I just think its a semantic issue we are having.

Did they give any references to textbooks or peer-reviewed papers? Can you give a link to the discussion?

I know a quantum particle doesn't have an exact position and an exact momentum at the same time, yes. I have not seen anything in a QM textbook or peer-reviewed paper about the claims you are making about the HUP and information.

What article? Can you provide a link?

This is silly. The reason you can't store infinite data on a hard drive is that it stores data in finite size cells and it has only a finite number of them. But this limitation is imposed by our limited technology, not by the laws of physics.

This is true. However, I don't think it means what you think it means.

There is a physical result called the "Bekenstein bound" which says that only a finite amount of information can be stored in a finite volume, and uses characteristics of black holes to make the argument for what that finite amount is. It's possible that you are reading garbled versions of this.

Know what? Know the vague, confused things you are claiming, taken from sources you have provided no links to, and paraphrased by you so I don't even know that what you think the sources said is what they actually said?

I have asked you repeatedly to provide references for where you are getting your understanding from, because the things you are saying do not seem like things that I know from textbooks and peer-reviewed papers and my understanding of them. It's possible that you are misunderstanding or mis-stating actual true pieces of physics that you've read. It's also possible that you are reading pop science sources that are misrepresenting the science. Unless you give some actual references, I have no way to tell. Either provide some references or this thread will be closed.

Also closing this thread would be immature and completely on you Peter. If I am dropping things that are not easily answered, then this thread is one of the few threads that you should want to guard with your life until an very adept person comes along and shows us that you and i were perhaps just arguing two sides of the same coin.
If you want to call me an arm chair physicist and say because i don't read stephen hawkings peer reviewed nonsense I am illegitimate go ahead. An office clerk physicist who basically freestyled GR because it followed the way he thought things should work is pretty much equivalent to an armchair physicist. Not bad company tbh. I am 20 iq pts below him but AP physics is something i could have learned when i was 10 years old so i know I am not as inept as you seem to believe.

Also, again, I am trying to find the articles.

closing this thread would be immature and completely on you Peter

No, it will be on you for not providing references after repeated requests.

i know I am not as inept as you seem to believe.

What you think you know is your business. So far you have not shown me any evidence that you have a good understanding of physics.

im trying to find the articles.

Good. When you have links, post them.

weirdoguy
I cleaned up my post just now and reinforced the points I am making please read through it.

Rather than editing an existing post, you should make a new one if you have more information to post.

infinite detail in a confined space would cause the creation of a black whole because of concentrated mass or energy density

No, that's not correct. What is correct is that if a physical system has anything close to the maximum information per volume that it can have, according to the Bekenstein bound, it is already a black hole. There is no such thing as having an object that is not a black hole but is "close" to one, and then packing a little more information into it and having it become a black hole. The system would collapse to a black hole well before you got anywhere close to the limit on information storage given by the Bekenstein bound.

Also, the Bekenstein bound has nothing whatever to do with the uncertainty principle. It has to do with applying classical thermodynamics in the context of a classical black hole as described by General Relativity.

The density of info on the hard drive is limited by the ability of transistors to function

Actually, the key limitation for hard drives is the ability to reliably distinguish the magnetic domains that signify 0 and 1 bits.

and raw information is limited by tbe HUP.

No, it isn't. A hard drive is not relying on quantum effects anywhere near the point where the uncertainty principle would significantly affect its operation.

I'm asking how much detail is packed into an atom. Like if the hup was smaller by a factor of a million, you would expect the amount of information present in an atom to be higher by a factor of 1 million. Follow?

The problen here is that the amount of information in bits is the logarithm to the base 2 of the number of states. Even if you could measure the atoms quantum numbers with an accuracy that is a million times bigger, the number of states would only increase by a factor 10^18, and this would add less than 60 bits for each atom.

atyy
No, it isn't. A hard drive is not relying on quantum effects anywhere near the point where the uncertainty principle would significantly affect its operation.

By raw information i was referring to the total system, not a computers memory.

The black hole stuff i don't disagree with at all. My understanding was rough around the edges but i don't think we had a crucial disagreement.

On the HUP, Peter how can the HUP not be considered the limiting factor for how detailed the universe is? Like i said, infinite detail is impossible. The Heisenberg uncertainty principle directly addresses not only how much you can know about a particle, but also how much THERE IS TO KNOW, about a particle. How could you not consider that as limiting the amount of detail/information present in a particle? I can't think of anything in physics that could be more glaring and explicit regarding the detail limit corollary of the HUP.

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Rather than editing an existing post, you should make a new one if you have more information to post.

No, that's not correct. What is correct is that if a physical system has anything close to the maximum information per volume that it can have, according to the Bekenstein bound, it is already a black hole. There is no such thing as having an object that is not a black hole but is "close" to one, and then packing a little more information into it and having it become a black hole. The system would collapse to a black hole well before you got anywhere close to the limit on information storage given by the Bekenstein bound.

Also, the Bekenstein bound has nothing whatever to do with the uncertainty principle. It has to do with applying classical thermodynamics in the context of a classical black hole as described by General Relativity.

Actually, the key limitation for hard drives is the ability to reliably distinguish the magnetic domains that signify 0 and 1 bits.

No, it isn't. A hard drive is not relying on quantum effects anywhere near the point where the uncertainty principle would significantly affect its operation.

I don't have any disagreement with what you said
except;
To use an example, say in another universe the HUP was shifted in the direction that would make it much harder to get precision measurements of position/momentum than it is in our universe. As if you could hardly know anything about a particles position/momentum duo. Wouldnt you consider this universe as being less detailed per unit mass/energy than ours is?
Wouldnt this be vaguely similar to having a computer monitor fudge together pixels whenever it is uncertain of the location of each colored pixel?

Why do you think a computer screens pixel density isn't a fair comparison to the intrinsic information content in matter or energy?

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I don't have any disagreement with what you said
except;
To use an example, say in another universe the HUP was shifted in the direction that would make it much harder to get precision measurements of position/momentum than it is in our universe. As if you could hardly know anything about a particles position/momentum duo. Wouldnt you consider this universe as being less detailed per unit mass/energy than ours is?
Wouldnt this be vaguely similar to having a computer monitor fudge together pixels whenever it is uncertain of the location of each colored pixel?

Why do you think a computer screens pixel density isn't a fair comparison to the intrinsic information content in matter or energy?

The HUP puts no constraint on how precisely you can measure the position of a particle. That's a common misconception of the HUP.

The HUP applies to all observables, some of which ( e.g energy and spin) theoretically have precise values. I.e. there is no uncertainty in them.

@Wolfenstein3d by the way, the armchair physicist from the patent office in Bern already had a PhD in physics!

how can the HUP not be considered the limiting factor for how detailed the universe is?

You seem to have the misconception that the HUP means the universe is discrete, not continuous. That's not the case. Position for a free particle is a continuous observable in standard QM, not a discrete one. The HUP doesn't change that.

As I mentioned before, there are speculations that spacetime might be discrete instead of continuous at the Planck scale, but those are just speculations.

Also, as has been discussed, what we know of black hole thermodynamics and the Bekenstein bound suggests that only a finite amount of information can be stored in a finite volume. But that has nothing to do with the HUP.

The Heisenberg uncertainty principle directly addresses not only how much you can know about a particle, but also how much THERE IS TO KNOW, about a particle.

No, it doesn't. The HUP says that a quantum system's allowed states do not include certain kinds of states that classically would have been expected--for example, a state which has both an exact position and an exact momentum. But that is not the same as the allowed states being discrete or the information that can be in principle stored in the state being limited. It just means the continuous state space in QM is not the same as the continuous state space you would expect from classical physics.

As above, there are indeed reasons to think that only a finite amount of information can be stored in a system with a finite volume; but those reasons have nothing to do with the HUP. I've said this repeatedly now and you have not appeared to grasp it.

Wouldnt this be vaguely similar to having a computer monitor fudge together pixels whenever it is uncertain of the location of each colored pixel?

No. The HUP is not the same as "uncertainty about the location of each colored pixel". It has nothing to do with pixels. I've said this repeatedly, and others have said it as well, and you have not appeared to grasp it.

Yeah, as if he needed a PhD to do his his thought experiments
I'm sure it helped!

Wouldn't you need a photon with a wavelength approaching 0 to locate a particle to an exact point location of the center of mass?
The consensus when I asked the hup detail question on this forum in 2013 was that the hup was the speed limit on detailedness of a particle. Like 4 people concurred about that. Did something happen in between then and now?

Wouldn't you need a photon with a wavelength approaching 0 to locate a particle to an exact point location of the center of mass?

You're assuming a "particle" like an electron is in fact a little billiard ball with a center of mass. It isn't.

The whole picture of the HUP being due to limitations of measurement (if you shoot a photon of short enough wavelength to pin down the position really precisely, it has so much momentum that it kicks the particle and makes its momentum uncertain) is not really correct.

when I asked the hup detail question on this forum in 2013

I'm unable to find this forum thread, so I can't comment on what was said there.

the hup was the speed limit on detailedness of a particle

I don't even know what this means. I suspect you have a garbled memory of whatever was actually said.

Yeah, as if he needed a PhD to do his his thought experiments

Of course he did! Without years of studying physics Einstein wouldn't have even known which thought experiments to think about, how to set them up, how physics would have worked in them, their consequences, etc. You can be absolutely certain that man needed the training and education he received while working on his PhD. After all, a PhD isn't just a sheet of paper (well, not usually). It represents the time and effort people spend learning their field. Do you need a PhD to understand physics at the level Einstein did? Certainly not. But if you're going to be spending years of your life learning physics to this extent, you might as well get something out of it that will let you get a job.

The consensus when I asked the hup detail question on this forum in 2013 was that the hup was the speed limit on detailedness of a particle. Like 4 people concurred about that. Did something happen in between then and now?

No, that answer was never correct if that's what the consensus came out as. As far as I understand it, the HUP puts constraints on measuring certain pairs of observables, such as position and momentum, preventing you from knowing both to infinite precision at the same time. If you choose only one of these to observe, you should be able to measure it to whatever precision you like.

PeroK
Of course he did! Without years of studying physics Einstein ...

It's the power of the myth. First, you learn that Einstein was a lowly patent clerk with no background in physics,who shook the scientific world with his humble thought experiments. And it's a great story.

Then you find out the man had a PhD and it's all a bit of a let down. I must admit I was very surprised, if not shocked, when I learned that. Like many people I had heard the myth first.

But, myths are not given up quite so readily by everyone.

Drakkith