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Can One Electron Hold Infinite Data?
Geoffrey Kidd writes: "There's a very interesting article
at EE Times about some research which seems to indicate
that an essentially unlimited number of bits can be stored in ONE electron. Hmmm. What if one
could encode every .mp3 file on Napster in one electron? :)"
Umm ... correction: the union of two infinite sets is always infinite, regardless of whether or not they are countable.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Each electron could hold the same set of infinite data but in a different order.
Hello Pete,
While I bask in the warm glow of your pity for me, let me point out what is ''obvious'' to us, now, was not even known 200 years ago and the bulk of it will probably be ludicrously outmoded 200 years hence. And that's us, the same race, in pretty much the same environment just separated by 200 of your Earth years.
If there are *aliens* out there with advanced technology, there is no reason for it to even be *possible* for a human to understand or even recognize it as a system; after all, our brains are of a finite size. In the same way that a dog will never truly appreciate music (howling tunelessly along because of a certain frequency content aside), surely more advanced races than us would beat us out with no more difficulty than we lock doors in front of our pets.
Anyway, the point was that the mere fact that we are still stumbling over these epoch-making concepts tells me - maybe you more advanced mutants don't need telling - that we may well still be too pathetic to imagine what medium would be the lingua franca for interstellar beacons &c used by hypothetical superadvanced civilizations.
> We'll have Heisenberg compensators to take care of that.
Life imitates Trek. IBM has invented just such a thing.
I've finally had it: until slashdot gets article moderation, I am not coming back.
Ok, I'll take the bait.
* Infinity isn't a recognised value in the Universe.
Prove it. All I see so far is hand-waving.
It's easy to show that it's _impractical_ to build a device with an infinite number of states, but it's certainly _possible_ (if you have an infinite amount of room).
* Whilst those orbits may be "theoretically" valid, any orbit which does NOT coincide with a valid point in space (which is also quantized, and not necessarily with the same step size), is an invalid orbit and cannot be entered.
Check that high-school physics textbook. Orbital radius goes up as the square of the energy level - even at it's smallest level, it's much too large to be affected by the granularity of space.
* Any orbit which is excluded due to any other phenomina (eg: Casimir Effect) also cannot be entered.
Other forms of noise will limit practicality long before the Casimir effect does. Regardless, the casimir effect wouldn't make any of the orbits impossible. If you had enough room for the electron shell to exist, the casimir effect would be irrelevent for orbits in that shell.
The Casimir effect also wouldn't have much of an effect period; it just affects the number and wavelength of virtual photons present in a region of space. So what?
* Of the remaining orbits, any orbit which would cause the electron to shift which nucleus or other particle it is orbiting, will negate that orbit and replace it with the corresponding new orbit around the new center point.
So suspend a single atom in a magnetic trap in vacuum, as the experiment in the article almost certainly did.
This (requirement that nothing else be nearby) also still doesn't affect whether the orbit is _possible_. As I said before, measurement concerns are already known to limit how many states you can use with practical equipment.
* Exact positioning of an electron is forbidden by the Uncertainty Principle, anyway
As above - this is irrelevant. It is the uncertainty principle that _gives_ us the wavelength of the electron, among other things. The electron orbits are _definitely_ large enough for this to be a non-issue (as they're more than a wavelength in size).
Summary: I'm afraid that your objections are based on a variety of assumptions that turn out not to hold, both about the nature of the experiment described in the article and about my own arguments. If you are genuinely interested in this topic, I'd strongly suggest picking up a first-year physics textbook and browsing the sections on quantum mechanics and atomic structure. It will be well worth it.
Before you object - yes, the number of states between the ground state and ionization threshold is infinite, even with quantum mechanics. Check a high school physics or chemistry textbook, or work it out yourself from the formulae in the textboks. Valid orbits have a circumference that is an integer number of electron wavelengths (from one to infinity).
Heisenberg's Uncertainty Principle states that certain pairs of properties can only be measured to a finite degree of precision. There are only a few such paired properties: position/momentum and time/energy are the only ones mentioned in my Physics text [Physics for Scientists and Engineers Volume 2, 3rd Ed., 1991 Paul A. Tipler, Worth Publishers, page 1180]. Electron phase is not one of the effected properties, so Heisenberg doesn't seem to be a limit here. Shannon, on the other hand, may have something to say in the matter.
Have you rad the article? In what I understood of the article, it says that with a lazer the scientist induces a wave into the elctron, and then it's possible to read the wave stored in the atom.
The infinity of bits encoded would be stored in the time dimension, witch is infinity as long as I know. Then is want to store more data you just have to wait more to store it. It is something like a endless backup tape.
Things I don't know is do we have to wait for a specific point in time to start reading? Is there a limitation in the wave length, probably yes, for the reason above (it's a quantic value)? Does it run on linux?
--
"take the red pill and you stay in wonderland and I'll show you how deep the rabitt hole goes"
[]'s Victor Bogado da Silva Lins
^[:wq
How is the data stored in the electron ever read or modified? Last I checked, there's a prevalent little theory known as the Heisenburg Uncertainty Priciple states that observing an electron inherently implies changing its position/state. Since this theory is generally accepted by just about every scientist I've ever met, how is it that we're supposed to read data without modifying it in a possibly unpredictable way here? It's the same situation with transporters in Star Trek - they simply can't exist as long as this principle holds true.
-- Imagine how much more advanced our technology would be if we had eight fingers per hand.
"Where'd my hard drive go? It was here a second ago!"
It seems that this is a step in the right direction for quantum computer, but how in the world would something allocate and infinite number of registers of memory. Would this "exciting" of the atom to which the electron belongs in someway eventually change the atom? How can it be possible that an infinite amount of data can be placed in one electron without it altering the spin or changing the atom in some adverse way. Anyway cool idea. How'd we get here anyway?
Good is never enough, when you dream of being great!
"Yeah, well, I got a new electron the other day, with the latest in quantum interfaces, so now I've got around 500 terrs of storage, more than enough to store my century of MP3s."
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Yes, but they aren't storing analog information.
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Energy levels in electrons can be raised to stable values. Only when you knock them off the shelf do the return to a lower energy level and release a photon with energy equal to the difference betweent the prior and new state.
Theoretically it's true, but is there a practical way of measuring the spin of an electron that finely? Wouldn't Heisenburg make it so that the electron would be both blank and fully formatted until you bothered to read it? Or would the process of reading the data actually alter the data on this disk?
That and I think an electron would be a bit too small for storage purposes... I have enough problems losing CD-Rs half the time... no less a storage media where I could only know the angular momentum or the location, but not both...
This is all well and fun, except that the second you get almost any bit of matter near it your data is lost. Now if you could apply this to some particle that doesn't interact as promiscuously as the electron (neutrino?). But then, the less it interacts with, the harder it is to read it, much less capture and adjust its properties.
Any sufficiently advanced civilization is indistinguishable from Gods.
yet ram prices are still going up??
how many electrons are there in ram? geez
when everything is working perfectly.. BREAK SOMETHING before something else FUCKS up!
"Now we want to find out how long information can be stored," he said.
Probably about 10 nanoseconds. Which is about as long as it takes for anything I put on a floppy to be lost.
:wq
-Pete
Like "Egon Spengler" of the Ghostbusters, but with an "I"---and say the "on" as "en"---then add states.
As far as what they are, I couldn't say, but it probably has something to do with the eigenvalues of a matrix describing the electron?
--8<--
--8<--
This kind of makes sense since more data would be stored by a longer signal...
--8<--
--8<--
That's one of the things I find so exciting. You could have a HUGE amount of redundancy built in. Why not store the same information on a bunch of electrons. Now if we can only get those electrons to change the state of other time and space separated electrons we would be in business! Instant communication and all that. I wonder how far we are from controlling THAT property? :)
--8<--
--8<--
It had all my homework and...
Badgers? Badgers! We don't need no stinkin' Badgers!
add compression and you can get past infinity.
Treatment, not tyranny. End the drug war and free our American POWs.
See my user info for links.
--
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We have fought the AC's, and they have won.
Only if you filled the whole address space with your data. If you use a finite portion of the space, you ought (one would think) to be able to find your data in a finite amount of time. And one would suppose that it would take you an infinite amount of time to write an infinite amount of data, so the seek time would be the least of your problems in that case. Or so it seems to my poorly educated mind at first blush.
On the other hand, if there are an infinite number of bits available, one would suppose the bits are in a random state before we begin to write to them. Perhaps this means that every .mp3 file on napster is already there, and you just have to find them. So perhaps the seek time is a big deal after all.
Now I just have to sit back and wait for the information theory people to set me straight... ;-)
"The best we can hope for concerning the people at large is that they be properly armed." - Alexander Hamilton
For those who like such things: For any set, take any function which maps it into it's power set (transforms each element of the set into a subset of the set). For this function, consider the set of all points which are not within the set which they map to. This set might be empty, but it is defined for the function. Whatever the subset, no point can be mapped to it by the function in question (think about it!). So there is an element of the power set which is not mapped to by the function. No matter what the function is. No matter what the set is.
perhaps its just a conspiracy, just one electron holds the data, and we pay the charge for "extra" memory. ;)
Well, I guess you would then have the biggest collection of badly encoded and half finished mp3's in the world.
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Basically, for those of you who haven't had any quantum mechanics courses:
The uncertainty principle says dXdP>=h. Where dX=delta X (position), and dP=delta P (momentum). h is Plancks constant (on the order of 10^-34). It basically says we can never know both the exact position and momentum of an electron. The more closely we measure one, the more error on the other.
As for the integral of the wavefunction, the probability of the electron existing from -infinity to +infinity will always be 1 (obviously). The weird part is that if you take an electron and put it in an infinite energy well, the electron is bounded to exist in the well. It gets funky in that there is a small probability that it will exist outside the well also!
This shit blows my mind.
-=God Hates Me=-
not the particle or "point". You're exactly right that the quantum world is so different than the macro world that most of the mental energies spent on the subject are wasted in translating abstract concepts between the two worlds. We humans have a lot to learn.
it seems very interesting to store infinite data into one single electron, but will it be possible to transfer this data to another electron?
Violence is the last refuge of the incompetent - Salvor Hardin
The fact that an observable (e.g. position) is quantized does not in itself mean it cannot have an infinite number of states. It's like the difference between integers and real numbers. Real numbers are continuous, whereas integers take discrete values (quantized if you like), however both has an infinite range of values (give me an integer, and I can alway add one to it.)
the union of two infinite sets is always infinite
That certainly sounds reasonable; however, as I understood the article, they are encoding their ''infinite data'' in the precise value assigned to what I think is called a scalar quantity (the phase, I assume, perhaps stupidly, expressed as an angle). So the first bit says whether it starts as 0 degrees or 180 degrees, the second bit adds 90 degrees if it is set, the third 45 degrees if set, and so on.
So this ''infinite'' data set boils down to a single infinitely precise number, say, 36.789...etc degrees. So that was one electron, perhaps full of an infinite number of Metallica albums. Now if we cp that electron to another one to give to a friend, but we added a Lene Marlin track at the beginning of it (having better taste than our friend), clearly it will end up with a different phase angle, even though it has an infinitude of contents (in different order). The phase angle will even be radically different if the first few bits of the added data are quite different.
Well, that is why I think your objection is wrong in this case:
-Andy
Like "Commander Taco" of Slashdot, but with an "I"--and say the "ommander Taco" as "gen"--then add states.
They're like a standing wave: they describe why electrons fall into particular orbits. You can read about it at [The Rotten Foundations of 20th Century Physics].
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This means that what "should" be inifinite, given a purely Newtonian view of the world, will always become finite in a Quantum Mechanical view of the world.
Um, this technique is _based_ on quantum mechanics. This is clearly described in the article.
An electron orbiting an atom can be at any of an infinite number of energy levels between the ground state and the ionization threshold. The researchers have found a clever way to arbitrarily set the probability of the electron being in each of these states, simultaneously - which gives them as many bits of data as they have states. They also have a clever way of reading back out all of this state probability information.
Limits to this are based on the time it takes the states to decay back to the ground state (which affects the lifetime of the data) and the time it takes to perform the read operation (which isn't stated, but which almost certainly lengthens for the closely-spaced energy states near the ionization energy).
No limits from newtonian/quantum mechanics, just ordinary engineering tradeoffs.
Altering the phase of the electron in an atom equals exciting the electron. And from what I remember from school physics, excited electrons tend to "fall back" into place (revert to it's previous waveform) after some time, sending out the extra energy as light.
This means that a memory made up of electrons is a dynamic RAM, and must be re-updated all the time.
Since altering the wave == exciting electrons, it takes energy. And the more improbable states you want (higher shells in the old atom-model), the more energy you have to inject. Thus, the number of states are not infinite, but restricted by the amount of energy available/feasable.
If I remember correctly, someone posted an article some weaks ago, calculating the theoretical limits of a computer of a certain weight and size. From what I can see, this aproach to storing information does not break this theoretical limit at all...
--The knowledge that you are an idiot, is what distinguishes you from one.
In an attempt to enforce this ruling, the FBI is developing a so-called "killer" electron known as "Quantumvore". Pending regulatory approval, the FBI plans to release large numbers of Quantumvores into the Internet infrastructure, in order to seek out and destroy banned electrons. Quantumvore is actually a type of positively-charged anti-electron known as a positron, which upon coming into contact with an MP3-encoded electron will annihilate with a release of energy determined by Einstein's famous formula, E=mc^2.
A number of physicists have expressed serious concern that the sheer quantity of MP3-encoded electrons now thought to be in circulation could mean that the release of Quantumvore will result in large explosions occurring within milliseconds of each other in countless locations throughout the world. Simulations indicate that such explosions are likely to be centered on college dormitories, which in some cases may have sufficient concentrations of MP3-electrons to trigger chain reactions, which collectively would be capable of utterly destroying the Earth.
An RIAA spokesperson responded to these concerns by saying "Without strong intellectual property protection, and the ability for monopoly content brokers to maximize revenue, the Earth may as well not exist anyway."
Stay tuned for further developments in this breaking story...
I got a question, hope somebody can poke holes in it. Say you have an unlimited number of states, and we ignore problems with how much energy or time you might need to get to that resolution.
Suppose you encode everything about a computer, its RAM contents and operating rules into a piece of data, basically a long number. Say you are doing something like dumping the VMWare PC emulator program and its memory buffers into this piece of data, along with your own program and also a bunch of other locations which are telltale bits that would only be set to true if certain instructions (your program) are executed in a certain order, so you can in a sense freeze a sequence of calculations, an overall machine state.
So in the end the last telltale will finally be set only if the results of the calculation which suposedly had been executed by this hypothetical (virtual) computer, was provably the answer you seek, i.e. the factors of a big prime number which could be multiplied together to show they are the right answer. A self-referential logic filter.
My conjecture (gleefully made without more knowledge of quantum physics than is available in lay publications..) is this. Could you use this huge number as a filter or reference beam to collapse the waveform of your recording medium, and read out the state of the virtual computer with the output of your program, in a picosecond?
It would seem that any Turing machine from a Cray to a ribosome (an rna tape device), could be simulated in this way, though smaller memory footprint/instruction set machines would be easier since they could be represented with less eigenstates. I wonder how many states would be the least amount necessary to simulate something useful.. if a full hardware abstraction is not needed and you can get away with just a language definition and virtual machine (yes like Java VM).
Would this mean you could run any program that can fit into the virtual machine in picosecond time? And if so, could you not in fact build a computer of any arbitrary capabilities by simply writing a pseudocode definition of how it ought to work? Final scary question.. The interior of a cell is a controlled environment and until the cell is queried by some process it is conceivable that some ribosomes could exist in superimposed states. Put another way, if you could solve the isolation problem it might end up to be cheaper to build the eigenstate computer with common cellular apparatus than by using big expensive lasers. What conclusions can you draw from this?
I think this is what was meant by a prediction I once came across.. that the coming century would create a new science of computing which is to today's computers as nuclear energy is to fire.
Like I said I hope someone can poke holes in this. The biggest problem seems to be universal laws about information, for example I understand that the recent sending of a light pulse at 300 times the ordinary speed of light was only possible because the leading edge of the pulse had enough information to reconstruct the rest of the pulse, suggesting that you could not send an entire packet of bits faster than the speed of light.
You're assuming that alien civilizations even know about radio waves. If they evolved with the ability to observe the "true quantum-wave reality" of our existence, then they might not be aware of the "radio waves" that appear as artifacts of some more fundamental medium. As far as we know, our precious "radio waves" are meaningless to other beings that may exist beyond our limited 4 dimensions.
If one electron holds infinite data, how much do two electrons hold?
First off, at the sort of level you're talking about (single electrons), you're talking about a world that obeys Quantum Mechanics, not Newtonian Mechanics.
This makes a big difference. Newtonian Mechanics is essentially continuous. Regardless of how close any two points are, Newtonian Mechanics assumes that there are still an infinite number of points between them, and that this can be repeated indefinitely.
Quantum Mechanics is a strange land of discrete points with NO space between them, as far as the particle(s) under consideration are concerned. Particles jump from one state to another, WITHOUT passing any intermediate point.
This means that what "should" be inifinite, given a purely Newtonian view of the world, will always become finite in a Quantum Mechanical view of the world.
Space, Time, Energy - these are ALL quantized.
The practical upshot? You may be able to store a LOT of information in an electron, but it won't be infinite. And how much you CAN store depends on what valid states there exist at that time, which may or may not remain the same over time.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
I didn't see it mentioned, but this must be taking place at very low temperatures.
When I hear about cool, promising advances like this is always makes me sorry for the SETI types. How the aliens will laugh themselves silly at our hopeful sifting of the *radio*/stone-age technology spectrum for traces of them, when an advanced civilization would have stupendously cooler ''magic'' at their disposal.
You are correct.....except that it is known that space-time _should_ also be quantized, so there is no such thing as "continuous eigenstates" , that's because QM is incomplete : we have not figured out quantum gravity yet (i.e. where it is believed that space-time curvature is also quantized).
I know..I know, all QM books say there are continuous eigenstates. But that's because QM works on the Minkowski flat space-time metric which is perceived as "background-fixed", i.e. not a dynamic metric like General Relativity's metric. The goal of physicists is to find a way to make QM "background-free", i.e. does not rely on a fixed-metric, or put it another way, to "quantize gravity" (which nobody really knows what it means, but people believed it means quantizing the dynamic metric, or "quantizing Space-Time").
So the people is pursuing a dream that is not viable.
Mode (3) smart-aleck mode. Press * to return to main menu.
One of the challenges encountered with increasingly smaller data storage media is the possible damage caused by stray radiation... at this scale, one alpha particle could ruin your whole database! (or maybe one x-ray, or static electric shock, etc.)
Although it is interesting to see just how much information could be encoded in a single electron, one would need some redundant electrons in other atoms to also encode the same information. (Think:RAQE a Redundant Array of Quantum Electrons.)
Further, if we can step away from the concept of trying to encode EVERYTHING in just ONE electron, and take a look at how much information can easily and reliably be encoded in one electron (pulls a number out of his hat) say 4 bits, and one has (pulling another number out of his hat), say 10 electrons for redundancy, that's still one heck of a dense recording medium! Several terabytes of data could be stored in a very small space!
How small a space? There's the unanswered question of just how close together these can be packed and uniquely targeted by the laser. (Or lasers, to speed reading/writing to the electrons.) I see issues with just trying to keep the atoms in a fixed location, how finely focused the laser beams can be adjusted, etc.
Still, this sure holds promise for one incredibly dense storage medium for all my MP3s!
Call me cynical, but do those guys up in Slashland use MadLibs as a base for their stories?
[person] writes, "[person, lab] has
[verb]'d a way to [verb] the [noun]".
Wow. How many [contested file format]'s
could you [verb] with this??
[person] writes, "the [hated industry]
is [verb]ing [loved individual]". Ya know,
there used to be a day when [verb] was not
only legal but encouraged.
[person] writes, "a [greek letter] release
of [obscure linux app] has just hit [release
site]'s page. Hoo boy, now our world is
[adjective].
</HUMOR>
.02
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Quux26
My
Quux26
www.crashspace.net
Don't you watch Star Trek?
= -=-=-=-=-=-=-
We'll have Heisenberg compensators to take care of that.
- JoeShmoe
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-- I wonder which will go down in history as the bigger failure: the War on Drugs or the War on Filesharing
Yes.
(though it depends wholy on the detail in which you can measure the state)
Imagine an arrow. It can spin on it's centre of gravity 360 degrees. If it points directly left the bit value is 1. If it points right the bit value is 0.
Going clockwise, pointing at the bottom half is for values the start with 0, the top half is for bit values starting with 1. Both have 180 degrees freedom of movement. Breaking the 180 degrees of each half into 2 points (3 sections) defines the second bit value. Iterate.
Keep going and breaking smaller and smaller sections to define further bit values. 60 degrees down left would be 00, etc...
Any real world thing (a bicycle for example) has an infinite number of possible states and your ability to reap binary values stops only at the limits of your measuring equipment.
(you know, I spend too much time amusing myself.)
--Giving to trolls for the benefit of us all