By "theoretical information storage" I mean future forms of information storage that can be stored, for example, atomically. I assume that atomic-level information storage is as small as information storage can get. What IS the smallest operational storage device with the largest capacity? How far can that go, and what are the limits of information storage. I mean 1TB of information can't fit in $0m^3$ obviously, but maybe $0.000000001m^3$ in the future, and so not knowing what the developments of tomorrow may bring, can one reconcile the global minimum of volume or whatever quantifying metric that universally measures information storage relative to the amount of data stored in that space/volume/etc.?
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$\begingroup$ Assuming future information storage is contained by the notion of volume, which seems reasonable. $\endgroup$– user149705Commented Mar 23, 2017 at 21:43
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1$\begingroup$ en.wikipedia.org/wiki/Limits_of_computation $\endgroup$– user126422Commented Mar 23, 2017 at 21:49
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1$\begingroup$ You're certainly not going to be able to store even a bit of information on the scale of a planck length. $\endgroup$– Señor OCommented Mar 23, 2017 at 21:49
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$\begingroup$ A key thing you will need to add in here is the lifespan of that data. With RAM and harddrives, we can keep the data "correct" without bit flips for long enough to just pretend it's "forever." When you start pushing the limits of science, however, you have to start including things like Mean Time Between Failures (MTBF). It's a lot easier to make memory that lasts a nanosecond than it is to make memory that lasts a thousand years. $\endgroup$– Cort AmmonCommented Mar 26, 2017 at 22:29
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2 Answers
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In practical terms we'd probably need at least an atom per bit for raw storage, but we'd need significantly more atoms to address the storage-atom individually. Let's say we need 100 atoms per bit stored (basically a random guess for the sake of doing it), then to store 1TB (that's B = byte not bit) we'd need at least 800,000,000,000,000 atoms, which is a pretty small number so we're being very optimistic here.
For Silicon :
- molar volume $\approx 12 \times 10^{-6} m^3\,mol^{-1}$
- Avogadro's number $\approx 6\times 10^{23} mol$
So our $8\times10^{14}$ atoms for 1TB requires some $1.6\times 10^{-14} m^{-3}$ or a cube about $2.5\times 10^{-5}m$ on each side ( about 0.025 mm per side )
Heat and practical requirements probably would never allow that, but it's smaller than your stated goal (although it's also probably wildly under-estimated).
answered Mar 26, 2017 at 22:10
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The theoretically smallest thing you can use to store 1 bit is not the determining factor in deciding the size of a 1TB storage module. A storage module is a system . It will need read/write hardware, possibly storage maintenance hardware, power supply, case, etc. You need to know what bits are where (addressing) and need to have the bits protected from interference from other bits. Simply considering the size of the "bit store" itself is woefully insufficient.
As you correctly say in your question it is the operational storage device that matters. We have no way of predicting what developments may or may not occur or even be possible with real world hardware. The minimum size of a transistor is still coming down, is there a practical limit ? We don't know, we might estimate a practical limit based on current manufacturing technology but I think we would all expect that some new development will occur at some time in the future which will push the boundaries.
In conclusion your question is not answerable, there is no way of theoretically calculating from physics where our practical limit will or could be.
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1$\begingroup$ I suggest using bold or italics for emphasis rather than capitals. On the web generally capitalizing is often used to shout, which is considered rude. $\endgroup$ Commented Mar 26, 2017 at 21:38