Answer: Standardized, Registered Tokens
(Or, "outer rim planets probably aren't going to take a check.")
Yep, that's right, "money". Even though you've moved away from a pure digital currency, you can make some technological improvements (some of which current world governments already use):
- Serial numbers, naturally. Not verified at the time of the transaction, but checked later, similar to how most real Earth money works. That way, if someone does manage to counterfeit bills, your banks can at least track the source, plus they have other benefits, in thefts, statistics, etc.
- The important bit: Include a small quantity of a radio-isotope such as Thorium from a single planet owned by the central bank (so no one else can gain access). The slow, predictable alpha decay signature of natural thorium (or any other stable radioactive solid) from a particular source into radium-228 can be easily verified, but it would be far harder to replicate. Even if a would-be counterfeiter could build the metallic strip on a twenty-token bill atom-by-atom, it will likely cost them far more than twenty bucks. The bank, on the other hand, has bins full of the stuff they just dig out of the ground, so it costs them comparatively very little.
- For very large amounts—where even today we wouldn't accept cash—might still have to be issued some other means, like specially-issued bank money orders with additional security and verification.
- Quantum money would be impossible to counterfeit, but also extremely impractical, so I won't be discussing it here, but it's worth a mention.
Backed by: Energy or virtual computing resources
Your currency ought to be fungible; that is, backed by something of value.
The key here is to imagine something unique to your universe that has value, and is interchangeable. (I.e., one type of frobnicator isn't superior to another.) The idea of "standardized" (and hence, fungible) computing opens up some interesting possibilities to back this currency:
- A unit of information transfer, like a terabyte
- A unit of information served storage, like a terabyte year or petaqubit-year
- Plain storage would not be as good for this purpose, as you'd essentially be backing your currency with hard disks or USB drives (or their future equivalent). I think the other options in this list are superior.
- A unit of computing effort, like a yottaflop
- A unit of energy, like a megawatt-hour or terajoule. Presumably backed by a partnership with planetary/regional energy providers, and the physical delivery system doesn't matter, as a joule is a joule, as long as you take transfer efficiency into account of course.
But how are computing resources fungible?
(Extended discussion here, in case of nay-sayers. Feel free to skip over the next paragraph if you're already convinced.)
It's my position that all of the above items meet the fungibility requirement even if multiple organizations actually provide the services, and even if there are slight variations in quality of service. Why? First, for example, a FLOP is a FLOP—i.e., either the operation was performed or not, and any FLOP is thus "substantially equivalent" to any other FLOP, regardless of how fast any given computer is. To wit: "a good is fungible if one unit of the good is substantially equivalent to another unit of the same good of the same quality at the same time and place." A futuristic society is likely to have better reliability than we do today, and in our world we're already pretty much at the point of "commodity" computing with reliability exceeding the 99.999% range. I would call any 0.0001% variation well within "substantially equivalent", and probably better than the purity of most fungible gold reserves! Issues of downtime, availability, speed, etc., are irrelevant to the issue of fungibility, although, like any currency, you want to make sure you have enough of the backed good to cover it! Finally, fungibility doesn't imply that your $1000 bill has a 1:1 mapping with a specific lump of gold, or terajoule, or whatever, just that the equivalence exists and can be backed up. As I said above, this paragraph was really for the doubters, so I've probably gotten rather nitpicky here as it is, so please keep the big picture in mind.
But what about Moore's law? This is the widely-known "law" that states that transistor density doubles every couple of years. People have misused it to draw similar conclusions about information storage or processor speed, but none of these figures are expected to continue to double indefinitely, as there are fundamental physical limits we are rapidly approaching, even now. Quantum computing (if it ever happens), would cause a big, albeit finite, jump. At any rate, if your future society hasn't already hit the fundamental limits of physics, there could be a little inflation, but it would be quite predictable, which makes it stable.
Why not a precious metal? Or diamonds? While things like gold will still be relatively rare in other star systems compared to say, iron, the differences would still be significant enough to give certain planets an unfair advantage. Larger, younger planets could have far more easily accessible gold, or platinum, or uranium, or whatever another planet might consider "rare", and hence, valuable.
Note that this differs from the alpha decay signature idea I mentioned above, as the metal used there is used to provide authenticity, not as an intrinsically valuable material like gold is to us now.
Aside: Why abandon electronic currency?
Although you've already stated the assumption to abandon digital currency, and offered a speculative reason, let me offer another one:
Propagation speed. I don't know if your universe has faster-than-light (FTL) travel or FTL communication, but either way, over interstellar distances, it could take a very long time (several minutes to many years) to query, hold, and withdraw funds to complete a typical transaction.