The reason that scarce metals like gold can be the real money is never because of its color but in fact an example of proof-of-work. The unit of work/energy is Joule which equals to the work done by a force of one newton when its point of application moves one meter in the direction of action of the force. To have some gold at the first place, you need to spend a lot of effort Joule by mining/digging and everyone understands there is no other way; not like a one gram stone which you might claim that it contains much value because you create it based on Einstein's statement that energy equals mass times square of light speed which is a big number of Joule, anyone would think you are lying and in fact picking up that stone casually on the way home which is a tiny small number of Joule because of your lack of proof of work. Joule is the money of the universe. By the First law of thermodynamics, the volume of this currency never inflates; when someone receives this money, there must be someone who pays this same amount of money. It shall be educative to those economist or policy makers that it always requires constant amount of energy to boiling 100 grams of water known by no-brainers while non-constant amount of equivalent fiat money while they try very hard to stabilize the CPI. If the effort Joule work behind an artifact can be proved/understood and shown to public, then that artifact can serve as money. In other words, the amount of proof-of-work is the proof or public understanding about the Joule number to produce one unit of the artifact. In economics terms, it means a constant marginal cost in term of energy work. Note that money is a physical concept, not a subjective value preference; one can spend 1000 Joules or spend 1000 coins to dig a hole or cut a tree and price his charge at 1000 Joules or 1000 coins to the market (if he doesn't want to take any profit) but one can not claim that hole is the same valuable as that tree to himself or to anybody.

Ideally, an ownership of energy storage "battery" (for example, food crop) is the best vehicle to be the money (see this energy-as-money game) where the proof of the work to cost X Joules energy is simply a battery containing X Joules energy; being an energy container, it is even immune to catastrophe such as famine where everyone prefers bread to gold to be money. But in a normal circumstance where the average energy amount of a battery remains, a battery tends to perish and leak its energy therefore no better than gold who is easier for storage and has the proof-of-work characteristic as well. In a planet far far away with gold spread all the way home, gold can not be money on that planet even with all the same physical properties as opposed to the claim by some people. The relationship between price level and money volume is detailed here.

It is interesting to derive some exchange rate formula based on this understanding. Examples as below.

North America Indian

Picture courtesy by Hibulb Cultural Center. Different kinds of shell have different values; the effort to find one particular shell can be spent on building a canoe alternatively. The most valuable shell is the one hardest to find or equivalently to demand greatest effort to find or to sacrifice greatest effort to find and now possibly is extinct. The exchange rate of different shells is decided by finding difficulty.

Some drawback is in this system. Trust as a demand in the cooperation society, its required amount is increasing/decreasing as the economy is expanding/shrinking. Because the proof-of-work of this shell money is set by Mother Nature to be a constant, this means the volume of the money will be not enough when the economy expands beyond a level. As the economy size expands, these shells are slaughtered to be used as money and extinct. After that, the economy will drop its use as money or find other types of money in addition. The same story repeats for the rare metal money whose proof-of-work is also said by Mother Nature; as people harvest more energy and the economy expands after 18th century, the gold and the silver were not enough so its use of money dropped in favor for paper money whose proof-of-work is the committed cost of counterfeit/policing (at least initially). The proof-of-work of the money defines money's price. When proof-of-work of a money differs from its price there will be energy arbitrage. people could not simply claim that 0.1g gold can be spent to boil one ton of water and 1g gold could be spent to accomplish the same task 10 years ago while gold's proof-of-work remains the same and the economy expands 10 times.

Karl Marx

Karl Marx thinks the only real resource with value is labor Joule. Any goods' value comes from the labor effort to produce the goods. Therefore, suppose it needs two times of working hours to dig out one gram of gold than one gram of silver and people understand there is no other ways to produce gold and silver. Then the exchange rate of Gold/Silver shall be 2. In addition, the more working hours needed to dig out one gram of gold, the more valuable of the gold is, for example, the higher the exchange rate Gold/Milk.

An obvious fault of Marx is that he omitted source of energy other than human labor; a bitcoin miner could take little human labor to mine the coin but consume a lot of electricity energy. Marx also forgot the impact of capital such as skills which are often the fruits of the previously devoted energy (training or experience) and materials.

Satoshi Nakamoto

Satoshi designs that the real resource behind bitcoin is electricity and time and the effort to generate a block or equivalently the resource to sacrifice is a ten minutes electricity of the bitcoin network. To be precise, we have the following (I do the calculation on someday 2016 so the number may be subject to change):

• electricity costs 8 and 12 cents USA dollar in China and USA per kilo watt hour respectively. However, because the majority of BTC miners are in China, I will use 8 cents for the calculation
• one kilo Watt hour is 3600000 Joule

Therefore the exchange rate of USD/Joule is 45,000,000.00

On the other hand:

• in current technology, by Bitfury white paper, the computation speed of one giga hash per second need 0.2 Joule
• current network computing power is 1,488,912,137.36 giga hash per second
• the current bitcoin miner get per block is 25.58180739 where 25 is the new BTC mined and 0.58180739 is the transaction fee

Then in ten minutes, we sacrifice 178,669,456,483.20 Joule to have 25.58180739 BTC. This activity is proved by finding the special hash with many leading zeros for the block and people understand there is no other ways to get the hash except brute force trial and error. Therefore, the exchange rate of BTC/Joule is 6,984,238,983.87. If we omit other costs for miners, the exchange rate of BTC/USD would be 155.21 which however we can treat as a lower bound of BTC/USD in addition to a possible upper bound.

Therefore many what-if below:

1. New mined BTC get half every four years. Currently the winner of the block generation will gain 25 BTC in addition to transaction fee. The new mined BTC is expected to become 12.5 BTC around 2016 July. The BTC/Joule and BTC/USD lower bound will be 13,657,845,874.32 and 303.51
2. All the 21M BTC are mined and the transaction fee per block is 0.01. Because the block generator (currently, we call them miners) still needs some profit gain for continuous operation of proof-of-work, the BTC/Joule and BTC/USD lower bound will be 17,866,945,648,320.00 and 397,043.24
3. The electricity cost gets higher to 35 USD cents per kilo watt hour, the BTC/Joule and BTC/USD lower bound will be 6,984,238,983.87 and 679.02
4. The network computing power advances to double, the BTC/Joule and BTC/USD lower bound will be 13,968,477,967.73 and 310.41
5. Technology advance and the Joule needed for 1 giga hash becomes half, the BTC/Joule and BTC/USD lower bound will be 3,492,119,491.93 and 77.60

Note that

• The new BTC getting half every four years is not really a what-if but a surely scheduled event of the design. Based on rational expectation in economics, double value for sure in four years is a very attractive earning. If people are clever enough, the BTC/USD exchange rate shall not jump higher at each four-year timing, but instead getting higher now by all the half events where all 21M BTC are mined. If people are clever enough, 1st what-if should not happen around 2016 July, instead, 2nd what-if should happen now. However, if people are not clever enough, 1st what-if and similar stories should happen every four years. A clever miner will calculate BTC/Joule by long term average energy usage and the price shall be much higher because of this halving design and treat current earning as the reserve for future energy cost.
• All the what-if may happen simultaneously. For example, when a new power-saving computer is introduced with double efficiency, the miners with the new computer will get higher profit advantage by simply deploying more new machines under the same electricity bill and then other miners will try to get the new machines too and phase out the old machines to compete with, therefore the whole network computing power grows and the Joule consumed by the network computing power for 1 gigahash remains roughly intact. But then the block generating time will be half to 5 minutes and the difficulty of the hash computing will be automatically adjusted to double to meet the 10 minutes design. Therefore the total Joule will double implying that the BTC/Joule and BTC/USD lower bound will get higher to double.

The design of mining difficulty allows a flexible number of proof-of-work to accommodate economy expansion/shrinking with constant volume. For ideal constant proof-of-work money, instead of adding new money with the proportional principle to the people, Satoshi Nakamoto mathematically appreciates the money's proof-of-work, aka money appreciation, to achieve the same equivalent result. The bitcoin network energy power is the substitute of energy of other money and its increasing either means the economy expansion or the substitution of other money.