Money - the obvious "index" - does not solve this problem, merely simplifies it and facilitates exchanges. It does not eliminate the necessity to negotiate an "exchange rate". It does not prevent market failures. In other words: money is not an index. It is merely a medium of exchange and a store of value. The index - as expressed in terms of money - is the underlying agreement regarding the values of resources in terms of other resources (i.e., their relative values).
The market - and the price mechanism - increase happiness and welfare by allowing people to alter the composition of their bundles. The invisible hand is just and benevolent. But money is imperfect. The aforementioned Rawles demonstrated (1971), that we need to combine money with other measures in order to place a value on intangibles.
The prevailing market theories postulate that everyone has the same resources at some initial point (the "starting gate"). It is up to them to deploy these endowments and, thus, to ravage or increase their wealth. While the initial distribution is equal - the end distribution depends on how wisely - or imprudently - the initial distribution was used.
Egalitarian thinkers proposed to equate everyone's income in each time frame (e.g., annually). But identical incomes do not automatically yield the same accrued wealth. The latter depends on how the income is used - saved, invested, or squandered. Relative disparities of wealth are bound to emerge, regardless of the nature of income distribution.
Some say that excess wealth should be confiscated and redistributed. Progressive taxation and the welfare state aim to secure this outcome. Redistributive mechanisms reset the "wealth clock" periodically (at the end of every month, or fiscal year). In many countries, the law dictates which portion of one's income must be saved and, by implication, how much can be consumed. This conflicts with basic rights like the freedom to make economic choices.
The legalized expropriation of income (i.e., taxes) is morally dubious. Anti-tax movements have sprung all over the world and their philosophy permeates the ideology of political parties in many countries, not least the USA. Taxes are punitive: they penalize enterprise, success, entrepreneurship, foresight, and risk assumption.