There is an ongoing debate over the "sustainability" of our resource use and/or our long-term standards of living.   This is largely driven by concerns for intergenerational equity.   The world provides us an endowment of resources to use and/or conserve.   Today's consumption and investment patterns will determine what endowment future generations--our own descendants--will receive, and how well they will live.  

John Rawls (A Theory of Justice) argues that there is a sort of altruistic imperative that insures intergenerational equity.   We can't know for sure what our own descendants' relative positions in society will be.   So our decisions about the future are made behind a "veil of ignorance" where we are motivated to look out for the welfare of the entire society.   (Consider how inheritance taxes promote intergenerational equity!)

Originally, "sustainability" meant harvesting a (renewable) resource at a rate that can be sustained more or less forever.   This is the strictest ("strong") form of sustainability that we will consider, and in the literal, physical sense it implies leaving the world exactly as we found it, generation after generation.   This is clearly impractical, since it implies virtually zero use of exhaustible resources and exclusive reliance on renewable resources.

But what do we want to sustain?   A more flexible ("weak") form of sustainability would insure that future generations enjoy at least as good standards of living as we enjoy, which implies that we must compensate them for reducing the stock "natural capital" by bequeathing them substitute forms of capital, including physical capital, technologies for more efficient resource use or better resource substitution, etc.

The big question then becomes how substitutable are other forms of capital for the natural capital we are gradually depleting?  Some forms of natural capital will have ready substitutes (e.g., solar power for coal-fired electricity generation); other will not (e.g., irreversible contamination of land with plutonium).

John Hartwick (1977) has developed a strong theoretical argument showing that the world can maintain constant consumption with a finite resource base as long as all resource rents are invested in capital.   One implication of the "Hartwick Rule" is that an inter-temporal allocation can only be sustainable as long as the total value of the capital stock (natural and man-made) is non-declining.

Here's a simple analogy: suppose your income derives from a $100,000 savings account that earns 10% compound interest each year, and assume there is zero inflation or risk.   The interest earned each year is $10,000, and as long as you don't withdraw more than that, your principal remains intact and you can draw $10,000 per year forever. If you withdraw less in the current years, the principal grows and you will be able to sustain withdrawals of somewhat more than $10,000 in future years. But if you withdraw more than $10,000 in the current years, you will reduce future sustainable withdrawals below $10,000.

We all make inter-temporal decisions for ourselves all the time.   For example, you get $100 for your birthday and have to decide whether to spend it now or save it now in anticipation of some future expenditure. In making these decisions, we generally discount the future relative to the present. There is no point in foregoing utility today unless we can expect some benefit (more utility later) from doing so. Banks typically pay interest on savings deposits that gives people an incentive to save some of their money for the future rather than spend it all today.

We also discount the future at the same rate even over very long time horizons.   We may be mortal, but financial markets and the estates we leave behind are not.   At first glance, it might seem unfair to discount the well-being of future generations relative to our current level of well-being.   But it's not necessarily unfair if we apply the same discounting in our own lives.

The further we project into the future, the more uncertain it is.   This gives us an ethical imperative to play it safe, so that we can guarantee future generations at least a "safe minimum standard." We don't know for certain that our technologies won't turn out to have devastating negative effects.