If we understand "cost"/"exchange" as transfer of energy from one component of a system to another anytime a "thing" occurs, the results of this thing occurring are what is now owned by the entities party to the exchange.

A hypothetical object in motion under no external forces will remain in motion until a force acts on it, upon this acting, energy will be transferred, thus a cost.

In our more familiar world, a ball rolling down a trail will continue rolling until the friction of the dirt provides sufficient cost/exchange of energy, or the ball encounters a change in grade on the trail such that a gravitational force extracts enough of a cost on the kinetic energy of the system to cause it to stop. For the ball to regain motion some other force must be applied to the ball at an energetic cost to the entity exerting the force.

We can see these costs/exchanges and any change of state in a system as equivalent because the total energy in the system remains the same. Anytime there is a change, there is a cost.

A "thing" is something that is identifiably different from other things. What causes differences to arise is fluctuation of energy in the system. A thing is a fluctuation, a fluctuation is an exchange, and exchange is a cost, things have/are costs.

At a less cerebral level, anytime you do a "thing" it comes at the cost of other "things" you could do. So whatever thing you're doing has this opportunity cost.

We've mapped the abstraction of money onto many types of costs, but costs can be at a level other than monetary.

"Capital should own things" because capital is the name we've given to the unit of energy in economic systems, and as we've seen above "things have costs," all things have costs. And as we've also seen above, "ownership" is the name given to the new state assumed following an exchange. The ball owns "at rest" after the exchange with the dirt.

It's not really "capital" that owns things, but the spenders/deployers of capital[0]. Just like it's not friction that owns the at rest state, friction was just a name for energy exchanged. The ball and the dirt conducted a transaction in friction, the ball got "at rest" and the dirt got "increased heat."

[0]So I guess at this point you'd say, in Socialism we'd prescribe that you can't spend money on things that confer ownership of future exchanges for money, or things that increase in value. But here is where the nature of reality is critically important, the universe is not perfectly flat, there are always going to be peaks and troughs in the distribution of energy so long as the universe is the one we recognize today. Not every cost will dissipate in it's returns because the total amount of energy in system is conserved. So if there are some costs that are net losses some must be net gains. And there must be variation in results of exchanges because otherwise we wouldn't see anything around us, we see things around us because of fluctuations in energy.

While Piketty's equation might need to be addressed, not understanding the reality from which it arises doesn't help in addressing it.

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II

You may have a broader understanding of this than me, but isn't "capitalism" simply the name we've given to the dominant economic system we've found that came to be through emergent processes of human social interaction stretching back thousands of years? Nobody ever said I'm going to start Capitalism!

Yes, there were some abstraction layers added on with the development of capital/share markets and limited liability corporations around 1400-1500AD, but it seems to me what we call capitalism is simply the name given to the economic system we've deduced to be present wherever we find things like coinage and contracts/exchange agreements in history. Were the ancient Greeks "capitalists"?

Adam Smith was for the most part describing what he saw around him and what already existed, was he not? I don't believe he was prescribing whole new systems of being.

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III

So you're saying Socialism is simply a restricted form of Capitalism?

Because the characteristics you give for Socialism, workers owning what they produce and co-ops, are not only possible in our capitalist system, but they are present in significant number.

In fact, in capitalism everyone owns the fruits of their labor. Were that not true, it would be more appropriately called slavery.

A computer programmer may or may not take home his code at the end of the day, depending on if he is employed by someone else and the agreements made between him and whoever may employ him, but he still owns what he has created even if he doesn't take the bytes home. He has just agreed to exchange it for something else upon creating it, most likely capital/currency.

So you're saying things would be better if such agreements were restricted by law?