Where does the wealth go when asset prices go down?

The Author misunderstands as badly as the people he is trying to explain to, conflating wealth and market value. If you own an asset, that is your wealth, no matter what dollar price you can sell it for, just the asset itself. You can trade it, but in aggregate, the amount of money and assets in the world stay the same. That's why the only real wealth increases are in GDP, someone creating some new wealth which never existed before. Price is just an estimate about the future, how large the money stream your assets might entitle you to capture over its lifetime, and one that has constantly to be revised. Value is subjective.

"It was never there to begin with" is my answer. When we say "$X is worth $Y billion dollars" it's an expression of hope, not a quantization of an actual potential. The financial industry's tolerance of such baseless metrics is one of the reasons to avoid the whole area of endeavor: they're willing to lie to themselves and everyone else about what they do.

Here is my non zero sum understanding.

Let's say there's a new company that develops technology to grow apples efficiently.

This company will be eventually able to sell its technology. But why would apple growing companies buy it? They can grow cheaper apples and thereby make more profits. So it follows that our apple tech company will be able to make profits.

Central to this example is that apples are valued by people. People WANT apples. And if they can eventually buy it for cheaper they are better off.

Now from the shares point of view, why will I buy shares of apple tech? Because I believe that this company will actually develop the technology, go on to make actual tangible profits by selling to companies. And I believe this because I believe apples are actually valued by people.

Now what will happen to the society if this company goes down under? The society on the whole lost the opportunity for cheaper apples (again valuable). And obviously the few investors who had put the money lost part of their wealth. (Similar to burning one's money)

So to answer the question, where did the wealth go? I think it's equivalent to a situation where if all my wealth were in eggs but they all rotted away.

Now to ascertain whether wealth vanishing is a good or a bad thing, i think that is directly dependent on your subjective opinion of the value the wealth was attached to. In the case of apples, it would clearly be a net loss to society.

But if we take shares of a porn company going down, there was no net loss to society because my subjective opinion on the value of porn is 0 or negative.

Where does the wealth come from when asset prices go up?

The numbers are irrelevant, because they are based on units that go up and down too.

My house was worth (say) 100,00 units 10 years ago. Now it's worth 200,00 units. The house hasn't changed, but the units have declined in value. So you need more of those worse units to pay the same amount.

A better way of looking at it is with an inert asset like gold. In the 1930s an ounce of gold was about $35, today that same ounce of gold costs about $1800. The gold itself hasn't varied. (It can't, it's a metallic element.) But the buying-power of the USD has declined tremendously; so much so that one dollar today has the roughly the same buying power that two cents did way back in 1935.

Price is a signalling protocol for resource allocation.

Perhaps the underlying resource has been degraded or is no longer useful in some sense, in which case real wealth has been lost. Otherwise it might just mean the signalling has changed (e.g. control of resources has shifted).

Don’t confuse wealth with value. In the described scenario, wealth just goes down.

Nowhere until the assets driving that wealth is liquified or you have debt against those assets that can no longer be repaid by them!