I definitely get your point. One difference between theoretical physics and just math is we have since we use math as just a tool to describe the world, we still have to input physical assumptions to make any sense of what we see. There are many instances of things being mathematically "OK" but we don't think physically exist. See "White Hole" for instance.

I will try to give a better explanation later today! Funny enough, I am off for the section for the QFT2 that Daniel teaches right now, hah. I can also ask him personally questions later in the week.

Who is the "we" who thinks White Holes don't exist?

https://en.wikipedia.org/wiki/GRB_060614

Black holes are hard to notice, except by side effects, but we know great many of them, end even portrayed one.

White holes would be relatively hard to miss, because they must be shining very brightly. One of the current theories suggests that the big bang (or "a big bang") was a white hole: every black hole is a white hole producing a big bang a parallel universe. We've already had ours, and are lucky enough to still register its echo as the CMB.

Without negative matter, it's impossible to build a wormhole that's shorter than the distance through normal space.

This piece of math shows that it may still be possible to build a wormhole which isn't shorter than that distance. Obviously that wouldn't be much of a shortcut, but the potential research and (maybe) real-world applications are still impressive.

That’s not what I was asking.

I was asking about the particular usage of the average null energy condition as justification to rule out wormholes: why isn’t that just begging the question by assuming your conclusion? and how does that particular assumption actually lead to the conclusion there can’t be wormholes?

It’s interesting the downvotes for asking someone to support a scientific claim, and be clear where they’re making assumptions versus reaching empirical conclusions.

That's right. When you have a mathematical theory, there are often extremal cases that predict strange things that have never been observed. At this point you have a choice to make:

1) Assume the mathematical theory is too permissive, and rule out the things you have no reason to exist, and hope to find a more elegant theory (on the controversial metaphysical assumption that simpler/elegant theories are more likely to be correct)

2) Assume that the mathematical theory is pointing you in a direction to search for a new phenomenon, and build things like superconducting supercolliders to search for empirical evidence.

With wormholes, we're a bit stuck in that we are decades to centuries away from empirically testing the theories, so physically the Average Null Energy Condition is moot -- it's fine math to do, as groundwork/scaffolding for future physics, but it doesn't say anything physically until we get empirical evidence for or against it.

Okay — and just to be clear, there’s nothing problematic to me about simplifying assumptions or effective theories.

Both are important tools for making predictions tractable.

But when we lose sight of what are conclusions, what are strongly justified assumptions, and what are simplifying assumptions we don’t have justification for (or even know to be untrue), we begin to create fundamentally inaccurate models or wrongly shut down others’ avenues of inquiry.

This happens in economics and business quite often, but simplifying assumptions become orthodox truth with surprising frequency in hard sciences like physics, as well.

If that condition didn’t hold, we would expect to see a lot of phenomena that we don’t see, which makes it a poor model for reality.