It’s kind of amazing to me that in a 100 years a whole lot of extremely smart, and very focused, people couldn’t arrive to a verifiable way of bringing together QM and GR. There’s something wrong with this situation.
Part of the reason little progress has been made is that it was considered career-ending in physics to work on those questions, because some of them dive into philosophy (What is knowledge? What is real? What is emergent?) Throughout the latter half of the twentieth century graduate students were counseled away from any work related to the field. Oppenheimer famously organized the shunning of Bohm for daring to publish (at Einstein's encouragement) on the subject. Hugh Everett was driven out of academia altogether.
Hard problems can be solved when people actually work on them. Often the problem is other people preventing the work. Thankfully this attitude seems to be easing thanks in part to the efforts of people like Sean Carroll and Lee Smolin.
One of Sean's papers, in fact, proposes a way to falsify Everettian mechanics through experiment (though the experiment would be exceedingly difficult in practice).
Copenhagen was "just an interpretation" but serious work on the subject is actually advancing work on new theories (with distinct mathematical models), not just hand-waving and dismissal.
I'm saying "you", not "author", because the paper's author seems to be interested in a very specific, somewhat niche question, which is studying the equation of motion of test particles (at rest) in alternative theories of gravity and in the situation where, in addition, the test particle is charged and interacting with a fixed gauge field. (One needs to be very careful with the term "gauge" here because the author confusingly uses it for both, the matter gauge theory / gauge group and the "gravitational gauge" group, i.e. coordinate invariance.)
This question might be interesting to a few select people but there is certainly no "problem of motion in gauge theories of matter" at large, at least not in the way you portrait it.
I mean, for classic gravity / General Relativity, one expects that, depending on whether the particle is charged or not charged, the equation of motion reduces to:
- the geodesic principle – i.e. the hypothesis that (uncharged) test particles at rest move along geodesics.
- a Lorentz-force-type law for gauge-charged test particles that (only) interact with a (fixed) gauge field and are otherwise at rest.
But both are quite well-established I'd say:
- The geodesic principle can actually be rigorously derived from the Einstein field equations for a large class of matter or situations[0]. Given this body of evidence, it's rather likely it's a mathematical theorem and does not actually need to be assumed as an axiom of General Relativity.
- The Lorentz law can already be derived[1] from the special-relativistic Lagrangian of the matter field and its coupling to the gauge field (where both fields are obviously classic, not quantum).
As for the latter, sure, strictly speaking the special-relativistic derivation (i.e. on a flat background) can only be a "local" one in light of General Relativity. In a fully relativistic derivation one should instead consider a curved background, i.e. the Einstein-Maxwell action (or a generalization thereof for arbitrary gauge fields). But then again – given the evidence for the geodesic principle – we know the Lorentz force must come from the interaction of the particle with the (fixed) gauge field (not gravity) and that interaction is largely "understood" – with the usual fine print that:
- forces are a classical concept but particles are actually quantum and there is backreaction (so the Lorentz force can only be the lowest-order term, anyway),
- obviously we don't really know how quantum fields work on curved backgrounds / in conjunction with General Relativity. Then again, we don't know how to make quantum fields mathematically rigorous on a flat background to begin with. So there is no point in asking for mathematical rigorisity in the context of deriving the Lorentz force from first principles when much larger issues would need to be tackled first.
So again, what "problem of motion" exactly would you like to see solved?
[0]: https://physics.stackexchange.com/questions/24359/why-do-obj...
[1]: https://math.stackexchange.com/questions/554488/derive-the-e...
What's wrong about it? If humans evolved, there's no good reason to think that even the smartest human has the mental capacity to do something like that, or to do it quickly. Science will hit a wall determined by human limits, and it's quite possible that limit has already been hit in some areas.
There are a lot of popular fairy tales that portray humans as universal understanders (with no limits as long as they Science™ hard enough), but they seem kind silly to me.
EDIT: I mean, who does revisit long established facts everybody just agrees upon, without checking, because they are long established?
The thing is there is no shortage of theories, or whole classes of theories, the problem is getting the data we need to verify and refine them.
Of the 4.4 million software developers in the US, most of them produce really bad code and have a lot of wrong ideas about development and don't think twice about what they're doing.
Same with the medical field - rife with dysfunction and malpractice.
Pretty much all fields work like this as far as I can tell. It sometimes takes hundreds of years for new correct ideas to be actually accepted and integrated into the mainstream knowledge/practice in any given field. Most people have giant egos and are resistant to change.
Note that we do teach classical mechanics (to a point) in high school, even though it was the cutting edge of physics at some point.
When you manage to write down your thoughts so future generations can build on prior work, and when you manage to formalize problems by abstract notation (math), and when you gain the capability of breaking down complex problems into small solvable chunks, then maybe, and I want to stress maybe, there is no limit to understanding things.
On the other hand, there also may be problems with irreducible complexity, so it really could be either way.
It took hundreds of years between Newton and Einstein and relativity was only possible once we were able to produce data about the speed of light.
Heck, that form might not even be consistent between "bubbles".
Or, there is something wrong with the theory?
Maybe his discrete, computable mathematics (which is merely alluded to) is the temporary step back we need to move forward again.
Although removing the continuum from QM seems questionable. AFAIK (which isn’t much) continuous change is a feature of QM. It’s one reason quantum computation has an advantage. No 0 or 1, but a continuous range of states somehow.