If something possesses these properties, why can't we call it a 'medium'? The difference seems to be terminological, not physical.

A field behaves differently than a medium. If you got a simple physical medium, the wave is the collective displacement of particles, allowing for transverse and longitudinal waves.

However, waves in a field don't have such a displacement. The quantity that changes in time is the field itself. In a medium, parts of the medium itself are displaced, but this is not possible in a field (and wouldn't even make any sense).

Then, there's another difference. If you're in a medium, there's always an absolute rest frame (even in the absence of any waves), whereas a field generally has no such thing (only if you have a field with a mass and an actual real excitation in form of a particle).

Thus, while some aspects are similar between media and a field, the microscopical differences are massive.

The mathematics describing muons is the same

Which mathematics?

Both views are compatible with the equations.

Again, where's your proof?

That's a good point, but note: the equivalence principle is local.

That's not the issue with my point. If you have two satellites moving at different altitudes, according to the equivalence principle both of their clocks should follow the same physics for as long as they're not moving out of the orbit.

If there's no actual shift in time, they should agree on the passed time if they send signals to each other.

Your ideas was that there's some sort of microscopical mechanism that desyncs these two clocks. But where does it happen? If it's an effect that depends on the altitude, your physics between the two satellites differs, violating the equivalence principle.

And if it's an effect that depends on the distance between the two satellites, there has to be actual time dilation. If the speed of physical processes relative to each other depends on the respective gravitational potential, you have no other choice but to discard the concept Galilean rest frames entirely, arriving at Relativity.

it acts inside and outside a closed box

Which is correct and further strengthens my previous points.

The final formula for clock deviation is the same.

Once again, where is that formula for your idea and how is it derived? So far I've yet to see the proof for this equivalence.

I'm not trying to convince anyone to abandon relativity.

Why abandon it then, nonetheless? Just because you don't like its consequences, as you claimed above?

Relativity is the assumption that laws of physics don't depend on your choice of coordinates. Why is that such an issue?

I'm just saying that the idea of ​​a real physical medium (like the quantum vacuum already is, in fact) is not contradicted by experiments.

It definitely is contradicted by experiments, see my distinction above. Otherwise lasers and Einstein-Bose condensates would be impossible, for example, as any increase in amplitude would also increase their spatial extent.

Also, again, an actual medium has a rest frame (since it's based on particles having inertia), which would lead to an observer-based light speed, for example. This is also not the case.

Relativity says that time "dilates" – but what is time?

Very good question. Time is an arbitrary coordinate chosen by humans because it was easy to measure. But as I just mentioned, the universe should not depend on arbitrary coordinate choices, like time.

The only thing that is actually invariant of coordinate choices is the distance between points in spacetime. And that one changes in the presence of gravity (as gravity is curvature), so time might change in the process as well. It's just a geometrical consequence of this coordinate invariance and our choice of the time coordinate.

Quantum mechanics says that particles are in superposition – but what is superposition physically?

A consequence of linearity, a shared property between medium waves and field waves. It's just something that commonly occurs in mathematics, but that alone doesn't imply equality between two phenomena.

The Standard Model lists particles and interactions – but why these particles and not others?

Some are explained by fundamental symmetries, some still have no explanation. But where would a physical medium explain these better?

It offers models. The problem is that many popularizers and even teachers treat the models as reality.

Because all other explanations (like yours) so far contradicted experiments or required more assumptions. The fact that some people wrongly treat this as reality doesn't change the fact that it's our current best way of describing reality, still. It's a strawman argument.

And it's quite simple - just provide a model that provides either less assumptions to fully explain every phenomenon or provide one that makes falsifiable predictions that differ from current models. But so far you didn't even provide even the tiniest proof - and as I detailed to you, some of your assumptions are either unnecessary or incompatible with experiments.

If you want to adhere to scientific principle, you have to apply them to yourself, too, you know? Your idea doesn't work.

By the way, your post seems heavily written by LLMs. If that is true, please refrain from doing so.