Running through this exercise with some honesty can give one a greater understanding of why our physics is framed the way it is, and why it is that while all sorts of reference frames are valid, "inertial" reference frames are still important on their own merits.
Is there a deeper meaning to "Consider the speed of light in the Andromeda galaxy" that I missed? The speed of light is known to be constant in every reference frame.
You can reformulate all of physics into your Earthly non-inertial reference frame. You can formulate all of physics into a reference frame in which you personally are always stationary! Nothing stops you from doing it, and the physics will work, as much as they ever do (i.e., we know something's wrong with our theories). To the extent that the result is a hideous monstrosity, well, such is my point. Pondering the nature of that hideous monstrosity is something I think worth doing, at least for a bit. Not to the extent of actually writing the equations, though. It brings clarity to why inertial reference frames are so important that we almost consider "inertial reference frame" to be a single atomic word, because non-inertial reference frames are in general not very useful. (In specific they can be.)
But now I understand why Einstein wrote in his last book, after much thinking, that this perspective is wrong. He called it "unthinkable" for a good reason. The model I'm using also has relativity, but with an absolute frame. It also behaves differently in extreme situations like the surface of super massive black holes and and near field of a proton. In fact, I have much more relativity but not everywhere and it's paradox free :)
What if I say there are frames of reference that are irrelevant to discovering the process that generates the observations?
Edit: Um, guys? I genuinely don't know what general relativity says and I didn't get the comment above. It'd be nice if someone explained.
The location, and speed with which you are travelling is what general relativity calls a "frame of reference", and none of them are "correct" or "incorrect", they're just predictors for what observations will be possible from that frame.
then the weirdest part is that one of the consequences is that planetery bodies are large enough for that “speed of light must remain constant” rule to matter in a particular way as to generate a warping of spacetime around them, the geometry of this warp perfectly explaining gravity. or put another way, we stick to the earth because time runs slightly faster at our heads than at our feet.
This youtube video explains it really well:
>> The location, and speed with which you are travelling is what general relativity calls a "frame of reference", and none of them are "correct" or "incorrect", they're just predictors for what observations will be possible from that frame.
OK, I see- "frame of reference" is a technical term, in General Relativity, that refers to your position in space, and determines what you can observe. Instead, I meant "frame of reference" as a more general "point of view" or "frame of mind" - a set of assumptions that give context to any observations and that inform interpretations of them.
Even going by the technical sense of a frame of reference, though, there are frames of reference that will not permit the cocrrect identification of a process that generates a set of observations- or at the very least, they will tend to favour incorrect interpretations of the observations.
I think that is in keeping with what your comment says about a frame of reference in General Relativity allowing a range of physical observations.
Going from observation, that the speed of light is constant, regardless of how fast the light emitter is travelling relative to you, he made that the unbreakable assumption, and made the shape of spacetime flexible to always satisfy a constant speed of light. This theory was then confirmed when the light of a distant star was observed to bend when travelling through the strong gravitational field of our sun during a total solar eclipse.
Therefore the physics described by General Relativity have greater predictive power.
Quantum physics, can also predict everything in general relativity, but doing so is a lot more complicated than using general relativity. However, Quantum Physics can explain things that happen on small scales that General Relativity cannot. Quantum Physics has greater predictive power, but it's more convoluted. Like Epicycles. Einstein didn't like quantum physics and spent a great deal of time trying to debunk it, but, well, he couldn't.
This is all to point out that one should not confuse predictive power with complexity. Ockham's Razor is a rule of thumb that prefers "simpler" explanations for things. But the predictive power of the two competing theories must be equal for that to apply.
My original comment is grounded in an assumption that predictive power is not enough to identify a theory as correct, and neither is simplicity. There's nothing to stop any number of theories to have the same predictive power and the same kind of complexity. Sometimes, it's just very difficult to choose one, above the others.
Did I come across as confusing predictive power with complexity?
EDIT: it's interesting you bring Occam's razor up. It's part of what I'm studying, in the context of identifying relevant information in (machine) learning. There are mathematical results (in the framework of PAC-learning) that say that, basically, the more complex your training data, the more likely you are to overfit to irrelevant details. At that point, you have a model that explains observations perfectly well, but is useless to explain unseen observations (the really unseen ones- not those pretending to be unseen for the puprose of cross-validation).
...iiish. The result is that large hypothesis spaces tend to produce higher error. But, the size of the hypothesis space in statistical machine learning depends on the complexity of the data, as in the number of features. Anyway, I'm fudging it some. I'm still reading up on that stuff.
Unfortunately, the two theories, while both being extremely successful and accurate in their predictions, are incompatible with one another. Quantum Field Theory has successfully combined Quantum Mechanics with Special Relativity, but that is all.
Which is to say: they break under conditions very unlike the every-day universe, which is important but also indicative that they are not that broken.
The incompatibility is important though, because if there's any more card tricks we can do with physics so we can do interesting things, somewhere in that bit of incompatibility is where we must find it.
maybe some day we’ll find the grand unifying theory of the universe.
Also, "frame of reference" has a specific meaning in relativity but it also has a more general meaning regarding the framework within someone understands something. It's pretty clear from the context (imo) that this latter is what was meant in this comment.
"I'm not that kind of geek" is a bit of an in-joke so my bad for using it where the context is missing, but I thought it would work even so. The missing context is that a colleague used to tease me for my deplorable lack of a science background, although we did hit it off in terms of our fantasy and science fiction tastes. So, I was not the science kind of geek, although I was the science fiction and fantasy kind of geek.
Like I don't understand either Australia or Argentina.. but I know that they are not the same!
According to General Relativity, there's no such thing as a "wrong" frame.