Lorentz Jr

No, the strong form of the principle (at least as interpreted by some people) means more than that. It goes beyond what observers experience and claims that there's nothing "under the hood", i.e. that no mechanism is required for time dilation because it's "just a matter of geometry". Anyway, I don't know how to explain this distinction more clearly, so let's drop the subject. We're repeating ourselves. Same thing. I criticize the metaphysical principle, and you respond by defending the mathematical theory. We're talking past each other. Yes, that's very different from both ordinary human intuition (maps are about space, not time) and the intuition of 19th-century physicists (science is about mechanisms). Most people outside the modern physics establishment would say that simple comparisons of observational data and theoretical predictions only require the ability to read charts and compare numbers and have nothing to do with intuition. Maybe so, although I'm not sure how new theories of any kind at all can be developed without some general principles or opinions to guide the theorists. Anyway, let's forget about the ether for now. I've been reading about emergent spacetime, and that looks like it may be close enough to what I have in mind.

You're confusing the mathematical theory with the metaphysical principle. The theory doesn't need excuses as long as people remember that it's just a theory. An abstract model that doesn't really explain anything and may be subject to further refinement. Curvature for GR, quantum complications for the ToE, etc.. The principle of relativity is a very different animal. It's only one possible interpretation of the theory. It's a platypus, with time for a nose and space for a tail. The extreme form of the principle says there's no reference frame with any special properties at all, which means time and space are somehow "interchangeable" or "made of the same stuff". That's an extraordinary claim, and as such, it requires extraordinary evidence. That's what people keep making excuses for. It's not what I've been demanding, it's what people have been claiming. They claim that SR "explains" things, but it doesn't. It's a shallow, phenomenological model that describes non-gravitational, non-quantum things very nicely, but it doesn't explain a damned thing. It doesn't explain time dilation, it only describes it. Yes, and I'll try to keep my mouth shut about this subject in the future unless someone else brings it up again. It only came up recently because of the "fabric" thing. I'm done with analogies, Markus. Other people may not understand this distinction, but one of the lessons that have been burned into my memory over the last year is that analogies aren't evidence of anything. They're just stories. They don't prove that what the person is saying is true, they only explain what the person is saying. And I understand what you've been saying. If I tell you life is like a bowl of cherries, that may explain how I feel about life, but it doesn't mean I'm right. So, to summarize, this is where we disagree. You can appeal to physical intuition, and you can talk about abstract mathematical models, but it's BS to conflate the two ideas. From an intuitive physical point of view, a "map" with time in it is very different from a map with only spatial dimensions. That's the lie of trying to "explain" time dilation by calling it "just a matter of geometry". Representations are mathematical models, not physical explanations, and the things that people intuitively understand as "maps" are only about space, not time. It's your two cents, and it's also the two cents of almost everyone else in the physics community. So the question is, why do I seem to be the only weirdo who doesn't believe in the principle of relativity but still believes in physics? I feel like I've gone from arguing with anti-establishment trolls on one website to arguing with pro-establishment trolls on another site! That's my two cents. 🙂 Sure, but any relationship requires a mechanism, and any nontrivial one requires a preferred reference frame to account for the traveler's motion.

Fundamental principles vs details of the problem at hand. Got it. 🙂

And I couldn't find anything about them in a quick internet search.

The feeling is mutual, Markus. Spacetime doesn't explain time dilation, it simply builds it into the abstract formalism, misleadingly calls the formalism "geometry", and declares that no mechanistic explanation for TD is necessary because it's already built into the "geometry". That's circular reasoning, and I've finally lost patience with the excuses that people keep making for it.

That's math. I was talking about physics.

Then it's not machinery. Thank you, martillo. When you're observing a turtle and trying to figure out how it behaves, mathematics can describe the behavior for you. To explain the behavior, i.e. to understand the machinery that makes the turtle behave the way it does, you need to examine and describe the next turtle down, the one that supports the turtle you're studying. An explanation for the behavior of one turtle requires a description of the next lower turtle.

No.

Derivations of the Lorentz transformations define localism in terms of a single speed limit that applies to all phenomena in the entire universe. That definition seems unnecessarily restrictive to me. After all, nobody complains that c is greater than the speed of sound. Light is defined at a lower level of abstraction than sound, so it's acceptable for it to be faster. Similarly, that also applies to phenomena at a lower level of abstraction than light. If the geometry of space is Newtonian, and matter and radiation are implemented by some mechanism in an ether, there's no reason that mechanism couldn't propagate at (VERY) superluminal speeds and simulate relativistic "geometry" for light. A more general form of localism only requires that the speed is finite. It would explain things like quantum entanglement and wave-function collapse without any tortured reasoning about fate or consciousness or invisible universes, all of which conflict with Occam's razor.

I'm pretty sure the range of physical conditions that have been observed is still fairly limited. There's plenty of room for disagreement between GR, which allows wormholes and time cycles, and gauge theory gravity, which doesn't.

There's a direct link between the theoretical formalism and the elapsed time. So what? That's the thing we're trying to explain. You said something about "causal efficacy", but things can't cause themselves, so that was nonsense. Your earlier point about detecting the ether's motion is also nonsense, because that's not the same thing as having an effect. It was established way back in Einstein and Lorentz's time that, for whatever reason, time dilation and length contraction are coordinated in such a way that they have the same effect regardless of the ether's velocity. As for proving the ether's existence, I've tried to explain that time dilation is evidence of something that causes time dilation, and an ether is one conceivable explanation but not the only one. So the relativistic argument seems to be that spacetime and real space are equally valid because they're both "models". But real space is simple, intuitive, and easy to explain. One can think of it as a network of little cells (Roger Penrose has called it a "spin network"), so proximity could be implemented as connections between cells, and distance along a path could be the number of cells on the path. And those cells could potentially be related to quantum-mechanical phenomena. What is the equivalent structure for spacetime? What underlying physics could it possibly represent? Why should people accept the apparently ridiculous proposition that a structure combining such obviously different phenomena as duration and extent can be anything more than a mathematical convenience? The final justification for relativity so far seems to be, not that spacetime provides a physical explanation for time dilation, but that theories in general don't have to provide explanations, because they're "just models". Which to me seems like blurring the distinction between science and religion. Maybe this would be a good place to end the thread. I'm not sure I can stand reading these excuses anymore without getting uncivil.

How do you measure the length of the path? In real space it's the number of meter sticks, laid end-to-end along the path, that are required to connect the two endpoints. What is the equivalent operation in Minkowski space?

Except in nonrealist interpretations of quantum mechanics, where Jack and Jill don't actually go up the hill, they just have an increasing probability of being detected there! 😄 You get today's award for worst analogy, swanson. Congratulations. 🙂 So what? I don't have to know how the engine in my car works to know that it's there and it propels the car. So what? We don't have to know things exist to speculate about them. Because we haven't finished with the first step yet. The next step is just Control Theory 101: You can't drive your car without turning the key in the ignition and operating the pedals and the shift lever and the steering wheel. You need to interact with your car in an absolute sense, not just wave your car keys in the air relative to the ignition switch or wiggle your toes near the gas pedal. An ether can affect a moving object, and the object can control the ether through its absolute motion. Not relative motion. Only absolute motion can have a real physical effect. All I'm doing is answering your questions, swanson. If you don't want me to soapbox, please stop provoking arguments with me with your false analogies and pointless comments. As for not arguing in good faith, you still haven't answered my question about your claim that "time moves at a slower pace in some reference frames". All you did was lecture me about derivations, cite generalities, refer to some "straw man" that I "fabricated" without specifying what it was, and ask some irrelevant question about "time" without specifying what you meant by it or what your question had to do with our discussion:

The effect is indistinguishable from the rules of SR. That's all the distinction means. It's not even absolute. It just means the ether's state of motion hasn't been detected yet, and it doesn't have to be detected for the ether to exist. I'm not going to deny that this is a bit of a stretch. An invisible ether sounds like IPUs or monsters under the bed. Although apparently the observed combination of time dilation and length contraction minimizes some relevant action, so maybe that could explain why they're so closely coordinated. The ether is just an attempt to make sense of frame-independent time dilation, because none of the answers from SR make sense to me. Quantum wave functions represent real physical phenomena, and their time evolution is a physical process. LET and SR were developed before QM, so I tack that on as a sort of "neo-LET". I do believe there's such a thing as universal time, and I think it's required in LET for time dilation to be a real effect. As for what time itself ultimately is, as I mentioned earlier, that may be too hard of a question for science to answer. I leave it as a question for the Creator and limit myself to thinking about physical processes.

No. To an observer viewing the glass from directly above, the rim is a circle and there is no ellipse. Observers will agree on the geometry of light rays reaching your eyes and creating elliptical images on your retinas, but that's not the rim of the glass itself or the surface of any liquid inside the glass. It's just your perception.