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I think it is best to just keep the situation fully classic, and consider only physical clocks to begin with, rather than wave functions. The question of evolution operators in RQM is complex and very non-trivial, and does little to illuminate this underlying question. Time dilation is a relationship between reference frames, and not something that physically “happens” to a single clock. Asking for a mechanism that “slows down” some clock is thus meaningless - clocks always tick at the same rate within their own frames. So the correct question would be why inertial frames are related via hyperbolic rotations in spacetime - that’s a very valid question, but it isn’t one that any of our present theories can answer. So to make a long story short, we don’t have an explanation of why this happens, only a description of it. That’s not the same thing at all. The length of a world line between given events in Minkowski spacetime is defined to be equivalent to the proper time of a clock travelling between these events that traces out that world line. In other words, it’s simply the total elapsed time that’s physically measured on a clock that travels along a specific spatial path between events. Intuitiveness is not a necessary condition for a mathematical model to be valid and useful. It just needs to be internally self-consistent, and produce results that can be verified using the scientific method. I think you would agree that SR does this quite well. Beside, something being intuitive (or not) is a very subjective measure - many things I find intuitive might appear otherwise to you, and vice versa. I would, by and large, agree with you - though I wouldn’t put into such strong terms. I just think many depictions of physical concepts get the differences between what is an explanation and what is a description muddled up, especially within pop-sci publications. We do not yet know the underlying mechanism of why spacetime is what it is, but we do have an excellent description of its features. To fully understand why spacetime gives rise to the phenomenology we see, we’d have to figure out first how spacetime itself comes to be, and if it can be broken down further into more fundamental concepts. Such attempts are under way, but at present they are just ideas and conjectures. I disagree. Physics makes models of the world around us, but not all of these models purport to be a fundamental explanation in ontological terms. As such, SR is a very good model that is in excellent agreement with experiment and observation. It’s just important to not confuse a model with an (ontological) explanation, because they are not the same.

The answer is “yes” If you measure the particle states and they do not have the expected correlation, you know there had been a prior interaction. This is the idea behind quantum key encryption. If there was no prior interaction, you can infer that the state is undetermined. You can choose the correlation. e.g. photons with the same polarization state or orthogonal polarization states. You can’t choose the state of one particle, since the individual states are undetermined.

What you're suggesting is measuring without interaction or measuring counterfactuals. It's better to deal with it for one particle in the double-slit experiment. You place a detector intercepting particles only in one of the branching paths. You fire your particles one by one and observe where they land in a faraway screen. You gather only the results that didn't do "click" at the detector. You do the statistics of all of those that didn't make the detector click. What's observed is that decoherence is broken. Counterfactual measurements, or interaction-free measurements --as they're also called-- break decoherence. This effect is so real that there is a bomb tester to know if a bomb would go off without actually making it go off: https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester Sorry for re-directing your question, but I think the essential aspect that you want to understand is contained here more simply than considering entanglement. I hope that has to do with your question at least. Look up for "interaction-free measurement," or perhaps, "counterfactual measurement." Also: https://en.wikipedia.org/wiki/Renninger_negative-result_experiment

Yes, that’s precisely my point. It is meaningless to speak of length contraction and time dilation “happening” to rulers or clocks. It’s always a relationship between two rulers, or two clocks. No. That would be like saying that a topographical map of your local area relies on an “aether” just because it uses a coordinate grid. To be sure, you can make that claim without affecting the usefulness of the map itself, if you so wish, but it doesn’t add anything to the information contained therein. Spacetime is just the same - it’s quite simply a map of events that allows you to determine separations and angles. There is no implication that we need to reify this into some kind of physical substance. This guy disagrees: Yes! Very important observation +1 This very lucidly demonstrates why a specific choice of coordinate system cannot carry physical relevance, so far as the form of physical laws is concerned.

It's easy to say "keep fighting" when you're not the pawn being used in another's game of chess...

Actually no. If we use τ = ict then we get an all positive metric. It is the squares of the space and time coordinate axes that have to be of opposite signs, not their first degrees.

The length of a world line between given events in Minkowski spacetime is defined to be equivalent to the proper time of a clock travelling between these events that traces out that world line. In other words, it’s simply the total elapsed time that’s physically measured on a clock that travels along a specific spatial path between event Excellent short answer +1 I would like to add to the second answer to the question "what does it mean....?" Minkowski imposes a cartesian coordinate system, which as Eddington pointed out a century ago, actually adds unneccessary mathematical structure. The same result could be achieved by a set of events and a set of the invariant intervals between them. This would form a network of linked events, with no cartesian structure superimposed. The sum of these invariants connecting any pair of events as a mathematical 'graph' (since this thread is partly about geometry, whch includes geometrical graph theory) then includes the shortest path. Ref Eddington The Mathematical Theory of Relativity pages 8 - 16, Cambridge 1923 (my ed 1954)

Durbin is right on with his urging Congress to pass a code of ethics for SCOTUS. Sorely needed. Leaks, failures to recuse themselves (this means you, Amy and Clarence), spousal influence and conflicts of interest... it's a cesspool atm.