It's not so hard to imagine that the rules of relativity are imposed and that outside of that imposition, they don't exist or are discontinuous to some degree. Indeed, it doesn't even take any imagination if one considers the theories and research related to what I linked above.
So personally I'd dismiss the conclusion given its predication on this idea. To me, time not being local is the controversial position.
As if some not widely accepted recent papers without empirical verification are the ultimate source of truth in physics? All kinds of bizarro ideas are a dime a dozen in papers...
Well, specifically, proper-time intervals are path-local in General Relativity (GR). There is a unique coordinate-invariant proper-time interval between two points on a timelike worldline.
I think that extending that to "time is a localized phenomenon" is harder than it seems, notably because worldlines depend on the full solution of the Einstein Field Equations. In a Big Bang cosmology (with a hyperbolization of the EFEs and ignoring constraints and diffeomorphism freedom), it's pretty brave to deny a relationship between the early boundary and the values of the fields at any point p on the manifold given that the causal cone at p of M contains the Big Bang.
> effect that local gravitational force has on the passage of time
It's the metric that leads to Lorentzian observables between observers at different points in the manifold. The metric near bodies like Earth closely approximates that of Schwarzschild spacetime in the way it generates geodesics including the null geodesics (among others) carrying information from one observer to another. Effects like gravitational redshift arise from the fact that in spacetime more-curved paths are shorter than less-curved paths (as opposed to how curved paths are longer than straight paths through Euclidean space).
The metric's generation of geodesics is difficult to relate to a classical force or potential in general. Two objects in vacuum free-fall can be at different gravitational potential while feeling no force whatsoever; the one at higher potential ticks faster. It's a bit easier in near-Schwarzschild. Consider two atomic clocks falling from different altitudes[1] towards the same point on the (practically atmosphere-free) moon; almost all observers will agree that the higher clock runs faster than the lower clock until they are both smashed together on the surface. Yet if each clock is equipped with an vector accelerometer, both accelerometers will point nowhere in particular with a magnitude of zero from the start of their free-fall trajectory until collision with the moon's surface -- the first time force is reported by the accelerometers is when "lithobraking" starts.
However, properly considering gravitational potential as a 4-vector generally requires some choices which eat the redundancies in the Einstein Field Equations. In General Relativity one has only the metric and Christoffel symbols and tedious arguments about which mathematical objects correspond to a Newtonian notion of a gravitational field (answer: "it depends" or "none of them"). Gauge-fixing lets one set a "depends" condition such that one can recover a vector potential field and a scalar field strength at each point; this approach is taken very seriously in Fedosin's covariant theory of gravitation for instance.
> effect that local gravitational force has on passage of time
Even if one takes steps to model some aspects of the gravitational interaction as a force, the proper time interval of an object doesn't change with the force acting on it. But the frequencies, lengths and related quantities of an object at some distance does depend on the force the object feels compared to the force the observer feels. (Moreover, if observers are in vacuum free-fall then they will feel no force at all, and can only infer the gravitational interaction from either a deviation from a straight-line track on a choice of coordinates, or by comparing the ticking rates of their own wristwatch with the wristwatch of several observer at some distance -- from [Synge 1960] this would take a minimum of five freely-falling wristwatches in total).
Generally the complexities of setting down this kind of gauge-and-coordinate conditions leads relativists away from worrying about relating GR's mathematical objects and Newton's, and it's easier to say "gravitation is not a force" rather than "with some effort you can treat gravitation as a force in local coordinates and in a local gauge but you'll still find yourself returning to the Special Relativistic forms of physics equations because they genuinely are the simplest form and are always valid in the neighbourhood around a point on a geodesic".
> if one considers the theories and research related to what I linked above
General Relativity is in extremely precise accord with observation at many length scales and direct experiment within the solar system. Deviations from General Relativity that are different in the limit of the parameterized post-Newtonian formalism (which applies at solar system scales) are almost entirely ruled out. Although it is perfectly reasonable to consider General Relativity to be an emergent theory, the theory it emerges from is (a) unknown (b) unobvious and (c) extremely difficult to take guesses at. Indeed, your offer of 1310.4691 is wholly rooted in this: canonically quantized GR conflicts violently with observations and experiments, and the usual workaround is to do some condition-fixing (which your referenced paper does) and then to try to get around the pseudo-forces brought in to describe local physics (in models like Page-Wooter these pseudo-forces appear as constraints in the theory ([2], which your authors reference in their first sentence and several times thereafter). The paper you point to also notes that the proposed experiment cannot select among a number of theories including General Relativity (where the Hamiltonian itself is a constraint).
> To me, time not being local is the controversial position.
I dunno, we do appear to live in an observable universe which admits an obvious equatorial 3+1 slicing in which there are an awful lot of Eulerian and nearly-Eulerian observers. Is the hill to die on the alignment of one's "natural" choice of timelike axis with the metric expansion or the way you put down coordinates on that axis? And how do you square either of those choices with the initial value formalism?
- --
[1] This is implicitly fixing a gauge wherein the surface of the moon is special; this is analogous to having a set of tunable air-pressure gauges at a point at sea level and setting it to 0 there, then using the readings of the tuned pressure gauges in helicopters riding above one another over the 0 point in order to say things about the state of each helicopter. In particular, one would use the reading of the pressure gauge as the basis of a coordinate axis (e.g. in marking coordinates on the radial axis in spherical coordinates on the 0-calibration point, or on the z axis in a choice of Cartesian coordinates on the 0-calibration point).
[2] K. Kuchař, in G. Kunstatter, D. Vincent, and J. Williams (eds), Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, (Singapore, World Scientific, 1992).
Indeed, you can consider the universe as this thing which is maybe boundless and has so much stuff and might go on forever but for some reason you think it's any harder than realizing that the street may be infinite in space as well, by virtue of continuous subdivision. Before trying to dive in on any estimate of the smallest thing, do remember that smart people once thought atoms were the smallest thing, and then particles, and so on. And remember that the street itself, even just the stretch you're concerned about, is composed of a ludicrously large number of the "smallest" things we current are aware of.
If we let go of this idea that at our own size, things are just some number of things that we can reason about (since that's clearly false, do you reason about the billions of living organisms in your own body right now? Could you?) then we can start to realize that smaller or bigger, we're merely consider a continuum at different scales and it's perfectly reasonable for the human mind to do so, it does so every day all the time.
Understanding is just a psychological phenomena. Its your brains who choose what ideas they mark as 'understood'. Thus its under your control what you understand and what you are not.
Once beeing a drunk teenager I felt myself understaning all the things in the whole Universe. Its pretty hard I'd say, because I never felt like this thereafter. Though I didn't tried to repeat it. Probably alcohol is not the best fit for it, maybe there are some drugs that can make you to understand.
I believe that somewhere in the brain there is some special spot, and all you need to understand everything is to thrust an electrode in that spot.
If you live your brain as I do and prefer not to control your brains in possible harmful way, than (I'm pretty sure) if one get some special training on this he could come eventually to everything-understanding state of mind. Maybe it even allow to switch by volition between that state of mind and state of mind of Socrates, who used to claim that he understands nothing. I didn't try it myself because I'm not sure about arbitrarily control option, and generally prefer Socrates' way of thinking.
But if you don't like to cheat, there is honest way to start understanding a very large distances. In general mind mark as understood all the things it is used to. You may train yourself at imagining large objects through some sort of succession. You should do all sorts of mental work with those objects in your imagination -- moving them, rotating, colliding, flying by or through them... Try to use different and constant kind of objects for every order of magnitude -- it might be really helpful. It will take time, but its still possible.
https://soundcloud.com/martin-adams-387371255/sets/lost-in-t...
There is no physical barrier stopping you from moving in any direction, but due to the shape of the Earth you have reached the southernmost point.
It is likely the same with our universe, and its inherent morphology, too.
Do we?
> boundaries
There's one at the Big Bang. You can go through contortions to try to remove it (Hartle & Hawking's "no boundary proposal"; Carroll & Chen's "two-ways-to-de-Sitter from arbitrary initial surface") but so far attempts have come at the cost of introducing a lot more conceptual baggage.
> outside
"more of mostly the same" unless you think that one metre or one light year or two hundred million light years beyond the Hubble radius the universe is vastly different from the stars and galaxies we have around here. What could have happened to early galaxies that 200 million years ago were in principle observable from the Milky Way, such that they wouldn't now resemble the descendants of early galaxies that are 200 million light years closer to us?
My high school physics prof had the best answer to "What is beyond the universe?" --> "Surely if we ever find something outside of the universe, we will be smart enough to call that the universe too"
He was referencing the idea that universe contains everything by definition.
Universe is our local observable space-time with the earliest event we can detect being the big bang.
So if we observe something beyond what is currently observable, would that not become observable and thus part of the universe?
Transitivit would say yes. If A implies B and B implies C then A implies C. That is, if you can observe A and that implies B, then you can observe B. Which makes it observable, no?
For now we're stuck in our universe, we know it's expanding (in something, potentially). So we preemptively give the name "cosmos" to EVERYTHING. It's entirely possible that cosmos is equal to universe. But it's also possible there are other universes out there, or something entirely different.
But you would still have something just as remarkable.