The simplest way I could ever wrap my head around this, is to understand that everything travels through spacetime at the same speed. There is no travelling faster or slower, just crossing the graph at a different angle.
For any space-time path, you can consider the coordinate system as an observer traveling that path would see it, in which that observer would see itself traveling through time at a rate of one second per second. Geometrically, if you were to draw where on the path the observer's clock ticks, the distance between ticks as measured along that path is constant regardless of the path.
The speed of light limit says something different. It limits what paths a physical observer can take.
Condsider a 1+1 dimensional universe (or our 3+1 universe with a test particle moving along a single spatial dimension).
Pick a non accelerating observer to construct the 'stationary' coordinate system. Plot spatial coordinates along the horizontal axis, and the time coordinate as the vertical axis. Pick units such that the speed of light is 1.
A particle moving at a constant velocity will follow a straight line. If the line is vertical the particle is stationary. If the line is at an angle, the speed of the particle is the inverse of the slope of the line. The speed of light limitation says that this line cannot be shallower than 45 degrees.
In more analytic terms, the distance metric for our 2 dimensional spacetime is given by ds^2 = dt^2 - dx^2. The speed of light limitation says that ds^2 cannot be negative for any path a particle actually takes.
In other words all particles must must have at least half of their travel be along the time dimension.
So given what you've described, that means that forces applied to bodies need to have a time component equal in magnitude to the spatial components. Forces must always exist along that 45° line. The limit of the force required to continue to rotate that spacetime velocity out of the time component and into the spatial components goes to infinity as the vector approaches that 45° line.
The fact that forces are unidirectional is the unexplained part. If they weren't, then we could rotate that vector further, and start traveling backwards in time. Then wouldn't B expect to see the objects moving apart, while A sees them moving closer together?
To me, the impossibility of the disparity in observations is a consequence of, dependant on, no-FTL, not an explanation thereof.
Addendum: I don't understand why you said 45° instead of 90°. I thought objects traveling at the speed of light would experience infinite time dilation, and thus be observed as having 0 passage of time.
Think about what the diagram shows: Every (s[pace], t[ime]) coordinate pair on the spacetime diagram shows an observation of a particle. So in natural units, a photon's wordline is given by s=t or s=-t (traveling in one or the other direction). If you draw that, it's a 45° line. It also gives you the light cone of the observer at (0, 0).
A horizontal wordline would be something moving at infinite speed, not the speed of light, as it is observed at every place at the same time.
The rate the simulators transmit data are irrelevant to our timeframe (since we’re a part of the computation).
I believe it’s more like a centralized interpreter with decentralized (NP) evaluation strategies. The limit reflects the minumium size of a recursive expression.
Consciousness (at least in this world) can perchance then be understood as the artifact of a feedback loop constructed by a (meta-circular) interpreter that converts the topologies of molecules into qualia, which then makes adjustment to the reflective tower (with physiological-changes-in-brain&body as correspondence).
Time perception then is the same consequence that follows relativity ie a direct result of this speed limit that reflects the minumium size of a recursive expression (but concerning only the viscosity and turbulence of neurotransmitters in relative to eletric signals?)
There was a talk with lawrence krauss I think, where he explained that at galaxy scales, everything is distributed, there's not one reality but an infinity since no point in space can be aware of far points in the universe.
I also wonder if there would be ways to tweak C.
(I also highly recommend their book "There Is No Antimemetics Division" if you're at all interested in SCP Foundation)
We can parametrize (as in make parametric) arbitrary curves through spacetime however we like. Parametric representations of unique curves are generally nonunique.
Some of the infinite possible parametrizations of a chosen curve have useful properties, such as uniquely labelling every point on the curve with some monotonically ordering value and keeping the form of some set of equations reasonably simple.
For timelike geodesics, particularly in the Minkowski space of Special Relativity, proper time (being a Lorentz scalar) is a good option. However that is not true for all geodesics in Minkowski space (as you note, the proper time is everywhere zero on a null geodesic, and so a bad option), much less all curves through general curved spacetimes.
For null geodesics, following the logic of GP's question, we may wish to preserve the tangent vector under parallel transport; this requires the parametrization to be affine. Some gory details at https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics and a brief useful summary at https://www.reddit.com/r/AskPhysics/comments/9aenid/what_act...
As is noted below the comment directly pointed to by the second link, labelling a timelike geodesic with proper time is choosing one specific affine parametrization on that geodesic, and that this choice is driven by convenience.
One of the neat outcomes of affine parametrization is that we can take a point on an affinely-parameterized null geodesic and look at the derivative with respect to the affine parameter there, and define a momentum k^{\mu} = \dot X^{\mu}. In a Lorentzian spacetime, with curvature, we can compare the momentum at two different points on the null geodesic, giving us the gravitational redshift between those two points of the photon's wavelength equiv. frequency.
It stops being conserved if there's suddenly more or less energy inside the volume without the same amount crossing the boundary
Conservation of energy says that it is impossible for energy to enter this volume with that same amount of energy exiting the volume.
Consider what it would mean for this to be violated. For the sake of argument, assume that all particles must move forward in time by a non zero amount at all points along there path. Since the volume is bounded, any particle with an infinite path must eventually have a time coordinate beyond the largest time coordinated in the volume. Therefore, the particle must eventually exit the volume. If you were to work out the geometry more carefully, you could show with relative ease that the particle must exit the volume an equal number of times as it enters. If a particle were to enter the volume without exiting the volume, it would mean that said particle was destroyed within the volume. Similarly, if a particle were to exit the volume without entering, it would have to have been created within the volume. Both of these situations are possible if an interaction occurs within the volume, but the net energy of the particles leaving such an interaction, must be the same as the net energy of the particles entering the interaction.
Put another way, assume that all interactions obey the conservation of energy. If our original volume was V, we can construct a new volume V' from V by carving out sub volumes in which an interaction occurs. Since all such sub volumes obey the conservation of energy (by assumption), the net energy flow into and out of V' must be the same as for V. However, since no interactions occur withing V', all particles entering V' must exit V' an equal number of times, so the net energy flow of V' must be 0. Therefore the net flow of V must also be 0.
At the other end of the scale, you're travelling through space (or practically-C on a relativistic scale), and you're not experiencing time.
So the whole theory of zipping around space and coming home to find you've barely aged, is just spending more time at a higher "angle" than everyone else.
Traveling at the speed of light results in infinite time dilation. Which means that from the perspective of an outside observer, no time at all is passing inside the spaceship.
One way I like to think of this is the term 'sun-kissed'. From the perspective of the photon, the sun is actually giving you a kiss on a summer day.
I would like to see the map of the universe at different potential speeds (or thrusts). E.g. you choose a point in space nearby the sun. At thrust zero you only see hot sun everywhere, because there you go anyway. But at greater thrusts the sun turns into a circle and you start to see sections of the “sky” where you could land, given the thrust is constant. Some areas would be still black because of blackholes, orbits and event horizon. I always wanted that simulation but never found it. It would be much more interesting than just looking around via reversed photons flying into your eyes.
But then that sounds like I'm describing the speed of sound, no? Maybe I'm confusing two concepts.
Xkcd style explainer: When you have two things going at noticeably different time rates, you typically prepend "relativistic" [0] to all interactions. "Relativistic collision" sounds almost like "changes into huge amounts of plasma escaping from contact point".