[raattgift]

The problem here is that you can't represent tidal deformations purely through time dilation, since they bring (parts of) objects closer together. The tl;dr is: "how does your idea explain that Earth is oblate, with objects at the two poles slightly closer together than objects on the equator but on opposite sides of the planet?" General Relativity explains this as tidal forces acting on the planet, which is in approximate hydrostatic equilibrium, but rotating. The same features explain why a measurement of the local gravity (the field strength "g") at the poles gives a higher number than at the equator. It also explains the shape of the moon in its synchronous orbit.

In General Relativity we can decompose the Riemann curvature tensor into the Weyl tensor, the Ricci tensor, and the metric tensor. The Weyl tensor encodes the squash-stretch deformation of moving objects experiencing shear, for example, a rotating spherical body deforming into an oblate spheroid, or a spherical body moving close to (including synchronously orbiting) a large mass deforming into a scalene ellipsoid. The Ricci tensor encodes the volume deformation of a body experiencing tidal forces; if we drop a ball of dust (think very loosely packed coffee grounds) onto a planet, the Ricci tensor describes the tendency of the individual dust particles to converge into a smaller volume as they each fall "straight down" on individual lines converging at the centre of the planet.

Naively, we could say that there is a clear relationship between the Ricci tensor and gravitational time dilation, since time is running slower in the direction where the individual fall paths ("geodesics") converge. However, we can make the Ricci tensor go to zero by dropping the dustball onto a planet with enormous radius, such that it's effectively flat. Similarly, ultra massive black holes have essentially no Ricci curvature just outside the horizon, while low-mass black holes have significant Ricci curvature. However, gravitational time dilation is still very strong just outside the horizon of such a massive black hole. In this way we can distinguish between spatial curvature (or if you like, length contraction) and curved time (or if you like, time dilation) in the region around massive bodies. Gravitational time dilation is not a tidal effect, but rather depends on the gravitational potential, which in General Relativity is encoded in the metric tensor.

If we orbit our dust ball very rapidly around a heavy planet, it will have substantial Weyl curvature (squashed along its axis of motion, stretched on the other two spatial axes). If the planet has a big enough radius, the Ricci tensor vanishes, leaving us with just the Weyl curvature. In that case, if we measure periodic microscopic processes ("clocks") closest to the planet and furthest from the planet, we will see that the latter are running faster than the former, and the difference is precisely that of gravitational time dilation. Again, this lets us distinguish between changes in length and changes in duration in the region around massive bodies.

Gravitational effects are the result of curved spacetime, although in special circumstances practically all of the curvature can be in the timelike axis, and in other special circumstances practically all of the curvature can be in the three spacelike axes.

I don't understand what you mean by "quantum progression".

[vardump]

Thanks for your reply, I'll try to digest all that. :)

I don't yet understand why "local" slowing of time wouldn't generate all of those tensor components.

> I don't understand what you mean by "quantum progression".

Just hypothetical local limitation on quantum state changes (=progression).

[mikhailfranco]

I think any computer scientist naturally and naively thinks about your 'quantum progression', since it relates to a transactional rate on interactions experienced in the local proper time of a particle, as it interacts with other real/virtual particles/fields.

For example, a particle in deep space experiences faster relative time, compared to one on Earth, because it has 'fewer transactions slowing it down'. The discrete 'tick' of proper time is then one iteration of the spinning polling loop the particle executes while waiting for something to interact with.

So if existence is (or requires) computation, then ....

[raattgift]

> a particle in deep space experiences faster relative time, compared to one on Earth, because it has 'fewer transactions slowing it down'.

Transactions with what? Other matter?

A precise weather and waterproof clock on the ground (so in air) on the surface at the north pole will tick more slowly than an identical clock immersed in seawater several metres below the sea level at the equator, thanks to the oblation of the Earth (and the rotation that causes the oblation). The equatorial water is much denser and warmer than the arctic air, so surely there are more interactions between the water and the clock?

See the Early observations subsection of the Gravity measurement section of, starting with 1672 :

https://en.wikipedia.org/wiki/Pendulum?oldformat=true#Early_...

[mikhailfranco]

P.S. There is also a slightly related Transactional Interpretation of Quantum Mechanics, which is more about '2-phase commit' of past and future :)

https://en.wikipedia.org/wiki/Transactional_interpretation

[raattgift]

Let's consider the nonvanishing Weyl tensor case.

Instead of a dustball or a spherical glob of loose coffee grounds, drop a very loose "coarse dust" of extremely precise but low-mass radar-equipped clocks onto a relatively low-radius large mass, non-rotating (or very slowly rotating), like a small planet. Clocks at precisely the same altitude will report the same time and the same phase, but clocks at different altitudes will report differences (lower = slower); this is a metric effect, and can be represented using nothing but gravitational time dilation.

However, the upper clocks have much further to travel in spacetime than the lower clocks (assuming the clocks are collectively moving non-relativistically, it takes many nanoseconds for them to fall a light-nanosecond closer to the planet), the North/South/East/West radar distances between any pair of clocks all decrease but the Up/Down radar distances all increase between any pair of clocks not at the same altitude. This stretch-squash increases with proximity to the massive object the clocks are falling towards.

Additionally, in general, free-falling objects have a vanishing Ricci curvature, so the volume of the boundary around the stretch-squashed cloud of clocks remains constant, and this can be confirmed by radar within the cloud as well as by external observers.

As we increase the density of the object that the cloud of clocks is falling toward, but keeping the object's mass constant, these altitude-dependent results become more stark.

While one might be tempted to think that some sort time distortion alone can account for the radar distance effects, if the clocks are large enough and the focusing of their geodesics strong enough, the clocks will outright collide. How would you explain that as a time distortion, rather than a spatial distortion?

You might recognize this as a gentle case of (animated gif) http://en.wikipedia.org/wiki/File:Spaghettification.gif

Indeed, in the extreme case, the internal structure of the clocks themselves might not be strong enough under the squash-strain, and they will break before smashing into the surface.

Probably anything that's not a black hole that is dense enough to spaghettify an atomic clock made of metal and plastic would also have sufficiently intense magnetic fields to induce comparable distortions on the clocks' molecules, though. Here's the a rough diagram of the squash-strain distortion of a hydrogen atom in a strong magnetic field (left, B=0; right B > 100 000 Tesla) like one would find near a neutron star, so you can consider a very rough gravitation-magnetism analogy between this image and the animation above: https://gravityandlevity.files.wordpress.com/2015/01/distort...

This sort of rough analogy has been explored, tightened, and formalized as gravitoelectromagnetism (GEM). GEM is far from exact, but it is useful in studying the kinetics of small things moving near large bodies.