How Space and Time Could Be a Quantum Error-Correcting Code

Actually, you would not have much time to hear, but what you would hear (among the other effects) would be the sound “in reverse”(!)

https://physics.stackexchange.com/questions/14880/hearing-a-...

What does t=0 even mean? If we switch to some coordinates where t_0 \def t_now = 0 and t_past \gt 0, as with the scale factor in cosmology, we don't have a special time coordinate at t_past ~ 13.8 Gyr, so we can still think about the stress-energy (and the mechanisms that generate it) and the curvature it sources locally.

We can also think about things under time-reversal:

A comoving test observer in vacuum just free falls without end. Our test observer is a point with no charges (including "active" gravitational charge) and no internal structure, so it feels no tidal effects.

If we have two such observers starting at arbitrarily large space-like separation, they eventually they come close to each other and ultimately end up freely falling on the same trajectory, forever.

If we complicate the test observers from this no-repulsive-interaction picture, we develop pressure (represented in the stress-energy tensor, T^11 T^22 T^33). The local increase in pressure generates local curvature in response, and if the repulsive interaction is finite then eventually the two interacting test observers end up freely falling on the same trajectory, forever. The eventuality is because the background has infinite curvature, and that and the contribution from the self-gravitation of pressure wins out over any finite repulsion.

We can complicate test object interactions further by introducing: repulsive and attractive interactions; extended observers that are composites of these test observers; and even have these objects obey the statistics for bosons and fermions. Same-charged fermions in effect resist being pushed onto the same trajectory, but the resistance is almost certainly finite. Eventually some daughter product free-falls forever.

(We can see some of this in sufficiently massive objects that repulsion or exclusion is overcome, as in the cores of stars or in neutron stars, where internal pressure tends to dominate the local stress-energy.)

What the daughter products of squashed-together Standard Model particles might be is a matter of research, both in terrestrial laboratories and in astrophysical processes (including black holes). Conversely, mirroring the time-reversal thinking above, the Standard Model particles have to freeze out of something hotter and denser that exists at greater lookback time. (cf. electroweak symmetry breaking).

Worse, at a(t_0) ("now") there is a lot of dark matter, and we don't know the details of how that interacts with the Standard Model. Those details will almost certainly matter in the time-reversal picture above.

Consequently we don't know that repulsion/exclusion is finite. Perhaps some crystalline structure develops in the time-reverse picture (or in black holes), and things just accumulate in that. Or perhaps there is a sudden drop in pressure where daughter products fly away from some ultrastrong squashing-together (cf. pair-instability supernovae).

There are quite a few options. And of course the Robertson-Walker background is already just an approximation; the real metric is likely to be very different at high lookback times.

Finally, Carroll has a nice deck (and it's filled with references) at https://www.slideshare.net/seanmcarroll/what-we-dont-know-ab...

> what does an infinite density even mean?

In the previous reply I asked what does t=0 mean and under time-reversal marched some late time test objects towards a big-bang style singularity. Infinite density means that you can put any amount of matter down as initial values on a spacelike hypersurface at a time far from the singularity, evolve that surface in time towards the singularity, and eventually up at the singularity. The problem of the singularity is that a spacelike hypersurface there doesn't admit a sensible set of initial values, so you can't predict much about what comes out of the singularity when marching forward towards late times.

I also talked briefly about the pressure components of the stress-energy tensor.

Let's treat the stress-energy tensor as a 4x4 matrix describing the flux of i-momentum in the i-direction, and slice up spacetime into time-indexed 3-spaces. If we make a little 3d "cell" (being a little loose with terminology) then T^{00} encodes the amount of momentum sourced within the cell at t_{now} and staying within the cell at t_{immediately adjacent to now}.

Let's look at only one spatial dimension.

T^{11} encodes the amount of momentum originating to our left or right entering and leaving the cell to the left or right. Lets send rightward-going momentum into the cell from the left and mostly bounce out again to the left as leftward-going momentum, with some of the sent-in momentum sticking behind in the cell as energy (T^{00}) and some leaking out as rightward-going momentum to the next cell to the right. This is how pressure works, and shows how the stress-energy tensor can evolve as you squash things together. Momentum that is sent into a region (a cell being a sort of region) can stick around as energy. The question is, "how does it stick around"? Perhaps by increasing the frequency of the particle(s) occupying the cell.

Since T^00 usually dominates the stress-energy tensor T, and that in turn usually determines the Einstein tensor G, as more momentum-energy enters the cell without leaving, local curvature around the cell also increases. That in turn drives the split of momentum reflected back out of the cell, momentum retained within the cell, and momentum passed in another direction. This is essentially the root of the nonlinearity of the Einstein Field Equations.

The split of what energy-momentum reflects back out, flows right through, or remains within a cell depends essentially on paths of least resistance, and those depend on how the contents of the cell behave locally and also on the geometrical background. Grossly, momentum will tend to exit a cell in a downwards direction if it can, and downwards is in the direction of cells with greater energy (T^00).

At ever higher density around a cell, practically any kind of momentum entering the cell stays in the cell. As we move towards infinite density, all the "higher" (in a gravitational potential sense) cells eventually lose all of their energy (and any newly arriving momentum) in the direction of the "lowest" cell, even as we take the sizes of all cells to zero.

(For black holes rather than collapsing whole universes (or time-reversed expanding universes) only the cells inside the horizon are guaranteed to leak their entire energy and future momentum-energy towards the lowest cell.)

Unanswered questions: what quantum numbers are found in the lowest cell, especially as we shrink cell sizes? If you have a lowest infinitesimal cell holding all the sources of stress-energy, do quantum effects transfer momentum-energy from it to neighbouring higher infinitesimal cells? What quantum numbers escape the singularity? Can this happen hierarchically so as to form jets or other structures?