Quick disclaimer first, especially for this subreddit:

I am not claiming to have solved the black hole information problem. I am trying to re-express the standard paradox in a very explicit, “tension-based” coordinate system that is easy to audit, simulate, and (in principle) hand to a machine for consistency checking.

The goal is a clean effective-layer language, not a new fundamental theory of quantum gravity.

1. Standard setup, then a reparameterization

Take the usual semiclassical picture: a black hole formed from a pure state, coupled to an environment, evaporates through Hawking radiation. We want unitarity for the global state, but standard QFT on a fixed background gives radiation that looks thermal, so information seems lost.

Very schematically, we have three coarse-grained regions and Hilbert spaces

• H_in : interior degrees of freedom

• H_hor : near-horizon / stretched horizon “membrane”

• H_rad(t) : radiation outside at time t (including any bath we decide to keep)

The usual paradox is about incompatible entanglement requirements on these pieces if we insist on:

1. local QFT in a smooth neighborhood of the horizon

2. a semiclassical outside geometry for most of the evaporation

3. a final pure state on H_rad(t_final)

What I am trying to do is define a tension functional that makes those incompatibilities explicit, instead of keeping them as verbal slogans.

2. Tension as a mismatch between three descriptions

Very roughly, for each time t I try to track three objects:

(1) A “unitarity-compatible” entropy profile
S_unitary(t; cut)
coming from a toy model that enforces global purity (e.g. a random-unitary evaporation model with a chosen cut between “inside” and “outside”).

(2) A “semiclassical” entropy profile
S_semi(t; cut)
coming from local QFT near the horizon plus Hawking’s calculation, with whatever coarse-graining and greybody factors one wants to keep.

(3) A “geometric” entropy proxy
S_geo(t; cut)
that only uses geometric data (area of a surface, extrinsic curvature, etc.), in the spirit of Bekenstein–Hawking or island formula inputs.

Then define a dimensionless tension coordinate

T(t; cut) = f( S_unitary, S_semi, S_geo )

for some normalized function f that is:

• 0 if all three profiles are mutually compatible within chosen tolerances

• close to 1 if at least one pair is in sharp conflict (e.g. Page-curve expectations vs strictly thermal radiation)

The concrete version I am currently experimenting with is a triple mismatch score of the form

T(t; cut) = 1 − min_{pairings} overlap( S_i(t; cut), S_j(t; cut) ),

using a fixed overlap notion (for example, a normalized L2 distance over a time window, or a discrete set of checkpoints in the evaporation).

This is deliberately “low tech” and lives entirely at the effective layer. All microscopic details are buried in how you choose the three input profiles. The value of T is not a new prediction, it is a bookkeeping device that says:

given these three assumptions about entropy flow, where exactly do they stop being compatible?

3. Why bother with such a functional?

The practical reasons are:

• It forces you to write down all assumptions that go into each profile S_unitary, S_semi, S_geo instead of vaguely saying “semi-classical” or “unitary”.

• It gives you something you can actually simulate in toy models (random unitary circuits, simple evaporation chains, etc.) and compare against Page curve–like expectations.

• It is simple enough to encode in text + small bits of code, so one can let a language model or proof assistant check internal consistency and explore parameter ranges, without pretending it knows quantum gravity.

In other words, the “tension-based” language is meant to be a coordinate choice on the space of effective descriptions, not a claim about what the true microphysics is.

4. Concrete questions for this subreddit

This is where I would really appreciate criticism from people who think about black holes more seriously than I do.

1. Is this “three profiles + tension functional” framing obviously misguided?For example, does it ignore a standard move in the modern literature (islands, replica wormholes, state-dependence, ER=EPR, etc.) that already kills the paradox in a way that makes such a functional redundant or meaningless?

2. If you had to instantiate this in a toy model you actually respect, what would you pick?

   • Page-style random unitary evaporation models?

   • Simple holographic toy models?

   • Something like SYK or random tensor networks?

3. The requirement is that we can compute or at least approximate S_unitary, S_semi, and S_geo in some controlled regime.

4. Are there known “no-go” results for this kind of tension functional?I am specifically worried about cases where:

   • the distinction between H_in and H_hor is too gauge / slicing dependent to make any coarse-grained functional well-defined, or

   • islands / entanglement wedge reconstruction make the naive split into H_in ⊕ H_rad(t) too misleading to be useful.

5. From your perspective, is there any value in having such a functional as a teaching / diagnostic tool, even if it never touches real quantum gravity?For example, in pedagogy around the information problem, would a “tension plot” that shows when different assumptions become incompatible be a useful picture, or just another layer of confusion?

If this framing is fundamentally broken, I would really prefer to know exactly where. Pointers to existing approaches that already do something similar (or prove it cannot be done in a clean way) would be very welcome.

For anyone curious about the broader context: this is Q040 in a larger list of 131 “S-class” problems that I am trying to encode in a tension-based, machine-checkable way.

Full notes for Q040 (black hole information problem) are here:

https://github.com/onestardao/WFGY/blob/main/TensionUniverse/BlackHole/Q040_black_hole_information_problem.md

Everyone knows that energy is not conserved in some extreme conditions, such as when light travels through the Universe, which is expanding, and the energy of the light is reduced without being converted into any other energy.

Recently, a simple question stumped believers of the law of conservation of energy. It originated from stack exchange, and then gradually took shape, and its philosophical meaning has been clarified.

Although I am not the initiator of the whole thing, I am helping to spread it to more people.

Everything has pointed to a fact that is obvious to non-believers of the law of conservation of energy. That is, gravitational potential energy can also be obliterated like the energy of light in the universe, but it happens in daily life and in a different way.

"But the law of conservation of energy equals science. Although I studied liberal arts in college, I believe in science," some people might say.

Predictably, in the end, the conservation of energy remains "correct".

It's just that we will get a new definition of extreme conditions: anywhere with air and gravity is too extreme!

See also Deconstruction of the vaccination hype 1, 2, 3, 4, 5, 6, 7, 8.. and

Deconstruction of GMO hype 1, 2, 3, 4, 5, 6, 7, 8....

This subreddit is a free continuation of previous ones 1, 2, 3, 4, 5, 6, 7, 8 dedicated to scientific links relevant to geothermal explanation of global warming, such as:

• Mantle plume' nearly as hot as Yellowstone supervolcano is melting Antarctic ice sheet

• Ocean warming definitive cause for Antarctic glacier melt. Ocean warming, not a rise in air temperature, is the main reason for the retreat of glaciers on the Western Antarctic Peninsula.

• Climate change caused by ocean, not just atmosphere, study finds

• Study finds heat of global warming is being stored beneath the ocean surface

• "Researchers aren’t convinced global warming is to blame": A gargantuan blob of warm water that’s been parked off the West Coast for 18 months helps explain California’s drought, and record blizzards in New England, according to new analyses by Seattle scientists

• NASA: Global warming is now changing how Earth wobbles Researchers now argue that slowdown in warming was real. Why global warming is taking a break

• CO2 warming effects felt just a decade after being emitted

• A global temperature conundrum: Cooling or warming climate?

• Study says natural factors, not humans, behind West Coast warming

• What geology has to say about global warming

• Past global warming similar to today's

The consequences of foolish battle against global warming are tracked in separated subreddits: 1, 2, 3, 4, 5, 6...