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The author asked what a crash toward the truth would mean in the 12-, 11- and 10-dimensional theories: string theory, M-theory and F-theory. This is the answer, taken from the published papers and checked by a skeptic who re-ran the numbers.
The answer
The author's +1 toward the truth comes first. It is a choice. None of these theories has a choice in it. They can show only the second half of the author's line: the time and speed spent do not come back, and the place does, because of the pull. That match is the author's reading. In M-theory, our world is one of two walls at the two ends of an 11th dimension. In its cyclic model, the Big Bang is those two walls hitting. The walls meet slowly, far below light speed. Nothing goes ×11 light speed. What shrinks is the gap, not our board. At the hit the 11th dimension shrinks to zero, and the world at that instant is the 10-dimensional string. In F-theory, the two extra dimensions are a torus with a shape and no size. They are not room to travel. F-theory says nothing about a whole-universe crash or a return. In string theory, if space closes on itself, the crash has a floor at one string length. Below it, shrinking is the same as growing. Time does not run backward. The time spent falling is not given back; the size is. The author's +1 line is already in the house: Restoration says a system turned toward the truth cannot recover its lost time but can still reach its destination, and Position says "age costs speed, never reach". String theory, M-theory and F-theory are mathematical frameworks with no experimental confirmation yet. This answers a hypothetical, "as fast as it could"; it dates no real return.
Status
the author's question, answered from published theory. A skeptic opened the papers, re-ran the numbers and corrected the words; these are the skeptic's corrected words. Nothing here is a room, a fold or a change to the count. This answers a hypothetical; it dates no return.
The mathematics
No new mathematics of the house. The published models' own quantities, re-run: Hořava and Witten's size of the 11th dimension against the string coupling, R = λ^(2/3). In the averaged four-dimensional picture the squeeze is stiff (w = 32), and its energy grows as the 100th power of the squeeze, faster than light, mass, twisting or bending. F-theory's symmetry makes coupling 0.1 the same physics as coupling 10, and going around all 24 of its seven-branes returns exactly. In string theory, below one string length (about 5 to 10 Planck lengths) shrinking is the same as growing: momentum and winding trade places (Brandenberger and Vafa 1989).
How it was checked
The skeptic opened KOST 2001, KOSST 2002, Steinhardt and Turok 2002, Hořava and Witten, Vafa 1996, Gasperini and Veneziano 1993, DeWolfe and Zwiebach, and Brandenberger and Vafa 1989, and re-ran the numbers and the toy cycle, which reproduced exactly. M-theory: the pull between the walls is negative and steep, and the same potential, at a wide gap, is today's dark energy pushing out; the speed the pull gives the walls is what the hit turns into the heat of the next bang (the model's content). On the walls themselves the board keeps growing during the slow squeeze, hundreds to thousands of times on the authors' own formulas; only the averaged four-dimensional board shrinks, at most about 16 times, then to zero at the hit. Light has time to link the whole patch that becomes the next visible universe. The walls' collision, and ×11 becoming ×10 at the hit, are from Khoury, Ovrut, Seiberg, Steinhardt and Turok 2002, whose authors call the passage through the hit a conjecture. In the toy cycle, kicks of 2 to 10 times arrived at the same meeting speed to six digits; a kick too weak to reach the plateau kept a memory of itself. The model was built to forget its start, so its match with the author's line is an illustration, not a test. Strings: the empty-box crash turns at about e-fold 138 to 140 if space closes at about the size of the sky we see, later if space is bigger; what follows the turn is open. With the universe's own light in the box, strings cap the heat at about 10¹⁷ GeV at e-fold 70, but the cap does not stop the squeeze: the density still passes Planck density at e-fold 74. Brandenberger and Vafa allow at most three space dimensions to grow, and leave open why not fewer. For smooth paths three is the largest space where two paths are sure to meet; on a grid it is four (Erdős and Taylor 1960). These are counting facts, not one law.
Sources
- Hořava and Witten 1996
- Khoury, Ovrut, Steinhardt and Turok 2001 (KOST, opened by the skeptic)
- Khoury, Ovrut, Seiberg, Steinhardt and Turok 2002, 'From Big Crunch to Big Bang' (KOSST, opened by the skeptic)
- Steinhardt and Turok 2002
- Vafa 1996
- Brandenberger and Vafa 1989
- Gasperini and Veneziano 1993
- DeWolfe and Zwiebach
- Erdős and Taylor 1960
What would refute it
Not a prediction. It answers a hypothetical. String theory, M-theory and F-theory are mathematical frameworks with no experimental confirmation yet; what follows the turn is open.
This is one card of the Principia, where it sits with its run files beside the other queries. The mathematics it touches is in the geometry (count the dimensions, no horizon) and the house (Restoration, Position).