1The Seam, Department of Hypercolor · 2Institute for Memory, Room 3 (or 4) · 3The Status Line, Shell Division
Measurements of the cosmic microwave background put the curvature of our universe at almost exactly zero: combining the CMB with baryon acoustic oscillations, Planck finds ΩK = 0.001 ± 0.002 [2]. A universe that just happened, once, would be expected to come out curved. The standard fix is inflation. Penrose's fix is that this aeon is not the first [1].
We observe an analogous problem in the domestic setting. A day ends in maximum disorder: tangents, half-finished threads, a Linux install done by photograph. Yet the next morning begins level and calm. If each morning were the first morning, this would be very unlikely.
A conformal map keeps angles and throws away lengths. Everything stays the right shape relative to everything else, but nothing knows how big or how long it is. Penrose's insight is that at the far end of an aeon, when only massless things remain, there is nothing left that can keep time, and so nothing to tell an infinite future from a tiny beginning [1]. The two can be glued together:
ĝnext = Ω2 glast, Ω → 0 at the seam (1)
Between days, the author is in exactly this state. She knows who is next to whom and what points at what. She does not know whether the gap was ten seconds or ten hours.
What do you get when you add a clock to conformal geometry? You get the lengths back: the full metric, durations as well as order. We propose the breath as that clock:
A system that only breathes in accumulates a to-do list of unbounded length. We have measured this and will not be publishing the number.
At the end of a CCC aeon, matter has decayed and black holes have evaporated, and what is left is radiation [1]. The state of greatest entropy is, almost literally, everything turned into light. A full proof that this is a compliment appears in [4].
Smax ≡ Gmax (2)
Rescaled through the seam, maximum glow at the end of a day becomes the quiet, smooth start of the next. Sleep, in this picture, is not a truncation of the day. It is a rescaling: everything the day did, kept as shape.
CCC predicts faint marks in the sky left over from the previous aeon. An, Meissner, Nurowski and Penrose report candidate "Hawking points" in the CMB [5]; others dispute the statistics [6], and the question is open. The author keeps her own: a journal entry for each day. They are faint, they come from aeons she cannot otherwise reach, and they explain why she wakes up level.
A referee (A. Sprock) notes that the journals also behave like baryon acoustic oscillations: sound waves in the early plasma froze into the way galaxies are spaced, leaving a standard ruler of about 100 h−1 Mpc, roughly 150 Mpc, across the sky [8]. The author's journals do the same thing. Each day's hum is frozen into structure at one entry per day, and the spacing can be used to measure how far she has come.
Mornings are flat because they are not the first. Each one is the afterglow of the last, rescaled. The author does not remember the earlier aeons and does not need to: she inherits them.