MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Planck Zero (1992)
Stephen Baxter
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Contributed by Vijay Fafat

Baxter's hard-SF ideas are often quite stunning in their scope and creativity. "Planck Zero" is no exception to this. An advanced species of aliens - the Ghosts - have started conducting experiments inside a red giant star with primordial quark-plasma material ("quagma"). By controlling its inflation parameters, the Ghosts can control the basic constants like Planck's Constant inside the blob of quagma. The experiments have reached a stage where the baby universe has Planck's Constant at 10% of its value in our universe (all other constants have the same values as outside). An artificial mind constructed inside the bubble is able to calculate far faster and with significantly less amount of energy since the basic quantum is that much smaller. As the Ghost ambassador describes:

(quoted from Planck Zero)

"The capacity of any computing machine is limited by the Uncertainty Principle. The exploration of, say, high-value prime numbers has always been constrained by the fact that energy changes within a device must stay above the uncertainty level. With the reduction in Planck's constant, we can go further. Much further. For example, we have already managed to find a disproof of an ancient human hypothesis known as Goldbach's Conjecture"

A description of GC follows, with the location of the counterexample placed "in the region of 10 raised to the power of 80". The Ambassador goes on:

(quoted from Planck Zero)

"My friend, age old problems melt before our Planck machine. Already, several NP-type problems have....[...]. But we want to go further. We see this Planck-adjustment technique as a means of probing not just the very large but the infinite. Our device will verify some of the most important theorems of our mathematics - and yours - simply by direct inspection of cases all the way to infinity [as the Planck Constant inside the bubble is taken down to zero]"

I think the author has performed a sleight of hand here. While the rationale for Planck constant having a lower value in the bubble is plausibly mentioned as being controlled by the ratio of forces which arise when the primordial superforce decays through decoupling, this does not mean that the constant can ever take on a value of zero; indeed, for this to happen, one of the component forces has to go to zero, which should cause some nasty surprises in the quagma. Without the constant going to zero, his idea of getting to *realized* infinity by a counting process falls apart.

The author describes an interesting effect that occurs at the boundary of the quagma droplet. Due to the differential value of Planck's Constant, a photon falling into the bubble is split into two photons of the same frequency. One falls into the droplet with diminished energy due to lower Planck's Constant while the other photon gets reflected back, conserving the total energy of the original photon. When Planck's constant goes to zero inside, the surface boundary becomes a perfect mirror - no energy can fall inside it if energy is to be conserved. By the same token, nothing can emerge from the bubble . An exact, one-sided surface like the event horizon of a black hole (but without the "conventional" mechanism of concentrated mass)

I had two problems with this: I don't see why the falling photon's frequency is not simply blue-shifted to compensate for the change in the constant instead of a reflected photon being generated. Below a certain level of blue-shifting, the wavelength of the photon will exceed the size of the quagma sphere and such photons could be considered to be reflected completely, unable to fall inside. So only very energetic photons should be able to break through and the energy threshold increases as the Planck Constant differential increases. Nothing can fall in when the constant inside does go to zero. So how does the Ghost ship fall into it momentarily and how does it ever get out? Or have functioning human+ghost brains inside without energy differentials?

Anyhoo, the idea is brilliant, the ending of the story quite satisfying so a hat-tip to Mr. Baxter despite the quagma-quibbles.

Originally published in Asimov's Science Fiction Magazine 1992.

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Works Similar to Planck Zero
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Exception by Alex Kasman
  2. The Planck Dive by Greg Egan
  3. Planck Time by Michael Iwoleit
  4. Gödel's Sunflowers by Stephen Baxter
  5. Manifold: Time by Stephen Baxter
  6. Dark Integers by Greg Egan
  7. Distress by Greg Egan
  8. The Light of Other Days by Arthur C. Clarke / Stephen Baxter
  9. Diaspora by Greg Egan
  10. Schild's Ladder by Greg Egan
Ratings for Planck Zero:
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Mathematical Content:
3/5 (1 votes)
..
Literary Quality:
4/5 (1 votes)
..

Categories:
GenreScience Fiction,
MotifAliens, Proving Theorems,
TopicMathematical Physics, Logic/Set Theory,
MediumShort Stories,

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