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"We are all repositories for genetically-encoded information that we're all spreading back and forth amongst each other, all the time. We're just lousy with information."
- Neal Stephenson

Husk of an Atom  
  A negative universe substance.  

There is a lot of pseudoscience stuff going on here, but the story mentions P.A.M. Dirac and his idea that a vacuum is an infinite sea of particles with negative energy - the Dirac sea. The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, before its experimental discovery in 1932.

These ideas seem to be referenced in this story, making it the first science fiction story about antimatter. Maybe.

“This is the strangest atom that I have ever seen. You will notice the complete absence of a nucleus. It seems to be composed entirely of negative electrons..."

“In this atom the positive charge seems to have been annihilated by a negative electron and escaped as electromagnetic energy. You will notice the almost identical shading of the entire atom. There are no concentric rings. This, in other words, is an atom in a state of disintegration which still maintains its essential integrity, which has not flown apart.

“All of you gentlemen, I suppose, are familiar with the theories of P. A. M. Dirac, the young British physicist. Dirac holds that there is no such thing as a completely empty vacuum, that a perfect vacuum is simply a region of space where all that exists is composed of negatively charged electrons. He holds that matter as we know it is simply a hole or vent in this sea of negative energy. In other words, only negative energy is real, basic.

"“We seem to have here the shell or husk of an atom, the maintenance of a kind of atomic pattern after the positive energy substance has been blasted out of existence. And this shell may represent basic reality..."

“It tore through the Earth annihilating matter wherever it spattered, or rather, knocking the protons from atoms, leaving a kind of seething vacuum, a yawning void in the Earth of negative universe substance.

“The small camera attached to the photoelectric eye contained six plates. Each plate came out of the developing tank the color of ink — no image, nothing. We do not know how far down the glowing matter went. But the failure of the eye to function indicates that the roaring blot is a true vacuum. Matter as we know it has simply been annihilated for hundreds, perhaps thousands of miles — perhaps to the Earth’s core."

From The Roaring Blot, by Frank Belknap Long, Jr..
Published by Astounding Science Fiction in 1936
Additional resources -

The story mentions a "cinder sun" made of regular matter, that approached our sun and tore stuff out of its core, which has who-knows-what exotic properties. Maybe even antimatter?

The positron is actually used in a 1934 story by Nat Schachner; see positron beam from The Great Thirst.

Another mention of antimatter is found in Minus Planet, a 1937 story by John D. Clark, Ph.D.; see the entry for antron. See also contraterrene matter from Collision Orbit (1942) by Jack Williamson.

Thanks to Mr. Beam Jockey for pointing this story out.

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Additional resources:
  More Ideas and Technology from The Roaring Blot
  More Ideas and Technology by Frank Belknap Long, Jr.
  Tech news articles related to The Roaring Blot
  Tech news articles related to works by Frank Belknap Long, Jr.

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