# It from Bit and Antibit

*“The appearance of a definite position of an electron during an observation is a creation outside the laws of nature” *Wolfgang Pauli [1]

Negative probabilities arose from Eugene Wigner’s calculations when he decided to correct (successfully) classical thermodynamics with the help of quantum mechanics. [2]

Paul Dirac tried (successfully) to combine quantum mechanics with Einstein’s special theory of relativity as applied to an electron with a near luminal velocity. He simultaneously came across negative energy and negative probabilities. [3]

Just like in Wigner’s case, they arose from Dirac’s calculations using a function that he constructed. The physical interpretation of the obtained results had to be sought after.

The physical interpretation of negative energy was found quite quickly albeit it stunned most physicists — antimatter — specifically an antielectron. Fortunately for Dirac, soon after his purely theoretical discovery, the existence of an antielectron, which was then called a positron, was confirmed experimentally.

The fate of the physical interpretation of negative probabilities was not so fortunate. Until now, the most common point of view is that they serve for the convenience of performing calculations and have no physical meaning. [4]

I had not yet finished reading Dirac’s article, where he described all this, but I had already asked myself: *Can an antibit exist?*

It turned out that this word is often found in the names of various means for fighting insects and the consequences of their bites. Perhaps, it is found somewhere in relation to information theory, but I did not get it on the first try.

Although, the *antibit* should look extremely simple. If a bit can take the values 0 or 1, then the *antibit* takes the values 0 or -1, respectively. If 1 is “yes” and 0 is “no”, then -1 in this case is “not yes” or, more precisely, “neither yes nor no”. The poor Schrödinger’s cat, tortured almost to death by science popularizers, immediately involuntarily comes to mind. Well, and, of course, the square root of -1 is an imaginary number *i*, with which Schrödinger’s equation of the wave function begins.

“Neither yes nor no” in this case includes all other values, except for the definite “yes” and “no”. It seems to me that *antiknowledge* should look like this. John Wheeler partially answered the question of what arises during the annihilation of knowledge and *antiknowledge*: “It from bit”. [4]

The full answer, in all likelihood, should sound like: “*It from bit and antibit*”. It is surprising that a lot of technical details, like Pauli’s exclusion principle, can be borrowed for defining a bit and an antibit relationship from the relationship of an electron and a positron, which is quite thoroughly investigated…

# References:

- Zeh, H.-Dieter. The Wave Function: It or Bit? Science and Ultimate Reality, J.D. Barrow, P.C.W. Davies, and C.L. Harper Jr., edts. (Cambridge University Press, 2004), pp. 103–120
- Wigner, E. On the Quantum Correction For Thermodynamic Equilibrium. Phys. Rev. 40, 749 — Published 1 June 1932
- Dirac, P. A. M. Bakerian Lecture. The Physical Interpretation of Quantum Mechanics.
*Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences*, vol. 180, no. 980, 1942, pp. 1–40.*JSTOR*, http://www.jstor.org/stable/97777. Accessed 4 Sept. 2024. - Feynman, Richard P . Negative probability. Quantum implications: essays in honour of David Bohm, pages 235–248, 1987.
- Wheeler, John Archibald. Information, Physics, Quantum: The Search for Links. In Wheeler John Archibald (ed.), Proceedings III International Symposium on Foundations of Quantum Mechanics. pp. 354–358 (1989)