ANALYTIC MESSAGES AND SUPERLUMINAL COMMUNICATION Louis M Houston

ANALYTIC MESSAGES AND SUPERLUMINAL COMMUNICATION Louis M. Houston The University of Louisiana at Lafayette, USA The Louisiana Accelerator Center

THIS WORK HAS BEEN PUBLISHED: THEORETICAL MATHEMATICS & APPLICATIONS, vol. 6, no. 1, 2016, 67 -73.

Superluminal Communication: sending information at faster-than-light speeds Consensus before this work: not possible! Speed of Light: c=3 x 10 8 m/s (Einstein’s Limit). Some Theories and Experiments include: Group Velocity >c Experiments. Evanescent Wave Coupling. Tachyons. Quantum Non-locality.

Greatest chance for superluminal communication: Quantum Entanglement. Theory that can simulate quantum entanglement: Coding Theory. Length of a message is k. Length of a codeword is n. A codeword is a function of a message:

Code Theory Example: Fractional Error Tolerance= Fraction of codeword error that can be tolerated with full message recovery:

ANALYTIC MESSAGE: message in which symbols are predictable from one another. EXAMPLE:

ANALYTIC MESSAGES create a greater fractional error tolerance: EXAMPLE:

THEOREM I. Message Speed due to ANALYTIC MESSAGES: THE MESSAGE SPEED IS DERIVED BY INTERPOLATING THE SPEEDS OF A COMPLETELY UNPREDICTABLE MESSAGE AND A COMPLETELY PREDICTABLE MESSAGE. PROOF:

The Information Content of a Message:

EXAMPLE OF AN ANALYTIC MESSAGE: After the entire message arrives, we discover more symbols than could have travelled at speed c.

COMPOSITION OF AN ANALYTIC MESSAGE: CAUSAL COMPONENT SUPERLUMINAL COMPONENT THE CAUSAL COMPONENT IS SENT BEFORE THE SUPERLUMINAL COMPONENT, BUT SINCE THE SUPERLUMINAL COMPONENT IS FASTER, THEY ARRIVE AT THE SAME TIME.

CODING ANALYTIC MESSAGES: TOTAL NUMBER OF MESSAGES: NUMBER OF EQUIVALENT MESSAGES WITH DISTINCT SYMBOLS: AN EQUIVALENT MESSAGE CONTAINS AN OCCURRENCE OF A floor(k/a)ELEMENT SET. HAVING EQUIVALENT MESSAGES DE-COUPLES THE CAUSAL AND SUPERLUMINAL COMPONENTS, ALLOWING THE SUPERLUMINAL COMPONENT TO CONTAIN INFORMATION.

SPECIFIC EXAMPLE: 4 -DIGIT SEQUENCES (MOD 10) WITH A BASE 10 ALPHABET: SPEED=4 c. 0123, 1234, 2345, 3456, 4567, 5678, 6789, 7890, 8901, 9012. TAG EQUIVALENT MESSAGES WITH A SPECIFIC DIGIT: (1 -ELEMENT OCCURRENCE OF A SET): TOTAL NUMBER OF MESSAGES=10. THERE ARE 4/10 EQUIVALENT MESSAGES.

INFORMATION CONTENT OF EXAMPLE:

DIGITAL ROOT NINE ANALYTIC MESSAGES successive sum of digits=9 EXAMPLE EQUIVALENT MESSAGES:

ANALYTIC MESSAGES explain quantum entanglement with correlated spins. Consider a system in which the total spin is zero. Let that condition be Let each possible spin be both a message and a symbol (i. e. composite system or two observers).

THE INFORMATION REDUCED TO CAUSAL SPEED: Ic PROPOSE THAT INFORMATION IS ESSENTIALLY MOMENTUM. THE INFORMATION IS GREATER THAN THAT OF A RANDOM MESSAGE. Þ ENERGY GETS CONVERTED INTO INFORMATION INCLUDING THE INFORMATION CONTENT OF b.

CONCLUSIONS: SUPERLUMINAL COMMUNICATION IS POSSIBLE. IT REQUIRES THAT A CAUSAL COMPONENT BE SENT BEFORE A SUPERLUMINAL COMPONENT. THE SUPERLUMINAL INFORMATION CONTENT IS ALWAYS LESS THAN THE CAUSAL INFORMATION CONTENT. WHEN THE ANALYTIC MESSAGE IS REDUCED TO CAUSAL SPEED, THE INFORMATION IS GREATER THAN THAT OF A RANDOM MESSAGE SO THAT ENERGY IS CONVERTED INTO INFORMATION.