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

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

3. 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.

4. 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:

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

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

7. ANALYTIC MESSAGES create a greater fractional error tolerance: EXAMPLE:

8. 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:

9. The Information Content of a Message:

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

12. 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.

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

14. SPECIFIC EXAMPLE:  4-DIGIT SEQUENCES (MOD 10) WITH A BASE 10 ALPHABET:  SPEED=4c.  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.

15. INFORMATION CONTENT OF EXAMPLE:

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

17. 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).

18. THE INFORMATION REDUCED TO CAUSAL SPEED: I c  PROPOSE THAT INFORMATION IS ESSENTIALLY MOMENTUM. THE INFORMATION IS GREATER THAN THAT OF A RANDOM MESSAGE.  ENERGY GETS CONVERTED INTO INFORMATION INCLUDING THE INFORMATION CONTENT OF .

19. 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.