Computation-Theoretic origin of Cosmic Inflation

1. Computation-Theoretic origin of Cosmic Inflation The secret behind Physical Laws By Hoi-Lai YU http://www.phys.sinica.edu.tw/~hoilai/

2. Bits to It 床前明月光，疑似地上霜 3 + 2 = ? Algorithms realization is material independent

3. Information and Entropy Minimum Free Energy needed to create a bit • F  kB  Log2 Or Entropy S  kB Log2 created for each bit Information in a message  amount of free energy to reset the memory bits to zero => Information Machines

4. Computing requires No Energy Irreversible computing needs energy Reversible computing consumes zero energy Reason: (1) Unitary transformation (2) Information known and can be recovered for all steps.

5. Maximum Computing Speed • Minimum time needed to jump from one Quantum state to another orthogonal state •   h/4E |0> =  Cn|En> • |t> =  Cn e -i (Ent / ) |En> Let S(t) = < 0 |t> =  |Cn | 2 e -i (Ent / ) Want to find smallest t such that S(t) = 0 Re(S) =  |Cn |2 Cos (Ent / ) •  |Cn | 2 ( 1 – 2/ (Ent /  + Sin(Ent /  ))) = 1- 2Et / ( ) => t  h/4E

6. Q: Why the world can be simulated? A: The world computes and processes information to determine its dynamical evolution or Physics is computable? Or approximately Computable Example(1) : Sun-Earth system from Information point of view Register update time between Sun and Earth  Distance • Area Law Kinematics, involves no dynamics, true in N-dimensional space Assume Computation time uniform everywhere (dynamical assumption) Elliptical and Third Law ( 1/r potential) Q: Would computability shed light on three body problem? i.e Only computability orbit are allowed

7. Q: Why the world can be simulated?(2) Example(2) Billiard Ball Model

8. Q: Why the world can be simulated?(3) The Billiard Ball Model = Fredkin Gate (control exchange gate) which is an universal gate (complete set, you can build everything out of it!)

9. The computing Universe The universe expands to gain computing power C =  c5 t4 /   ( t / tp)2 tp  5.3x10-44 sec, t  1017 sec => c = 10120 bits Gain in computing capacity in unit time is: C (t)  t / tp The number of registers S = s/kB Log2 = ( t / tp) 3/2 =1090 bits Problem: S grows faster then C(t)

10. What can the universe do? (1)Can’t increase computing power without violating Energy, Momentum,…conservation etc (2)C(t) only depends on average energy but not the form of energy (3)Vacuum energy won’t give entropy but give C(t) (5)Can distinguish vacuum and particle energy in Enistein Equation (4)Fix Hubble radius,C(t)=constant within universe’s Horizon (5)Inflate away entropy S by exponential expansion i.e. S = So e -3tH t 3/2 (6)And the Universe therefore recover her computing power

11. Predictions • Multiple inflations • Time need to communicate data from one side of Horizon to another = Inflation time => tf = ti Hi / Hf =10-33 x1024 /10-28 sec =1017 sec for the new inflation • Computational cost Cp = Const x S => tN = e 9tH/(6-4) to => tN = 3x1019 sec and =2.2 for tH=60 and to = 10-36 sec Consistent with present observation to see the universe began to accelerate at z=0.3

12. Summary (1)The universe is computing (2) The universe expands to get computing power (3) Multiple inflations, no big problem with accelerating universe (4) Universal computing gives serious constraints on Physical Laws i.e universe bears only limited total information but infinite time to decode => very special initial condition of early universe (5) Bits can be as or even more fundamental than it (Physical Laws) (6)  = 2.2 indicates that the universe is solving an easy problem