Is Reality An Error Correcting Code?
Transcript of Is Reality An Error Correcting Code?
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Is Reality An Error Correcting Code?
Christopher RoseRutgers University, WINLAB
S. James GatesUniversity of Maryland
February 2013
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1 Is Reality an Error Correcting Code
MODEST PHYSICIST
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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2 Is Reality an Error Correcting Code
Credit Where Credit Is Due
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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3 Is Reality an Error Correcting Code
(even more) MODEST STRING THEORIST
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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4 Is Reality an Error Correcting Code
Or to Some ...
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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5 Is Reality an Error Correcting Code
Communication Theorist
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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6 Is Reality an Error Correcting Code
Popular Culture Doesn’t Help
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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7 Is Reality an Error Correcting Code
Tricia Rose
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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8 Is Reality an Error Correcting Code
Stephanie Bell-Rose
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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9 Is Reality an Error Correcting Code
S. James Gates
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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10 Is Reality an Error Correcting Code
Can’t Beat ’Em?
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10 Is Reality an Error Correcting Code
Can’t Beat ’Em?
DEMYSTIFY ’EM!
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10 Is Reality an Error Correcting Code
Can’t Beat ’Em?
DEMYSTIFY ’EM!(show physics looks just like comm theory)
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10 Is Reality an Error Correcting Code
Can’t Beat ’Em?
DEMYSTIFY ’EM!(show physics looks just like comm theory)
SUBSUME ’EM!!
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10 Is Reality an Error Correcting Code
Can’t Beat ’Em?
DEMYSTIFY ’EM!(show physics looks just like comm theory)
SUBSUME ’EM!!(show physics IS comm theory)
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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11 Is Reality an Error Correcting Code Classical
It’s All About Energy (classical)
Mk
x(t)
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11 Is Reality an Error Correcting Code Classical
It’s All About Energy (classical)
Mk
x(t)
• Hamiltonian:
H(x, p) = Epotential + Ekinetic =12
[k1x
2 +1Mp2
]
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11 Is Reality an Error Correcting Code Classical
It’s All About Energy (classical)
Mk
x(t)
• Hamiltonian:
H(x, p) = Epotential + Ekinetic =12
[k1x
2 +1Mp2
]
• Differential Equations:
x = ∂H()∂p p = −∂H()
∂x
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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12 Is Reality an Error Correcting Code Classical
Different Formulations
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
• Statespace:
x =[xx
]=[
0 1− k
M 0
]x
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
• Statespace:
x =[xx
]=[
0 1− k
M 0
]x
• Add Noise, Choose Right Basis Set:
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
• Statespace:
x =[xx
]=[
0 1− k
M 0
]x
• Add Noise, Choose Right Basis Set:
– Colored noise channel
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
• Statespace:
x =[xx
]=[
0 1− k
M 0
]x
• Add Noise, Choose Right Basis Set:
– Colored noise channel– MAC Channel
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12 Is Reality an Error Correcting Code Classical
Different Formulations• Frosh:
x+k
Mx = 0
• Statespace:
x =[xx
]=[
0 1− k
M 0
]x
• Add Noise, Choose Right Basis Set:
– Colored noise channel– MAC Channel– Odd Macro-Heisenbergishness
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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13 Is Reality an Error Correcting Code Quantum
It’s Still All About Energy (quantum)
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13 Is Reality an Error Correcting Code Quantum
It’s Still All About Energy (quantum)
• Hamiltonian:
H = Epotential + Ekinetic = − e2
4πε0r− ~2
2m∇2︸ ︷︷ ︸
(non-relativistic electron)
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13 Is Reality an Error Correcting Code Quantum
It’s Still All About Energy (quantum)
• Hamiltonian:
H = Epotential + Ekinetic = − e2
4πε0r− ~2
2m∇2︸ ︷︷ ︸
(non-relativistic electron)
• H is now an operator
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13 Is Reality an Error Correcting Code Quantum
It’s Still All About Energy (quantum)
• Hamiltonian:
H = Epotential + Ekinetic = − e2
4πε0r− ~2
2m∇2︸ ︷︷ ︸
(non-relativistic electron)
• H is now an operator
• Schrodinger:
i~∂ψ
∂t= Hψ
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
• You can’t actually measure ψ
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
• You can’t actually measure ψ
• Measurement: 〈ψk|ψ〉 (yes, it’s a projection operation)
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
• You can’t actually measure ψ
• Measurement: 〈ψk|ψ〉 (yes, it’s a projection operation)
• 〈ψ|ψ〉 = |ψ|2
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
• You can’t actually measure ψ
• Measurement: 〈ψk|ψ〉 (yes, it’s a projection operation)
• 〈ψ|ψ〉 = |ψ|2
• |ψ|2 ↔ probability density on (r, t)
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14 Is Reality an Error Correcting Code Quantum
What is ψ?
• Solution of Schrodinger equation
• Complex function
• You can’t actually measure ψ
• Measurement: 〈ψk|ψ〉 (yes, it’s a projection operation)
• 〈ψ|ψ〉 = |ψ|2
• |ψ|2 ↔ probability density on (r, t)
• In general (system of particles)∫|ψ(r1 · · · rN , t)|2 dr1 · · · drNdt = 1
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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15 Is Reality an Error Correcting Code Quantum
Static Schrodinger
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
Eψ = Hψ(just Fourier with a dash of Heisenberg)
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
Eψ = Hψ(just Fourier with a dash of Heisenberg)
Hamiltonian Eigenfunctions⇔ System Wave Functions
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
Eψ = Hψ(just Fourier with a dash of Heisenberg)
Hamiltonian Eigenfunctions⇔ System Wave Functions
Hamiltonian Eigenvalues⇔ System Energy Spectrum
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
Eψ = Hψ(just Fourier with a dash of Heisenberg)
Hamiltonian Eigenfunctions⇔ System Wave Functions
Hamiltonian Eigenvalues⇔ System Energy Spectrum
Arbitrary Orthonormal Bases {|i〉}: |ψ〉 =∑
i |i〉〈i|ψ〉
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15 Is Reality an Error Correcting Code Quantum
Static SchrodingerSuppose H Is Not a Function of Time
Eψ = Hψ(just Fourier with a dash of Heisenberg)
Hamiltonian Eigenfunctions⇔ System Wave Functions
Hamiltonian Eigenvalues⇔ System Energy Spectrum
Arbitrary Orthonormal Bases {|i〉}: |ψ〉 =∑
i |i〉〈i|ψ〉
NOT So Mysterious, Huh?
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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16 Is Reality an Error Correcting Code Quantum
Add Special Relativity
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16 Is Reality an Error Correcting Code Quantum
Add Special Relativity• Bosons:
– Force carriers– 2 or more with same wave function? YES!– Integer “spin”
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16 Is Reality an Error Correcting Code Quantum
Add Special Relativity• Bosons:
– Force carriers– 2 or more with same wave function? YES!– Integer “spin”
• Fermions:
– Matter particles– 2 or more with same wave function? NO! (Pauli Exclusion)– Half integer spin
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16 Is Reality an Error Correcting Code Quantum
Add Special Relativity• Bosons:
– Force carriers– 2 or more with same wave function? YES!– Integer “spin”
• Fermions:
– Matter particles– 2 or more with same wave function? NO! (Pauli Exclusion)– Half integer spin
• Composites:
– Schizophrenic, but ...– STILL either integer or half-integer spin
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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17 Is Reality an Error Correcting Code Quantum
WEIRDNESS!
• Nature can always tell if you peeked
• Spooky action at a distance (instantaneous communication)
• Atoms flowing through atoms (Bose-Einstein condensates)
• Etc. Etc. (but not our concern here)
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17 Is Reality an Error Correcting Code Quantum
WEIRDNESS!
• Nature can always tell if you peeked
• Spooky action at a distance (instantaneous communication)
• Atoms flowing through atoms (Bose-Einstein condensates)
• Etc. Etc. (but not our concern here)
GRAVITY gums up the works
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17 Is Reality an Error Correcting Code Quantum
WEIRDNESS!
• Nature can always tell if you peeked
• Spooky action at a distance (instantaneous communication)
• Atoms flowing through atoms (Bose-Einstein condensates)
• Etc. Etc. (but not our concern here)
GRAVITY gums up the works
SuperSymmetry helps
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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18 Is Reality an Error Correcting Code SuperSymmetry
SuperSymmetry Disclaimer
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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19 Is Reality an Error Correcting Code SuperSymmetry
Enter SuperSymmetry (SUSY)
Fermions: {ψm} Bosons: {φn} Operators: {Qi}
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19 Is Reality an Error Correcting Code SuperSymmetry
Enter SuperSymmetry (SUSY)
Fermions: {ψm} Bosons: {φn} Operators: {Qi}
Bosonφn
Qi
→←Q†i
Fermionψm
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19 Is Reality an Error Correcting Code SuperSymmetry
Enter SuperSymmetry (SUSY)
Fermions: {ψm} Bosons: {φn} Operators: {Qi}
Bosonφn
Qi
→←Q†i
Fermionψm
• On-Shell (has defined Hamiltonian): {Qi, Qj} = δijH
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19 Is Reality an Error Correcting Code SuperSymmetry
Enter SuperSymmetry (SUSY)
Fermions: {ψm} Bosons: {φn} Operators: {Qi}
Bosonφn
Qi
→←Q†i
Fermionψm
• On-Shell (has defined Hamiltonian): {Qi, Qj} = δijH
• Off-Shell (“normalized” Hamiltonian-Free): {Qi, Qj} = 2iδij∂t
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19 Is Reality an Error Correcting Code SuperSymmetry
Enter SuperSymmetry (SUSY)
Fermions: {ψm} Bosons: {φn} Operators: {Qi}
Bosonφn
Qi
→←Q†i
Fermionψm
• On-Shell (has defined Hamiltonian): {Qi, Qj} = δijH
• Off-Shell (“normalized” Hamiltonian-Free): {Qi, Qj} = 2iδij∂t
The {Qi} are sorta like dimensions(but not really)
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
• “Dashing” links: flips operator sign (Pauli exclusion)
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
• “Dashing” links: flips operator sign (Pauli exclusion)
NO NO NO!!! bosonk{Operators}A→ {fermion subset} {Operators}A← boson` 6=k
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
• “Dashing” links: flips operator sign (Pauli exclusion)
NO NO NO!!! bosonk{Operators}A→ {fermion subset} {Operators}A← boson` 6=k[
Also from anticommutation: {Qi, Qj} = QiQ†j +QjQ
†i = 0 i 6= j
]
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
• “Dashing” links: flips operator sign (Pauli exclusion)
NO NO NO!!! bosonk{Operators}A→ {fermion subset} {Operators}A← boson` 6=k[
Also from anticommutation: {Qi, Qj} = QiQ†j +QjQ
†i = 0 i 6= j
]• Raising/Lowering nodes
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20 Is Reality an Error Correcting Code SuperSymmetry
ADINKRAS
• Nodes: bipartite hypercube node coloring (“bosons” and “fermions”)
• Links: direction-k → operator-k (color-k)
• “Dashing” links: flips operator sign (Pauli exclusion)
NO NO NO!!! bosonk{Operators}A→ {fermion subset} {Operators}A← boson` 6=k[
Also from anticommutation: {Qi, Qj} = QiQ†j +QjQ
†i = 0 i 6= j
]• Raising/Lowering nodes
Many Different Possible Graphs (systems)
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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21 Is Reality an Error Correcting Code SuperSymmetry
Construction Illustration
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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22 Is Reality an Error Correcting Code SuperSymmetry
Adinkras and Fields of Particles
• Nodes can be rearranged according to “engineering dimension”(bosons on the bottom for our-world SUSY)
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22 Is Reality an Error Correcting Code SuperSymmetry
Adinkras and Fields of Particles
• Nodes can be rearranged according to “engineering dimension”(bosons on the bottom for our-world SUSY)
• Each is a Feynman-like self-consistent particle-operator system
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22 Is Reality an Error Correcting Code SuperSymmetry
Adinkras and Fields of Particles
• Nodes can be rearranged according to “engineering dimension”(bosons on the bottom for our-world SUSY)
• Each is a Feynman-like self-consistent particle-operator system
EXACT Representations of Potential Realities
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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23 Is Reality an Error Correcting Code SuperSymmetry
Some Adinkras Can Be Folded
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23 Is Reality an Error Correcting Code SuperSymmetry
Some Adinkras Can Be Folded• Un-dash
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23 Is Reality an Error Correcting Code SuperSymmetry
Some Adinkras Can Be Folded• Un-dash
• Find appropriate boson-boson, fermion-fermion pairings
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23 Is Reality an Error Correcting Code SuperSymmetry
Some Adinkras Can Be Folded• Un-dash
• Find appropriate boson-boson, fermion-fermion pairings
• Collapse
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23 Is Reality an Error Correcting Code SuperSymmetry
Some Adinkras Can Be Folded• Un-dash
• Find appropriate boson-boson, fermion-fermion pairings
• Collapse
⇒
(link to video)
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
• LBC (yeah, that’s a linear block code!): G =[
g1 · · · gK
]
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
• LBC (yeah, that’s a linear block code!): G =[
g1 · · · gK
]• Code set C = {ci} =
⋃n,k
gn ⊕ gk
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
• LBC (yeah, that’s a linear block code!): G =[
g1 · · · gK
]• Code set C = {ci} =
⋃n,k
gn ⊕ gk
• A folds iff ∃ a doubly-even self-dual generator G s.t.⋃n,i
an ⊕ ci = A
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
• LBC (yeah, that’s a linear block code!): G =[
g1 · · · gK
]• Code set C = {ci} =
⋃n,k
gn ⊕ gk
• A folds iff ∃ a doubly-even self-dual generator G s.t.⋃n,i
an ⊕ ci = A
• Previous picture:G> = [ 1 1 1 1 ]
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24 Is Reality an Error Correcting Code SuperSymmetry
Which Adinkras Can Be Folded?• Derive node addresses (codewords) {an} = A, n = 1, ...N
• LBC (yeah, that’s a linear block code!): G =[
g1 · · · gK
]• Code set C = {ci} =
⋃n,k
gn ⊕ gk
• A folds iff ∃ a doubly-even self-dual generator G s.t.⋃n,i
an ⊕ ci = A
• Previous picture:G> = [ 1 1 1 1 ]
LBC Controls Adinkras Folding!
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
– Fluke?
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
– Fluke?– Nature “protects” telescoping (folding) “realities”?
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
– Fluke?– Nature “protects” telescoping (folding) “realities”?– What are perturbations?
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
– Fluke?– Nature “protects” telescoping (folding) “realities”?– What are perturbations?– Natural Selection during the Big Bang?
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25 Is Reality an Error Correcting Code SuperSymmetry
What Does This Mean?• A few Jim-Facts:
– Irreducible Adinkras⇔ No embedded LBC– Smallest (irreducible) SUSY representations consistent with
Feynman’s “sum over histories formulation of quantum theory,” arecontrolled by block-linear self-dual error correcting codes.
– This is STRANGE!• Speculation:
– Fluke?– Nature “protects” telescoping (folding) “realities”?– What are perturbations?– Natural Selection during the Big Bang?
What Do I Hope It Means?
WINLAB ITA, February 2013 Chris Rose & Jim Gates
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26 Is Reality an Error Correcting Code SuperSymmetry
Structure of Reality⇔ BEC Codes
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26 Is Reality an Error Correcting Code SuperSymmetry
Structure of Reality⇔ BEC Codes
Communication Theory PWNS EVERYTHING!
WINLAB ITA, February 2013 Chris Rose & Jim Gates