The Fitness of the Holographic Universe

[RR Edwards]

Introduction

The “Black Hole Wars” was a series of debates, over many years, that involved prominent physicists and concerned the nature of reality under conditions where local gravity is strong enough to affect local Quantum Mechanics (QM). The conclusion of these debates was to embraced Black Hole Complementarity (BHC) and popularized the Holographic Principle (HP). On further examination, however, it seems to have put Quantum Information Theory (QIT) itself into mortal peril.

 

Glossary of terms

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Gödel's Incompleteness Theorems

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Two theorems that establish the inherent limitations of expressive axiomatic systems in that a system cannot demonstrate its own consistency (e.g. the liar paradox).

 

Quantum Information Theory (QIT)

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A postulate largely compatible with the Copenhagen Interpretation of Quantum Mechanics (QM) whereby the quantum wave function is considered fundamental reality.

 

de Sitter space

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A description of our universe that is analogous to a reverse black hole, where the de Sitter space event horizon is a boundary surrounding our universe and nearly mathematically identical the event horizon of a black hole.

 

Holographic Principle (HP)

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A widely accepted principle that the description of a volume of space can be encoded on a “film” outside the boundary of the space itself.

 

Black Hole Information Paradox (BHIP)

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The concern that information could disappear into a black hole where it would violate QIT in that the complete information about a system must be encoded in its wave function.

 

Black Hole Complementarity (BHC)

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The proposed solution to the Black Hole Information Paradox (BHIP), that the information of a system is both reflected at the event horizon where it conforms to the Holographic Principle (HP) and passed through the event horizon without possibility of escape and thus avoiding a violation of the no-cloning theorem.

 

No-cloning theorem (NCT)

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A fundamental principle of QIT that forbids the creation of identical copies of an arbitrary unknown quantum state.

 

Holographic Universe (HU)

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Any of a number of postulates proposing that the de Sitter space event horizon of our universe is the fundamental seat of our reality.

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The Fitness of the Holographic Universe

The Holographic Principle (HP) was proposed as the mechanism and seat for a solution to the Black Hole Information Paradox (BHIP) built on Black Hole Complementarity (BHC). It has been further postulated as a universal solution for Quantum Gravity (QG) in the form of a Holographic Universe (HU), but such solutions simply fail to comport with a consistent homogony and Gödel's Incompleteness Theorems.

 

The HP/BHC solution for QIT in the black hole case, when either mass or energy crosses the event horizon, two copies of its quantum information arise. Each copy exists and proceeds through time in separate forms on its own side of the event horizon. Functionally, it’s as if a holographic foto is painted onto a film on the surface of the black hole as the mass or energy crosses the event horizon. Critically, there cannot be an intelligible connection between these two copies. If there was an intelligible connection between these two copies, information would escape the black hole, violating the NCT. If there could ever be a way to reliably correlate the inside copy to the outside copy and use it to know about its opposite, it would violate the NCT and overturn the entirety of QIT.

 

Additionally, it is important to remember that in BHC, the HP “film” is on the outside of event horizon of a black hole and it only records the information of things that pass across the event horizon, into the black hole. The de Sitter space equivalent at the big bang event horizon then would be a film on the inside recording things that pass across the de Sitter space event horizon as it leaves our universe. The de Sitter space HP is not suitable to describe the universe, it only describes things that left the universe and could no longer affect the universe in any way at any time in the future. The final effect of HP applied to the event horizons of black holes and the the de Sitter space event horizon of our universe is to isolate QIT into a single functional axiomatic system which would violate Gödel's theorems.

 

Thus the de Sitter space event horizon of our universe functionally guarantees three things:

1 - If any information from outside the universe penetrated into our universe, QIT would be overturned. Not only does this seem to be an inescapable side effect of HU, it violates Gödel's incompleteness theorems.

2 - All information that has ever left our universe is painted on our side of its de Sitter space event horizon and in no way representative of the content of our universe. If it could be correlated to the universe itself, it would violate NCT.

3 - All the information on all the “films” that conform to the Holographic principle correlate to copies of information that has left our reality and could never return or take part in our reality again in any possible way without violating the NCT.

With these points in hand, there seems to be no room for a possible mechanism for HU.