time in physics and computer science - hpts · 2017. 10. 27. · patents pending | earth computing...

Patents Pending | Earth Computing Inc. | Paul Borrill

Time in Physics and Computer Science

Paul Borrill EARTH Computing


Time emerges from entanglementEverything you thought you

knew about time is now obsolete


Time is change we can count

There is no evidence whatsoever for a smooth background of spacetime

Bell’s Inequalities have been telling us for a while now that there’s something wrong with Minkowski’s 4D “spacetime”


Time is not continuous

Everything we measure is discrete


Time is not irreversible

All our theories are time reversal invariant

Classical (Newtonian) Relativistic (Special and General)

Standard Model (Quantum Field Theory)


Everything Moves at SOL


Everything Moves at SOL

You can’t see photons coming;

you can only see them

arrive


So What?


We cannot achieve exactly once delivery unless it is paired

(intimately) with exactly once transmission

not guaranteed by the “end to end principle”


Switches are DReDDful (they Drop, Reorder, Delay and

Duplicate packets)

We Need Something Else


Compare and set atomicity cannot be guaranteed across a

switched network, or any network that can be partitioned



Heartbeats don’t scale



Timeouts create cascade failures



CellAgent

A∅

Half Link AHalf-Edge

Entangled (Hidden ENTL Packets)

ENTL

Circulating ENTL Event

ENTL

ENTLw x

z y

EARTH Computing Link• Reversible

• No-Copying

• Atomic Information Transfer (AIT)Guaranteed in the sense that both sides can “know” if it failed or succeeded

CellAgentA

CellAgentB

HalfLink A

HalfLink BTx/Rx Media


Mathematical Foundation

Groupoid semantics for timeless networksand secure classical key distribution

David ReutterDepartment of Computer Science, University of Oxford

[email protected]

Jamie VicaryDepartment of Computer Science, University of Oxford

[email protected]

Abstract—We provide a mathematical foundation for timelessnetworks, a new paradigm for distributed communication whichhas recently been proposed. Our approach is based on groubits,generalizations of classical bits arising from groupoids with spe-cial properties. Our techniques give a clean mathematical modelfor timeless networks, and allow the description and verificationof a number of interesting protocols, including message routingwithout timeouts, and information theoretically–secure classicalkey distribution, under minimal security assumptions. We alsobuild classical-physics implementations of a number of quantumprotocols on networks of groubits, including dense coding andteleportation.

I. INTRODUCTION

A. Overview

In this paper we study the foundations of timeless networks,a new paradigm for distributed communication presented re-cently by Borrill [1] and currently under commercial devel-opment by Earth Computing1. We study a mathematically-idealized form of timeless networks based on groubits—group-theoretical generalizations of classical bits, with similarbehaviour to qubits in quantum information—and go on toshow that groubits can be manipulated to achieve a wide rangeof surprising informatic tasks.In the simplest nontrivial case, a groubit is computational

device storing two ordinary bits (AL, AI), a logical bit AL

and an internal bit AI , and supporting the primitive operationsInit, Swap, Read, Write and Tick. Some of these operationsin turn make use of the procedure Rand, a function with noarguments which returns either 0 or 1 nondeterministically.We describe these procedures as follows, in their simplest

instantiations. The Init operation takes no arguments, andcreates a new groubit in the following state:• Init = (Rand, 0)Here and throughout, we intend that the Rand function isexecuted freshly each time. The Swap operation acts on agroubit, exchanging the logical and internal bits:• Swap(AL, AI) = (AI , AL)Conventional single bits [B] can be stored in groubits, usingthe following read and write procedures:• Read(AL, AI) = [AL]• Write[B] = (B,Rand)1See http://www.earthcomputing.io.

The read operation destroys a groubit and creates a conven-tional bit, while the write operation destroys a conventionalbit and creates a new groubit. Pairs of groubits can also beconnected by a link, enabling the Tick operation, where A andB label the two connected nodes, and ⊕ is addition modulo 2:• Tick((AL,AI),(BL,BI)

!=((AL,AI⊕BL),(BL,BI⊕AL))

Intuitively, for each node in the pair, we flip the internal bitjust when the other node has logical bit equal to 1. Nodes canbelong to multiple links, in general forming a graph topology.

B. Assumptions

We make some assumptions about these groubit operations.• Atomicity. The operations Init, Swap, Read, Write andTick are implemented atomically.

• Security. A user can never discover any information aboutthe state of a node, except via Read.

We emphasize that claims we make about the functionalityof timeless networks—in particular, security properties—reston the validity of these assumptions.2 We suggest that theseassumptions are within the realm of technological plausibility;for example, separation kernels [3] are a well-developed tech-nology for guaranteeing strong security properties of privatememory states within embedded devices. Also, note thatwe do not assume that devices cannot fail; to satisfy theseassumptions, it would therefore be valid for a device to self-destruct if tampering was detected.

C. Significance

We claim that groubits have exotic properties making theminteresting to study. In particular, they allow timeout-freeatomic message routing (the origin of the term ‘timelessnetwork’), and they have the ability to replicate a variety ofquantum protocols.

Message routing. Linear chains of groubits allow messagerouting between nodes with guaranteed message atomicity,and without timeouts3 (see Section III-A). We understand thatdeveloping this idea is the primary commercial interest ofEarth Computing, with a focus on high-resilience networkarchitectures for data centres; this is potentially significant,since the timeout properties of the standard TCP transport2For quantum protocols such as quantum key distribution, security is

derivable from the laws of physics; this is not the case here [2].3This is the origin of the timeless network terminology.

arxi

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0966

https://arxiv.org/abs/1707.00966


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Why Can’t Links be Reversible?

the snapshot problem


Thank You

EARTH Computing Solid Ground Beneath The Clouds


Spare Slides


EARTH Non Time Liveness (ENTL)

“Reliable”

Failure Detector

CellAgent

A∅

Half Link AHalf-Edge

Entangled (Hidden ENTL Packets)

ENTL

Circulating ENTL Event

ENTL

ENTLw x

z y


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ENTT Converts to ENTL

ENTT

ENTL

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EARTH Non Time Transaction (ENTT)

A Better Idea:

Conserved/Exchanged

Quantities


The EndofLink to Endof Link

Principle

Replaces the “end to end principle”


Reversible Link ProtocolTECK

TACK

TICK

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TICK

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Forward

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Einstein’s Unfinished Revolution•A new revolution in our understanding of the

nature of time; bigger than relativity

•Profoundly important to computer science

•A new way of looking at:

•Consistency

•Transactions •Resilience

•Security


Lamport’s Unfinished Revolution• Shared Memory Atomic Register • Message Passing Atomic Link

• THE MISSING ENTITY?Process A Process B

Process BProcess A

On One Machine On Two Machines[1] Lamport, Leslie. “Arbitration-Free Synchronization.” Distrib. Comput. 16, no. 2–3 (September 2003): 219–37.

SharedLinkState

SharedMemory

State

CAS AIT


Classical Emulation of Entanglement

QuBit Gray Codes

0 0

0 0

0 -1

0 0

1 0

0 0

1 -1

0 0

0 0

1 1

1 0

1 1

0 -1

1 1

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1 0

1 0

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1 -1

1 0

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1 0

0 1

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0 1

0 0

1 0

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1001

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0 0

0 0

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LOV

GEV

Information

Information

Entropy

Entropy

0 0

0 0

0 0

1 0

1 0

0 0

1 0

1 0

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0 1

1 -1

0 1

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0 0

1 -1

1 0

0 0

0 1

0 0

1 1

1 0

1 1

0 -1

0 0

0 0

0 0

Conjugate Transpose

1 -1

1 1

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Matrix Decomposition

Entangled State

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References• Stanford 2016: “The Time-Less DataCenter" (November 2016)

• Video: https://www.youtube.com/watch?v=IPTlTmH-YvQ• Slides: http://web.stanford.edu/class/ee380/Abstracts/161116-slides.pdf• Info: http://web.stanford.edu/class/ee380/Abstracts/161116.html

• Papers We Love 2016: “Lamport’s Unfinished Revolution” (July 2016)

• Video: https://www.youtube.com/watch?feature=youtu.be&t=32m27s&v=CWF3QnfihL4• Slides: https://speakerdeck.com/pborrill/time-clocks-and-the-reordering-of-events-pwl-san-francisco-14-jul-2016• Info: https://www.meetup.com/papers-we-love-too/events/228341271/

• Stanford 2014: “Time in Physics, and Implications for Computer Science”:

• Video: https://www.youtube.com/watch?v=SfvouFIVCmQ• Slides: http://web.stanford.edu/class/ee380/Abstracts/140416-Borrill-slides.pdf• Info: http://web.stanford.edu/class/ee380/Abstracts/091111.html

• Time’s arrow emerges from observers. https://www.wired.com/2016/09/arrow-of-time/

• PBS SpaceTime https://www.youtube.com/watch?v=GguAN1_JouQ

• Groubits https://arxiv.org/abs/1707.00966

https://www.youtube.com/watch?v=IPTlTmH-YvQ

http://web.stanford.edu/class/ee380/Abstracts/161116-slides.pdf

http://web.stanford.edu/class/ee380/Abstracts/161116.html

https://www.youtube.com/watch?feature=youtu.be&t=32m27s&v=CWF3QnfihL4

https://speakerdeck.com/pborrill/time-clocks-and-the-reordering-of-events-pwl-san-francisco-14-jul-2016

https://www.meetup.com/papers-we-love-too/events/228341271/

https://www.youtube.com/watch?v=SfvouFIVCmQ

http://web.stanford.edu/class/ee380/Abstracts/140416-Borrill-slides.pdf

http://web.stanford.edu/class/ee380/Abstracts/091111.html

https://www.wired.com/2016/09/arrow-of-time/

https://www.youtube.com/watch?v=GguAN1_JouQ

https://arxiv.org/abs/1707.00966

time in physics and computer science - hpts · 2017. 10. 27. · patents pending | earth computing...

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