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Deriving quantum theory from information processing axioms

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Russ Abbott

Deriving quantum theory from information processing axioms

From APS Physics.

We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields.
...

They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρ_A of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state Ψ_AB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B).

Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory.

-- Russ Abbott
_____________________________________________

Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
_____________________________________________

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Russ Abbott

Re: Deriving quantum theory from information processing axioms

I expected this to have more of an impact than it seems to be having. What am I missing?

-- Russ Abbott
_____________________________________________

On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott <[hidden email]> wrote:

From APS Physics.

We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields.
...

They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρ_A of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state Ψ_AB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B).

Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory.

-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
_____________________________________________

Grant Holland

Re: Deriving quantum theory from information processing axioms

Russ,

I had the same feeling about my recent missive - entitled "Uncertainty vs Information - redux and resolution" - in which I too make various claims about information theory. I believe I had only one response - from Eric. I expected more, maybe from Owen and Frank and yourself.

The APS Physics review you attached discussed an Italian paper from the U of Pavia. About that paper the review says "They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory." Understandably, such a view is likely to be sacrosanct among many.

I must confess however that I have considerable sympathy with it. In my recent posting on Uncertainty and Information, I cited the Oxford Info Theorist Vlatko Vedral. In his book Decoding Reality: The Universe as Quantum Information, he states:

“This book will state that information (and not matter or energy or love) is the building block on which everything is constructed. Information is far more fundamental than matter or energy because it can be successfully applied to both macroscopic interactions, such as economic and social phenomena, and, as I will argue, information can also be used to explain the origin and behavior of microscopic interactions such as energy and matter.”

Evidently, there is a body of information theorist out there who are making a play for the proposition that Information Theory is more fundamental than physics.

Of course, my recent posting argues that uncertainty is more foundational then information (even though, according to Shannon, entropy measures them both). This is because, as argued by Khinchin, information derives from uncertainty through realization.

Maybe together we can get a thread started about the primacy of physics, information or uncertainty - or maybe something else? Oh, yeah, there is already one going about the primacy of physics vs philosophy. Maybe we can add information and uncertainty to the mix!

On 7/26/11 11:37 AM, Russ Abbott wrote:

I expected this to have more of an impact than it seems to be having. What am I missing?

-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
_____________________________________________

On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott <[hidden email]> wrote:

From APS Physics.

We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields.
...

They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρ_A of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state Ψ_AB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B).

Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory.

-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
_____________________________________________
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Rich Murray-2

Re: Deriving quantum theory from information processing axioms

As a universal layman, with a BS in physics and history from MIT in
1964, I have always been keenly interested as to the actual deep
meaning of quantum theory.

Can someone give a simple dynamic geometrical model which can embody
these axioms, fleshing out their abstract meanings in a simple way,
somewhat accessible to common sense?

A video game or YouTube video?

Thanks, Rich Murray [hidden email] 505-819-7388

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Russell Standish

Re: Deriving quantum theory from information processing axioms

In reply to this post by Russ Abbott

Of course, I published a paper in 2004 (Why Occams Razor) doing
essentially the same thing (I expanded on this somewhat in my 2006
book, Theory of Nothing).

I would also say, that Lucien Hardy did something similar in 2001
(Quantum theory from five reasonable axioms). Also, there have been
other works linking the uncertainty principle to the Cramer-Rao
inequality from information theory.

I expect this current paper (when I finally get around to read it), will be
equivalent to what I've done. Ultimately, it may come down to history
which method is preferred, or if some uber-clear version is presented
(like Dirac did to Schroedinger and Heisenberg's theories).

It would be all the more remarkable if this approach was fundamentally
different.

All I have to say now...

On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote:

> I expected this to have more of an impact than it seems to be having. What
> am I missing?
>
> *-- Russ Abbott*
> *_____________________________________________*
> *** Professor, Computer Science*
> * California State University, Los Angeles*
>
> * Google voice: 747-*999-5105
> * blog: *http://russabbott.blogspot.com/
> vita: http://sites.google.com/site/russabbott/
> *_____________________________________________*
>
>
>
> On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott <[hidden email]> wrote:
>
> > From APS Physics <http://physics.aps.org/articles/v4/55>.
> >
> > We know how to use the “rules” of quantum physics to build lasers,
> > microchips, and nuclear power plants, but when students question the rules
> > themselves, the best answer we can give is often, “The world just happens to
> > be that way.” Yet why are individual outcomes in quantum measurements
> > random? What is the origin of the Schrödinger equation? In a paper [1<http://physics.aps.org/articles/v4/55#c1>]
> > appearing in Physical Review A, Giulio Chiribella at the Perimeter
> > Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo
> > Perinotti at the University of Pavia, Italy, offer a framework in which to
> > answer these penetrating questions. They show that by making six fundamental
> > assumptions about how information is processed, they can derive quantum
> > theory. (Strictly speaking, their derivation only applies to systems that
> > can be constructed from a finite number of quantum states, such as spin.) In
> > this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s
> > belief that one obtains “it from bit,” in other words, that our account of
> > the universe is constructed from bits of information, and the rules on how
> > that information can be obtained determine the “meaning” of what we call
> > particles and fields.
> > ...
> >
> > They assume five new elementary axioms—causality, perfect
> > distinguishability, ideal compression, local distinguishability, and pure
> > conditioning—which define a broad class of theories of information
> > processing. For example, the causality axiom—stating that one cannot signal
> > from future measurements to past preparations—is so basic that it is usually
> > assumed a priori. Both classical and quantum theory fulfil the five
> > axioms. What is significant about Chiribella et al.’s work is that they
> > show that a sixth axiom—the assumption that every state has what they call a
> > “purification”—is what singles out quantum theory within the class. In fact,
> > this last axiom is so important that they call it a postulate. The
> > purification postulate can be defined formally (see below), but to
> > understand its meaning in simple words, we can look to Schrödinger, who in
> > describing entanglement gives the essence of the postulate: “Maximal
> > knowledge of a total system does not necessarily include maximal knowledge
> > of all its parts.” (Formally, the purification postulate states that every
> > mixed state ρA of system A can always be seen as a state belonging to a
> > part of a composite system AB that itself is in a pure state ΨAB. This
> > pure state is called “purification” and is assumed to be unique up to a
> > reversible transformation on B).
> >
> > Chiribella et al. conclude there is only one way in which a theory can
> > satisfy the purification postulate: it must contain entangled states. (The
> > other option, that the theory must not contain mixed states, that is, that
> > the probabilities of outcomes in any measurement are either 0 or 1 like in
> > classical deterministic theory, cannot hold, as one can always prepare mixed
> > states by mixing deterministic ones.) The purification postulate alone
> > allows some of the key features of quantum information processing to be
> > derived, such as the no-cloning theorem or teleportation [7<http://physics.aps.org/articles/v4/55#c7>].
> > By combining this postulate with the other five axioms, Chiribella et al. were
> > able to derive the entire mathematical formalism behind quantum theory.
> >
> >
> >
> > *-- Russ Abbott*
> > *_____________________________________________*
> > *** Professor, Computer Science*
> > * California State University, Los Angeles*
> >
> > * Google voice: 747-*999-5105
> > * blog: *http://russabbott.blogspot.com/
> > vita: http://sites.google.com/site/russabbott/
> > *_____________________________________________*
> >
> >

> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [hidden email]
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Grant Holland

Re: Deriving quantum theory from information processing axioms

Exciting, Russ. I've downloaded your 2004 paper, and will take a look.

Thanks,
Grant

On 7/26/11 3:16 PM, Russell Standish wrote:

Of course, I published a paper in 2004 (Why Occams Razor) doing
essentially the same thing (I expanded on this somewhat in my 2006
book, Theory of Nothing).

I would also say, that Lucien Hardy did something similar in 2001
(Quantum theory from five reasonable axioms). Also, there have been
other works linking the uncertainty principle to the Cramer-Rao
inequality from information theory.

I expect this current paper (when I finally get around to read it), will be
equivalent to what I've done. Ultimately, it may come down to history
which method is preferred, or if some uber-clear version is presented
(like Dirac did to Schroedinger and Heisenberg's theories).

It would be all the more remarkable if this approach was fundamentally
different. 

All I have to say now...

On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote:

I expected this to have more of an impact than it seems to be having. What
am I missing?

*-- Russ Abbott*
*_____________________________________________*
***  Professor, Computer Science*
*  California State University, Los Angeles*

*  Google voice: 747-*999-5105
*  blog: *http://russabbott.blogspot.com/
  vita:  http://sites.google.com/site/russabbott/
*_____________________________________________*



On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott [hidden email] wrote:

From APS Physics <http://physics.aps.org/articles/v4/55>.

We know how to use the “rules” of quantum physics to build lasers,
microchips, and nuclear power plants, but when students question the rules
themselves, the best answer we can give is often, “The world just happens to
be that way.” Yet why are individual outcomes in quantum measurements
random? What is the origin of the Schrödinger equation? In a paper [1<http://physics.aps.org/articles/v4/55#c1>]
appearing in Physical Review A, Giulio Chiribella at the Perimeter
Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo
Perinotti at the University of Pavia, Italy, offer a framework in which to
answer these penetrating questions. They show that by making six fundamental
assumptions about how information is processed, they can derive quantum
theory. (Strictly speaking, their derivation only applies to systems that
can be constructed from a finite number of quantum states, such as spin.) In
this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s
belief that one obtains “it from bit,” in other words, that our account of
the universe is constructed from bits of information, and the rules on how
that information can be obtained determine the “meaning” of what we call
particles and fields.
...

They assume five new elementary axioms—causality, perfect
distinguishability, ideal compression, local distinguishability, and pure
conditioning—which define a broad class of theories of information
processing. For example, the causality axiom—stating that one cannot signal
from future measurements to past preparations—is so basic that it is usually
assumed a priori. Both classical and quantum theory fulfil the five
axioms. What is significant about Chiribella et al.’s work is that they
show that a sixth axiom—the assumption that every state has what they call a
“purification”—is what singles out quantum theory within the class. In fact,
this last axiom is so important that they call it a postulate. The
purification postulate can be defined formally (see below), but to
understand its meaning in simple words, we can look to Schrödinger, who in
describing entanglement gives the essence of the postulate: “Maximal
knowledge of a total system does not necessarily include maximal knowledge
of all its parts.” (Formally, the purification postulate states that every
mixed state ρA of system A can always be seen as a state belonging to a
part of a composite system AB that itself is in a pure state ΨAB. This
pure state is called “purification” and is assumed to be unique up to a
reversible transformation on B).

Chiribella et al. conclude there is only one way in which a theory can
satisfy the purification postulate: it must contain entangled states. (The
other option, that the theory must not contain mixed states, that is, that
the probabilities of outcomes in any measurement are either 0 or 1 like in
classical deterministic theory, cannot hold, as one can always prepare mixed
states by mixing deterministic ones.) The purification postulate alone
allows some of the key features of quantum information processing to be
derived, such as the no-cloning theorem or teleportation [7<http://physics.aps.org/articles/v4/55#c7>].
By combining this postulate with the other five axioms, Chiribella et al. were
able to derive the entire mathematical formalism behind quantum theory.

*-- Russ Abbott*
*_____________________________________________*
*** Professor, Computer Science*
* California State University, Los Angeles*

* Google voice: 747-*999-5105
* blog: *http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
*_____________________________________________*

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Russ Abbott

Re: Deriving quantum theory from information processing axioms

I just looked at Theory of Nothing on Amazon. Two very nice reviews. Amazon's "Look Inside" doesn't show much, but the book looks very much worth reading. The Introduction talks about Schrodinger's cat. It had never occurred to me that the cat always experiences a boring hour and then comes out alive--at least according to the Many Worlds View of QM. It's on my reading list.

-- Russ Abbott
_____________________________________________

On Tue, Jul 26, 2011 at 3:13 PM, Grant Holland <[hidden email]> wrote:

Exciting, Russ. I've downloaded your 2004 paper, and will take a look.

Thanks,
Grant

On 7/26/11 3:16 PM, Russell Standish wrote:

Of course, I published a paper in 2004 (Why Occams Razor) doing
essentially the same thing (I expanded on this somewhat in my 2006
book, Theory of Nothing).

I would also say, that Lucien Hardy did something similar in 2001
(Quantum theory from five reasonable axioms). Also, there have been
other works linking the uncertainty principle to the Cramer-Rao
inequality from information theory.

I expect this current paper (when I finally get around to read it), will be
equivalent to what I've done. Ultimately, it may come down to history
which method is preferred, or if some uber-clear version is presented
(like Dirac did to Schroedinger and Heisenberg's theories).

It would be all the more remarkable if this approach was fundamentally
different. 

All I have to say now...

On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote:

I expected this to have more of an impact than it seems to be having. What
am I missing?

*-- Russ Abbott*
*_____________________________________________*
***  Professor, Computer Science*
*  California State University, Los Angeles*

*  Google voice: 747-*999-5105
*  blog: *http://russabbott.blogspot.com/
  vita:  http://sites.google.com/site/russabbott/
*_____________________________________________*



On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott [hidden email] wrote:

From APS Physics <http://physics.aps.org/articles/v4/55>.

*-- Russ Abbott*
*_____________________________________________*
*** Professor, Computer Science*
* California State University, Los Angeles*

* Google voice: 747-*999-5105
* blog: *http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
*_____________________________________________*

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Eric Charles

Re: Deriving quantum theory from information processing axioms

Russ,
That was actually a very good article! I remain amongst those skeptical that one can really test the theory, but it is nice to see the theory explained such a straightforward way, and to know there are people making solid attempts to test it.

One major cop-out / overtly-overstated-claim though is Vilenkin's speculation that:
           "This picture of the universe... explains the long-standing mystery of why the constants of nature appear to be fine-tuned for the emergence of life. The reason is that intelligent observers exist only in those rare bubbles in which, by pure chance, the constants happen to be just right for life to evolve."
That, at least in my mind, sidesteps the question, as it can be reduced to:
           "The reason nature appears to be fine-tuned for the emergence of life is because it is."
Another way to phrase this is that if we are going to be happy (as scientists) with the answer that things are the way they are due to "pure chance," we didn't need multiverse theory to be happy.

Also, my favorite bit is in Tegmark's article. He states:
     "Remember: Parallel universes are not a theory—they are predictions of certain theories."
Speaking with most of my sociology-of-science knowledge revolving around the field of psychology, the ability to maintain that distinction is admirable, incredibly valuable to the progress of a field, and I wish more people could do it.

Eric

On Wed, Jul 27, 2011 04:28 PM, Russ Abbott <[hidden email]> wrote:

And speaking of multiverses, this was just published on the <a href="http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe" onclick="window.open('http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe');return false;">Scientific American website.

In the August issue ofScientific American, cosmologist George Ellis describes why he's skeptical about the concept of parallel universes. Here, multiverse proponents <a class=" snap_noshots" href="http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 1px; padding-right: 3px; padding-bottom: 1px; padding-left: 1px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 1px; border-left-width: 0px; border-style: initial; border-color: initial; outline-width: initial; outline-style: none; outline-color: initial; font-size: 16px; vertical-align: baseline; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; color: inherit; text-decoration: none; cursor: url(http://cdn.apture.com/media/imgs/crsr/socialLink.png), default; border-style: initial; border-color: initial; border-collapse: collapse; clear: none; float: none; display: inline; width: auto; height: auto; font-weight: normal; position: relative; border-bottom-color: rgb(0, 102, 204); border-bottom-style: dotted; top: -1px; border-top-left-radius: 2px 2px; border-top-right-radius: 2px 2px; border-bottom-left-radius: 2px 2px; border-bottom-right-radius: 2px 2px; background-position: initial initial; background-r! epeat: i nitial initial; " onclick="window.open('http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#');return false;">Alexander Vilenkin and <a class=" snap_noshots" href="http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 1px; padding-right: 3px; padding-bottom: 1px; padding-left: 1px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 1px; border-left-width: 0px; border-style: initial; border-color: initial; outline-width: initial; outline-style: none; outline-color: initial; font-size: 16px; vertical-align: baseline; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; color: inherit; text-decoration: none; cursor: url(http://cdn.apture.com/media/imgs/crsr/socialLink.png), default; border-style: initial; border-color: initial; border-collapse: collapse; clear: none; float: none; display: inline; width: auto; height: auto; font-weight: normal; position: relative; border-bottom-color: rgb(0, 102, 204); border-bottom-style: dotted; top: -1px; border-top-left-radius: 2px 2px; border-top-right-radius: 2px 2px; border-bottom-left-radius: 2px 2px; border-bottom-right-radius: 2px 2px; background-position: initial initial; background-repeat: initial initial; " onclick="window.open('http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#');return false;"><a class=" snap_noshots" href="http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 1px; padding-right: 3px; padding-bottom: 1px; padding-left: 1px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 1px; border-left-width: 0px; border-style: initial; border-color: initial; outline-width: initial; outline-style: none; outline-color: initial; font-size: 16px; vertical-align: baseline; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; backgro! und-colo r: transparent; color: inherit; text-decoration: none; cursor: url(http://cdn.apture.com/media/imgs/crsr/socialLink.png), default; border-style: initial; border-color: initial; border-collapse: collapse; clear: none; float: none; display: inline; width: auto; height: auto; font-weight: normal; position: relative; border-bottom-color: rgb(0, 102, 204); border-bottom-style: dotted; top: -1px; border-top-left-radius: 2px 2px; border-top-right-radius: 2px 2px; border-bottom-left-radius: 2px 2px; border-bottom-right-radius: 2px 2px; background-position: initial initial; background-repeat: initial initial; " onclick="window.open('http://www.scientificamerican.com/article.cfm?id=multiverse-the-case-for-parallel-universe&WT.mc_id=SA_WR_20110727#');return false;">Max Tegmark offer counterpoints, explaining why the multiverse would account for so many features of our universe—and how it might be tested.

-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: <a href="http://russabbott.blogspot.com/" style="font-style:italic" target="" onclick="window.open('http://russabbott.blogspot.com/');return false;">http://russabbott.blogspot.com/
vita: <a href="http://sites.google.com/site/russabbott/" style="font-style:italic" target="" onclick="window.open('http://sites.google.com/site/russabbott/');return false;">http://sites.google.com/site/russabbott/
_____________________________________________

On Wed, Jul 27, 2011 at 12:54 PM, Russ Abbott <russ.abbott@...> wrote:

I just looked at Theory of Nothing on <a href="http://www.amazon.com/Theory-Nothing-Russell-Standish/dp/1921019638" target="" onclick="window.open('http://www.amazon.com/Theory-Nothing-Russell-Standish/dp/1921019638');return false;">Amazon. Two very nice reviews. Amazon's "Look Inside" doesn't show much, but the book looks very much worth reading. The Introduction talks about Schrodinger's cat. It had never occurred to me that the cat always experiences a boring hour and then comes out alive--at least according to the Many Worlds View of QM. It's on my reading list.

-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles

Google voice: 747-999-5105
blog: <a href="http://russabbott.blogspot.com/" style="font-style:italic" target="" onclick="window.open('http://russabbott.blogspot.com/');return false;">http://russabbott.blogspot.com/
vita: <a href="http://sites.google.com/site/russabbott/" style="font-style:italic" target="" onclick="window.open('http://sites.google.com/site/russabbott/');return false;">http://sites.google.com/site/russabbott/
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On Tue, Jul 26, 2011 at 3:13 PM, Grant Holland <grant.holland.sf@...> wrote:

Exciting, Russ. I've downloaded <a href="http://arxiv.org/pdf/physics/0001020v6" target="" onclick="window.open('http://arxiv.org/pdf/physics/0001020v6');return false;">your 2004 paper, and will take a look.

Thanks,
Grant

On 7/26/11 3:16 PM, Russell Standish wrote:

Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing). I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote:

I expected this to have more of an impact than it seems to be having. What am I missing? *-- Russ Abbott* *_____________________________________________* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *<a href="http://russabbott.blogspot.com/" target="" onclick="window.open('http://russabbott.blogspot.com/');return false;">http://russabbott.blogspot.com/ vita: <a href="http://sites.google.com/site/russabbott/" target="" onclick="window.open('http://sites.google.com/site/russabbott/');return false;">http://sites.google.com/site/russabbott/ *_____________________________________________* On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott <russ.abbott@...> wrote:

From APS Physics <a href="http://physics.aps.org/articles/v4/55" target="" onclick="window.open('http://physics.aps.org/articles/v4/55');return false;"><http://physics.aps.org/articles/v4/55>. We know how to use the “rules” of quantum physics to build lasers, microchips, and nuclear power plants, but when students question the rules themselves, the best answer we can give is often, “The world just happens to be that way.” Yet why are individual outcomes in quantum measurements random? What is the origin of the Schrödinger equation? In a paper [1<a href="http://physics.aps.org/articles/v4/55#c1" target="" onclick="window.open('http://physics.aps.org/articles/v4/55#c1');return false;"><http://physics.aps.org/articles/v4/55#c1>] appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory. (Strictly speaking, their derivation only applies to systems that can be constructed from a finite number of quantum states, such as spin.) In this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s belief that one obtains “it from bit,” in other words, that our account of the universe is constructed from bits of information, and the rules on how that information can be obtained determine the “meaning” of what we call particles and fields. ... They assume five new elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—which define a broad class of theories of information processing. For example, the causality axiom—stating that one cannot signal from future measurements to past preparations—is so basic that it is usually assumed a priori. Both classical and quantum theory fulfil the five axioms. What is significant about Chiribella et al.’s work is that they show that a sixth axiom—the assumption that every state has what they call a “purification”—is what singles out quantum theory within the class. In fact, this last axiom is so important that they call it a postulate. The purification postulate can be defined formally (see below), but to understand its meaning in simple words, we can look to Schrödinger, who in describing entanglement gives the essence of the postulate: “Maximal knowledge of a total system does not necessarily include maximal knowledge of all its parts.” (Formally, the purification postulate states that every mixed state ρA of system A can always be seen as a state belonging to a part of a composite system AB that itself is in a pure state ΨAB. This pure state is called “purification” and is assumed to be unique up to a reversible transformation on B). Chiribella et al. conclude there is only one way in which a theory can satisfy the purification postulate: it must contain entangled states. (The other option, that the theory must not contain mixed states, that is, that the probabilities of outcomes in any measurement are either 0 or 1 like in classical deterministic theory, cannot hold, as one can always prepare mixed states by mixing deterministic ones.) The purification postulate alone allows some of the key features of quantum information processing to be derived, such as the no-cloning theorem or teleportation [7<a href="http://physics.aps.org/articles/v4/55#c7" target="" onclick="window.open('http://physics.aps.org/articles/v4/55#c7');return false;"><http://physics.aps.org/articles/v4/55#c7>]. By combining this postulate with the other five axioms, Chiribella et al. were able to derive the entire mathematical formalism behind quantum theory. *-- Russ Abbott* *_____________________________________________* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 * blog: *<a href="http://russabbott.blogspot.com/" target="" onclick="window.open('http://russabbott.blogspot.com/');return false;">http://russabbott.blogspot.com/ vita: <a href="http://sites.google.com/site/russabbott/" target="" onclick="window.open('http://sites.google.com/site/russabbott/');return false;">http://sites.google.com/site/russabbott/ *_____________________________________________*

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