Quantum mechanics anyone? Dozens have been disappointed by UCLA’s administration ineptly standing in the way of Dr. Mike Miller being able to offer his perennial Winter UCLA math class (Ring Theory this quarter), so a few friends and I are putting our informal math and physics group back together.

We’re mounting a study group on quantum mechanics based on Peter Woit‘s Introduction to Quantum Mechanics course from 2022. We’ll be using his textbook Quantum Theory, Groups and Representations:An Introduction (free, downloadable .pdf) and his lectures from YouTube.

Shortly, we’ll arrange a schedule and some zoom video calls to discuss the material. If you’d like to join us, send me your email or leave a comment so we can arrange meetings (likely via Zoom or similar video conferencing).

Our goal is to be informal, have some fun, but learn something along the way. The suggested mathematical background is some multi-variable calculus and linear algebra. Many of us already have some background in Lie groups, algebras, and representation theory and can hopefully provide some help for those who are interested in expanding their math and physics backgrounds.

Everyone is welcome! 

Yellow cover of Quantum Theory, Groups and Representations featuring some conic sections in the background

Bookmarked Lecture Notes by Arun DebrayArun Debray (web.ma.utexas.edu)
I LATEXed up lecture notes for many of the classes I have taken; feel free to read through them or use them to review. If you find a mistake or typo, please let me know. If you want to look over the .tex source for any of these notes, please send me an email.
A great set of LaTeXed notes from a variety of coursework.

via Rama Kunapuli.

Liked a tweet by Tai-Danae Bradley (@math3ma) (Twitter)
Bookmarked At the Interface of Algebra and Statistics by Tai-Danae Bradley (arXiv.org)
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.

Quantum theory cannot consistently describe the use of itself | Nature Communications

Bookmarked Quantum theory cannot consistently describe the use of itself by Daniela Frauchiger & Renato Renner (Nature Communications)
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity. The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory. Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. The agents’ conclusions, although all derived within quantum theory, are thus inconsistent. This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.
Published version of arXiv paper at https://arxiv.org/abs/1604.07422v1

hat tip: https://boffosocko.com/2019/01/01/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-quanta-magazine/

[1604.07422v1] Single-world interpretations of quantum theory cannot be self-consistent

Bookmarked Single-world interpretations of quantum theory cannot be self-consistent by Daniela Frauchiger & Renato Renner (arXiv.org)
According to quantum theory, a measurement may have multiple possible outcomes. Single-world interpretations assert that, nevertheless, only one of them "really" occurs. Here we propose a gedankenexperiment where quantum theory is applied to model an experimenter who herself uses quantum theory. We find that, in such a scenario, no single-world interpretation can be logically consistent. This conclusion extends to deterministic hidden-variable theories, such as Bohmian mechanics, for they impose a single-world interpretation.
Hat tip: https://boffosocko.com/2019/01/01/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-quanta-magazine/

👓 Frauchiger-Renner Paradox Clarifies Where Our Views of Reality Go Wrong | Quanta Magazine

Read Frauchiger-Renner Paradox Clarifies Where Our Views of Reality Go Wrong by Anil AnanthaswamyAnil Ananthaswamy (Quanta Magazine)
A thought experiment has shaken up the world of quantum foundations, forcing physicists to clarify how various quantum interpretations (such as many-worlds and the Copenhagen interpretation) abandon seemingly sensible assumptions about reality.

👓 The End of History? | Francis Fukuyama

Read The End of History? by Francis FukuyamaFrancis Fukuyama (The National Interest | No. 16 (Summer 1989), pp. 3-18)

IN WATCHING the flow of events over the past decade or so, it is hard to avoid the feeling that something very fundamental has happened in world history. The past year has seen a flood of articles commemorating the end of the Cold War, and the fact that "peace" seems to be breaking out in many regions of the world. Most of these analyses lack any larger conceptual framework for distinguishing between what is essential and what is contingent or accidental in world history, and are predictably superficial. If Mr. Gorbachev were ousted from the Kremlin or a new Ayatollah proclaimed the millennium from a desolate Middle Eastern capital, these same commentators would scramble to announce the rebirth of a new era of conflict.

And yet, all of these people sense dimly that there is some larger process at work, a process that gives coherence and order to the daily headlines. The twentieth century saw the developed world descend into a paroxysm of ideological violence, as liberalism contended first with the remnants of absolutism, then bolshevism and fascism, and finally an updated Marxism that threatened to lead to the ultimate apocalypse of nuclear war. But the century that began full of self-confidence in the ultimate triumph of Western liberal democracy seems at its close to be returning full circle to where it started: not to an "end of ideology" or a convergence between capitalism and socialism, as earlier predicted, but to an unabashed victory of economic and political liberalism.

In general, while I’ve been reading Stuart Kauffmann’s At Home in the Universe, I can’t help but thinking about the cascading extinctions he describes and wonder if political extinctions of ideas like Communism or other forms of government or even economies might follow the same types of outcomes described there?   
August 29, 2018 at 09:37AM

Building on this, could we create a list of governments and empires and rank them in order of the length of their spans? There may be subtleties in changes of regimes in some eras, but generally things are probably reasonably well laid out. I wonder if the length of life of particular governments follows a power law? One would suspect it might.   
August 29, 2018 at 09:43AM

Highlights, Quotes, Annotations, & Marginalia

The triumph of the West, of the Western idea, is evident first of all in the total exhaustion of viable systematic alternatives to Western liberalism.  

Total exhaustion?
August 29, 2018 at 08:53AM

What we may be witnessing is not just the end of the Cold War, or the passing of a particular period of postwar history, but the end of history as such: that is, the end point of mankind’s ideological evolution and the universalization of Western liberal democracy as the final form of human government.  

What if, in fact, we’ve only just found a local maximum? What if in the changing landscape there are other places we could potentially get to competitively that supply greater maxima? And possibly worse, what if we need to lose value to get from here to unlock even more value there?
August 29, 2018 at 08:56AM

Hegel believed that history culminated in an absolute moment – a moment in which a final, rational form of society and state became victorious.  

and probably not a bad outcome in an earlier era that thought of things in terms of clockwork and lacked the ideas of quantum theory and its attendant uncertainties.
August 29, 2018 at 08:59AM

Believing that there was no more work for philosophers as well, since Hegel (correctly understood) had already achieved absolute knowledge, Kojève left teaching after the war and spent the remainder of his life working as a bureaucrat in the European Economic Community, until his death in 1968.  

This is depressing on so many levels.
August 29, 2018 at 09:05AM

Paul Kennedy’s hugely successful “The Rise and Fall of the Great Powers”, which ascribes the decline of great powers to simple economic overextension.  

Curious how this may relate to the more recent “The End of Power” by Moisés Naím. It doesn’t escape one that the title of the book somewhat echoes the title of this particular essay.
August 29, 2018 at 09:18AM

But whether a highly productive modern industrial society chooses to spend 3 or 7 percent of its GNP on defense rather than consumption is entirely a matter of that society’s political priorities, which are in turn determined in the realm of consciousness.  

It’s not so much the percentage on produced defense goods, but how quickly could a society ramp up production of goods, services, and people to defend itself compared to the militaries of its potential aggressors.

In particular, most of the effort should go to the innovation side of war materiel. The innovation of the atomic bomb is a particularly nice example in that as a result of conceptualizing and then executing on it it allowed the US to win the war in the Pacific and hasten the end of war in Europe. Even if we otherwise had massive stockpiles of people or other weapons, our enemies could potentially have equaled them and dragged the war on interminably. It was the unknown unknown via innovation that unseated Japan and could potentially do the same to us based on innovation coming out of almost any country in the modern age.
August 29, 2018 at 09:24AM

Weber notes that according to any economic theory that posited man as a rational profit-maximizer, raising the piece-work rate should increase labor productivity. But in fact, in many traditional peasant communities, raising the piece-work rate actually had the opposite effect of lowering labor productivity: at the higher rate, a peasant accustomed to earning two and one-half marks per day found he could earn the same amount by working less, and did so because he valued leisure more than income. The choices of leisure over income, or of the militaristic life of the Spartan hoplite over the wealth of the Athenian trader, or even the ascetic life of the early capitalist entrepreneur over that of a traditional leisured aristocrat, cannot possibly be explained by the impersonal working of material forces,  

Science could learn something from this. Science is too far focused on the idealized positive outcomes that it isn’t paying attention to the negative outcomes and using that to better define its outline or overall shape. We need to define a scientific opportunity cost and apply it to the negative side of research to better understand and define what we’re searching for.

Of course, how can we define a new scientific method (or amend/extend it) to better take into account negative results–particularly in an age when so many results aren’t even reproducible?
August 29, 2018 at 09:32AM

FAILURE to understand that the roots of economic behavior lie in the realm of consciousness and culture leads to the common mistake of attributing material causes to phenomena that are essentially ideal in nature.  

August 29, 2018 at 09:44AM

“Protestant” life of wealth and risk over the “Catholic” path of poverty and security.[8]   

Is this simply a restatement of the idea that most of “the interesting things” happen at the border or edge of chaos? The Catholic ethic is firmly inside the stable arena while that of the Protestant ethic is pushing the boundaries.
August 29, 2018 at 09:47AM

Hence it did not matter to Kojève that the consciousness of the postwar generation of Europeans had not been universalized throughout the world; if ideological development had in fact ended, the homogenous state would eventually become victorious throughout the material world.  

This presupposes that homeostasis could ever be achieved.

One thinks of phrases like “The future is here, it just isn’t evenly distributed.” But everything we know about systems and evolving systems often indicates that homeostasis isn’t necessarily a good thing. In many cases, it means eventual “death” instead of evolving towards a longer term lifespan. Again, here Kauffmann’s ideas about co-evolving systems and evolving landscapes may provide some guidance. What if we’re just at a temporary local maximum, but changes in the landscape modify that fact? What then? Shouldn’t we be looking for other potential distant maxima as well?
August 29, 2018 at 09:52AM

But that state of consciousness that permits the growth of liberalism seems to stabilize in the way one would expect at the end of history if it is underwritten by the abundance of a modern free market economy.  

Writers spend an awful lot of time focused too carefully on the free market economy, but don’t acknowledge a lot of the major benefits of the non-free market parts which are undertaken and executed often by governments and regulatory environments. (Hacker & Pierson, 2016)
\August 29, 2018 at 10:02AM

Are there, in other words, any fundamental “contradictions” in human life that cannot be resolved in the context of modern liberalism, that would be resolvable by an alternative political-economic structure?  

Churchill famously said “…democracy is the worst form of Government except for all those other forms that have been tried from time to time…”

Even within this quote it is implicit that there are many others. In some sense he’s admitting that we might possibly be at a local maximum but we’ve just not explored the spaces beyond the adjacent possible.
August 29, 2018 at 10:08AM

For our purposes, it matters very little what strange thoughts occur to people in Albania or Burkina Faso, for we are interested in what one could in some sense call the common ideological heritage of mankind.  

While this seems solid on it’s face, we don’t know what the future landscape will look like. What if climate change brings about massive destruction of homo sapiens? We need to be careful about how and why we explore both the adjacent possible as well as the distant possible. One day we may need them and our current local maximum may not serve us well.
August 29, 2018 at 10:10AM

anomie  

I feel like this word captures very well the exact era of Trumpian Republicanism in which we find ourselves living.
August 29, 2018 at 10:37AM

After the war, it seemed to most people that German fascism as well as its other European and Asian variants were bound to self-destruct. There was no material reason why new fascist movements could not have sprung up again after the war in other locales, but for the fact that expansionist ultranationalism, with its promise of unending conflict leading to disastrous military defeat, had completely lost its appeal. The ruins of the Reich chancellery as well as the atomic bombs dropped on Hiroshima and Nagasaki killed this ideology on the level of consciousness as well as materially, and all of the pro-fascist movements spawned by the German and Japanese examples like the Peronist movement in Argentina or Subhas Chandra Bose’s Indian National Army withered after the war.  

And yet somehow we see these movements anew in America and around the world. What is the difference between then and now?
August 29, 2018 at 11:46AM

This is not to say that there are not rich people and poor people in the United States, or that the gap between them has not grown in recent years. But the root causes of economic inequality do not have to do with the underlying legal and social structure of our society, which remains fundamentally egalitarian and moderately redistributionist, so much as with the cultural and social characteristics of the groups that make it up, which are in turn the historical legacy of premodern conditions.  

August 29, 2018 at 11:47AM

But those who believe that the future must inevitably be socialist tend to be very old, or very marginal to the real political discourse of their societies.  

and then there are the millennials…
August 29, 2018 at 11:51AM

Beginning with the famous third plenum of the Tenth Central Committee in 1978, the Chinese Communist party set about decollectivizing agriculture for the 800 million Chinese who still lived in the countryside. The role of the state in agriculture was reduced to that of a tax collector, while production of consumer goods was sharply increased in order to give peasants a taste of the universal homogenous state and thereby an incentive to work. The reform doubled Chinese grain output in only five years, and in the process created for Deng Xiaoping a solid political base from which he was able to extend the reform to other parts of the economy. Economic Statistics do not begin to describe the dynamism, initiative, and openness evident in China since the reform began.  

August 29, 2018 at 11:58AM

At present, no more than 20 percent of its economy has been marketized, and most importantly it continues to be ruled by a self-appointed Communist party which has given no hint of wanting to devolve power.  

If Facebook were to continue to evolve at it’s current rate and with it’s potential power as well as political influence, I could see it attempting to work the way China does in a new political regime.
August 29, 2018 at 12:04PM

IF WE ADMIT for the moment that the fascist and communist challenges to liberalism are dead, are there any other ideological competitors left? Or put another way, are there contradictions in liberal society beyond that of class that are not resolvable? Two possibilities suggest themselves, those of religion and nationalism.  

August 29, 2018 at 12:19PM

This school in effect applies a Hobbesian view of politics to international relations, and assumes that aggression and insecurity are universal characteristics of human societies rather than the product of specific historical circumstances.  

August 29, 2018 at 12:30PM

But whatever the particular ideological basis, every “developed” country believed in the acceptability of higher civilizations ruling lower ones  

August 29, 2018 at 12:37PM

Perhaps this very prospect of centuries of boredom at the end of history will serve to get history started once again.  

Has it started again with nationalism, racism, and Trump?
August 29, 2018 at 12:48PM

Reply to Kartik Singhal about Webmention

Replied to a tweet by Kartik SinghalKartik Singhal (Twitter)
Let me know if you need help finding resources. I see you have a Hugo site and I’m pretty sure someone has set it up for Webmention use before. https://indieweb.org/Hugo

Following Mark Stanley Everitt

Followed Mark Stanley Everitt (Qubyte Codes)

Mark Stanley Everitt headshot Welcome to qubyte.codes! The personal site of Mark Stanley Everitt.

I'm a programmer specialising in JavaScript, living and working in Brighton, UK. This blog is a place for me to write about stuff I find interesting or useful. Probably JavaScript for the most part, but certainly not limited to it. By day I spend most of my programming time writing Node.js applications, with a little browser stuff when I can.

I'm also interested in the social side and ethics of software development. I'm a regular mentor at Codebar in Brighton.

I lived and worked in Tokyo for a number of years, initially as an academic (I hold a PhD in quantum optics and quantum information), and later as a programmer. I speak a little Japanese.

If you have and questions of comments, tweet to me @qubyte or toot to me at @qubyte@mastodon.social .

If you're interested in code I've published, I'm qubyte on GitHub.

A blogger/coder who was into quantum mechanics, information theory, supports webmentions, and speaks some Japanese? How could I not follow?!

👓 Andrew Jordan reviews Peter Woit’s Quantum Theory, Groups and Representations and finds much to admire. | Inference

Read Woit’s Way by Andrew Jordan (Inference: International Review of Science)
Andrew Jordan reviews Peter Woit's Quantum Theory, Groups and Representations and finds much to admire.
For the tourists, I’ve noted before that Peter maintains a free copy of his new textbook on his website.

I also don’t think I’ve ever come across the journal Inference before, but it looks quite nice in terms of content and editorial.

🔖 The Theory of Quantum Information by John Watrous

Bookmarked The Theory of Quantum Information by Tom Watrous (cs.uwaterloo.ca)

To be published by Cambridge University Press in April 2018.

Upon publication this book will be available for purchase through Cambridge University Press and other standard distribution channels. Please see the publisher's web page to pre-order the book or to obtain further details on its publication date.

A draft, pre-publication copy of the book can be found below. This draft copy is made available for personal use only and must not be sold or redistributed.

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.

h/t to @michael_nielsen via Nuzzel

Following Ilyas Khan

Followed Ilyas Khan (LinkedIn)
Ilyas Khan Co-Founder and CEO at Cambridge Quantum Computing
Dear god, I wish Ilyas had a traditional blog with a true feed, but I’m willing to put up with the inconvenience of manually looking him up from time to time to see what he’s writing about quantum mechanics, quantum computing, category theory, and other areas of math.

👓 Something New For Baby To Chew On: Rocket Science And Quantum Physics | NPR

Read Something New For Baby To Chew On: Rocket Science And Quantum Physics by Lynn Neary & Julie Depenbrock (NPR)
The books introduce subjects like rocket science, quantum physics and general relativity — with bright colors, simple shapes and thick board pages perfect for teething toddlers. The books make up the Baby University series — and each one begins with the same sentence and picture — This is a ball — and then expands on the titular concept.
Ooh! We definitely need more books like these in early childhood education.