One must bring in some basic notions of quantum theory if one wants to reduce de- and reconstruction to quantum physics. The key mathematical fact is that in quantum theory each particle in many-particle state corresponds to a tensor factor of state space of the entire system. This notion is very difficult to explain without actually having a lecture series about quantum theory and I prove in the following that this is indeed the case.
1. The space of quantum states of system is the basic notion: technically it is known as Hilbert space, which can have finite or even infinite dimension and also infinite dimension (and this in many senses!).
The basic idea is that one can build bigger Hilbert spaces as their tensor products. If you have Hilbert spaces of dimensions n1 and n2, the tensor product has dimension n1× n2. This is algebraically like multiplying numbers and one can indeed identify prime Hilbert spaces as those with prime dimension. Also direct sums of Hilbert spaces are possible.
Hilbert spaces represent physical systems: say electron and proton. To describe a world consisting of proton and electron one forms the tensor product of electron and proton Hilbert spaces. This is somewhat like playing with legos.
I was cheating a little bit. Life is not quite so simple. One can also form bound states of two systems - say hydrogen atom from proton and electron, and the bound states of hydrogen atom represent only a sub-space of the tensor product. Connes tensor product is more exotic example: only certain kind of entangled states in tensor product for which the composites are strongly correlated are allowed. As a matter of fact, also the gluing the legos together creates strong correlations between them so that it serves as a good analogy for Connes tensor product and tensor product assignable to bound states.
How disputes over privacy and security have shaped the relationship between the European Union and the United States and what this means for the futureWe live in an interconnected world, where security problems like terrorism are spilling across borders, and globalized data networks and e-commerce platforms are reshaping the world economy. This means that states’ jurisdictions and rule systems clash. How have they negotiated their differences over freedom and security? Of Privacy and Power investigates how the European Union and United States, the two major regulatory systems in world politics, have regulated privacy and security, and how their agreements and disputes have reshaped the transatlantic relationship.The transatlantic struggle over freedom and security has usually been depicted as a clash between a peace-loving European Union and a belligerent United States. Henry Farrell and Abraham Newman demonstrate how this misses the point. The real dispute was between two transnational coalitions—one favoring security, the other liberty—whose struggles have reshaped the politics of surveillance, e-commerce, and privacy rights. Looking at three large security debates in the period since 9/11, involving Passenger Name Record data, the SWIFT financial messaging controversy, and Edward Snowden’s revelations, the authors examine how the powers of border-spanning coalitions have waxed and waned. Globalization has enabled new strategies of action, which security agencies, interior ministries, privacy NGOs, bureaucrats, and other actors exploit as circumstances dictate.The first serious study of how the politics of surveillance has been transformed, Of Privacy and Power offers a fresh view of the role of information and power in a world of economic interdependence.
Highly Commended by the 2020 Business Book Awards
Digital influencing is one of the most exciting and disruptive new media industries, forecast to be worth over £10bn by 2020. Influencers now dominate the digital world and, when it comes to growth, they are consistently outperforming traditional media and brand advertising.
Despite their prominence, digital influencers continue to be misunderstood and undervalued by many people, as those charged with incorporating the influencer space into their digital strategy rarely comprehend how this extremely powerful industry works. As one of the leading authorities on the influencer space, Sara McCorquodale demystifies exactly how it operates, as she interrogates the phenomenon, analyses its problems and forecasts its future.
Influence draws upon first-hand interviews with world-renowned influencers, providing an invaluable insight into the inner-workings of digital culture and how it can best be used as an effective marketing and branding platform. This compelling guide on how to effectively identify and utilise the power of influencers is a must-read for anyone who wants their business to succeed and prosper online.
From the bestselling author of A More Beautiful Question, hundreds of big and small questions that harness the magic of inquiry to tackle challenges we all face--at work, in our relationships, and beyond.
When confronted with almost any demanding situation, the act of questioning can help guide us to smart decisions. By asking questions, we can analyze, learn, and move forward in the face of uncertainty. But "questionologist" Warren Berger says that the questions must be the right ones; the ones that cut to the heart of complexity or enable us to see an old problem in a fresh way.
In The Book of Beautiful Questions, Berger shares illuminating stories and compelling research on the power of inquiry. Drawn from the insights and expertise of psychologists, innovators, effective leaders, and some of the world's foremost creative thinkers, he presents the essential questions readers need to make the best choices when it truly counts, with a particular focus in four key areas: decision-making, creativity, leadership, and relationships.
The powerful questions in this book can help you:
- Identify opportunities in your career or industry
- Generate fresh ideas in business or in your own creative pursuits
- Check your biases so you can make better judgments and decisions
- Do a better job of communicating and connecting with the people around you
Thoughtful, provocative, and actionable, these beautiful questions can be applied immediately to bring about change in your work or your everyday life.
Hedgehogs, with their quiet determination and bristling, bumbling ways, are seen by many of one of life's most enduring symbols of the countryside and town gardens. This shy, snuffling, enigmatic animal has captured the imagination of children and adults for centuries – from Beatrix Potter's Mrs Tiggywinkle to Sonic the Hedgehog.
Full to the brim with fascinating insights and countryside lore, The Hedgehog Handbook explores different facets of this much-admired mammal – from its wildlife habits to its literary heritage, how different cultures have viewed the hedgehog and what we can do to help preserve this icon of rural life.
Fun, sweet and warm hearted, The Hedgehog Handbook is a month by month celebration of one of the countryside's best-loved creatures. Packed with inspirational quotes, entertaining facts, folklore and literary references, it's the perfect gift for anyone with a penchant for prickles.
'The Internet was supposed to be for everyone... Millions found their voices in this brave new online world; it gave unheard masses the space to speak to each other without limits, across borders, both physical and social. It was supposed to liberate us from gender. But as more and more of our daily lives migrated on line, it seemed it did matter if you were a boy or a girl.'
It's a tough time to be a woman on the internet. Over the past two generations, the political map of human relations has been redrawn by feminism and by changes in technology. Together they pose questions about the nature and organisation of society that are deeply challenging to those in power, and in both cases, the backlash is on. In this brave new world, old-style sexism is making itself felt in new and frightening ways.
In Cybersexism, Laurie Penny goes to the dark heart of the matter and asks why threats of rape and violence are being used to try to silence female voices, analyses the structure of online misogyny, and makes a case for real freedom of speech – for everyone.
Laurie Penny's forthcoming book, Unspeakable Things: Sex, Lies and Revolution, will be published in 2014.
Thank you for your interest in this booklet. The "The Basics" series, is a series of booklets designed to help you get the basics or foundations about a subject. Time is one of our most precious resources and as such it does not comeback, for that reason the Amber siblings have created this series. It is a series of small quick and easy to read and understand booklets, designed to give you a quick idea on a subject. Instead of spending a lot of time and money on a subject to find out that it is not what you expected, this series allows you to get a quick overview, without spending a lot of time or money. If you then find that it is a subject of interest you can invest more time and/or money. Since this is a booklet it is short in pages as it is designed to get to the point quickly.
This booklet is titled "Social Media: The Basics" and covers:
Social Media Basics
Benefits of Social Media
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