What does it mean for two things to be identical?
Intuition tell us that if you are able to do a measurement or experiment such that you can detect a difference, then those two items are not identical. However, this statement of identical seems to be dependant on the abilities of the experimentalist. But what about if instead of considering some classical macroscopic objects whose distinguishability is dependant on the experimentalist, we instead consider fundamental particles, such as two electrons, existing in the quantum realm. As these particles are fundamentally the same the definition of identical is no longer dependant on the abilities of the experimenter to distinguish them but is a characteristic of the particles themselves.
This quantum nature of indistinguishable has an important consequence when considering systems of these identical particles. This consequence is called the symmetrisation principle, interested readers should resort to Feynman’s lecture notes (Vol III Ch 4.). A consequence of this symmetrisation is that the state of the full system now appears to have an important quantum property, known as entanglement. This is the quantum property once described by Einstein as “Spooky action at a distance” but is now expected to play an essential part in quantum computation and communication. However, we now have a problem, despite these identical particles being formally entangled how do we utilize it when we can’t tell which particle is which?
The problem and solution is described in the following situation…
Our blog Quanta Rei has been online for three and a half years. We’ve been exploring a variety of ways to convey our passion for science. Some of our posts have been rather technical, some more philosophical, some quite artistic. This post is about poetry.
Earlier this year, during a morning run, I suddenly remembered about my passion for rhymes. When I was in high school and later studying Physics at the University of Salerno (Italy), I spent many a hour composing sonnets – in Italian. Some of them being love poems, others being more humorous and satirical ones to be posted on the now defunct portal Risateonline.com – often in response to challenges set by my then competitor and now friend Rullianus. Then, not sure why, but I haven’t been writing poetry in almost two decades, till now.
Cross posted from FQXi’s blog: https://fqxi.org/community/forum/topic/3253
I recently completed a collaborative art-physics project, with award-winning artist Joseph Namara Hollis, to produce a short, illustrated book about the quantum mechanical reality in which we live.
From the start, this was an ambitious project. Our aim was to introduce quite challenging philosophical concepts deeply embedded in quantum mechanics. Our target audience was broad: we hoped that anyone from school science students to academic quantum physicists would both learn something, and be entertained, by the book. And finally, the book is short – only six double page spreads – and contains minimal text, with the intention that the illustrations play a central part in conveying the concepts we introduce. So, have we succeeded? You can find out by reading the book online here.
Humankind has a fantastically deep and complex understanding of many of the scientific and philosophical puzzles that have baffled our ancestors. We understand the inner workings of the sun, and what lives in the most remote places on Earth; we have a good idea of what happened a fraction of a second after the Big Bang, and how distant galaxies were formed; and we can explain the basic structure and the evolutionary emergence of the complex organisms that roam our planet. But there are some mysteries that still elude us, and perhaps none are as close, personal, and important as the question of how our brains work – how they produce such a rich variety and complexity of thoughts and feelings, and how they perform such a huge range of tasks, from communication to mathematics to movement. And while AI is making great progress, our computers are still far behind most everyday cognitive tasks, such as the activity in your brain right now while you are reading this post. Furthermore, how can such a lump of meat produce the rich first-person experience that we are all consumed by throughout our lives?
Roger Penrose’s book Shadows of the Mind confronts these problems head-on, by giving a detailed assessment of the question: Is the human mind a computer? Can it be simulated by a computer, and can its workings be understood and explained only using computation? Penrose is conclusion is a resounding no: he concludes that the human mind is not a computer, and the workings of the human mind cannot be explained by computation alone.
The vast body of scientific knowledge is a whole divided into three parts, or layers. The first falls under the name of empirical knowledge, and includes the descriptions and the results of all experiments ever attempted. The second part comprises the mathematical systematisations of those experiments and the rules to predict the outcomes of future ones, that is, the physical theories of Nature. There is also a third part, to which one may ascribe the abstract study of physical theories themselves, seen as mathematical and logical objects. The purpose of this blog post is to advocate the importance of this ‘meta-theoretical’ layer of knowledge from a conceptual and foundational standpoint, and to illustrate how it is possible to investigate it.
There is not a deep divide between science and arts. Rather the opposite! I have long been interested in unveiling links between these two seemingly distinct spheres of knowledge. Scientists are typically seen as rational beings who pursue the truth and are not afraid of dissecting the most beautiful manifestations of nature into a set of basic analytical rules, often formalised as mathematical equations, even going as far as reducing the feelings of love to a series of biochemical reactions. Artists, on the other hand, are often perceived as creative characters who synthesise and embellish emotions by expressing them in languages which touch deeper chords in humanity, such as music or imagery.
Yet for those doing science with a passion, beautiful equations are perceived as equally if not more touching than a work of art, and creativity is a fundamental requirement for reaching beyond the state of the art on our understanding of how the universe works. Similarly, an increasing number of artists resort to analytical methods to explore novel ways to communicate inner expressions of self. And let’s not forget that a streak of polymaths, in which a combination of scientific and artistic skills has resulted in universally acclaimed masterpieces which made history, can be traced back many centuries: Leonardo da Vinci is perhaps the brightest example.
Quantum Roundabout 2018 was the fourth iteration of a series of dedicated conferences looking at foundational mathematical topics within quantum physics.
The etymology of the conference stems from the so called “Magic Roundabout” on the outskirts of Swindon. This roundabout boasts five mini-roundabouts arranged around a sixth central anticlockwise roundabout. It was decided that such a strange junction could only be quantum in nature, hence the conception of Quantum Roundabout. Continue reading