European Mathematical Society - 81 Quantum theory
https://euro-math-soc.eu/msc/81-quantum-theory
enBreakfast with Einstein
https://euro-math-soc.eu/review/breakfast-einstein
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Orzel is a physicist who authored several popularizing books already. How to teach quantum mechanics to your dog is probably the best known because it was a bestseller. In this book, Orzel does something similar and explains all the quantum effects that we are constantly (and probably unknowingly) experience as one gets out of bed and have breakfast at sunrise.</p>
<p>For example the sun is a gigantic nuclear reactor essential for our existence. What is happening in the sun? Why it exists the way it does? And more generally how to explain the whole existence of the universe? These are the first topics to be explained. It is all a matter of particles being attracted, and repulsed as they are subject to several forces. This causes the collapsing of stars, evolving into a white dwarf, a neutron star, or a black hole depending on its total mass. It is all an interplay of gravity, electromagnetism, and strong and weak nuclear interaction. This introduces some model of atoms consisting of a kernel and electrons, forming a system that is kept in a stable state by all these forces. In fact the growing insight into the structure and the physics that take place at an atomic scale is used to lead us throughout the historical evolution sketched in this book.</p>
<p>The next trigger is the observation that heated material shows a red glow (like in the toaster). This is a reason to discuss light, wavelength and photons. It was Einstein's suggestion in his analysis of the photoelectric effect that light might be a particle. Recall that it was this, and not relativity theory, that eventually resulted in his Nobel Prize. So now that we got Einstein involved, we have a complete explanation of the title of the book. The alarm clock is triggering reflections on time keeping, which in modern times depends on the oscillations of a cesium atom. This requires a more detailed analysis of the atomic structure and the physics that happen there.</p>
<p>The Internet is the next trigger. This chapter is an exploration of glass fibers and deals again with the interaction of light and atoms. We are introduced to the physics of lasers. The smell of a cup of coffee is a reason to explain why and how we can smell something. This is related to how atoms bond and form molecules. The planetary model of an atom with kernel and electrons needs to be replaced by atoms that are sharing electrons. The Schrödinger equation characterizes the probability distribution of the position of the electron and we are confronted with the Heisenberg uncertainty principle. Next is the question why solid objects are solid. Why do they not collapse like stars do and cause a nuclear explosion? To answer this, one needs to look at the global behaviour of many atoms. And of course this can be applied to how we experience a loaf of bread as well as to how we can explain some astrophysical phenomena.</p>
<p>Computer chips, require semiconductors and diodes. These are explained starting from a single molecule with a discrete energy spectrum emitting particular wavelengths of light, but many molecules together emit a certain continuous frequency band. In this context Orzel explains a surprising fact about some parrot feathers that seem to be blue, while consisting of filaments of keratin which is actually grey and slightly translucent. It is all a matter of matching wavelengths. Ordinary magnets are even more mysterious to explain. It depends on the spin of the electrons and how they are paired in different states of excitation, taking into account Pauli's exclusion principle and how they interact when in bulk.</p>
<p>A smoke detector depends on light being reflected by tiny smoke particles. More advanced ones can detect particles that do not reflect light well and these use a small ionization chamber and detect disturbances. The latter depends on alpha particles generated during the decay of an artificial radioactive element. Radioactivity and quantum tunnelling are explained and these effects are also important for X-ray radiography and other medical applications. The final application explains entanglement, the EPR (Einstein-Podolsky-Rosen) paradox and sketches the related Bell theorem and the Aspect experiment. It explains how this can break down our whole encryption system when quantum computing becomes a common reality.</p>
<p>Orzel uses physics, not mathematics in his explanations of the quantum effects. These are mostly related to the structure of the atom and the interaction of electrons in molecules. All the atomic models are explained with the increasing complexity that grew as physicists got more and more insight. Historical context is given of all the physical models proposed and the related experiments but also about the application that is being considered like time keeping, the Internet, the use of the magnetic compass by sailors, etc. It is interesting to note that in this context some puzzling observations could only be explained by breaking with traditional views. The new model that was proposed depended partly on intuition and it was often only later confirmed by mathematical computations and experiments. Original ideas are what makes the quantum leap advances in science just like an original angle of approach from a different area can solve a long standing problem in mathematics. It is also noteworthy that in the course of history, several breakthroughs were proposed by scientists who spent some time away from their usual research environment. Newton is a well known example who proposed calculus when he returned from his stay in the countryside during the plague, and Orzel gives other examples.</p>
<p>Orzel often refers to some scientist "who did the mathematics" and could confirm what he or somebody else had proposed, or, that in a more complicated situation of more than just one atom "the mathematics become much more involved". Thus it is clear that Orzel suggests that there is mathematics underlying all these models, but he does not go anywhere into the mathematics itself. So it may be a bit disappointing that with Einstein in the title, there is not more mathematics. Even relativity theory is absent. It is not relevant at this level of detail anyway. Neither is Orzel visiting the zoo of subatomic particles that have been proposed more recently. He is not even hinting at the Theory of Everything, a theory where theoretical physicists are nowadays wandering is an almost purely mathematical maze. Some have criticized this modern evolution as pure mathematical speculation which is not even scientific because it is not verifiable by experiment any more.</p>
<p>Thus if you expect to find mathematics in this book you may be disappointed, but you will find a readable introduction of the quantum physics that are connected to atomic models and you will know that you walk on solid ground since it is all supported by mathematics as well as by experimental verification. There are some effective illustrations and exceptionally a formula, but most of the book is just text. Since there is a lot of material presented, even in a popular science book, (and perhaps especially in such a book), one might have expected a subject index which would facilitate to look up something from a previous chapter that you need to recall later. Orzel gives cross references in the text, but sometimes a reader will like to recall some concept, and then it is difficult to find it in previous chapters.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is a popular introduction to quantum physics, somewhat following the historical development. It illustrates that quantum physics is not an exotic theory but that we constantly experience its effects in our everyday life.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/chad-orzel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Chad Orzel</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oneworld-bloomsburry-publishing" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Oneworld / Bloomsburry Publishing</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9781786076403 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 26.99 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">288</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://www.bloomsbury.com/au/breakfast-with-einstein-9781786076403/" title="Link to web page">https://www.bloomsbury.com/au/breakfast-with-einstein-9781786076403/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a79" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a79</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/70-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">70-01</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/78-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">78-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/82-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">82-01</a></li></ul></span>Mon, 25 Nov 2019 09:16:52 +0000Adhemar Bultheel49947 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/breakfast-einstein#commentsThe Universe Speaks in Numbers
https://euro-math-soc.eu/review/universe-speaks-numbers
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The title of the book may suggest that this is about numbers, but there are nu numbers in the book, at all. So the subtitle: "How modern mathematics reveals nature's secrets", is a better description of the content. Because the book is about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" as Eugene Wigner formulated it back in 1960. Especially with physics, there has been a close and successful interaction with mathematics. But Farmelo explains that this is not so unreasonable and in fact it goes also the other way around since there is also "A Reasonable Influence from Theoretical Physics on Mathematics". Perhaps, there can even be a superstructure that has mathematics and nature as two of its realizations that we humans, with our limited intellectual capabilities, are able to experience, without yet understanding the superstructure, an idea that has been proposed before by Max Tegmark in <a target="_blank" href="/review/our-mathematical-universe-my-quest-ultimate-nature-reality">Our Mathematical Universe</a>.</p>
<p>Clearly both communities, physicists and mathematicians, have their own culture. Mathematics expands in the minds of mathematicians that are driven by abstraction and a mathematical result is true and remains true beyond discussion after it has been proved once and for all. The (traditional) physicists are driven in their urge to explain nature. They care somewhat less about rigour and their models are inspired by observation, and perhaps less by strict abstract deduction. Their models are accepted if they are confirmed by nature itself after appropriate experiments, but acceptance of the model is only guaranteed until it is contradicted by new or better experiments. The latter situation seems to have changed for current theoretical physics that has moved to the mathematical approach.</p>
<p>Since antiquity mathematics and physics have developed in parallel. Even mathematics developed and progressed often driven by practical physical problems. Yet, Greek philosophers already discussed whether mathematics was created by humans or provided by nature and left for humans to be discovered. Farmelo sketched in the first half of the book this on-off relationship between mathematics and physics up till about the 1970's. He tells the history by staging the people who have contributed to the major steps in the evolution of both mathematics as well as physics.</p>
<p>Of course Newton and the scientists of the Enlightenment who envisioned a mechanical clockwork world. It was promoted by Laplace that if all the details of the current state age given, then this would allow to predict the future perfectly. Much of this resided on an atomic idea about the world consisting of particles subject to forces.</p>
<p>The electromagnetic theory of Maxwell introduced the concept of a field. His theory is condensed in the Maxwell equations named after him, but written down by Heaviside. The "beauty" and symmetry in the equations were a source of inspiration for later developments.</p>
<p>Gravity, the source of inspiration for Newton, coupled to a geometric vision, and thought experiments, were the instruments used by Einstein to develop his special relativity theory, only to be confirmed afterwards by practical experiments. At first he was not convinced that physics required advanced mathematics but he had to abandon this idea when he got in trouble for the development of his general relativity theory. Early twentieth century were turbulent times, shaking the foundations of both physics and mathematics. This was promptly followed by a steep increase in our understanding of the world.</p>
<p>Heisenberg and Schrödinger developed quantum mechanics, but it was Dirac who could link this new model, which inherently involved uncertainty, with classical world view of Laplace. He endorsed Einstein's revised view that mathematics is unavoidable for the development of physics. But then, during the war and in the post war period came, what Farmelo calls, "The Long Divorce" where mathematics and theoretical physics each went their own way for about two decades. However, physicists in search for their unifying theory got stuck and were confronted with a zoo of subatomic particles. Feynman made some progress, and Yang and Mills tried to generalize the symmetry of the Maxwell equations, but Freeman Dyson in his 1972 talk to the AMS pointed to the missed opportunities because the physicists were not aware of the most recent developments in mathematics and mathematicians were not interested in physics. Until in November 1974 (hence called the November Revolution) the psion (J/ψ meson) was discovered, a particle that lived much longer than other elementary particles, and gauge theory became the common interest of physicists and mathematicians, also because of the Atiyah-Singer theorem which had shown the power of differential geometry in explaining subatomic quantum mechanics. The Standard Model was realized in the 1970's.</p>
<p>This is where the first part of the book ends, surveying about 3 centuries from Newton till the Standard Model. The second half deals with the 4 decades that follow. Veneziano had written down the formula forming the model for string theory on a napkin already in 1968. It was however abandoned because quantum chromodynamics and quantum gravity (the quantum mechanical approach to study gravity near black holes) had stolen the hearts and minds of physicists. But strings were later reinstalled as the road to take for a Theory of Everything. String theory introduced extra dimensions because supersymmetry is the only way to extend the symmetry between space and time as in Einstein's special relativity theory. Farmelo continues to illustrate the intense interaction between theoretical physicists and mathematics. They mutually helped each other to make progress, with Witten, Deligne, Seilberg, Penrose, Arkani-Hamed and many others as main contributors. However the Large Hydron Collider (LHC) of CERN didn't provide the many particles that were predicted by the theory, the detection of the Higgs boson in 2012 being the last success.</p>
<p>However the state of affairs have brought mathematicians and theoretical physicists closer together than ever before. They are collaborating in the new emerging field of mathematical physics. In the last chapter Farmelo concludes his arguments defending what he has illustrated in this book: it is predestined and the fate of mathematics and physics to work together. He even makes some predictions about ideas that will stand the test of time like space and time are not fundamental but are aspects of a more fundamental concept. He also believes that supersymmetry will be verified experimentally thereby affirming the beauty of mathematics to be basic. And he has a few more like those. So with this book he contradicts Sabine Hossenfelder who in her book <a target="_blank" href="/review/lost-math-how-beauty-leads-physics-astray">Lost in Math</a> complains about the state of affairs that physics is at a dead end caught up in theoretical imaginations remote from reality and just because this vision happens to be mainstream, it absorbs all the research money. Who is right? Time should bring the answer, but in my opinion it doesn't look like it will come in the very near future, despite what mathematicians and physicists may think or hope for.</p>
<p>It is remarkable that this book, that is from the first till the last page about mathematics and mathematical physics, has no formulas (well almost none, I counted five very simple ones and that includes E = mc²). Farmelo does not go into technical details in the sense that he avoids confusing the reader with technicalities. If that reader does not know the exact meaning of the terms (gauge theory, quark, gluon,...) then it does not really harm the basic story that he wants to tell and it does not hinder reading on. He keeps the reader hooked. This alone is a tour de force. Farmelo's style is very entertaining, describing the moments and the circumstances when it was realized that some breakthrough had been found. This is only possible because he interviewed the people involved or he himself was a witness of the events in the second half of his book. He also frames the time and the setting by referring for example to the fact that some physics event took place "in the year that the Beatles produced their first LP" or "when nearby a large group of music lovers flocked together" (referring to Woodstock), or "a few weeks after Obama was inaugurated". He discusses throughout the book the, sometimes subtle, interplay between the mathematics and the physics, and he is as generous about mathematics as he is about physics. I also appreciated how he analyses the important lectures of Dyson, Witten, and others where they made some important statements about the state of affairs. He claims that it is the book he has been writing since his childhood, and I can believe that. A recommended read, and Hossenfelder can be a comparable complementary read to keep the balance.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The book describes without being technical, the close collaboration between mathematics and physics in the course of history. In particular the mutual influence of mathematics and theoretical physics since the 1970's till now.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/graham-farmelo" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Graham Farmelo</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0465056651 (hbk), 9781541673922 (ebk) </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£ 24.00 (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">336</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://www.basicbooks.com/titles/graham-farmelo/the-universe-speaks-in-numbers/9781541673922/" title="Link to web page">https://www.basicbooks.com/titles/graham-farmelo/the-universe-speaks-in-numbers/9781541673922/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-03</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/01-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/00a79" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a79</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/81-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-03</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/83-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83-03</a></li></ul></span>Mon, 03 Jun 2019 08:43:09 +0000Adhemar Bultheel49420 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/universe-speaks-numbers#commentsTotally Random
https://euro-math-soc.eu/review/totally-random
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a popular science book explaining quantum mechanics (QM), in particular the key element called entanglement, which is surprisingly conceived as a graphical comic. The graphics are in greyscale (but mostly black) and almost all are either collages of drawings and real pictures, or just plain text.</p>
<p>
The book has three parts. The first one brings the essential concept of entanglement to the reader, but without any mathematics. The main instrument is a kind of toaster (the Super Quantum Entangler PR01) that is used throughout the book. Two coins can be inserted in parallel slits and the toaster ejects the two coins landing head or tails as if they were entangled like the spins of entangled photons are. This is actually Bell's theorem stating the dependence of the quantum states of entangled particles. This 'curious correlation' of 3/4 is an upper bound for a kind of instantaneous non-local communication that cannot be explained by classical mechanics, and which Einstein called 'spooky action at a distance'. This is expressed here as an operating scheme of the toaster that will result in the landing of the two tossed (or toasted) coins to end up with a different face (tails-heads or heads-tails) if both are tossed starting heads up. For all other initial conditions, the two coins will land with equal face up (heads-heads or tails-tails). Thus the tossed coins land with different faces up in three quarters of the cases. This correlation can not be explained by randomness if the two coins are uncorrelated, and neither can it be explained by rigging the coins. These entangled coins are called <em>quoins</em> in the book. The authors take their time and quite a number of pages to imprint the concept of quoins on the reader. The off-line characters here are the authors Jeffrey Bub (a physicist at the University of Maryland) explaining this to his daughter Tanya (who attended Art School and develops websites). They initiate the discussion, but the narrator does the explanation, and the reader (we see only the hands) does the tossing.</p>
<p>
The `spooky action at a distance' brings us to Einstein and part 2 in which the main characters of last century's QM debaters are explaining their vision on how it should be interpreted. Einstein is the first and next comes Schrödinger and his cat in the box with a theory that the state describes the whole past and future (the wave function, a term not used here). The wave function collapsing by our observation means that what we measure is different from what the real state actually is if not observed: a mixture of all possible states. Enters Hugh Everett with a universal splitter: All outcomes of a measurement do exist, but in different universes. Since we cannot probe another universe, this is impossible to verify. The Pauli effect (critical equipment tends to fail when someone is present) kills Everett. So Pauli and a private eye (von Neumann) appear to investigating what went wrong. The culprit is the witness who consciously observed the outcome of the coin toss that made the state collapse. The whole bunch ends up in the consultation room of doctor (Niels) Bohr where they investigate the causality involved (which quoin defines the outcome of the other?), but since time is relative, causality becomes difficult to define. There is a pun here because (David) Bohm (who defended the hidden variables theory) is mentioned among the characters, but he seems not to appear in the story. He has hidden himself, disguised in the form of the Einstein character who plays a double-role.</p>
<p>
The third part takes on a more comic kind of style with invented characters and situations. It is about what applications one could think of if we had these quoins, in other words, what are the (practical) applications of QM? The first application is about quantum cryptography. It is presented as if the classical characters Alice and Bob want to escape from some room where the outcome of a toss from one side of the room must be passed to another side. However, every information crossing can be observer by E.V.E., an eavesdropper in the form of a sphinx that sends an all intercepting beam dividing the two parts of the room.<br />
Quantum computing is illustrated by animals (chickens and foxes dressed as humans) who are gambling in a casino.<br />
The last application is about teleportation, at least teleporting Spock's soul, leading to the dissociation of everything in a whirling cloud of particles, referring the reader to page 1.</p>
<p>
If we make abstraction of the QM content, it is also interesting as a comic book. The scenario is witty and has some nice findings like involving the reader as one of the characters. At some point, the reader is sucked inside the story. The scientists sitting in a van with the unconscious Everett, directly address the reader asking to come inside and close the door of the van so that they can bring Everett to doctor Bohr. Another fun element are the dog-eared graphics showing comments of the Bubs with grumpy critique on how the story develops. Most of the graphics combine a collage of pictures with minimal drawing interventions. Sometimes what is being discussed is illustrated with pictures of (the first page of) the actual historic publications in a scientific journal. I guess that to obfuscate the unwanted artefacts from the collage, the graphics are a bit fuzzy and dark-ish. Since there is a lot of explanation to do, there are also frames that are just white text in a black window. Some of the better graphics are in the third part and in the apotheosis.</p>
<p>
This is an interesting experiment. Quantum mechanics is not easy to grasp. What the book somehow makes clear is what entanglement really means, or in this case how quoins (entangled coins) actually behave. The historical discussions by the physicists are reflecting the different opinions that they represent but it has to remain necessarily superficial. I guess that a complete layman can fully understand the discussions they have here in this book, but if not everything is clear, it could of course be an incentive to read more about this. For example with the guidance of a teacher who is using this book as a guideline. There is an appendix with notes, some of which refer to the literature, and there is also a website for the book <a href="http://totallyrandom.info" target="_blank">totallyrandom.info</a> which has some extra material but (at the time of writing this review) it is more a brief summary, serving as teasers to buy the book, rather than adding extra new material. In my opinion, the third part is the most interesting one since it illustrates the power of what could be done with QM. That should be easy to understand once the result of part 1 is accepted.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a graphical version of a popular science book, which has a lot of humour, but its serious purpose is to explain what makes quantum mechanics (QM) so unearthly and how it relates (or not) to reality. In particular the focus is on entanglement, which makes QM so difficult to understand, but, if entanglement is accepted, it also allows to illustrate the miracles QM is capable of.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/tanya-bub" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Tanya Bub</a></li><li class="vocabulary-links field-item odd"><a href="/author/jeffrey-bub" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jeffrey Bub</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2018</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-691-17695-6 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">22.95 USD (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">280</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://press.princeton.edu/titles/11232.html" title="Link to web page">https://press.princeton.edu/titles/11232.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81p40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P40</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/81p05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P05</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/00a79" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a79</a></li></ul></span>Tue, 26 Feb 2019 10:31:52 +0000Adhemar Bultheel49151 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/totally-random#commentsLost in Math: How Beauty Leads Physics Astray
https://euro-math-soc.eu/review/lost-math-how-beauty-leads-physics-astray
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The title of the book says it all, but it may need some explanation. Physicists have learned by experience that mathematics is very effective in describing the physical laws. It has also turned out to be effective when a simpler explanation is preferred over a more complicated one. Simpler means fewer equations, fewer assumptions, and fewer parameters. These simplifications are often the result of symmetry. So physicists came to accept symmetry as a synonym for beauty. This was a success when in astronomy the paradigm shifted from a geocentric to a heliocentric system, and it was useful in particle physics to unify the theory of different forces as in the standard model. But physicists should be warned by the disaster of the models designed and loved by economists for their mathematical beauty but that dramatically crashed in the 1980s with many years of global recession as a consequence.</p>
<p>
To arrive at a Grand Unified Theory (GUT) and design the mathematics for quantum gravity, physicists, intoxicated by this concept of symmetry, could only think of going one rung further up the ladder, and blindly proposed supersymmetry (susy for the intimi) as the logical next step. And mathematically, it is indeed a beautiful theory: a supergroup that incorporates all the symmetries of the underlying laws as subgroups. However mathematics is not physics, and physics requires experimental confirmation. Unfortunately the physicists are now erring in the dark since the Large Hadron Collator (LHC) did not reveal all the expected particles predicted by susy. The Higgs boson observed in 2012 was the last success. But the Higgs is at a scale that is so far off the scale of the other particles that it conflicts with another paradigm of physics: <em>naturalness</em>. This means that a dimensionless constant should at approximately the same scale as the other parameters. If it is not, then it might be a statistically irrelevant outlier. However if statistics shows that it is an important parameter of the theory, then it needs to be shifted or renormalized, which is called <em>fine tuning</em>. The cosmological constant is an example of fine tuning and it is ugly and still a source of much debate. Einstein was the first to introduce the cosmological constant Λ but he did not like it. It was reintroduced to explain the expansion of the universe and dark energy in the ΛCDM (Cold Dark Matter) model, but dark energy is poorly understood.</p>
<p>
So the question that Hossenfelder as a theoretical physicist asks herself is whether physicists are blinded by this mathematical symmetry principle of beauty and naturalness and do not realize that they are barking up a dead end. Mathematics should not lead the way for physics. It should be the other way around: the appropriate mathematics should be derived from the physics. In the past this ideal of symmetry and naturalness were not the lead. Symmetry was observed a posteriori when the paradigm shift was made. Also naturalness has not always been avoided. The parallax of the stars that could explain the heliocentric system, was way off the scale of distances in our solar system, and so are the distances between stars and between galaxies as compared to our solar system.</p>
<p>
She sets on a mission to ask many of the specialists in the field about their opinion. Skyping and travelling all over the world to interview the leading scientists and everyone who might have an opinion on this matter, trying to convince them (and herself) that physicists have driven research into a cul de sac. This book is a report of her crusade searching for answers. It is clearly her conviction that there is something rotten in the state of physics.</p>
<p>
To explain the problem and to understand the arguments given, she also has to discuss the terms and claims of particle physics, cosmology, etc. So at the same time, this book is a very readable popular science book on the subject. Of course there are no technical details, but for the layman, just enough insight into the concepts and problems are given to know what the discussion is about. All this information is nicely interwoven with her travelling experiences, and the interviews. These interviews are related in a very lively and personal way, often in the form of dialogues that she reconstructed from her recordings. So the reader is painlessly introduced to a broad spectrum of concepts. Of course supersymmetry, but also the standard model in particle physics and the concordance model in cosmology, multiverses, strings and branes, dark matter and WIMP, vortex theory, QBism, symmetry and Lie groups, cosmic background radiation, a simplified particle zoo, and many more. But only just enough info to understand the context.</p>
<p>
The interviews are also very personal. These "big shots", sometimes very busy running a research group, sometimes old retired emeriti, they are only humans, yet convinced of their opinion, defending the foundations on which they built their career. The place and circumstances in which the interview takes place, the hesitation or silence in the discussion, that sometimes drifts off to a philosophical discourse, it all contributes to an entertaining story. And there are many she has interviewed. From Nobel Prize winners Frank Wilczek, Murray Gell-Mann, and Steven Weinberg, to a wind-surfing non-academic Garrett Lisi, enjoying life and research on Maui, Hawaii, who proposed a so far not very successful Theory of Everything based on the exceptional E8 Lie group, and there are about a dozen more people that are staged.</p>
<p>
The frustration of Hossenfelder is that theoretical physicists just go on chasing after mathematical results following these assumptions of beauty and naturalness, and they do not even care about experimental verification, which technically means that they leave science behind. Moreover, they live in a closed, isolated environment, publishing in journals refereed by peers that have the same opinions. The pressure of publishing, getting finances, being accepted by peers, all means that young researchers have to conform themselves to these mainstream ideas. In 2016 the LHC detected something that could not be explained by the standard model. A few months later hundreds of papers had appeared in refereed journals about this so-called diphoton anomaly, when it was announced that the observed bump should be disregarded since it could be explained as noise. This illustrates that theoretical physics can invent explanations for whatever data are presented but so far, no experimental data occurred to confirm susy. Susy is called beautiful, but the concept of beauty can change. Perhaps there are physical laws that are beautiful in an unfamiliar way. Clearly Hossenfelder is throwing a bat in the henhouse. Her message is not very welcome in the community. Will she remain a voice calling in the desert? As a mathematician, (not involved in theoretical physics), I would like the math to triumph, but I think Hossenfelder has some good arguments, and in the past paradigm shifts away from what was considered to be perfect and beautiful have been rewarding. For example it was difficult to abandon the perfectly beautiful circular motion of the planets on epicircles in a geocentric system. However, even though the circles had to be replaced by ellipses in a heliocentric system, it only resulted in an even more general and beautiful mathematical theory. Thus there is no doubt that mathematics will prevail, but nature should be the guide and not the other way around.</p>
<p>
I loved reading this bird's-eye vision of the state of confusion and hope against all odds that theoretical physics is in today. It is written in an entertaining and convincing, yet very human way, showing that science is only produced by people. Perhaps it is worthwhile that scientists take a step back from the rat race of producing papers and that they reflect on what they are doing and recall what the ultimate goal of their science is. Reading this book, can be a good start.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
In this book Hossenfelder complains about the current state of theoretical physics. She shows that currently the mathematical beauty of supersymmetry is the guideline for researchers while so far none of it has been experimentally verified. Her plea is to invert the engine and let nature drive theoretical research instead of unverifiable mathematical assumptions. She tells her story by reporting on interviews that she had with peers all over the world.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/sabine-hossenfelder" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Sabine Hossenfelder</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2018</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-4650-9425-7 (hbk), 978-0-4650-9426-4 (ebk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 30.00 (hbk); USD 17.99 (ebk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">304</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://www.basicbooks.com/titles/sabine-hossenfelder/lost-in-math/9780465094257/" title="Link to web page">https://www.basicbooks.com/titles/sabine-hossenfelder/lost-in-math/9780465094257/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span>Tue, 05 Feb 2019 08:26:43 +0000Adhemar Bultheel49081 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/lost-math-how-beauty-leads-physics-astray#commentsQuantum Information Theory
https://euro-math-soc.eu/review/quantum-information-theory
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a massively comprehensive work that can be used as lecture notes or for self study. Quantum information theory is not the easiest topic and it is still in full expansion. So besides many other books devoted to the subject (I. Chuang and M. Nielsen: <em>Quantum Computation and Quantum Information</em>, Cambridge University Press, 2000, has become a kind of standard) this book has the advantage that it includes the more recent developments of the field. What I have in front of me is the first edition of 2013. A second edition comes out in 2017. In fact a preprint version of 2016 is available on <a href="https://arxiv.org/abs/1106.1445" target="_blank">arxiv.org/pdf/1106.1445</a> and can be modified by teachers under the Creative Commons non-commercial licence. Besides little changes throughout, and additional exercises, the text has been extended and modified at several places with modified proofs and extra results and it has an extra chapter on <em>Quantum Entropy Inequalities and Recoverability</em>, there is a different appendix and of course extra references.</p>
<p>
Despite the many pages, the author does not claim completeness or to have covered all possible protocols. Much has been achieved, yet much has to be investigated before we will be able to deal with a quantum version of the Internet. He has chosen to concentrate on channels. So channel capacity is the key concept here. It expresses how much information can be sent over it and most importantly whether we are able to reach this optimal capacity.</p>
<p>
The book is self-contained in the sense that, besides assuming a solid background in probability and linear algebra, it starts with some basic elements from classical Shannon information theory as well as from quantum theory, although some prior knowledge is advisable. Consider these introductory parts I and II more as an executive summary, rather than a basic course on these topics, even though they fill already some 150 pages. The second part on quantum information theory covers some aspects that may not be found in a classical book on quantum mechanics (quantum channels, channel capacity, purification systems to simulate noisy quantum systems etc.). Basic unit protocols of teleportation, super-dense coding and entanglement distribution assuming a noiseless channel are the core subjects of part III.</p>
<p>
The bulk of the preparatory work comes with part IV defining the basic tools for quantum information theory where the practical, but much more complicated situation of noise channels are taken into account. Distance measures are needed, entropy is revisited, different measures for quantum information are needed, both in a static and in a dynamic (i.e., for channels) situation and these measures should be such that asymptotically as the number of samples in typical sequences goes to infinity, the error or uncertainty should vanish (quantum typicality). Finally the packing lemma and its dual the covering lemma are the last tools introduced. In the first, one party packs its messages in a subspace so that it is easily recognizable for another party, and in the second the goal is the opposite, namely to make the messages indistinguishable.</p>
<p>
With all these tools prepared, the results are developed first in part V for noiseless channels and the main results of the book in part VI for the noisy situation. In the first case this is the Schumacher compression (based on von Neumann entropy) and the related, yet incompatible entanglement concentration (based on entropy of entanglement). Part VI is the present state of the noisy quantum Shannon theory is the culmination of the whole book. It amply illustrates that quantum information theory is so much richer than classical information theory and not everything is fully understood. Channel capacity and optimal communication of classical information over a noisy quantum channel, without or with entanglement, and coherent communication, private or public. Some of this is combined and refined in a chapter on quantum communication and in the subsequent one on communicating classical and quantum information, which unifies all the channel coding theorems seen before. The book concludes with a brief survey and outlook.</p>
<p>
The many possibilities to be considered make it easy to get lost. So the author takes care to proceed step by step, starting from the situation closest to the classical one to proceed to more involved cases. Each chapter starts with an introductory text explaining what this chapter is about and how it fits into the rest of the book with backward and forward references. Many of the chapters also end with a short summary to recapitulate the material just introduced. Each chapter has also a short section with some historical remarks and references for further reading. Exercises are sprinkled throughout the text, often it is a way to shortcut the exposition.</p>
<p>
Conclusion: this is an excellent textbook for graduate students to be introduced to the topic of quantum information theory. I trust this qualification will be prolonged in the second edition. It is probably too much to be dealt with in just one course, but if the students are really graduate, they may be familiar with either or both of quantum theory and information theory, otherwise it may be tough to assimilate the whole theory. There are suggestions for students and teachers on how to use the book and make selections.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a comprehensive course on quantum information theory. analyzing is how much (quantum) information can be transmitted over a (noisy) channel in a quantum world. The basics of classical information theory and of quantum mechanics are recalled. The many protocols and different channel capacities that can be defined result in a much richer theory than in the classical situation.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mark-m-wilde" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mark M. Wilde</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/cambridge-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">cambridge university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978110703425-9 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 54.99 (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">671</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.cambridge.org/catalogue/catalogue.asp?isbn=1107070236" title="Link to web page">http://www.cambridge.org/catalogue/catalogue.asp?isbn=1107070236</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81p45" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P45</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span>Sun, 19 Feb 2017 09:42:16 +0000Adhemar Bultheel47467 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/quantum-information-theory#commentsA Beautiful Question
https://euro-math-soc.eu/review/beautiful-question
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The relation between mathematics and art has been discussed in several books already. In this book Frank Wilczek answers the Question whether Nature itself is a piece of art (he always writes Question and Nature with a capital). Frank Wilczek is theoretical physicist and 2004 Nobel prize winner (together with Gross and Politzer) for work on the strong nuclear interaction force. Physical laws were originally derived from everyday observations, but once it comes down to particle physics, observations of everyday events are not helpful anymore, and experiments are scarce because they require more and more energy. In fact, the direction is reversed and the theory is now driving the experiments. Hence it is becoming less obvious what the model should be. Theoretical physics has turned to mathematics and draws its credibility from the mathematical models that show the most symmetry. Although there is symmetry breaking in practice, but that is only putting extra conditions on the model. It turns out that it is easier to start from the general symmetric solution and add extra conditions, instead of trying to lift an unsymmetric solution into the symmetric model.</p>
<p>
Wilczek's work as a theoretical physicist is exactly in the tension field just described. He contributed to the worldwide efforts to find an overall model that should join the quantum theory of the four fundamental forces of Nature: Maxwell's electromagnetism, strong and the weak interaction and gravitation. The fourth, gravitational force is so weak that it does not fit as well as the others do. Even though, Einstein's relativity theory was the first that lifted space-time to a higher dimension and was integrated with Maxwell's equations while quantum physics was in its infancy.</p>
<p>
Seen in this context, it is not difficult to imagine that Wilczek sees symmetry (or supersymmetry in the most recent model) as an indication of beauty, and therefore his answer to the Question he states at the beginning is whole-heartedly super-affirmative in the end. The core of his argumentation (or meditations as he calls it) is centered around his own work, but it requires to survey many other ingredients that preceded. So he walks through the whole evolution meandering from Pythagoras to Plato to Newton to Maxwell to Einstein to finally plunge into quantum dynamics, and in particular quantum chromodynamics, his own playground. In this ocean of subatomic particles the question about beauty finally gets an answer and symmetry is born like Venus from sea foam generated by the quantum waves. With this allegory of Venus, I imitate a technique that also Wilczek uses in his book. References to work of art is introduced alongside the physical and mathematical theories, and this includes music, poetry, and paintings.</p>
<p>
Pythagoras studied music, vibrating strings, and related ratios of numbers, already relating mathematics and art. Music was part of the quadrivium alongside arithmetic, geometry, and astronomy. So Wilczek in his meditation on Pythagoras already raises a question of beauty: why certain combinations sound harmonic and others don't? That is connected with a particular discrete set of ratios in the length of the string (like quanta). Had Pythagoras pushed a bit harder, quantum theory would have emerged much earlier.</p>
<p>
From Plato we know the platonic solids, the five symmetrical objects that inspired Kepler to use them as a model for the solar system. This shows Kepler's belief that Nature's design is one of symmetry. The model turned out to be wrong but it is an example where the beauty (i.e., the symmetry) of the mathematics inspired a model for reality. From Plato we also remember the allegory of the cave. We are limited by our senses so that we only see a two-dimensional black-and-white image of what is in reality a very colorful three-dimensional world outside. (Wilczek elaborates on the invention of perspective as an illustration of how we manage to represent reality within the limitations of a rectangular canvas.)</p>
<p>
From Newton we have to remember his decomposition of light into the different colors of the rainbow and of course his mechanics. Light and mass need two different approaches, one being a wave and the other being related to a material object. But light is just a particular example of an electromagnetic wave. So they obey Maxwell's electromagnetic equations. These equations are another triumph of symmetry and simplicity. Clearly a beautiful theory to describe Nature. But it does not embrace gravity that acts on particles at a distance through a void intermedium. On the other hand, electromagnetism introduces fields visualized by fieldlines, forming the fluid filling the void in between particles attracting or repulsing each other.</p>
<p>
Maxwell is one of Wilczek's heros. It is perhaps less generally known that Maxwell has also experimented a lot with colors. Although the sunlight contains an infinity of frequencies, the human eye pics up only three components (R,G,B) and we can compose all other colors by combining these in our mind. A strange saving in the design that evolution has bestowed upon us. Certain shrimps for example register many more frequencies. We see white light by adding red green and blue, but this is quite different from the white light that is reflected by white paint where pigments absorbs frequencies that are not reflected.</p>
<p>
When it comes to quantum theory, Wilczek reflects on the eigenmodes of a string and of other music instruments. These remind us of Pythagoras' ratios of numbers.<br />
The discussion of Einstein's theory is relatively short. It is used to introduce the importance of local (Galilean) invariance, which is a form of symmetry. This is an unusual approach, but it is central in Wilczek's view of gravitons and metric fields.<br />
After an intermezzo on the symmetry of carbon structures (fullerenes, nanotubes, buckminsterfullerenes), Wilczek embarks on Core Theory (a term he prefers over the usual naming Standard Model which sounds to him too common, too much like a bucketful of conventions). Arriving on his own domain, he moves to a higher level of detail, to a higher gear for the reader, and to the higher dimension of quantumchromodynamics with its many particles, For the latter purpose he associates with every spacial point a property space. Each of the four fundamental forces has its own property space. He treats in some details all the quantumchromodynamics of the three forces with the particles these require as they show up in his own work, with a triumph of the supersymmetry (SUSY) and hence the answer to the Question. He links this to the mathematics of Emma Noether's (first) theorem about the conservation of energy (but he does not explain).</p>
<p>
It should be clear that Wilczek, although he hops through the history and he is very fluent in juggling with all the electron, lepton, gluon and whateveron particles, he is primarily interested in answering his Question and hence is looking for the beauty that becomes more and more apparent as theoretical physics evolves. Therefore, this book is not the place to learn about all the mathematics and the formulas supporting this. He assumes that this is more or less known to the reader. If your theoretical physics is a bit rusty, you will need the 57 page small print supplement providing a dictionary defining and explaining the most important "terms of art" as he calls all these physical concepts. It is a factual list arranged in two columns per page from 'absorption' to 'z-particle'. There are a few references for further reading too. What Wilczek wants to communicate in this book is not the theory itself, he is not teaching a physics course, but he gives an idea of how theoretical physicists have struggled with the problem. He somehow communicates the satisfaction, the sensation, the joy, and the sense of beauty that it must have brought when they succeeded in nicely matching the three fundamental forces together, with a possibility to eventually include gravity as well.</p>
<p>
It is very difficult to convince a reader, who is not involved in the research, of the overwhelming sensation it brings when after working very hard and meeting dead ends many times, finally the pieces of the puzzle just fall naturally into place. This is is not restricted to research in physics, but mathematicians and probably others may have experienced something similar. Like the three lines of the theory finally meet in one point on page 317 in the graph 'Why I ♡ SUSY', also the human quest for beauty and truth of all ages seem to converge here in the end. By starting at the beginning and collecting the star dust that makes up the jewel in the end (the timeline at the end of he book that takes several pages shows how long this road is and how many have contributed) Wilczek is able to convey some of his experience to the reader. He regularly makes comparisons and he illustrates some physical ideas or achievements with pieces of art that may be more familiar to the lay reader. The book is also richly illustrated with pictures and two sets of color plates, and some care has been taken by the publisher to make it stand out from the more common and discrete scientific books. The colorful cover that only peaks through a hole in the dust jacket is for example notable.</p>
<p>
It is quite an experience to read this book, but the reader should have a keen interest in the crusade of theoretical physics currently storming the walls that border our understanding of Nature. But should not every human being be interested in the outcome that brings the truth? and should not everybody rejoice in the beauty that it brings along? Probably the answer to this question is also yes, though some may have more down-to-earth everyday worries to take care of for the moment being.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Nobel prize winner Frank Wilczek meditates on the question: Is Nature's design beautiful, hence is Nature a piece of art? He makes it quickly clear that in his view beauty can be found in symmetry and since supersymmetry seems to be the mathematical tool to be applied to complete our understanding of what Nature is made of, his answer is whole-heartedly: Yes it is.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/frank-wilczek" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Frank Wilczek</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/allen-lane-penguin-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Allen lane / Penguin Books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9781846147012 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">19.38 USD</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">448</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.penguin.co.uk/books/a-beautiful-question/9781846147012/" title="Link to web page">http://www.penguin.co.uk/books/a-beautiful-question/9781846147012/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81t30" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81T30</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81v25" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81V25</a></li></ul></span>Sat, 07 May 2016 15:46:13 +0000Adhemar Bultheel46925 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/beautiful-question#commentsEinstein Was Right!
https://euro-math-soc.eu/review/einstein-was-right
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
To place this book in context one has to know about Einstein's vision on quantum mechanics. Einstein believed in quantum mechanics (QM) but he thought it was incomplete. In the EPR paper (Einstein, Podolsky, Rosen) of 1935 quantum entanglement was described. The wave function factored in two separate parts, so that the momentum and position of the two particles were intimately connected by some "spooky" action at a distance, exchanging information at a speed higher than the speed of light in vacuum. Einstein believed that there were some hidden local variables, not yet observable that should be taken into account. This started a war between Einstein and Bohr. This yes-no discussion between believers in Einstein and the QM adepts is still going on till the present day.</p>
<p>
Experiments performed by groups supervised by Aspect (1982) and by Zeilinger (2007) however confirmed the existence of entanglement, hence the action at a distance. The latter was measuring polarized entangled photons at the Canary Islands Tenerife and La Palma. It was shown that there was a significant correlation between the observations, although no communication was possible. What was shown in fact was that the Bell inequality was violated. This inequality says that if variables A,B,C can take randomly any of the two values +1 or -1 (corresponding to the polarization), then AB + AC - BC ≤ 1. The experiment showed that averaging this (i.e., computing correlations), the inequality was significantly violated when A, B and C represented observations of the polarization under different circumstances characterized by parameter settings a,b and c (i.e., different orientations of the detectors): a and b on Tenerife and a and c on La Palma. Violation means that the observations are not random but there is indeed entanglement between both islands.</p>
<p>
The book is a personal account of Hess about his attempts with his coworker Walter Philipp, and after Philipp succumbed to heart failure during a mountaineering trip in 2006, with his collaborators Hans De Raedt and Kristel Michielsen. Hess graduated in Physics in Vienna, Austria, and is now retired professor from the University of Illinois, Urbana. Philipp also was Austrian, specialized in probability theory and a colleague of Hess at the University of Illinois. Together, they have published several papers refuting the application of the Bell inequality to prove the non-locality of QM. Their main point is that the inequality only holds if all the stochastic variables are independent. However, in their opinion they are not because the hidden local variables that are not taken into account is time, or spacetime in a more general setting. This would explain the violation of the inequality in the experiment without the need for the spooky action.</p>
<p>
Hess gives a chronological account of his collaborating conquest of the material. Their publications got opposition from the QM establishment, and not always in the most amicable or respectful way. The material of course is not very simple, but Hess avoids a mathematical treatment and explains again and again with different analogies and rephrasings that it all comes down to countering their opponents with the dependency on spacetime. To read the text, one is not required to know anything about relativity theory or quantum mechanics. Just adding plus and minus ones suffices. At some point Hess explains the basic notion of probability and stochastic variables, but that is about the most 'difficult' part. On the other hand conditional probability is not really explained and the very nature of the physical and mathematical background is largely handwaved and that leaves you as a reader somewhat in a foggy oversimplification of what is actually going on and the discussion of the successive papers seem to repeat the same thing all over and over. One could of course consult the actual papers to know their actual contents.</p>
<p>
Another little bombshell is thrown in the QM camp when Hess discloses that Boole had an inequality equivalent to the one of Bell one century earlier. That appears in his later work with De Raedt and Michielsen. Here the discussion treats also commuting operators and macroscopic realism (the moon is there also when it is not observed). Big words, but nothing to be afraid of as an unexperienced reader.</p>
<p>
The account is interlaced with personal anecdotes, friendships that were built up during his collaboration and the problems he and his wife had to go through when in 2006 Philipp died, he retired from the university, and they moved to live permanently in Hawaii. Also the unpleasant experience with a paper that got positive referee reports, but was nevertheless rejected for publication. The latter are all too realistic when one wants to publish results that are not streamlined with the mainstream belief. For the moment, the mainstream is formed by a majority of the believers of QM, although also Nobel prize winner Gerard 't Hooft has expressed some doubts and proposes alternatives.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a personal chronological account of Karl Hess on his conquest to show that Einstein was right by contesting the experimental verification of 'spooky action at a distance'. His arguments basically reduce to the fact that the violation of the Bell inequalities that are instrumental in these experiments have been misinterpreted and that the results can be be explained by Einsteinian local hidden variables which in Hess's vision is time or more generally spacetime.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/karl-hess" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Karl Hess</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/pan-stanford-publishing" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Pan Stanford Publishing</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-981446369-0 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 33.20</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">220</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.crcpress.com/product/isbn/9789814463690" title="Link to web page">http://www.crcpress.com/product/isbn/9789814463690</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81p15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P15</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-05</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/81-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-03</a></li></ul></span>Wed, 04 Feb 2015 15:13:14 +0000Adhemar Bultheel46004 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/einstein-was-right#commentsQuantum Mechanics
https://euro-math-soc.eu/review/quantum-mechanics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
<a href="http://theoreticalminimum.com/"><em>The theoretical minimum</em></a> is an online lecture series given by Leonard Susskind, professor of theoretical physics at Stanford University. The first volume in the book series with the same name treated <em>Classical Mechanics</em>, a course given in the <a href="http://theoreticalminimum.com/courses/classical-mechanics/2011/fall">fall 2011</a>, and the current volume on Quantum Mechanics resulted from the <a href="http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter">winter 2012</a> lectures. The course consists of a sequence of 10 lessons, which correspond to the 10 chapters of the book. The co-author Art Friedman is computer scientist who attended the lessons. The books can be considered as the elaborated lecture notes for Susskind's courses.</p>
<p>
The name of the series and subtitle <em>what you need to know to start doing physics</em> explains the concept. This is intended for the amateur scientist who really wants to learn and understand the subject. It is Susskind's conviction that this can only be achieved if one masters the mathematics that describe the physics. In this second volume it is assumed that the reader is familiar with elements about classical mechanics explained in volume 1 of the series. Furthermore, the reader should not be afraid of the abstraction of mathematics. The ideal situation would be that the reader is familiar with the basic mathematics at the level of a bachelor university degree. On the other hand, introducing the necessary mathematics is exactly what this course is about, so in principle no mathematics of this level is assumed. But if mathematics scares you off, then this is not for you, which implies, if we believe Susskind, that you will never be able to properly understand quantum physics.</p>
<p>
</p>
<p>
Susskind obviously is addressing the reader who has some (classical) physics background. He starts from the intuitive physical description, and then illustrates that this can be perfectly described by introducing the necessary mathematical concepts. For example: what is spin? Not just an ordinary 3-vector. If you measure it there are only two possible outcomes, say +1 and -1. But before it is measured, it can be in different (coherent) states. The outcome of the measurement will depend on this state and on the "orientation" of the measuring apparatus. So the reader is taken along on an exploration tour and it takes a while (in fact 3 chapters) before a proper mathematical concept sublimates. In this case, the Pauli matrices. Given an orientation for the measuring apparatus, it will be possible to combine the Pauli matrices to a matrix and its eigenvalue decomposition will allow you to compute the probabilities of either outcome of the experiment. So the mathematics do not come gratuitously, but come to the help of the physicist who just needs it at some point.</p>
<p>
On the other hand, if you are a mathematician, then the content may somewhat disappoint you because the mathematics is relatively elementary knowledge. Since I assume that a mathematician feels comfortable with abstraction, he or she might have preferred a more axiomatic approach. For example, the above state vector is a 3D unit vector and hence has two degrees of freedom. The Pauli matrices are 2x2 unitary matrices with eigenvalues +1 and -1 and the eigenvectors are orthonormal basis vectors. Of course, the line of thought that Susskind uses, has the advantage of explaining why a certain mathematical concept is needed to catch a particular physical phenomenon. So, if the mathematical abstraction is the more challenging part for the physicist, for a mathematician it also requires an effort to detach from the oh so familiar laws of mechanics in our everyday life and to accept the sometimes paradoxical physical interpretation imposed by the mathematics of the quantum mechanical game.</p>
<p>
To summarize, this is more about mathematics for physicists than about physics for mathematicians. Whatever the approach or background, quantum mechanics remains a difficult subject because it is often counter intuitive. The reason is that humans normally observe the world they live in at a scale that is hugely different from the scale needed to describe the physics at a quantum level. As Susskind claims at some point: conceptually quantum mechanics should be the first approach to describe mechanical phenomena because that corresponds to reality and classical mechanics is a simplification that is a good approximation only at a much larger scale.</p>
<p>
However, as is usually the case, that top-down approach is not the best way to learn things. It is much better to start with a simple special case and when that is properly understood, one may step up to generalizations. However, supposing you can assimilate all the material as it is intended by the authors, you will not be at a level where you can directly involve in current research on quantum mechanics. You will be at an elementary level still, and it will take much more mathematics to reach the level of current research. There are many more advanced courses available on the courses website, so one may expect several more volumes in the <em>Theoretical Minimum</em> book series to come.</p>
<p>
Let's go quickly through the contents of the book. It takes three lessons/chapters to explain the notion of a state of a system. For this, Susskind uses the easiest example of a system of just one simple observable: the spin or a qubit. While explaining this concept, Susskind introduces on the mathematical side the complex numbers, vector spaces, orthogonal basis vectors and Gram-Schmidt orthogonalization, (Hermitian) operators and their eigenvalues, and of course the bra-ket notation that was introduced by P. Dirac.<br />
The next two chapters deal with time dependency. Here the notion of Lie bracket (the authors prefer to use commutator as an alias), Hamiltonian, Schrödinger equation, Cauchy-Schwartz, unitary operators, and the general uncertainty principle is introduced.<br />
The two following chapters are on observation and state of a combination of systems. Again, the simplest case is observing two spins. Susskind shows that the tensor product of the bases for the states of the separate systems does not form a complete basis for the states of the combined system. Hence some extra basis vectors (singlet and triplets) are needed to describe the whole state space. These vectors are responsible for entanglement. The mathematical concepts here are the outer product, density, and correlation.<br />
The remaining chapters are about particles and waves. This duality is probably the best known aspect of quantum mechanics: a photon behaves as a wave and at the same time it is like a particle. I believe the reader who has been hanging on till this point of the course will have to fasten seat belts and shift to a higher gear now. The first thing is to move from eigenvectors of a matrix to eigenfunctions of an operator, and from finite sums to integrals. Position, velocity, momentum, Hamiltonian all become operators and can best be studied in the Fourier domain, the latter resulting for example in the classical Heisenberg uncertainty principle. To know how particles move, one has to reconsider time dependency in this continuous setting. The equation of motion with kinetic and potential energy and the classical form of the Schrödinger equation, waves, wave packages and the harmonic oscillator are the results with which this course comes to an end. Several exercises are inserted where the reader is asked to prove some of the properties or to work out some formulas. Usually they are not very hard and they help to assimilate the material. In an appendix some of the basic formulas are summarized so that they can be easily looked up, for example when going through the formulas to solve the exercises. Also the subject index is handy when studying the material.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the second volume in the <em>Theoretical Minimum</em> series to accompany a lecture series given by L. Susskind. The material covers only the basics and is intended for the layman, but a layman that is interested in understanding the mathematics needed to go beyond a general descriptive approach of quantum physics.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/leonard-susskind" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">leonard susskind</a></li><li class="vocabulary-links field-item odd"><a href="/author/art-friedman" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">art friedman</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-4650-3667-7 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£17.99</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">384</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.basicbooks.com/full-details?isbn=9780465036677" title="Link to web page">http://www.basicbooks.com/full-details?isbn=9780465036677</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span>Tue, 06 May 2014 06:05:35 +0000Adhemar Bultheel45560 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/quantum-mechanics#commentsLove and Math. The heart of hidden reality
https://euro-math-soc.eu/review/love-and-math-heart-hidden-reality
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Ever since he grew up as a boy in Kolomna (Russia), Frenkel was fascinated by elementary particles and quantum physics. It was pointed out to him that to understand these, he should start learning mathematics. So he started reading mathematics in his free time. An obvious choice would be to study at the department of Mechanics and Mathematics (<em>Mekh-Mat</em>) of the Moscow State University (MGU). However, back in 1984, his father being Jewish, this was impossible by the ruling anti-Semitism. His second choice was the Institute of Oil and Gas (<em>Kerosinka</em>), but he sneaked into the GMU to attend some courses and seminars by Gelfand. On the side he worked on a problem of braid groups proposed by D. Fuchs which resulted in his first paper published in <em>Funct. Anal. Appl.</em> at the age of 20. This brought him to study symmetry, (braid) groups and curves over finite fields. Further work brought him straight to the <em>Langlands Program</em> that was proposed by <em>Robert Langland</em> in 1967 and more formally in 1970. It is based on an earlier idea of <em>André Weil</em> who, while imprisoned in 1940 (having a disagreement with the French authorities), wrote a letter to his sister explaining the idea of a mathematical <em>Rosetta Stone</em> which would allow to translate results between three seemingly different fields in mathematics into each other: number theory, curves over finite fields, and Riemann surfaces. Exploring this connection has been shown successful by the proof of Fermat's Last Theorem. This connection is the mathematical analog to what the theoretical physicist call the <em>Grand Unifying Theory</em> in their study of quantum physics. The mathematical or physical aspects are just two different interpretation of the same theory. So quantum physics is like a fourth column to be added to Weil's <em>Rosetta Stone</em>. Frenkel's work with B. Feigin on Kac-Moody algebras came just in time because he got an invitation to spend a semester at Harvard in 1989 at the very time that <em>perestroika</em> was emerging. Because of the worsening situation in Russia with an unclear outcome, he decided after his 3 months stay, that it was better not to return home. So he stayed at Harvard where he got his PhD in 1991. Later he became professor of mathematics at UC Berkley. In 2003 he got directly involved in a multi-million DARPA grant to work out more elements of Weil's Rosetta Stone. Since then, his mathematical career is largely devoted to building the bits and pieces of this <em>Grand Unifying Theory</em>.</p>
<p>
Frenkel makes it crystal clear that he is a passionate lover of mathematics and that his enthusiasm for the <em>Langlands Program</em> is immense. This love and passion is what he wants to convey to the reader. The math that most people learn in school is like learning to paint a fence in an art class, while true painting is about creating master pieces like Da Vinci or Picasso did. Mathematics is also a moral duty. Our world is ruled by mathematics that are hidden to most of us. The financial crisis in 2008 was caused by applying mathematics by people that were not controlled in a democratic way because our society does not care about mathematics and most people tend to stay away from it as far as possible. Mathematics should not be restricted to the "initiated few" but it should be shared by everybody. There is nothing more democratic than mathematics. There are no patents for formulas, its a universal language, and a correct formula can only represent truth, the universal truth.</p>
<p>
With this conviction, Frenkel wants to transfer not only his love for mathematics but he also wants to show us the beauty of the mathematics that he is devoting most of his life to, and not just the "fence painting" bits. Of course reading this book will not make you a mathematician, but he succeeds by describing his life (at least the part related to his mathematical career) and gradually taking the reader along in his conquest of the mathematics he needed. So he explains symmetries, groups, finite fields, SU(3), manifolds, Galois groups, Lie algebras, sheaves, supersymmetry, strings, branes, etc. All things that are far beyond the low-fi kind of math that one usually finds in popular science books. Of course this is not easy, but I can imagine that his charismatic account will make some readers regret that they are not mathematicians, rather than the usual conviction that mathematics is a natural habitat where only nerds can survive. Many of the more technical details are removed from the main body as (sometimes quite extensive) notes that are collected at the end of the book. For a mathematical reader, they are of course useful, but others may want to skip them and still follow the essence of Frenkel's Conquest of Paradise.</p>
<p>
But Frenkel is not only a mathematician. The last chapter of the book is still about mathematics and love, but now revealing the artistic talents of Frenkel. After a visit to Paris, he got the idea to make a film about math. With his neighbour, the author T. Farber, he wrote a screen-play called <em>The two-body problem</em> about two men in the South of France, one is a writer, the other a mathematician. They exchange their experiences, their passion for their profession and for women. It was published as a book in 2010. Before starting on the movie project, he wanted to get some cinematographic experience at a smaller scale and decided to produce a short movie. During another visit to France, he joined in with Reine Graves, a young film director. Inspired by a Japanese film of Y. Mishima <em>Rites of Love and Death</em> in which a lieutenant commits a ritual suicide together with his wife. Frenkel and Graves imitate the movie more or less. It shows a man (Frenkel) and a women (K.I. May) with in the back a poster with the text istina (Russian for truth). The man tattoos a mathematical formula (the formula of love) on the body of the women. The film is called <a href="http://ritesofloveandmath.com/"><em>Rites of Love and Math</em></a>. It was well received, and you will find pictures on the Web of Frenkel teaching in Berkeley, but also where he shows up at the Cannes film festival. In fact by different media, Frenkel tries to transmit the same message: a mathematical formula or mathematics in general can be a thrilling thing of beauty, it can give you goose bumps, one may fall in love with it, it represents the ultimate truth, and it is worth committing your life to. The return you get from it is overwhelming.</p>
<p>
One final remark. It is of course a side remark after Frenkel's plea for beauty, but I do not think that the cover design of the book is a success. It shows text in slightly tilted rectangles on a background image that is a detail of Van Gogh's <em>The Starry Night</em> painting. The symbolism is obviously well chosen, but it looks terribly chaotic, and I would have preferred a more stylish design representing the mathematical purity and beauty of its contents.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Partly a story of his life, partly an introduction to the essence of his work: the Langlands Program. Frenkel displays his enthusiasm, and love for mathematics and in particular for this "Grand Unifying Theory" of mathematics and quantum physics by taking the reader along on this journey from his first contact with SU(3) to what he now is, a leading mathematician at the forefront of this exciting development in mathematics and quantum physics.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/edward-frenkel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">edward frenkel</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-465-05074-1 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">27,99 USD (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">304</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.basicbooks.com/full-details?isbn=9780465050741" title="Link to web page">http://www.basicbooks.com/full-details?isbn=9780465050741</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span>Wed, 12 Feb 2014 06:06:55 +0000Adhemar Bultheel45553 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/love-and-math-heart-hidden-reality#commentsA first course in Loop Quantum Gravity
https://euro-math-soc.eu/review/first-course-loop-quantum-gravity
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>As it is said in the preface of the book, Loop quantum gravity has emerged<br />
as a possible avenue towards the quantization of general relativity. This is<br />
one of the main streams to attack this outstanding problem in mathematical physics,<br />
although one has to recognize that it has had less impact than string and superstring<br />
theories.</p>
<p>Before starting to read the book, I was delighted to have in my hands what<br />
it seemed to be a leisurely introduction to a topic of such novelty, in<br />
which my background as differential geometer and (mathematical) gauge<br />
theorist could be well suited. The first chapters give overall<br />
introductions in differential geometry, general relativity, semi-riemannian<br />
geometry, always keeping an informal style. So informal that at some points<br />
in touches the incorrectness. However, when reading these chapters, some of<br />
the times even skipping parts (so basic for a mathematician), this was<br />
to be forgiven. Around the second third of the book, physical<br />
(and more interesting) ideas enter the discussion (Yang-Mills theories, quantum mechanics,<br />
quantum field theory), and then the book swaps to the usual "physics<br />
jargon", so extraneous to a mathematician. No much<br />
intention not to lose people not already familiar with the theory<br />
is shown in the text, accompanied by a lack of motivation when introducing physical concepts.<br />
Moreover, not even for the experts the material is<br />
going to be of much use, since details are skipped once and again. The third<br />
part of the book (loop general relativity, loop quantum cosmology) is basically<br />
a review of very technical material. This is where the book touches the topic<br />
announced in the title, but by then all arguments follow a physics line of<br />
reasoning: no rigorous proofs, renormalizations, divergences, etc.<br />
Again, I have gone through a text in mathematical<br />
physics on which my expectations have not been fulfilled. Maybe next time.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Vicente Muñoz</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">UCM</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Loop quantum gravity has emerged as a possible avenue towards the<br />
quantization of general relativity. This book is an introduction to this<br />
topic, which is at the level of a graduate student in Theoretical Physics.<br />
The book covers: general relativity, hamiltonian mechanics, Yang-Mills<br />
theories, quantum mechanics, quantum field theories and loop quantum<br />
gravity.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/rodolfo-gambini" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">rodolfo gambini</a></li><li class="vocabulary-links field-item odd"><a href="/author/jorge-pullin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">jorge pullin</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-19-959075-9</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span>Tue, 19 Jun 2012 09:46:14 +0000Anonymous45452 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/first-course-loop-quantum-gravity#comments