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The Ultimate Guide to Booking Frankfurt Flights from New York

If you’re planning a trip to the beautiful city of Frankfurt, Germany from New York, USA, you’ll need to find the best flights that suit your needs. With numerous airlines offering flights between these two destinations, it can be overwhelming to choose the right one. But fear not. In this ultimate guide, we will provide you with all the information you need to book Frankfurt flights from New York hassle-free.

Finding the Right Airlines

When it comes to booking Frankfurt flights from New York, one of the first things you should consider is which airlines operate on this route. Some popular airlines that offer direct flights include Lufthansa, United Airlines, Delta Air Lines, and American Airlines. These airlines not only provide convenience but also offer excellent service and competitive prices.

Comparing Prices and Deals

Once you’ve identified the airlines that fly between New York and Frankfurt, it’s time to compare prices and deals. The cost of airfare can vary significantly depending on factors such as travel dates, booking time in advance, and seat availability. To ensure you get the best deal possible, consider using flight comparison websites or apps that aggregate fares from different airlines. Additionally, keep an eye out for special promotions or discounts offered by airlines during specific seasons or holidays.

Choosing Your Travel Dates Wisely

Choosing the right travel dates can make a significant difference in terms of price and availability when booking Frankfurt flights from New York. Generally, weekdays tend to have lower fares compared to weekends when demand is higher. If your travel plans are flexible, consider opting for off-peak seasons or shoulder periods when airfares are usually more affordable. It’s also worth noting that booking your tickets well in advance can help secure better deals.

Making Your Reservation

Once you’ve compared prices and decided on your preferred airline and travel dates, it’s time to make your reservation. Most airlines offer online booking systems that allow you to conveniently select your flights, choose seats, and make secure payments. Before finalizing your booking, double-check all the details, including departure and arrival times, layovers (if any), baggage allowances, and any additional charges or fees. If you have specific requirements or preferences, such as dietary restrictions or special assistance needs, make sure to inform the airline in advance.

In conclusion, booking Frankfurt flights from New York doesn’t have to be a daunting task. By following this ultimate guide, you can find the right airline that suits your needs, compare prices and deals effectively, choose travel dates wisely, and make a smooth reservation process. So go ahead and start planning your trip to Frankfurt – an enchanting city waiting to be explored.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.


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December 21, 2023

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Steven Weinberg and the Puzzle of Quantum Mechanics

April 6, 2017 issue

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In response to:

The Trouble with Quantum Mechanics from the January 19, 2017 issue

To the Editors :

My article “The Trouble with Quantum Mechanics” [ NYR , January 19] provoked a flood of comments. Some were from nonscientists charmed to learn that physicists can disagree with one another. Here there is only room to outline a few comments from physicists who offered arguments in favor of interpretations of quantum mechanics that would make it unnecessary to modify the theory. Alas, these interpretations differ from one another, and none seems to me to be entirely satisfactory. (Several letters on this matter received by The New York Review appear in full following this letter.)

N. David Mermin of Cornell argued with characteristic eloquence for what I (but not he) would call an instrumentalist approach. In his view, science is directly about the relation between each person’s total experience and the outside world that includes that experience. I replied that I hoped for a physical theory that would allow us to deduce what happens when people make measurements from impersonal laws that apply to everything, without giving any special status to people in these laws. I suggested that our difference is just that Mermin thinks I had been hoping for too much. He agreed, with the understanding that those hopes are mine, not his.

In contrast, Thomas Banks of Rutgers in our correspondence and the draft of a new book, Quantum Mechanics: An Introduction , described his elegant efforts to avoid bringing human measurement into the laws of nature. He describes measurement as an interaction of the system being measured with a macroscopic system, in which probabilities appear much as they do in classical physics. But it is still necessary to bring into the laws of nature assumptions about these probabilities that I can only understand as probabilities of the values found when humans decide what to measure.

I had an interesting correspondence with Robert Griffiths of Carnegie Mellon and James Hartle of the University of California–Santa Barbara regarding an approach to quantum mechanics variously known as “decoherent histories” or “consistent histories,” which was introduced in 1984 by Griffiths and further developed by Hartle and Murray Gell-Mann. The laws of nature are supposed to attribute probabilities to histories of the world, not just to the results of single measurements. I had described this approach in detail in my textbook Lectures on Quantum Mechanics but did not cover it in my article, because I thought it has the same drawbacks that I attributed to all instrumentalist approaches.

The wave functions for these histories involve averaging over most quantities, with a few held fixed, as if they were being measured, but histories with different things held fixed are incompatible, and it is humans who must choose the particular kind of history to which to attribute probabilities. Griffiths developed a sort of quantum logic consistent with his approach, but it leaves me uncomfortable. Hartle and Gell-Mann may share some of this discomfort, for they have moved toward identifying one “true” kind of history that does not have to be selected by people; but they have to attribute weird negative probabilities to histories of this kind. My discomfort remains.

Jeremy Bernstein, a contributor to these pages, thinks like Mermin that there is no trouble with quantum mechanics as it stands, but he supplied an anecdote that runs in the opposite direction. A visitor to Einstein’s office in Prague noted that the window overlooked the grounds of an insane asylum. Einstein explained that these were the madmen who did not think about quantum mechanics.

Steven Weinberg Austin, Texas

Selected letters in response to Steven Weinberg’s article on Quantum Mechanics:

I agree with Steven Weinberg that “it is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means” [“The Trouble with Quantum Mechanics,” NYR , January 19]. This ninety-year failure to reach anything like a common understanding of such a spectacularly successful theory indicates that physicists might share an unrecognized prejudice about the nature of scientific explanation that prevents each of them from seeing what quantum mechanics actually means.

In explaining why he finds untenable what he calls “the instrumentalist approach,” Weinberg gives voice to just such a widespread prejudice: “Humans are brought into the laws of nature at the most fundamental level.” Weinberg is not ready to give up the goal of understanding the relation of humans to nature by deducing it “from laws that make no explicit reference to humans.” And so he endorses, with a touch of pessimism, a long-term goal of seeking modifications of quantum mechanics that “are not only speculative but also vague.” He embraces this bleak prospect because he cannot accept incorporating the relation between people and nature into “what we suppose are nature’s fundamental laws.”

But why not? Science is a human activity. As empiricists most scientists believe that their understanding of the world is based entirely on their own personal experience (which, importantly, includes the words of others that they have heard and read). Why shouldn’t the science that I use to understand the world be directly about the relation between my total experience and the world outside of me that induces that experience?

Erwin Schrödinger (a David Levine cartoon of whom illustrates Weinberg’s essay!) traced this deep prejudice of scientists back to the ancient Greeks. He thought it was essential for the early development of science, but that it removed an important part of the story. He did not suggest that abandoning it dissolved the puzzles of quantum mechanics, but in the early twenty-first century Christopher Fuchs and Rüdiger Schack argued that it does.

For example Weinberg and many others complain that there is “no way to locate the boundary between the realms in which, according to Bohr, quantum mechanics does or does not apply.” Fuchs and Schack have a simple answer: the boundary is elusive because it depends on the scientist who is using quantum mechanics, but for each such user it is unambiguous: I apply quantum mechanics to the world I infer from my own experience; the role of my classical world is played for me by that experience.

Last year Hans Christian von Baeyer published a beautiful exposition of this new point of view, QBism: The Future of Quantum Physics. I recommend von Baeyer’s little book to readers of Weinberg’s essay. It addresses Weinberg’s concerns, is written at an entirely nontechnical level, and makes it clear that the resolution applies not only to quantum mechanics but also to even older, if less vexing, puzzles in classical physics.

N. David Mermin Horace White Professor of Physics Emeritus Cornell University Ithaca, New York

Steven Weinberg’s article on quantum mechanics is written with his usual clarity and brilliance. But I think that it is misguided. The probabilistic interpretation of the Schrödinger wave function was introduced by Max Born in a very brief note in 1926. He considered the collision of an electron with a target and studied the wave function that represented the electron after the collision. It is a function of position and he said that the wave function determined the probability that the electron would occupy that position. Later he modified it to say that it was the square of the wave function and still later he said the absolute value determined the probability. The notion that this is “derived” is absurd. It was a postulate. Now the present generation of quantum theorists—some of them—find this unsatisfactory and want to produce a derivation. Of course it can’t be derived from quantum mechanics as we understand it so they want to introduce “quantum” mechanics from which it can be derived, In the most recherché versions of this, “quantum” mechanics has slightly different predictions from quantum mechanics. If they are right it would be revolutionary but to me the whole enterprise is a solution looking for a problem.

Jeremy Bernstein Aspen, Colorado

Early on, students of quantum mechanics rhymed: “Erwin with his psi can do calculations quite a few, but one thing has not been seen: just what does psi really mean?” The answer was first given by Max Born, who received the Nobel Prize for giving meaning to psi, the wave function of a system, stating that the absolute square of this function is the probability of finding the system under observation in a given state. Steven Weinberg claims that the trouble with quantum mechanics is that the wave function “is governed by an equation, the [Erwin] Schroedinger equation, that does not involve probabilities .” Since this equation is perfectly deterministic, he asks, “how do probabilities get into quantum mechanics?”

But also in classical mechanics, given the inevitable uncertainties in the initial conditions, the situation is actually similar, because only probabilities of the outcome at a later time can be predicted. The main difference with quantum mechanics is that in this theory there is a limit on the relative size of the initial uncertainties, e.g., the position and velocity of an object. In his Nobel Prize speech, Born stated that “ordinary mechanics must also be statistically formulated…the determinism of classical physics turns out to be an illusion…and cannot be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.” The nature of reality in the atomic world, however strange, is revealed by experiments, and not by requiring that it fit some prejudices from classical mechanics as Weinberg indicates.

Michael Nauenberg Professor of Physics, Emeritus University of California Santa Cruz, California

Steven Weinberg has stated clearly and unambiguously that there is something rotten in the kingdom of the “Copenhagen interpretation” of quantum mechanics. Though they often continue to pay lip service to that “interpretation” in their courses and papers, an increasing number of physicists realize this, and nobody is quite sure nowadays what that interpretation really means. As Weinberg says, “It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means.”

Weinberg identifies the basic problem with quantum mechanics: that one applies a different rule of evolution to the wave function of a system when it does not contain an observer or measuring device (one then uses the deterministic Schrödinger evolution) from when it does (one then collapses the wave function in a random fashion, following a rule, due to Max Born, for the probabilities of the result). That not only puts the “observer,” whether it is a human subject or an instrument in a laboratory, outside the ordinary laws of physics, but also renders that “observer” indispensable to make sense of those laws. We agree with Professor Weinberg that this is deeply unsatisfactory.

Weinberg mentions two “ways out” of the problems of quantum mechanics: the “many-worlds interpretation” of Hugh Everett and the “spontaneous collapse” theories of Gian Carlo Ghirardi, Alberto Rimini, and Tullio Weber. For the first option, Weinberg observes that he doesn’t see how to justify the use of the usual quantum mechanical probabilities, given by Born’s rule, within that framework, though he is aware of a variety of attempts to do so. According to the second option, the predictions of quantum theory are not quite correct, but only a very good approximation to the more correct predictions of the spontaneous collapse theory. Many experiments are being carried out in order to decide between spontaneous collapse theories and quantum mechanics. So far, there is no indication that quantum mechanics is wrong and its spectacular successes show that, if its predictions are indeed violated in some situations, this will not be easy to demonstrate.

Weinberg presents the Copenhagen interpretation on the one hand, and many-worlds and spontaneous collapse theories on the other, as corresponding respectively to what he calls an instrumentalist and a realist approach to the wave function. In the instrumentalist approach the wave function is not regarded as something to be taken seriously as real or objective, but merely as a convenient tool for describing the behavior of measuring devices and the like. In the realist approach, according to Weinberg, the wave function is not only real and objective but also exhaustive, providing a complete description of the physical state of affairs. In other words, the alternatives for the wave function for Weinberg are either that it is nothing or it is everything.

However, Weinberg does not mention a third possibility, the de Broglie–Bohm theory or Bohmian mechanics, in which the wave function is something but not everything. This theory, which we consider to be, by far, the simplest version of quantum mechanics, does not require any modification of the predictions of ordinary quantum mechanics, nor a bizarre (to say the least) multiplication of parallel universes. It was proposed by Louis de Broglie in 1927 and rediscovered and developed by David Bohm in 1952. For several decades its main proponent was John Stewart Bell, the physicist who did more than any other to establish the existence of the quantum non-locality mentioned by Weinberg.

In Bohmian mechanics a system of particles is described by actual positions of actual particles in addition to its wave function: particles actually do have positions at all times, hence trajectories and also velocities. Their time evolution is guided in a natural way by the wave function, which functions as what is often called a pilot wave. This should be contrasted with the role of the wave function in the instrumentalist approach: to predict the behavior of (clearly nonfundamental) measuring devices. Thus the wave function in Bohmian mechanics is somewhat similar to the forces or the electromagnetic waves guiding the particles in classical physics.

The wave functions of closed systems in Bohmian mechanics, even systems containing observers and measuring devices, always follow Schrödinger’s equation and never collapse. Thus, observations are no longer a deus ex machina in that theory. When one analyzes in Bohmian mechanics what is called a “measurement” in ordinary quantum mechanics, one finds that the behavior of the particles yields a world in which measurement results conform precisely to the quantum mechanical predictions. Such an analysis of quantum measurements also explains why the fact that particles have both positions and velocities at all times does not contradict the Heisenberg uncertainty principle. In particular, although Bohmian mechanics is perfectly deterministic, one can recover the statistical predictions of ordinary quantum mechanics (the Born rule mentioned by Weinberg) by making natural assumptions on the initial conditions of physical systems (something which has become familiar among physicists with the development of modern “chaotic” dynamical systems theory).

While Bohmian mechanics is a version of nonrelativistic quantum mechanics and not of quantum field theory, the basic idea of Bohmian mechanics—that the wave function should be something but not everything—applies to any quantum theory. In fact there are a variety of Bohmian versions of quantum field theory, though it would be fair to say that there is no agreed-upon best or canonical version for relativistic physics.

Jean Bricmont Professor of Theoretical Physics University of Louvain Louvain-la-Neuve, Belgium

Sheldon Goldstein Distinguished Professor of Mathematics, Physics and Philosophy Rutgers University New Brunswick, New Jersey

Tim Maudlin Professor of Philosophy New York University New York City

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Steven Weinberg 1933-2021

I heard this morning the news that Steven Weinberg passed away yesterday at the age of 88.  He was arguably the dominant figure in theoretical particle physics during its period of great success from the late sixties to the early eighties.  In particular, his 1967 work on unification of the weak and electromagnetic interactions was a huge breakthrough, and remains to this day at the center of the Standard Model, our best understanding of fundamental physics.

During the years 1975-79 when I was a student at Harvard,  I believe the hallway where Weinberg, Glashow and Coleman had offices close together  was the greatest concentration of the world’s major figures driving the field of particle theory, with Weinberg seen as the most prominent of the three.  From what I recall, in a meeting one of the graduate students (Eddie Farhi?) referred to “Shelly, Sidney and Weinberg”, indicating the way Weinberg was a special case even in that group.   I had the great fortune to attend not only Coleman’s QFT course, but also a course by Weinberg on the quantization of gauge theory.

Weinberg was the author of an influential text on general relativity, as well as a masterful three-volume set of textbooks on QFT.  The second volume roughly corresponds to the course I took from him, and the third is about supersymmetry.   While most QFT books cover the basics in much the same way, Weinberg’s first volume is a quite different, original and highly influential take on the subject. It’s not easy going, but the details are all there and his point of view is an important one.  When you hear Nima Arkani-Hamed preaching about the right way to understand how QFT comes out uniquely as the only sensible way to combine special relativity and quantum mechanics, he’s often referring specifically to what you’ll find in that first volume.

Besides his technical work, Weinberg also did a huge amount of writing of the highest quality about physics and science in general for wider audiences.  An early example is his 1977 The Search for Unity: Notes for a History of Quantum Field Theory (a copy is here ). His 1992 Dreams of a Final Theory is perhaps the best statement anywhere of the goal of fundamental physical theory during the 20th century. His large collection of pieces written for the The New York Review of Books covers a wide variety of topics and all are well worth reading.

At the time of the 1984 “First Superstring Revolution”, Weinberg joined in and worked on string theory for a while, but after a few years turned to cosmology. In early 2002 he was one of several people I wrote to about the current state of string theory, and here’s what I heard back from him:

I share your disappointment about the lack of contact so far of string theory with nature, but I can’t see that anyone else (including those studying topological nontrivialities in gauge theories) is doing much better. I thinks that some theorists should go on pushing as hard as they can on string theory, and others should do something else, but it is not easy to see what. I have myself voted with my feet (if that is the appropriate organ here) and switched entirely to work in cosmology, which is as exciting now as particle physics was in the 1960s and 1970s. I wouldn’t criticize anyone for their choices: it’s a tough time for fundamental physics.

A couple years after that time, Weinberg’s 1987 “prediction” of the cosmological constant became the main argument for the string theory multiverse. This “prediction” was essentially the observation that if you have a theory in which all values of the cosmological constant are equally likely, and put this together with the “anthropic” constraint that only for some range will galaxy formation give what seem to be the conditions for life, then you expect a non-zero CC of very roughly the size later found. I’ve argued ad nauseam here that this can’t be used as a significant argument for string theory in its landscape incarnation. One way to see the problem is to notice that my own theory of the CC (which is that I have no idea what determines it, so any value is as likely as any other) is exactly equivalent to the string landscape theory of the CC (in which you don’t know either the measure on the space of possible vacua, or even what this space is, so you assume all CC equally likely). One place where Weinberg wrote about this issue is his essay Living in the Multiverse , which I wrote about here (the sad story of misinterpretation of a comment of mine there is told here ).

Weinberg’s death yesterday, taking away from us the dominant figure of the period of particle theory’s greatest success is both a significant loss and marks the end of an era. His 2002 remark that “it’s a tough time” is even more true today.

Update : Scott Aaronson writes about Weinberg here , especially about getting to know him during the last part of his life.

Update : For Arkani-Hamed on Weinberg, see here .

Update : Glashow writes about Weinberg here .

18 Responses to Steven Weinberg 1933-2021

Weinberg was the last of the physics giants who produced fundamental theories validated by experiments. After half a century his Standard Model still holds, so maybe now is the fist time in physics history without scientific giants.

A tribute to him from one Astrophysics colleague who had recently joined UT Austin https://twitter.com/MBKplus/status/1418972769509855236

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His last book “Foundations of Modern Physics came out a few months ago. From the preface: “This book treats such a broad range of topics that it is impossible to go very far into any of them. Certainly its treatment of quantum mechanics, statistical mechanics, transport theory, nuclear physics, and quantum field theory is no substitute for graduate-level courses on these topics, any one of which would occupy at least a whole year. This book presents what I think, in an ideal world, the ambitious physics student would already know when he or she enters graduate school. At least, it is what I wish that I had known when I entered graduate school.” Does anybody have an opinion about how well he succeeded?

It is sad news that Weinberg is not with us anymore but I cannot agree with Alessandro Strumia that “Weinberg was the last of the physics giants who produced fundamental theories validated by experiments…so maybe now is the fi(r)st time in physics history without scientific giants.” Please be reminded that C. N. Yang and T. D. Lee still are healthily living.

@Ricardo: I wrote the following review on one of my piazza sites a few weeks ago. I am currently half way through the book, and I am enjoying the book, although I am familiar with most of the content already. As I indicated below it is more of a review book, than a teaching book.

Steven Weinberg had come out with a new book: Foundations of Modern Physics.  I have read the first 2 chapters, and scanned the rest of the book – the book is a short 300 pages and the hardcover is about $40.  The level of the book is intermediate to advanced undergraduate.

I often encounter online students who have taken several of the MIT physics MOOC’s but often feel that they either lack some background, or don’t see what they have learned (especially in the QM sequence) and how it will be applied.  To many of these students my advice is usually to read the Feynman Lectures on physics, to get the big picture and for more background in QM prerequisite physics, and/or find a good textbook on modern physics.

When I was in college almost half a century ago, I remember using Leighton’s classic book Principles of Modern Physics 1959 (about 700 pages in length), and suggest students try and find a more recent book covering roughly the same material – I haven’t seen one, so let me know if you have. There seem to be many freshman/sophomore level books covering modern physics, but I don’t think these are sufficient.

Weinberg’s book is less of a textbook (while there are 25 problems at the end of the book, there are no exercises at the end of chapters, and no worked out examples).  It is written in Weinberg style, few pictures or diagrams, unusual symbols ($m_1$ for the atomic mass unit, usual notation is u), nice but sometimes terse arguments, and excellent content with interesting historical asides.  The math level is low at the beginning (algebra – elementary calculus), and rises a little with the level of the material, but not nearly as difficult as his graduate level books.

There are seven chapters in the book:  

Early Atomic Theory Thermodynamics and Kinetic Theory Early Quantum Theory Relativity Quantum Mechanics Nuclear Physics Quantum Field Theory So the coverage is exactly what a student should be looking for in a modern physics book (perhaps astrophysics and cosmology are left out, because Weinberg just published a set of lectures on astrophysics, and has a whole book on Cosmology). The book seems more of a review or plug holes in background, and less of a teaching masterpiece.  

I recommend that students looking for a book on this type of material take a look at the book and see if it is for them.  I think students who are taking or have finished the MITx 8.04-8.06 sequence might find the book worthwhile as a review and also as filling out some material, and get a preview of quantum field theory as well.

Steven Weinberg – a great, highly creative physicist and wonderfully involved teacher of fundamental physics who shaped my own education in quantum field theory and cosmology during essential steps. I’ll miss him and his sober views very much.

Dear Wei, thank you, let me try to explain better. Historians like to choose a somehow arbitrary moment to symbolise a gradual change. If the change I mentioned will really happen, I expect they will choose this moment.

Alessandro, Glashow is still around, isn’t he? So not quite the last. As a sophomore, I attended a talk by GSW when they were here in Stockholm to collect their Nobel prize, and I understood absolutely nothing.

Btw. I learned from Lubos that Miguel Virasoro has passed away as well.

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I was working at Cambridge University Press in 1995 when the first volume of his “Quantum Theory of Fields” was released. I recall speaking briefly with him on the phone about something trivial like distributing review copies, and picking up a copy of the book that had been delivered to our office. I read the first page and then put it back down—it was just a *bit* over my head…

My PhD thesis was a measurement of the Weinberg angle (sin^2\theta_W) using polarized electrons at the SLAC linear collider. Some people insisted the W stood for Weak but I always held it is W for Weinberg. I read and reread his paper A Model of Leptons many times until I could reproduce it at my defense. I wish all theory papers were as clear and understandable.

Miguel Virasoro died the same day

Amitabha: From what I understand the “Weinberg” angle was first introduced by Glashow.

Shantanu, that is funny because I was told to call it Weak Mixing Angle (and not Weinberg angle) after I gave this talk at Harvard. Glashow was in the room but he was not the one who made that comment. I made the correction with a marker on my transparencies right there. This was a while ago, but I also vaguely remember some chatter about “well if this is right it means the higgs is light”. We were, and it was.

Amitabha: This is also mentioned on Peter’s blog https://www.math.columbia.edu/~woit/wordpress/?p=17 I have also heard this mentioned in many HEP seminars I attended as a grad student.

Dreams of a Final Theory is available on Audible. It’s read by Weinberg himself. It’s written for a general audience, so even untutored but interested readers like me can understand it.

That is sad news, but it was a long life well-lived. He was an authentic giant. His book on GR is still my favorite (tied with that of Fock) and I was lucky to learn the subject in detail mostly from that. Agree also about QTF II. I wish we had made more progress in his last years for him to enjoy and contribute to. RIP.

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‘To Explain the World,’ by Steven Weinberg

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By Sam Kean

  • March 6, 2015

Steven Weinberg doesn’t think much of Plato or Pythagoras. Nor does he hold René Descartes or Francis Bacon in ­especially high regard. But in his new book on the origins of science, “To Explain the World,” Weinberg casts particular aspersions on science historians themselves.

A Nobel Prize-winning physicist, Weinberg has set out to write a broad historical overview that can explain how humanity invented science. But he finds that historians disdain nearly everything that excites him. They mistrust overarching narratives and notions of progress. Some dispute the very idea of a scientific revolution. Above all, they argue that we can’t cherry-pick winners and losers based on what later scientists believed to be true. They insist on judging people in the context of their own times.

Weinberg rejects all that. He’s perfectly happy judging the past by today’s standards. After all, scientists can’t well overlook the fact that some theories work and some don’t. And it’s this willingness to ignore pieties that makes “To Explain the World” so refreshing. Much of the ­history is standard fare, however well written. But every 15 or 20 pages, the old lion rouses himself and roars in defense of Whig history.

The book has virtually nothing to say about biology or chemistry, focusing ­instead on physics and astronomy. That’s partly because those fields proved more important to early science — and probably because Weinberg knows those fields so well. (Indeed, almost too well: The astronomy chapters especially get pretty dense. After reading them, I was half-afraid to peek at the “technical notes” in the appendix — what horrors must be buried there!)

The book begins with the ancient Greeks — from Thales to Aristotle — sometimes described as early scientists, but Weinberg classifies them as poets instead. They chose their words “for aesthetic effect,” he writes, not clear communication, and they made no serious attempt to justify their theories with evidence. This echoes Bertrand Russell’s famous jab at Aristotle, who claimed that women had fewer teeth than men. He could have avoided this mistake, Russell noted, “by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted.”

Weinberg thinks more highly of the ­Hellenistic Greeks of the fourth through the first centuries B.C. Unlike Plato and Aristotle, who erected grand metaphysical schemes that attempted to encompass all of reality, they were more modest. They took on smaller, more tractable problems like calculating the size of the Earth, moon and sun — and made real progress.

After Greece, the book takes a very ­cursory tour of non-Western science. Weinberg argues that while “the West borrowed much scientific knowledge from elsewhere — geometry from Egypt, astronomical data from Babylon, the techniques of arithmetic from Babylon and India,” it alone developed scientific methods, like building hypotheses and testing them with experiments. ­Moreover, while China gave the world wonderful technologies, including the magnetic compass, Weinberg draws a hard line between technology and science proper — an unpopular stance nowadays. He does make an exception for Arab scientists, who made important advances in optics, astronomy and medicine. The Arab scientist Ibn al-Nafis, for instance, first determined that blood from the heart enters the lungs and returns to the heart after absorbing air.

After this detour, the action returns to Europe, and Weinberg resumes sorting out the saved from the damned. He can be quite wry doing so. Historians praise René Descartes’s philosophical contributions, especially his prescriptions for avoiding errors when thinking about ­nature. But Weinberg is characteristically skeptical: “For someone who claimed to have found the true method for seeking reliable knowledge, it is remarkable how wrong Descartes was about so many ­aspects of nature.”

Weinberg does find much to admire in a few near contemporaries of ­Descartes: Galileo and Isaac Newton. It’s not that these two didn’t have wrong or even kooky ideas (Newton spent much of his life hunting through the Bible for coded messages about the apocalypse). But they developed important new ­approaches. Galileo experimented ­aggressively, rolling balls down ramps, for instance, to test different theories about falling objects, trials Weinberg calls “a distant ancestor of today’s particle accelerators, with which we artificially create particles found nowhere in nature.” In outlining his theory of gravity, Newton developed simple equations that, mirabile dictu, ­applied just as readily to planets circling stars as to apples falling from trees — an incredible range of phenomena. “By comparison,” Weinberg writes, “all past successes of physical theory were parochial.”

Despite the sparring, Weinberg ­deserves credit for at least engaging with historians; too many practicing scientists are ignorant of history. And Weinberg provides several nice examples of how history can illuminate modern science. In the late 1500s, the astronomer Johannes Kepler wanted to know why each planet in our solar system orbited the sun at the distance it did. He eventually created a model with giant cubes, pyramids and other shapes hovering in space, with each figure nested inside the next like Russian dolls. Planets then orbited on spheres crammed between them. Inevitably the whole scheme fell apart. Most scientists today believe there’s no deep reason the planets orbit at the distances they do. It’s random, an accident — news that would have crushed Kepler.

Scientists of today may face similar disappointments. Certain numbers, called constants of nature, come up over and over in studying physics, and many physicists want to know the reason those numbers have the values they do. Why is gravity as strong as it is? Why do electrons have one specific mass and charge and not another? Scientists haven’t made much progress here, and Weinberg suggests that perhaps there isn’t any deep reason. Perhaps we live in one of many universes, each of which has constants with essentially random values. The universe is the way it is just because.

It’s a prospect that would have horrified Newton, and probably depresses any number of modern scientists. It amounts to abandoning the search for deeper meaning. As Weinberg wrote in his book “The First Three Minutes,” “The more the universe seems comprehensible, the more it also seems pointless.”

But “To Explain the World” ultimately undercuts such nihilism. It tells a rich, meaningful tale about the emergence of science, and evokes a sense of “how difficult was the discovery of modern science, how far from obvious are its practices and standards.” Maybe the universe at large is pointless and random, but we still have the triumph of science, Weinberg reminds us, this “extraordinary story, one of the most interesting in human history.”


The discovery of modern science.

By Steven Weinberg

Illustrated. 416 pp. Harper/HarperCollins Publishers. $28.99.

Sam Kean’s latest book is “The Tale of the Dueling Neurosurgeons.”

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From The New York Review of Books: Steven Weinberg “The Crisis of Big Science”


In The New York Review of Books , May 10, 2012 Dr. Weinberg writes, as beautifully as ever, about some of the past and future of what is essentially Basic Scientific Research, in the field of Physics. This article is copyright protected, so I will not even quote from it, out of respect for Dr. Weinberg. I will just suggest that you go to the link provided below and read the article.


Suffice it for me to say that in this article he is concerned with the future of the U.S. budget for basic research, specifically in Physics and Astronomy. But he does spend some time describing where we have been before talking about where we are or are not going. I have read him before in NYRB, and he never fails to properly set a context for his major thesis. But, while this is one of the most eminent people in our scientific community, still, in his description of our history of support and the lack of it for basic research, Dr Weinberg seems to make the defining point of his interest the 1993 cancellation by the U.S. Congress of the Superconducting Super Collider , to have been built in Texas. I have seen it in his previous articles, I have seen him speak about it in videos of his lectures. On the one hand, he is not wrong. On the other hand, let it go. This failure to proceed in a program in the State of Texas, where he has been at the University of Texas, is in no way any sort of defining moment in his incredible and Nobel winning career.

If Dr Weinberg can be criticized for anything at all in his writing, it is his too quick mentions of various sub-atomic particles and forces which are the elements of the Standard Model . While it might be reasonable for him to expect that his readers would already be familiar with these terms, still he is writing in a journal of popular press, no matter how erudite the journal or its readership. He might just keep some quickie descriptions of quarks, leptons, muons, and bosons , etc., in his word processing files and dump them in for his less learned readership.

steven weinberg new york review of books

The U.S. D.O.E. Office of Science funds about seventeen major research laboratories, such as Berkeley Lab , Brookhaven , Argonne , and Fermilab . There is a lot of concern about the future of many projects in these labs. At Fermilab, the Long Baseline Neutrino Experiment (LBNE) has been pushed back to economic re-design. That is a biggie. Dr. Weinberg comments that things are not rosy in Europe. But the European Southern Observatory , an incredible organization in Astronomy, seems to be pushing ahead with its long range telescope building program. Also, in a previous post here, we saw that Director Oddone of Fermilab had recently returned from meetings in which he was quite impressed with the planning he saw in both Europe and Asia.

I highly recommend that you read Dr. Weinberg’s article. I always recommend that you read Dr Weinberg. The article can be found here .

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September 2021 (Volume 30, Number 8)

Steven weinberg 1933-2021.

By Daniel Garisto

Steven Weinberg, a theorist who unified two fundamental forces and shaped the way physicists and the public thought about the universe, died July 23 in Austin at 88.

Weinberg shared the 1979 Nobel Prize in Physics with Abdus Salam and Sheldon Glashow for contributions to the theory that unified the weak and electromagnetic forces. He continued to win academic honors and awards for the next half century, including the 2020 Breakthrough Prize. In addition to his academic research, Weinberg wrote prolifically about science in popular books and publications such as the New York Review of Books . He was also a Fellow of APS.

“Steve was one of the last figures from this heroic era of particle physics that culminated in the development of the Standard Model,” said Scott Aaronson, a theoretical computer scientist at the University of Texas at Austin, where Weinberg was a professor for forty years.

If he achieved mythic status through physics, it was from humble beginnings. Steven Weinberg was born in New York City to Frederick and Eva Weinberg, a court stenographer and homemaker respectively. Weinberg’s interest in science was cultivated at the Bronx High School of Science, where he was—famously—classmates with Glashow, who would also go on to attend Cornell.

Steven Weinberg

Credit: Larry Murphy, University of Texas at Austin

Steven Weinberg

After Cornell, Weinberg married Louise Goldwasser, and the newlyweds spent a year in Copenhagen. He then went back to America and finished his PhD with Sam Treiman at Princeton on weak decays and renormalization, the mathematical technique for wrangling annoying infinities. Over the next decade, he bounced from Columbia to Berkeley before landing in Cambridge, MA, where he held appointments at MIT and Harvard.

In the early 1960s, Glashow and Salam attempted to unify electromagnetism and the weak force by proposing massive W and Z bosons as force carriers. But giving the W and Z mass made the theory nonrenormalizable. Weinberg took the idea of spontaneous symmetry breaking and in three brisk pages showed how the mechanism could lead the W and Z to appear massive at lower energies. One of the most impactful papers in particle physics, “ A Model of Leptons ” went mostly unnoticed: for two years after it was published in Physical Review Letters , it garnered only two citations.

“Why doesn't anybody quote his paper between 1967 and 1970? The reason is nobody could do that calculation,” said Helen Quinn, a professor emerita at SLAC. Weinberg knew that his model was “probably renormalizable,” but it wasn’t until a 1970 paper by Gerard t’Hooft that the dam burst and citations flooded in. When Quinn and her coauthors did the first one-loop calculation for Weinberg’s theory, “he was so happy he invited us to sherry at his house,” she said.

As a theorist, Weinberg was not particularly focused on model building. “It is ironic that his Nobel Prize was for a specific model, because he was really interested in the general picture and not in the specific models, no matter how beautiful,” Howard Georgi, a Harvard physicist, wrote in an email to APS News .

“He told me why once: Models are almost always wrong. But if you have general arguments that follow from general principles, that has a chance of being correct in the long run,” said John Preskill, a physicist at Caltech and one of Weinberg’s students.

Quinn recalls an argument between Julian Schwinger and Weinberg during a student’s thesis defense. “Julian's position was effectively that that theory is best which is flexible enough to accommodate all new data and be adapted to it,” she said. “Steve's position was that that theory is best which is very well defined, and thus can be tested and ruled out.”

Some of Weinberg’s colleagues argue that his real seminal contribution to particle physics was not electroweak unification but articulating how to think about effective quantum field theories (EQFTs). Though EQFTs had been in use for decades, Weinberg’s insight was that physics lurking at much higher energies would appear in terms suppressed by heavy masses. This perspective shaped the hunt for unknown particles and “underlies almost everything we do from LHC physics to string theory to dark matter,” Georgi wrote.

Beyond particle physics, Weinberg also made contributions to astrophysics and cosmology, in particular by reintroducing the cosmological constant as a problem—prior to the discovery of dark energy—and working on matter-antimatter asymmetry in the early universe. He expounded on his view that the very small and very large were connected in The First Three Minutes , a popular science text, which both introduced the public to cosmic microwave background radiation for the first time and inspired a generation of practicing physicists to hone their cosmological queries.

In 1981, Weinberg followed his wife Louise to UT Austin, where she was already a professor at the law school. He established a theoretical physics department where his Tuesday pre-colloquium lunches became de rigeur . “The discussion was basically led by him,” said Willy Fischler, a theorist at UT Austin. “Often, it was about history, poetry, and literature.”

Despite his laurels and seniority, Weinberg continued teaching. This fall, he was set to teach a course on thermodynamics and statistical mechanics. “I was amazed. I mean Steve is 88, and he's going to teach a course that he has never taught,” said Fischler.

Colleagues noted Weinberg’s intensity and testified to his single-mindedness when attacking a physics problem. “He wasn't going to come to your office and say, ‘How are you doing? How was your weekend?’ He wasn't that kind of person,” said Sonia Paban, a theoretical physicist at UT Austin.

Weinberg was known for his solitary style, and he was frequently a sole author. When working from home, Weinberg kept a TV on his desk and enjoyed listening to old movies in the background to feel less isolated. But earlier in his career, Weinberg frequently collaborated with physicists like Quinn, Glashow, and Benjamin Lee.

When Quinn and Roberto Peccei published their approach to the strong CP problem, they did not predict an axion. “Weinberg actually called me up and asked me, ‘Did you notice that your theory has this property that there's a pseudo-Goldstone boson?’ And I said, ‘Well, no, I didn't. But you're absolutely right. Obviously, it does.’ And he said, ‘Well, in that case, I'll publish it myself.’” Quinn said. “So what he was doing was giving me the opportunity to be a co-author of the paper with the axion.”

Others also spoke to Weinberg’s sense of fairness. Paban recalls an incident when a visiting Nobel laureate dismissed a question by a student during a colloquium. “The speaker looked at [the student] and said, ‘I see you don't understand’ and he proceeded,” she said. “Steve raised his hand and said, ‘I don't understand that—and don't give me that answer.’”

For Weinberg, the pursuit of understanding was not an idle matter. “Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough,” he wrote in The First Three Minutes .

“Steve said, ‘I think we don't take our theories seriously enough, because it's so hard to believe that the squiggles that you make on a piece of paper are actually the way nature works.’” Preskill said. “In his case, and in a few spectacular examples, they were indeed.”

The author is a science writer based in Bellport, New York.

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Staff Science Writer: Leah Poffenberger Contributing Correspondents: Sophia Chen, Alaina G. Levine

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