What was it like being a student of Richard Feynman?

Updated on : January 17, 2022 by Gerardo Calderon



What was it like being a student of Richard Feynman?

Unfortunately, I was not an RPF thesis student, so I didn't have to try to keep up with him on a regular or formal basis. Or maybe that was a good thing: I could be inspired by the contact without "responsibility."

In some of his writings, I remember him saying that he was always disappointed in his students - none of them ultimately lived up to it. I guess it would be hard to do it!

But he had some PhD thesis students - a Wikipedia article lists:

  • FL Vernon, Jr.
  • Willard H. Wells
  • Al Hibbs
  • George zweig
  • Giovanni rossi lomanitz
  • Thomas curtright
  • James M. Bardeen


It would be interesting to get views of them!

My favorite story about Feynman and mathematics is (as with so many other things) in James Gleick's great biography, Genius. However, I loaned the book to a friend, so I tried to find the story online. It is an account of a talk he gave in Los Alamos during the Manhattan Project, entitled "Some Interesting Properties of Numbers." I remembered that he said that all "powerful minds" were "deeply impressed" by his tour de force.

So an internet search finally turned up the passage - someone else had been so impressed by it that they had folded that page in Gleick's book and immediately found it 20 years ago.

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My favorite story about Feynman and mathematics is (as with so many other things) in James Gleick's great biography, Genius. However, I loaned the book to a friend, so I tried to find the story online. It is an account of a talk he gave in Los Alamos during the Manhattan Project, entitled "Some Interesting Properties of Numbers." I remembered that he said that all "powerful minds" were "deeply impressed" by his tour de force.

So an internet search finally turned up the passage - someone else had been so impressed by him that he had folded that page in Gleick's book and found it immediately 20 years later, it was the only page he had marked this way. : Bent corners.

Here is the full passage:

Meanwhile, under the influence of this primordial dissection of mathematics, Feynman withdrew from pragmatic engineering long enough to organize a public lecture on "Some Interesting Properties of Numbers." It was an amazing exercise in arithmetic, logic and, although I would never have used the word, philosophy. He invited his distinguished audience ("all mighty minds," he wrote to his mother a few days later) to discard all knowledge of mathematics and start from the first principles, specifically, from a child's knowledge of counting in units. He defined sum, a + b, as the operation of counting b units from a starting point, a. He defined multiplication (counting b times). He defined exponentiation (multiply b times). He derived simple laws of the type a + b = b + ay (a + b) + c = a + (b + c), laws that were generally assumed unconsciously, although quantum mechanics itself had shown how crucially some mathematical operations depended on their ordering. Taking nothing for granted, Feynman showed how pure logic made it necessary to devise inverse operations: subtraction, division, and taking logarithms. He could always ask a new question that necessarily required a new arithmetic invention. Thus he expanded the class of objects represented by their letters a, b and c and the class of rules with which he manipulated them. By its original definition, negative numbers didn't mean anything. Fractions, fractional exponents, imaginary roots of negative numbers - these had no immediate connection to counting, but Feynman kept pulling them out of his silver logic engine. He turned to irrational numbers and complex numbers and complex powers of complex numbers; these came inexorably as soon as one was faced with the question: What number, I, when multiplied by itself, is equal to a negative one? He reminded his audience how to calculate a logarithm from zero and showed how numbers converged by taking successive square roots of ten and thus, as an inevitable by-product, derived the "natural base" e, that ubiquitous fundamental constant. He was recapitulating centuries of mathematical history, but not quite recapitulating, because only a modern shift in perspective made it possible to see the fabric in its entirety. Having conceived complex powers, he began to calculate complex powers. He made a table of his results and showed how they oscillated, oscillating from one to zero to negative one and vice versa in a wave that he drew for his audience, although they knew exactly what a sine wave looked like. He had arrived at the trigonometric functions. Now he posed one more question, as fundamental as all the others, but encompassing all of them in the round, recursive web that he had been weaving for a mere hour: To what power must we rise to reach i? (They already knew the answer, that eyi and π were linked as if by an invisible membrane, but as he told his mother, “I was quite fast and I did not give them much time to exercise the reason for one fact before I was showing them another even more amazing. ”) Now he repeated the statement he had happily written in his notebook at the age of fourteen, that the strangely polyglot statement e πi + 1 = 0 was the most remarkable formula in mathematics. Algebra and geometry, despite their different languages, were one and the same, a little abstract child arithmetic and generalized for a few minutes of the purest logic. “Well,” he wrote, “all powerful minds were tremendously impressed by my little arithmetic feats.

For me, this story says a lot. First, Feynman was never happy until he broke something in his essence, especially something mathematical. It did not accept "black boxes" that produced regular results, but whose internal operations were not understood. Second, he would intuit a general principle for the system he was studying, and he would use this principle to activate and guide the mathematical machinery to "shake up" a suitable proof or formalism.

Here, he used Euler's identity (sorry, I can't find a way to superscript on Quora, so I hope you understand what is previously meant by e πi + 1 = 0) to guide his systematic breakdown and construction. of the entire complex number system that we use. It's the rabbit that he pulls out of the hat at the end and everything builds up to that point.

Another example is his acceptance of the principle of least action - which he was initially very reluctant to use, because it seems magical, as in, how does light know this is the shortest way - to formulate his final version of quantum mechanics.

Third: Even as the youngest physicist in Los Alamos, among all the powerful minds that solved all the world's problems, he was not afraid to be playful, lead everyone to first principles, and keep a fundamental perspective on everything they were doing. . .

However, there is another aspect of Feynman's arithmetic, and the way he broke down the numbers, that deserves attention. This was his ability to play crossover rhythms on drums. I seem to remember "11 against 12", but online I can only find: "Do you remember Feynman and bongo drums? It was said that he could play 10 beats with his right hand and 11 with his left."

(That's a top conga, by the way, not bongos).

How did Feynman do this? How can you separate your left brain from your right brain and tell something as crazy as this? Can any of you do this? I must say that I have never met another physicist who knew how to even try it, although I have met a mathematician who could play two against three.

I don't know how Feynman did it, but I did describe some of the tricks African musicians use in my first Quora post: Karl Muller's answer to Is Music Really Mathematical?

If you work the rhythm slowly and then assign a mnemonic to the beats, it is actually quite easy (with practice) to spread your hands. However, there is a more mathematical way of doing it, which I often use when first working on a crossover rhythm from early beginnings. This is actually an arithmetic modulo app.

To play 3 beats in your left hand and 4 beats in your right hand: Count 4 x three beats in your right hand and 3 x four beats in your left hand.

I use a wonderful system called TaKeTiNa to count these rhythms, this is by far the best rhythm system I have come across in my life: Home

To count three times, you say "Ga Ma La". To count four times, say "Ta Ke Ti Na".

So: 4 x "Ga Ma La" = 3 x "Ta Ke Ti Na".

Now just play the right hand rhythm, I usually use my right hand for the faster rhythm, this says "Ga Ma La Ga Ma La Ga Ma La Ga Ma La ..."

Your right hand hits the drum every time you say "Ga" and you do it four times. If you are counting as an orchestral musician, you say: “One, two, three; Two, two, three; Three, two, three; Four, two, three… ”—and you get 4 x 3 = 12 beats.

In his left hand, he now wants 3 x "Ta Ke Ti Na". However, he is busy counting the "Ga Ma La" in his right hand. So how do you do both?

Begin by saying “Ta Ke Ti Na Ta Ke Ti Na…”, beating the drum with your left hand each time you say “Ta”, maintaining the same pulse as before. Just do this with one hand, until you're on the beat. Then, still hitting every fourth beat, you start saying "Ga Ma La". So now you are doing this with your left hand:

"Ga Ma La Ga Ma La Ga Ma La Ga Ma La ...", and now you have 3 x 4 = 12.

Hope you can see some of the similarities with the arithmetic lesson.

Now look closely at what you are saying as you hit the drum with your left hand. You're saying “Ga… Ma… La… Ga… Ma… La…”.

That's not that difficult, is it? All you have to count is Ga, Ma, La.

So now you put it together: using bold for the right hand, italic for the left, and bold italic for both hands together, you get:

Ga Ma La Ga Ma La Ga Ma La Ga Ma La, Ga Ma La Ga Ma La Ga Ma La Ga Ma La, ... "

So both your left hand and your right hand are saying the same thing, Ga Ma La, in an interlocking sequence. Once you get used to it, you don't have to count.

To fit a mnemonic to this: to pick up the rhythm of the right hand, I say the following (this is my own invention, if you can find a better one, do it, I have tried for years, this one is completely stuck in my head):

“Don't say it, do the action. "

To raise your left hand, you keep the rhythm exactly the same, but you say:

"Don't forget the Coff-ee ..." (using bold now to indicate the heartbeat of the left hand).

In this way, you can shift your attention at will to focus and improvise with one hand, while the other keeps your rhythm unchanged.

However, another way to do this is to use a metronome and just watch your hands work. If T = Together, R = Right, and L = Left, you can do a quick calculation and solve this:

T 2 RL 1 R 1 LR 2, T…

You tell it like this to the rhythm of a metronome: "Together, one, two, right left, one, right, one, left right, one two, together ..."

If you take this sequence and run it back and forth, it is, of course, symmetrical; this is true for all crossover rhythms.

One of the tricks that a "higher intelligence" could perform, they say, would be to spontaneously compose a piece of music that is symmetrical, that is, it can be played both backwards and forwards. You can see that this trick is actually a completely normal skill among African drummers. When we start to play a crossover rhythm, from the beginning, we can immediately hear how it will change at the end.

Now: If you do this long enough, you will eventually find that these rhythms circulate within you, and you can switch from one to the other without even thinking. I can play three beats with my left hand and do 1, 2, 3, 4, 5 and 6 with my right hand at will (I'm still working on 3 vs. 7 ... 4 vs. 7 is much easier).

I must admit that I have never tried 10v11, but I have a fully crafted composition 11 times. In fact, I count it in two measures of five and a half, which is why it is called "The Take Five-and-A-Half Cha-Cha-Cha." You find these weird melodies just popping up as you work on your crossover beats.

According to neurologist Oliver Sacks, the only profession one can recognize just by looking at someone's brain is "musician." The cerebral cortex is much more developed, as a result of what is called "long-term enhancement" of the brain - the brain synapses actually physically grow and form stronger connections to reinforce repeated brain wave patterns. Musicians are not born with such a brain: tens of thousands of hours of physical practice make the brain develop in this way.

Sacks also says that the corpus callosum, the thick fiber that links the left and right brains, is especially enhanced in musicians.

With all the incessant drumming Feynman was making, on desks, doors, walls, pots, pans, wine glasses, literally anything at hand, he constantly kept his left and right brains working together, but autonomously. And perhaps this is one of the secrets of the Feynman algorithm to solve a problem: http://wiki.c2.com/?FeynmanAlgorithm:

  1. Write down the problem.
  2. Think about it.
  3. Write down the solution.

Maybe it should be "Think well while playing with your fingers."

One last point: Reinhard Flatischler, the creator of the TaKeTiNa system, makes a big distinction between actions that are automatic and those that are autonomous. By definition, doing something automatically means that you are doing it without thinking about it. The moment you start thinking about it, it is no longer automatic. Now ask any pianist who has honed his skills and may be playing something perfectly if he gets in trouble when he starts looking at his fingers and thinking about what he is doing. This can be disastrous and it happens to the best performers.

When you can look at your left hand and find that it keeps that rhythm on its own - "Ga Ma La Ga Ma La Ga Ma La ..." - and that when you pay attention to it, you don't miss a beat, rather, the beat says: "Thanks for finally paying attention to me, now, you can start to improvise a bit with this hand, don't worry, I have this ..."; In other words, your two hands are both quite autonomous, each of them is under its own control and they can move quite independently, just as you wish:

So, you can say that you are counting on your whole brain. It's easy enough to count to three fours with one hand, but try to do it when the other hand counts four three. This is African higher mathematics. Even highly skilled Western orchestral musicians are completely lost in the moment when they play complex African music. Take Tubular Bells as an example of difficult western beats - this starts with 7, 7, 7, and 9 beats, making 30 in total, but it's pretty linear, there are no real crossover beats in it. An African musician would take a look at this and say, hm, 30 beats, let's try six 5-beat bars ... Ga, Ma, La, Ta, Ki, Ga, Ma, La, Ta, Ki ... it could be a bit boring, but it's a good start ...

I think the answer is: you can't, but there's a lot that can be learned from how you approached things that are worth trying to emulate.

Mark Kac memorably said that there are two types of geniuses: ordinary ones (who are just like you if you were simply much, much smarter) and wizards (who think in ways you simply cannot conceive of). Feynman was, according to Kac, a magician of the highest caliber.

Feynman's father gave him a great foundation on how to think critically: The messages he received as a child included the point that people are the same under their uniforms, that they know

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I think the answer is: you can't, but there's a lot that can be learned from how you approached things that are worth trying to emulate.

Mark Kac memorably said that there are two types of geniuses: ordinary ones (who are just like you if you were simply much, much smarter) and wizards (who think in ways you simply cannot conceive of). Feynman was, according to Kac, a magician of the highest caliber.

Feynman's father gave him a great foundation for how to think critically: the messages he received as a child included the point that people are the same under their uniforms, that knowing the name of a thing is not knowing the thing itself, and, conversely, that just because we can name and describe a phenomenon like inertia, it doesn't mean that we can explain why it happens. That's a great foundation for having an inquisitive mind and not being impressed by who you're talking to, and it's something we can all try to remember (though it's harder to do if you've grown up without thinking that way).

Feynman also developed his own mental bag of tricks, such as solving the integral path mathematics to calculate the path of a ball, essentially alternative but mathematically equivalent approaches to standard problems that gave him different perspectives on things. The comprehensive path was, of course, central to his QED formulation many years later. You can learn to do that too, but the challenge is being able to recognize when and how to apply it.

It seems to me that much of Feynman's magic came from the ability to detect patterns that were deeper and more fundamental than what other people could see. The reason your QED formulation has been so successful, with Feynman diagrams and all, was essentially a matter of ergonomics. Schwinger's formulation was mathematically identical but much more complex to work with; Feynman's approach broke the whole thing down into diagrams, each line and node of which represented a precise event that could be described mathematically, reducing a horrendous monolithic calculus into a series of simpler calculations.

And each of those events represented a possible physical interaction between particles, with a calculable probability of happening. Seeing a deeper reality, Feynman was able to unravel a complex web of mathematics into something that "allowed second-rate men to do first-rate work."

Could ordinary mortals learn to see new bonds between nature's lego blocks that way? I doubt it. I remember one of his Los Alamos stories, where he is presented with the blueprint of a uranium separation facility and asks (says randomly) what a particular symbol does ... only for the designers to realize that it is identified a big flaw in the design. He downplays his own role, stating that he didn't know what he was looking at, but it seems to me that he had the kind of mind that recognizes patterns that might have been drawn to a symbol that somehow looked strange, even if he couldn't consciously frame. why (or just thought it was a better story not to state that)

"If one fool can learn to do it, so can another" may be so, but he has to be the right fool, and I'm not sure the right fool is born yet.

(Like Charles, I have no personal knowledge of Feynman, but have read a lot about him.)

Richard Feynman was an exceptionally broad and accomplished physicist, but he was not equal to Einstein. However, I would say that it is debatable whether even Newton was equal to Einstein. Einstein, particularly in regards to his theory of general relativity, was a historical anomaly that cannot be easily categorized.

In the case of special relativity, if Einstein hadn't thought of it, someone else would almost certainly do it in a couple more years. However, if Einstein hadn't come up with general relativity, it's quite possible that we still wouldn't have a theory like I do.

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Richard Feynman was an exceptionally broad and accomplished physicist, but he was not equal to Einstein. However, I would say that it is debatable whether even Newton was equal to Einstein. Einstein, particularly in regards to his theory of general relativity, was a historical anomaly that cannot be easily categorized.

In the case of special relativity, if Einstein hadn't thought of it, someone else would almost certainly do it in a couple more years. However, if Einstein hadn't come up with general relativity, it's quite possible that we still wouldn't have a theory like this to guide us. Einstein was not first a visual thinker; that was Minkowski. Instead, he had an intuitive style that allowed him to see how different things could be the same on a deeper level. This novel approach took him to places where no one else had been or ever would have gone.

I once analyzed Einstein's articles on special relativity once in extreme detail, and it was quite fascinating. He was downright clumsy and a bit inept at algebra, which is the only kind of math he used in those jobs; He didn't even try advanced math. Trying to understand how his mind worked in these and other articles from his "miracle year" (he should have actually won about five Nobel prizes) convinced me that he was a bit wise, in the literal psychological sense of the word. He could "see" how physics worked, but he couldn't easily put into words how his intuition worked or why it seemed so obvious to him. This made it difficult to transmit his ideas to others, and is part of why it took him so long to learn the math he needed to create General Relativity.

Newton was amazing, especially for his time, but in terms of skills and knowledge, I would compare him more to Maxwell. Maxwell was a truly amazing and influential physicist who sadly died young, which is why he is better known to scientists than the general public. Most people have heard of his equations, but have no idea that Maxwell also initiated both the use of differential equations for physics and the importance of the methodical use of units. Ironically, the four equations Maxwell is best known for are not even his equations. They were created by Heaviside many years after Maxwell's death, and are both a massive translation and a condensation of Maxwell's original twenty-odd quaternion-based equations (!). Despite all your work, Heaviside was adamant in giving all the credit to Maxwell, whom he deeply respected. And a bit of trivia: This was the same Heaviside whose name is used for Cat Heaven (the "Heaviside cape") on the Broadway show and in the 2020 movie Cats. It is one of the earliest names for the ionosphere.

I was hugely surprised to see Feynman portrayed in an answer here as being unfairly unworthy of Schwinger, as they won a Nobel Prize together and just had different approaches to the same problem. If anyone came up short in history for that particular award, it was the third co-winner, Sin-itiro Tomonaga… have you heard of him lately? Tomonaga did his work on the same problem in near total isolation, an astonishing feat. He was also probably the kindest of the three, if you consider simple humanity as a relevant topic.

It is inevitable that the Schwinger and Feynman approaches are mathematically equivalent on some level, since they give the same answers! Quantum mechanics has a very old history of allowing very different conceptual models to produce the same result, a point that Spekkens discusses in some of his writings. If anything, I'd always thought that, far from being looked down upon, Schwinger has had a very good reputation in the physics research community and has been highly influential in ways other than Feynman. It is not always a zero sum game! Feynman did not seem to think of Schwinger as a "competitor" and he certainly knew and respected his methods. Feynman spent a lot of time in his lectures explaining coupled harmonic oscillators and their value, for example. For Feynman,

Yes, Feynman absolutely won the popular vote for his methods, but nothing I've seen indicates that Schwinger even cared or was "behind" that part of the "market." Schwinger's comment that Feynman brought QFT to the masses was, for example, a slight, not a compliment! Schwinger had his greatest impact exactly where he wanted, which was the Ph.D. and post-doctorate-level physics communities.

The subject of particles is fascinating! I should mention that I myself am a very solid "nonbeliever" in particles as reality, since everything we call a "particle" is always a much smaller wave function. The real universe seems to have a very deep aversion to true points, since ordinary Planck uncertainty ensures that creating a particle the size of a real point in any real experiment would only have an infinite energy cost.

However, to say that for this reason Feynman's astonishingly efficient methods (this was in the era of manual calculus) were "wrong" just because he adapted the particle end view rather than the wave end view misinterprets the flexibility of quantum mechanics, which positively seems to encourage human minds to take their models to an extreme and somehow get away with it, often with real benefits. Bell, for example, had his own version of point particles, in his case in combination with pilot waves (the de Broglie-Bohm model), that is, particles-Y-waves. While pilot wave models are not very popular in English-speaking culture, according to their own statement, Bell's use of them contributed directly to how he came up with his astonishing inequality. Feynman simply showed that if you take the particles, ONLY extreme,

The fact that Feynman used ONLY particles (and particles AND Bell waves) in no way excludes or contradicts the ONLY Schwinger wave perspective. In fact, if anything, the success of both (for example, that joint Nobel Prize) and their identical predictions demonstrate a larger lesson: There is never just one way to describe quantum mechanics. If you insist on such an approach, all you'll end up doing is unnecessarily excluding some useful set of additional computational and conceptual tools.

Finally, I have to say this: Calling Julian Schwinger the equivalent of Einstein misses the real reason why Schwinger's methods, while powerful, did not fully take over physics. If anything, decades of searching for spin 2 gravitons to explain gravity has been one of the biggest reversal disasters in the history of physics. The problem with that specific attempt to convert everything to quantized fields is remarkably straightforward - it just didn't work. But for whatever reason, everyone kept trying really hard to make it work anyway, both through quantum gravity and less directly through string theory. To this day, those models have yet to produce useful and experimentally meaningful mathematical models.

The fact that Schwinger gave impressive pre-quark talks on such topics, making it seem like everything was going to fit together beautifully in a few years, is forgivable the moment he did. But we now know, unfortunately at a cost of tens, if not hundreds of millions of dollars of research lost and lives of researchers downright wasted, that Schwinger's impressive and persuasive insight was simply not entirely correct.

Finally, I must mention that, as a reductionist, Schwinger's concept of simply establishing new fields for new particles is distressingly unsatisfactory to me. I suspect that perspective is not mine alone, and that it is much more a factor of why Schwinger was not hailed as the new Einstein than a silly competition with Feynman for the equivalent of the Facebook likes of the 1900s. More specifically The inevitable focus of the accelerator community on "particles" made it much easier to describe their efforts in terms of Feynman's QED model similarly centered on particles. That, in turn, made it conceptually easier for them to search for a deeper simplicity in physics by trying to break "particles" down into smaller, simpler pieces. This particle-biased approach,

RICHARD PHILIPS FEYNMAN vs STEPHEN HAWKING

No they were just different

They were different, although good friends.

The contribution to the physics of both has been great.

Esteban lived overcoming death.

Feynman was a very nice person. And besides, he was an expert playing the bongos. My great pain was not being able to attend any of his great classes.

In return, I met Stephen personally in Cambridge. He was a very happy person. He was only three years older than me.

RICHARD PHILIPS FEYNMAN

He revised the big picture of quantum electrodynamics and revolutionized the way science under

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RICHARD PHILIPS FEYNMAN vs STEPHEN HAWKING

No they were just different

They were different, although good friends.

The contribution to the physics of both has been great.

Esteban lived overcoming death.

Feynman was a very nice person. And besides, he was an expert playing the bongos. My great pain was not being able to attend any of his great classes.

In return, I met Stephen personally in Cambridge. He was a very happy person. He was only three years older than me.

RICHARD PHILIPS FEYNMAN

He reviewed the whole picture of quantum electrodynamics and revolutionized the way science understood the nature of elementary particles and waves.

In 1965 he shared the Nobel Prize in Physics with the American Julian S. Schwinger and the Japanese Tomonaga Shinichiro, scientists who independently developed theories analogous to those of Feynman, although the latter's work stands out for its originality and scope.

The tools that he devised to solve the problems that were posed to him, such as, for example, graphical representations of the interactions between particles known as Feynman diagrams, or the so-called Feynman integrals, allowed progress in many areas of theoretical physics. throughout the period beginning after the Second World War.

He studied physics at the Massachusetts Institute of Technology, and later received his doctorate from Princeton University, where he collaborated in the development of atomic physics between 1941 and 1942. In the following three years he led the group of young theoretical physicists who collaborated in the Manhattan Project in the secret laboratory of Los Alamos, under the direction of Hans Bethe.

In the 1950s, he justified, from the point of view of quantum mechanics, the macroscopic theory of the Soviet physicist LD Landau, which explained the superfluid state of liquid helium at temperatures close to absolute zero, a state characterized by the strange absence of forces friction. .

In 1968 he worked at the Stanford particle accelerator, a period in which he introduced the theory of partons, hypothetical particles located in the atomic nucleus, which would later lead to the introduction of the modern concept of quark.

His contribution to theoretical physics has been reflected in titles such as Quantum Electrodynamics (1961) and The Theory of Fundamental Processes (1961).

On top of all this, his classes at Caltech were a show.

The late Richard P. Feynman, a former Caltech physics professor and Nobel laureate, would have turned 100 on May 11, 2018. Although he passed away more than 30 years ago, he left a lasting legacy as a brilliant physicist. and a master storyteller and teacher. To celebrate Feynman's 100th birthday, Caltech recalled a special two-day event (May 11-12) in which his friends and family and some of today's best scientists participated.

STEPHEN HAWKING

After high school, Hawking entered the University College of Oxford, graduating in 1962 with degrees in mathematics and physics. At that time he was a young man of normal life, whose singularities were only his brilliant intelligence and a great interest in science.

He was diagnosed with a degenerative neuromuscular disorder, ALS, or amyotrophic lateral sclerosis. Stephen's life was not the same from then on, but his physical limitations did not interrupt his intellectual activity at any time; in fact, they increased it.

With Jane Wayline on the wedding day (1965)

Stephen Hawking set himself the ambitious goal of harmonizing general relativity and quantum mechanics, in search of a unification of physics that would make it possible to account for both the universe and subatomic phenomena.

His studies on mini black holes would lead him to combine for the first time the theory of relativity and quantum mechanics to solve the problem of studying these structures of very small dimensions and extraordinarily high density, about which it was not believed that one could have any knowledge. . acquired.

In 1974 he proposed, according to the predictions of quantum physics, that black holes emit thermal radiation until their energy is depleted and extinguished. Hawking has also explored some singularities of the space-time binomial.

In 1974 Hawking was appointed a Fellow of the Royal Society and three years later, Professor of Gravitational Physics at Cambridge, where he was awarded the Lucasian Chair of Mathematics (1980), a chair that had been taught by such eminent figures as Isaac Newton and, most recently, Paul Dirac.

Hawking would continue to occupy this chair until his retirement in 2009.

A great popularizer

It is a great paradox that a man who was fully endeavoring to clarify scientific concepts for the average public had to grapple with the difficulty of communicating.

His most famous books, such as A History of Time: From the Big Bang to Black Holes (1988), which has been translated into thirty-seven languages ​​and sold more than twenty million copies in a few years. In his intention to bring the book to a wide audience, he renounced formulas and exhibitions by specialists, but did not abandon the rigorous treatment of the subject.

In History of Time he addresses topics such as black holes and, in addition to the origin, the possible destiny of the universe.

Other later books, such as Black Holes and Small Universes (1994), The Universe in a Nutshell (2002) or The Great Design (2010), manifest an even greater informative intention than their previous books.

As for his more specialized bibliography, his efforts to describe the properties of black holes from a theoretical point of view, as well as the relationship that these properties have with the laws of classical thermodynamics and quantum mechanics, have been collected in works such as The Large Scale Structure of Space-Time (1973, in collaboration with GFR Ellis), Superspace and Supergravity (1981) and The Very Early Universe (1983).

Feynman felt compelled: high-level algebra, integral calculus, he consumed them as if we were consuming a Netflix series. I would recommend reading 'You are surely joking, Mr. Feynman', his autobiography. You get a glimpse of his psyche, and that may be unpopular to say, but I think for Feynman a lot of ego was involved in his upward spiral.

Consider their jokes. They were often aimed at an audience, he wanted people to see how smart he was. In Los Alamos, working on 'the bomb,' he broke people's safes numerous times, in front of high-ranking military personnel, and then simply took out t

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Feynman felt compelled: high-level algebra, integral calculus, he consumed them as if we were consuming a Netflix series. I would recommend reading 'You are surely joking, Mr. Feynman', his autobiography. You get a glimpse of his psyche, and that may be unpopular to say, but I think for Feynman a lot of ego was involved in his upward spiral.

Consider their jokes. They were often aimed at an audience, he wanted people to see how smart he was. In Los Alamos, working on 'the bomb', he broke people's safes numerous times, in front of high-ranking military personnel, and then simply took out top-secret contents that could have influenced the war effort had they fallen into the hands German. Shock, horror, colorless faces, amazement at his technical skills as a safe-thief, Feynman loved these things. However, his safe opening was not a remarkable stroke of genius, as it appeared to be, he had actually discovered a trick, by examining safes when they were open, he could come back later and easily break them when they were closed. Of course,

In fact, this pattern of seeking intellectual glory played out in Feynman's life many times, again I implore you to read his autobiography and you will get the flavor I'm talking about. The Challenger disaster, of which he was an investigator, is one of his famous last exploits. He appeared before a panel of judges and 'proved' that the mishap was caused by the cold weather on launch day, which caused the rubber O-rings to deform. People were shocked, Feynman does it again, he solved it! But what Feynman didn't say was that Donald Kutyna tipped him off to this end, and he certainly didn't solve the problem himself.

I cite these examples, of which there are many of a similar kind, not to demean Feynman but to offer you another perspective on his psyche. He was a genius, but a lot of people are smart, what interests you are their motivations. From what I know of him from studying his lectures and indeed his life somewhat, Feynman was partially motivated by the impression he had on others, along with his love of problem solving. He loved the audience, the applause, the open mouth that is usually reserved for magicians and miracles. You could call this ego, if you want. But we all need a carrot on a stick.

I sat in Physics X at Caltech for a year - this is where Feynman would take questions from freshmen and sophomores and try to answer them. He did not like the more "formal" questions posed by graduate and senior students: he wanted questions prompted by real curiosity.

I had a lot of fun on Physics X: I once mentioned something that had bothered me the most for a long time: "Why is the gamma function generally considered the 'natural generalization' of n-factorial (n!)?" He did not respond directly; instead, he turned to the classroom and issued a challenge: "During the break, think about this

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I sat in Physics X at Caltech for a year - this is where Feynman would take questions from freshmen and sophomores and try to answer them. He did not like the more "formal" questions posed by graduate and senior students: he wanted questions prompted by real curiosity.

I had a lot of fun on Physics X: I once mentioned something that had bothered me the most for a long time: "Why is the gamma function generally considered the 'natural generalization' of n-factorial (n!)?" He did not respond directly; instead, he turned to the classroom and issued a challenge: "During the break, think about this: 'What is (1/2)!, the factorial of (1/2)?' Okay, Merry Christmas! "

Three students really thought about this during the holidays. A girl pointed out that (d / dx) ^ n x ^ n = n!; I thought something could be done with that. Another colleague expanded the factorial function in a complex series of powers over z = (1 / 2,0), imposing the conditions that (z +1)! = (z + 1) * z! and also that 1! = 1 = 0!; He carried it out on more and more terms.

I took the idea about repeated differentiation and combined it with the fact that a repeated integral also incorporates the factorial function. (See
mathworld.wolfram.com/RepeatedIntegral.ht ml; you'll need to remove the space.)
For integer values, the relationship between n! and the nth repeated integral is simply true. I co-defined non-integral values ​​of n! And repeated integrals not integrals so that the relationship remains true. Then I tested that relationship between gamma function and beta function (See:
http://en.wikipedia.org/wiki/Beta_function#Relationship_between_gamma_function_and_beta_function)
also held for my factorial extension. I was 95% of the way, but got stuck at one point: once I was able to figure out a value, for n = 1/2, I was able to immediately show that any continuous function that was defined in my path had to be the famous gamma function .

On the first Monday night of the new calendar year, only 4 people showed up: the three factorialists and Feynman. Feynman was delighted with what we had found: it all reminded him of things he had worked on before. I think he pointed out something very easy that I hadn't finished thinking about (basically piecemeal integration; can't find my notebook to see why that would have been a problem), and then boom !, I had (1/2)! = square root (pi) / 2; knew my definition of n! = gamma (n + 1); and it had a definition for non-integer iterations of integration and differentiation, all together.

Feynman dug it. Then he gave me a little advice: "Don't tell anyone. Just wait. Someday, someone will have a problem, and this will be the answer. Just take it out then. And then when they ask you," How did you notice that?

I ran into Feynman in the Caltech cafeteria and he invited me to lunch with him three different times. This was the highlight of my year at Caltech.

Although IQ is still very popular in psychometrics, I have strong reasons for classifying it among the 'not even wrong' (not even wrong) constructs:

  1. The "No Free Lunch" Theorem. In short, it is not possible for a cognitive system to optimize various kinds of tasks without a collateral load. As such, it is highly unlikely that similar systems (i.e., Homo sapiens brains) will have different overall abilities to solve arbitrary problems.
  2. External validity. The correlations between IQ and external measures (that is, professional performance) vary widely. Basically, you get high correlations with t-tests
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Although IQ is still very popular in psychometrics, I have strong reasons for classifying it among the 'not even wrong' (not even wrong) constructs:

  1. The "No Free Lunch" Theorem. In short, it is not possible for a cognitive system to optimize various kinds of tasks without a collateral load. As such, it is highly unlikely that similar systems (i.e., Homo sapiens brains) will have different overall abilities to solve arbitrary problems.
  2. External validity. The correlations between IQ and external measures (that is, professional performance) vary widely. Basically, you get high correlations with tests that are similar to the IQ itself. The simplest instruments (Miller test of analogies) provide similar correlations, suggesting that IQ is not special as a proxy for "general intelligence."
  3. Different problems have different requirements to meet. Sages make use of their atypical brain function to do things like play a song right after hearing it or factor large prime numbers. Both are tasks that require "intelligence", but IQ tests fail catastrophically in these cases.

The big problem is: IQ maps (a) the ability of a complex neural network to solve an infinity of arbitrary problems to (b) a real number.

This is only possible if you place strong restrictions on the kinds of problems you face. Otherwise it will be clearly wrong.

Could you assign different animals to real numbers? Rabbit -> 142.3; Horse -> 109.4. You could do it with a dimension, like its volume, but not the concept of 'animal'. I think the same applies to general intelligence.

If you read Feynman's "Surely You're Kidding, Mr. Feynman", you'll notice that he enjoyed looking outside the box: playing bongo, meditating in sensory deprivation chambers, joking, picking locks ... Perhaps the reinforcement patterns related to exploration of alternative (creative) paths led him to devise innovations like the Feynman path diagram, which are not so complex, but useful and elegant.

On the other hand, consider people like John von Neumann. He was extremely conservative and pure mathematics came naturally to him. These features are likely related to his work, such as creating a unifying formal framework for quantum mechanics (Dirac-von Neumann axioms in Mathematical Foundations of Quantum Mechanics).

Notice that they both solved important problems, although their brains functioned very differently. Could von Neumann walk into a room full of other sapiens and entertain people like Feynman did? Computationally, this is NOT an easy task for a neural network: reading non-verbal behavior in real time, inferring internal states of other neural networks, predicting reactions to different actions, etc. However, an illiterate Hollywood movie star may outperform Feynman at this.

It's not amazing and it fits the data.

I think it is more likely to be true.

The average IQ of a PhD. The physics student is 130. So if the SD is like 15, Feynman's IQ fits the data. There would also be some people with an IQ of 110 or less with a Ph.D. in physics.

You don't have to have a very high IQ to achieve anything. With an IQ of 125, he could do everything Feynman did ... what's hard to believe about it?

People often cite things like Feynman mastering algebra at 13, calculus at 15, and high scores, but those things don't necessarily mean someone has a very high IQ.

With an IQ of 125 you

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It's not amazing and it fits the data.

I think it is more likely to be true.

The average IQ of a PhD. The physics student is 130. So if the SD is like 15, Feynman's IQ fits the data. There would also be some people with an IQ of 110 or less with a Ph.D. in physics.

You don't have to have a very high IQ to achieve anything. With an IQ of 125, he could do everything Feynman did ... what's hard to believe about it?

People often cite things like Feynman mastering algebra at 13, calculus at 15, and high scores, but those things don't necessarily mean someone has a very high IQ.

With an IQ of 125, you will be able to get perfect high scores and learn things like algebra and calculus. If you are really interested in or obsessed with math and physics and your IQ is 125, you will be able to learn it and get really good at it ... why would you need a super high IQ to be good at math or physics? ?

You can't tell what someone's IQ is using just their subjective perception because very few things absolutely REQUIRE someone to be super good at IQ puzzles. There are also some people who mentally cannot solve many IQ puzzles, but with writing and time they would solve it.

The correlation between tertiary academic performance and IQ is only r = 0.23 (Poropat, AE (2009). A meta-analysis of the five-factor model of personality and academic performance. Psychological Bulletin, 135, 322–338.). .which means that more than 94% of the total variation in tertiary academic achievement would be inexplicable by IQ (if you use the coefficient of determination).

Many of the people who score 100% don't have a super high IQ ... just an IQ between 100 and 120 ... neither super high nor super low. I know a lot of people in college with super high SAT scores who had a 2.0-2.5 GPA ... some even failed.

I doubt you need an adult IQ above 80 to accomplish most things ... it seems like an adult IQ of 115 would be enough for everything.

I don't understand what's hard to believe about Feynman having an IQ of 125, as studies show a very low correlation between IQ and a lot of things.

In reality, based on all the evidence and data, an IQ of 125 would be more than enough to accomplish what Feynman did even though many people imagine or speculate that "you need to be really super good at IQ puzzles to achieve things ", which is not supported. by the evidence.

An IQ of 125 is above average or "much higher" on the Stanford-Binet scale.

Many people in history imagined or speculated that they had a very high IQ, they probably had an IQ of 140 or less.

There is also evidence showing that working memory (WM) predicts many things better than IQ.

This story was shared with me by the late David Olive, who was my supervisor for a short time when I thought I would like to specialize in superstring theory.

We were sitting in the theoretical physics common room when one of the graduate students asked about Feynman. And, of course, people like David Olive, Tom Kibble, Abdus Salam, and others in the same group had been at the forefront of theoretical physics research, and spending time in the group had also been done by many others. Steven Weinberg and Sheldon Glashow, who shared the 1979 Nobel Prize with Salam, for example, had also spent time in the group.

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This story was shared with me by the late David Olive, who was my supervisor for a short time when I thought I would like to specialize in superstring theory.

We were sitting in the theoretical physics common room when one of the graduate students asked about Feynman. And, of course, people like David Olive, Tom Kibble, Abdus Salam, and others in the same group had been at the forefront of theoretical physics research, and spending time in the group had also been done by many others. Steven Weinberg and Sheldon Glashow, who shared the 1979 Nobel Prize with Salam, for example, had also spent time in the group.

(And contrary to popular impression, Steven Weinberg has always said that it was Kibble's 1967 article on breaking local symmetry that really cleared it all up. For this reason, some professional physicists refer to the Higgs mechanism and the Higgs boson as the Higgs-Kibble mechanism, and the Higgs-Kibble boson.)

So this was not your average company. And yet Feynman being Feynman, and everything we did Feynman diagrams, or path integrals, someone asked the question. I just hope it wasn't me.

You see it is a little like asking Novak Djokovic to tell you Rafael Nadal stories. Or maybe like asking Andy Murray to tell you Roger Federer stories. Or Ivan Lendl to give away stories about John McEnroe.

I just hope I wasn't the one asked the question.

So David Oliver, never very talkative, explained the one incident he remembered vividly. They had all arrived at a conference in the US and went off to to hotel where either Feynman had asked to discuss with them - or they had asked to discuss with him - the day before the conference started.

As their taxi pulled into the hotel, they saw Feynman run out of the foyer, throw his bag into a cab, and drive off. “Catch you later” he said.

So he was leaving as soon as he arrived? Huh?

But as they were checking in, another cab arrived with someone asking for Mr Feynman. They were told Mr Feynman had gone back to the airport.

So they turned around and rushed back.

An hour our two later, Feynman returns, and asks hotel management if someone had shown up asking for him. The said a guy had and they had told him Feynman had rushed back to the airport.

So they had rushed back too and were likely at the airport, and so Feynman now rushed back to airport too.

So no discussion on physics that day. They said Feynman was just seen rushing back and forth between the hotel and airport.

Here my memory is a bit hazy, because in of one those trips his bag may have also fallen off the top of a shared limousine etc. I don’t fully recall the detail.


So you can guess what happened. Someone took Feynman’s bag or vice versa, and then they were both trying to retrieve their own. And if in one of the rushes Feynman’s bag had fallen off, then Feynman had to go back to find it. I'm kind of 90% sure that is what happened - but not 100%.

Either way he was rushing back and forth the whole day. In David Olive’s words, “Always in a taxi, comimg or going. “

So they never had that discussion the day.


All physicists mentioned above:

David Olive - WikipediaEarly Years and Education Edit David Olive was born in Middlesex in 1937 1 and educated at the Royal High School, Edinburgh and the University of Edinburgh. He then moved to St John's College, Cambridge, where he obtained his PhD under John Taylor in 1963. 2 He has 2 daughters and a granddaughter. After a brief postdoctoral appointment at the Carnegie Institute in Pittsburgh, Olive returned to Cambridge as a fellow at Churchill College, becoming a professor in the Department of Applied Mathematics and Theoretical Physics (DAMTP) in 1965. Here he made key contributions to the physics approach of particles known as S-matrix theory. His 1966 book The Analytic S-matrix, co-authored with Richard Eden, Peter Landshoff, and John Polkinghorne, it remains a definitive text on the subject and is known as ELOP. 2 In 1971, Olive made what she has described as a "momentous personal decision" to sacrifice her tenure at Cambridge and move to CERN's Theory Division as a fixed-term staff member. He was part of a team brought together by Daniele Amati to work on the theory originally known as the dual resonance model, but soon to be recognized as string theory. At CERN, Olive initiated collaborations with the circle of string theorists, many of whom are featured in her memoirs From Dual Fermion to Superstring. His work at CERN, in part in collaboration with Lars Brink and Ed Corrigan, initially focused on the consistent formulation of dual fermion amplitudes, generalizing existing bosonic models. This period saw several of Olive's major contributions to string theory, including the Gliozzi-Scherk-Olive (GSO) projection that elucidated the role of space-time supersymmetry in ensuring the consistency of the dual fermion model and was an essential step in establishing 10-dimensional superstring theory. He was one of the first to be convinced of the conceptual revolution according to which string theory is considered a unified theory of all particle interactions, including gravity, rather than simply a hadron model. This was the subject of his plenary talk at the 1974 Rochester conference in London. 2 In 1977, Olive returned to the UK to take a professorship at Imperial College, becoming Professor in 1984 and Head of the Theoretical Physics Group in 1988. He had already begun to collaborate with Peter Goddard and together they produced a series of articles on the mathematical foundations of string theory, notably on the Virasoro and Kac-Moody algebras. and their representations and relationship with vertex operators. One result of their work on algebras and lattices was the identification of the special role played by the two Lie groups SO (32) and E8 x E8, which Michael Green and John Schwarz would show shortly to show the cancellation of anomalies that led to the rebirth of string theory in 1984. 2 This body of work from 1973 to 1983 was recognized with the award of the prestigious Dirac Medal in 1997 to Goddard and Olive "in recognition of their fhttps: //en.m.wikipedia . org / wiki / David_Olive Tom Kibble - Wikipedia British physicist Tom Kibble Born Thomas Walter Bannerman Kibble (1932-12-23) December 23, 1932 Died June 2, 2016 (2016-06-02) (83 years old) British Nationality Alma mater University of Edinburgh, BSc, MA, PhD Known for quantum field theory, broken symmetry, Higgs boson, Higgs mechanism, Kibble-Zurek mechanism, cosmic strings Awards Scientific career Fields Theoretical physics Institutions Imperial College London Thesis Topics in quantum field theory: 1. Schwinger's principle of action; 2. Scattering relationships for inelastic scattering processes (1958) Doctoral advisor John Polkinghorne Doctoral students Seifallah Randjbar-Daemi citation needed Jonathan Ashmore 2 Sir Thomas Walter Bannerman Kibble CBE FRS MAE 1 (; December 23, 1932 - June 2, 2016), was a British theoretical physicist, principal investigator at the Blackett laboratory, and emeritus professor of theoretical physics at Imperial College London. 3 His research interests focused on quantum field theory, especially the interface between high-energy particle physics and cosmology. He is best known as one of the first to describe the Higgs mechanism and for his research on topological defects. Since the 1950s he has been concerned with the nuclear arms race and since 1970 he has assumed leading roles in promoting the social responsibility of the scientist. 4 Early life and education edit Kibble was born in Madras, in the Madras presidency of British India, on December 23, 1932. 5 6 He was the son of statistician Walter F. Kibble, and the grandson of William Bannerman, an Indian Medical Service officer, and author Helen Bannerman. His father was a mathematics professor at Madras Christian College, and Kibble grew up playing on the university grounds and solving mathematical puzzles his father gave him. 7 He was educated at Doveton Corrie School in Madras and later in Edinburgh, Scotland, at Melville College and at the University of Edinburgh. 3 He graduated from the University of Edinburgh with a BA in 1955, an MA in 1956, and a Ph.D. in 1958. 5 8 Kibble worked on the mechanisms of symmetry breaking, phase transitions and topological defects (monopoles , cosmic strings or domain walls) that can be formed. He is best known for his joint discovery of the Higgs mechanism and the Higgs boson with Gerald Guralnik and CR Hagen. 9 10 11 As part of the Physical Review Letters 50th anniversary celebration, the journal recognized this discovery as one of the most important articles in the history of PRL. 12 For this discovery, Kibble was awarded the 2010 JJ Sakurai Prize from the American Physics Society for Theoretical Particle Physics. 13 While Guralnik, Hagen and Kibble are considered to be the authors of the most comprehensive of the earliest articles on Higgs theory, but controversially they were not included in the 2013 Nobel Prize in Physics. 14 15 16 17 18 19 20 21 In 2014, Nobel laureate Peter Higgs expressed disappointment that Kibble had not been chosen to share https: //en.wikipedia. org / wiki / Tom_Kibble Abdus Salam - Wikipedia Mohammad Abdus Salam 4 5 6 NI (M) SPk (/ s æ ˈ l æ m /; pronounced əbd̪ʊs səlaːm; January 29, 1926 - January 21 November 1996) 7 was a Pakistani theoretical physicist. He shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for their contribution to the theory of electroweak unification. 8 He was the first Pakistani and the first from an Islamic country to receive a Nobel Prize in science and the second from an Islamic country to receive a Nobel Prize, after Anwar Sadat of Egypt. 9 Salam was a scientific advisor to the Pakistan Ministry of Science and Technology from 1960 to 1974, a position from which he played an important and influential role in the development of the country's scientific infrastructure. 9 10 Salam contributed to numerous developments in particle and theoretical physics in Pakistan. 10 He was founding director of the Commission for the Investigation of Space and the Upper Atmosphere (SUPARCO), and responsible for the establishment of the Theoretical Physics Group (TPG). 11 12 for this, he is seen as the "scientific father" 5 13 of this program. 14 15 16 In 1974, Abdus Salam left his country in protest, after the Pakistani Parliament unanimously passed a parliamentary bill declaring members of the Ahmadiyya Muslim community non-Muslims, to which Salam belonged. 17 In 1998, after the country's Chagai-I nuclear tests, the Pakistani government issued a commemorative stamp, as part of "Pakistan Scientists", to honor Salam's services. 18 Salam's notable achievements include the Pati-Salam model, the magnetic photon, the vector meson, the Grand Unified Theory, work on supersymmetry, and, most importantly, the electroweak theory, for which he was awarded the Prize. Nobel. 8 Salam made an important contribution to quantum field theory and the advancement of mathematics at Imperial College London. With his student, Riazuddin, Salam made important contributions to modern theory on neutrinos, neutron stars, and black holes, as well as work on the modernization of quantum mechanics and quantum field theory. As a professor and promoter of science, Salam is remembered as the founder and scientific father of mathematical and theoretical physics in Pakistan during his tenure as the president's chief scientific adviser. 10 19 Salam contributed greatly to the rise of Pakistani physics within the global physics community. 20 21 Until shortly before his death, Salam continued to contribute to physics and advocate for the development of science in third world countries. 22 Biography Edit Youth and education Edit Abdus Salam was born to Chaudhry Muhammad Hussain and Hajira Hussain, in a Punjabi Muslim family that was part of the Ahmadiyya Movement in Islam. His grandfather, Gul Muhammad, was a religious and medical scholar, 7 while his father was an education officer at the Punjab State Department of Education in a poor agricultural district. Salam was established very early https: //en.m.wikipedia. org / wiki / Abdus_Salam Steven Weinberg - Wikipedia Steven Weinberg was born in 1933 in New York City. 7 His parents were Jewish immigrants 8; 9 his father, Frederick, worked as a stenographer at court, while his mother, Eva (Israel), was a homemaker. 10 11 Taking an interest in science at age 16 through a chemistry game given to him by a cousin, 12 10 he graduated from Bronx High School of Science in 1950. 13 He was in the same graduation class. such as Sheldon Glashow, 11 whose research, independent of Weinberg's, resulted in them (and Abdus Salam) sharing the 1979 Nobel Prize in physics. 14 Weinberg received his BA from Cornell University in 1954. There he resided at Telluride House. He then went to the Niels Bohr Institute in Copenhagen, where he began his graduate studies and research. After a year, Weinberg moved to Princeton University, where he earned his Ph.D. in physics in 1957, completing his dissertation, "The role of strong interactions in decomposition processes," under the supervision of Sam Treiman. 3 15 After completing his doctorate, Weinberg worked as a postdoctoral researcher at Columbia University (1957–59) and the University of California, Berkeley (1959) and was later promoted to professor at Berkeley (1960–66). . . He did research on a variety of particle physics topics, such as the high-energy behavior of quantum field theory, symmetry breaking, 16 pion scattering, infrared photons, and quantum gravity. 17 It was also during this time that he developed the approach to quantum field theory described in the first chapters of his book The Quantum Theory of Fields 18 and began writing his textbook Gravitation and Cosmology, having become interested in general relativity after the discovery of cosmic microwave background radiation. 10 He was also appointed chief scientist at the Smithsonian Astrophysical Observatory. 10 The Quantum Theory of Fields spanned three volumes and over 1,500 pages, and is often considered the leading book in this field. 10 In 1966, Weinberg left Berkeley and accepted a teaching position at Harvard. In 1967 he was visiting professor at MIT. It was in that year at MIT that Weinberg proposed his unification model of electromagnetism and weak nuclear forces (such as those involved in beta decay and kaon decay), 19 with the masses of the force carriers of the weak part . of the interaction that is explained by the spontaneous breaking of the symmetry. One of its fundamental aspects was the prediction of the existence of the Higgs boson. Weinberg's model, now known as the electroweak unification theory, had the same symmetry structure as that proposed by Glashow in 1961: both included the then-unknown weak interaction mechanism between leptons, known as neutral current and mediated by the Z boson. . The 1973 experimental discovery of weak neutral currents 20 (mediated by this Z boson) was a verification of electroweak unification. Weinberg's article in which he presented this theory is one of the most cited https://en.m.wikipedia.org/wiki/Steven_Weinberg Sheldon Lee Glashow - WikipediaSheldon Lee Glashow (USA: / ˈ ɡ l æ ʃ oʊ /, 1 2 United Kingdom: / ˈ ɡ l æ ʃ aʊ /; 3 born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and the Eugene Higgins Professor Emeritus of Physics at Harvard University, and is a member of the Board of Sponsors for the Bulletin of Atomic Scientists. Birth and education Edit Sheldon Lee Glashow was born in New York City, the son of Jewish immigrants from Russia, Bella (née Rubin) and Lewis Gluchovsky, a plumber. 4 He graduated from the Bronx High School of Science in 1950. Glashow was in the same class as Steven Weinberg, whose own research, independent of Glashow, would result in Glashow, Weinberg and Abdus Salam sharing the 1979 Nobel Prize in Physics. (see below). 5 Glashow received a Bachelor of Arts from Cornell University in 1954 and a Ph.D. Graduated in Physics from Harvard University in 1959 with Nobel Prize-winning physicist Julian Schwinger. Subsequently, Glashow became a member of the NSF at NORDITA and joined the University of California, Berkeley, where he was an associate professor from 1962 to 1966. 6 He joined the Harvard physics department as a professor in 1966, and was appointed Eugene Higgins Professor of Physics in 1979; he became emeritus in 2000. Glashow has been a visiting scientist at CERN and a professor at Aix-Marseille University, MIT, Brookhaven Laboratory, Texas A&M, the University of Houston, and Boston University. 5 In 1961, 7 Glashow extended the electroweak unification models due to Schwinger by including a short-range neutral current, the Z 0. The resulting symmetry structure proposed by Glashow, SU (2) × U (1) , forms the basis of the accepted theory of electroweak interactions. For this discovery, Glashow, along with Steven Weinberg and Abdus Salam, received the 1979 Nobel Prize in Physics. In collaboration with James Bjorken, Glashow was the first to predict a fourth quark, the charm quark, in 1964. This was in a by which time 4 leptons had been discovered but only 3 quarks were proposed. The development of his work in 1970, the GIM mechanism showed that the two pairs of quarks: (ds), (u, c), would largely cancel the neutral currents that change the taste, which had been observed experimentally at levels much more lower than theoretically predicted on the basis of 3 quarks only. The charm quark prediction also eliminated a technical disaster for any quantum field theory with unequal numbers of quarks and leptons, an anomaly, where the symmetries of classical field theory do not carry over to quantum theory. In 1973, Glashow and Howard Georgi proposed the first great unified theory. They discovered how to fit the gauge forces in the standard model in a SU (5) group and the quarks and leptons in two simple representations. His theory qualitatively predicted the general pattern of constant-running coupling, with plausible assumptions, he gave approximate mass rats https://en.m.wikipedia.org/wiki/Sheldon_Lee_Glashow Richard Feynman - WikipediaAmerican theoretical physicist Richard Phillips Feynman (; 11 de May 1918 - February 15, 1988) was an American theoretical physicist, known for his work on the integral pathway formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of superfluidity of supercooled liquid helium, as well as his work in particle physics for which he proposed the parton model. For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 along with Julian Schwinger and Shin'ichirō Tomonaga. Feynman developed a widely used pictorial representation scheme for mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams. During his life, Feynman became one of the best known scientists in the world. In a 1999 survey of 130 leading physicists around the world by the British magazine Physics World, he was ranked the 7th greatest physicist of all time. 2 He aided in the development of the atomic bomb during World War II and became known to a wide public in the 1980s as a member of the Rogers Commission, the panel that investigated the Challenger space shuttle disaster. Along with his work in theoretical physics, Feynman is credited with pioneering the field of quantum computing and introducing the concept of nanotechnology. He held the Richard C. Tolman Chair of Theoretical Physics at the California Institute of Technology. Feynman was a great popularizer of physics through books and lectures, including a 1959 top-down nanotechnology talk called There 's Plenty of Room at the Bottom and the publication in three volumes of his undergraduate lectures, The Feynman Lectures on Physics. Feynman also became known through his autobiographical books You are surely kidding, Mr. Feynman! And what does it matter what other people think? , and books written about him like Tuva or Bust! by Ralph Leighton and James Gleick's biography Genius: The Life and Science of Richard Feynman. Early life edit Feynman was born on May 11, 1918 in Queens, New York, 3 the son of Lucille née Phillips, a housewife, and Melville Arthur Feynman, a sales manager 4 originally from Minsk in Belarus 5 (then part of the Russian Empire). Feynman was a late talker and did not speak until after his third birthday. As an adult he spoke with a New York accent 6 7 strong enough to be perceived as an affectation or exaggeration 8 9, so much so that his friends Wolfgang Pauli and Hans Bethe once commented that Feynman spoke like a homeless man. 8 Young Feynman was strongly influenced by his father, who encouraged him to ask questions to challenge orthodox thinking, and who was always ready to teach Feynman something new. From his mother, he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, 10 he kept an experimental laboratory at home and was delighted to repaihttps: //en.wikipedia.org/wiki/Richard_Feynman Peter Higgs - Wikipedia British physicist Peter Ware Higgs CH FRS FRSE FInstP ( born May 29, 1929) is a British theoretical physicist, professor emeritus at the University of Edinburgh, 6 7 and Nobel laureate for his work on the mass of subatomic particles. 8 In the 1960s, Higgs proposed that broken symmetry in electroweak theory could explain the origin of mass for elementary particles in general and for W and Z bosons in particular. This so-called Higgs mechanism, which was proposed by several physicists other than Higgs at around the same time, predicts the existence of a new particle, the Higgs boson, whose detection became one of the great goals of physics. 9 10 On July 4, 2012, CERN announced the discovery of the boson in the Large Hadron Collider. 11 The Higgs mechanism is generally accepted as an important ingredient in the Standard Model of particle physics, without which certain particles would be massless. 12 Higgs has been honored with several awards in recognition of his work, including the 1981 Hughes Medal from the Royal Society; the 1984 Rutherford Medal from the Institute of Physics; the 1997 Dirac Medal and Prize for Outstanding Contributions to Theoretical Physics from the Institute of Physics; the 1997 Prize for High Energy and Particle Physics awarded by the European Physical Society; the 2004 Wolf Prize in Physics; the 2009 Oskar Klein Memorial Lecture Medal from the Royal Swedish Academy of Sciences; the 2010 JJ Sakurai Award from the American Physical Society for Theoretical Particle Physics; and a unique Higgs Medal from the Royal Society of Edinburgh in 2012. 13 The discovery of the Higgs boson led physicist Stephen Hawking to point out that he thought Higgs should receive the Nobel Prize in Physics for his work, 14 15 which he eventually did, he shared with François Englert in 2013. 16 Higgs was named a member of the Order of Companions of Honor at the 2013 New Years Honors 17 18 and in 2015 the Royal Society awarded him the Copley Medal, the oldest scientific award in the world. 19 Early life and education edit Higgs was born in the Elswick district of Newcastle upon Tyne, England, to Thomas Ware Higgs (1898-1962) and his wife Gertrude Maude née Coghill (1895-1969). 13 20 21 22 23 His father worked as a sound engineer for the BBC, and as a result of childhood asthma, along with the family moving away due to his father's work and later to the World War II, Higgs lost some early studies and was taught at home. When his father moved to Bedford, Higgs stayed in Bristol with his mother and largely grew up there. He attended Cotham Grammar School in Bristol from 1941 to 1946, 13 24 where he was inspired by the work of one of the school's pupils, Paul Dirac, founder of the field of quantum mechanics. 22 In 1946, at the age of 17, Higgs moved to the City of London School,

Without comparison. Feynman by far. J. Robert Oppenheimer was a very talented and very competent theorist: he worked on stellar collapse and corrected the error that Dirac purposely put in his paper on the interpretation of the sea from the Dirac equation, showing that holes in the sea had to ser have the same mass as positive energy electrons, which was in effect an early version of the CPT theorem, or rather that he used CPT explicitly to prove the result. I always suspected that Dirac already knew about this result, but that he simply did not have the courage to predict a new particle, the position.

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No comparison. Feynman by a long shot. J. Robert Oppenheimer was a very talented, very competent theorist - he did work on stellar collapse, and he corrected the error that Dirac purposefully put into his paper on the sea interpretation of the Dirac equation, by showing that holes in the sea had to have the same mass as positive energy electrons, which was in effect an early version of the CPT theorem, or rather which used CPT explicitly to prove the result. I have always suspected that Dirac already knew this result, but that he just didn’t have the courage to predict a new particle, the positron. So he tried to interpret holes in the sea of negative energy electrons as protons, but this was not done at all convincingly when you actually read Dirac’s paper on the subject. Dirac was just too smart to have believed that stuff or so I always thought.

But Feynman was groundbreaking. He finished Dirac’s initial work towards path integrals, based on timeslicing in the Hamiltonian formalism, and gave the path integral formulation to physics. The Feynman diagrams and that put his achievements on a different level from Oppenheimer’s.

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