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Thu Jan 19, 2012, 02:39 PM

Science's "most beautiful theories"

By Sharon Begley

NEW YORK, Jan. 15, 2012 (Reuters) From Darwinian evolution to the idea that personality is largely shaped by chance, the favorite theories of the world's most eminent thinkers are as eclectic as science itself.

Every January, John Brockman, the impresario and literary agent who presides over the online salon Edge.org, asks his circle of scientists, digerati and humanities scholars to tackle one question.

In previous years, they have included "how is the Internet changing the way you think?" and "what is the most important invention in the last 2,000 years?"

This year, he posed the open-ended question "what is your favorite deep, elegant or beautiful explanation?"

more

http://www.newsdaily.com/stories/tre80e04y-us-feature-sciences-most-beautiful-theories/

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Arrow 18 replies Author Time Post
Reply Science's "most beautiful theories" (Original post)
n2doc Jan 2012 OP
DetlefK Jan 2012 #1
caraher Jan 2012 #2
Lionel Mandrake Jan 2012 #9
xocet Jan 2012 #18
laconicsax Jan 2012 #3
QED Jan 2012 #4
laconicsax Jan 2012 #5
caraher Jan 2012 #6
QED Jan 2012 #7
Lionel Mandrake Jan 2012 #8
laconicsax Jan 2012 #10
Lionel Mandrake Jan 2012 #11
caraher Jan 2012 #12
laconicsax Jan 2012 #13
Lionel Mandrake Jan 2012 #14
laconicsax Jan 2012 #15
xchrom Jan 2012 #16
jimlup Jan 2012 #17

Response to n2doc (Original post)

Thu Jan 19, 2012, 04:15 PM

1. Noether's theorem, hands down.

"If there's a symmetry, then there's a conserved physical parameter."

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Response to DetlefK (Reply #1)

Thu Jan 19, 2012, 09:46 PM

2. A real favorite of mine as well

Though interestingly enough, I understand that's not as well-known among mathematicians as some of her other work!

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Response to caraher (Reply #2)

Sun Jan 22, 2012, 07:04 PM

9. Her isomorphism theorems are better known.

Every book on abstract algebra includes the first, second, and third isomorphism theorems.

Oddly enough, few of these books mention that these fundamental theorems are due to Emmy Noether (18821935).

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Response to DetlefK (Reply #1)

Tue Jan 31, 2012, 03:20 PM

18. "If there's a continuous symmetry...."

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Response to n2doc (Original post)

Fri Jan 20, 2012, 01:13 AM

3. I like Quantum Electrodynamics.

 

You can explain everything except gravitation and radiation simply by drawing little arrows on a piece of paper.

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Response to laconicsax (Reply #3)

Fri Jan 20, 2012, 09:07 PM

4. I'm still trying to understand it.

I've read Feynman's book - do you have another suggestion?

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Response to QED (Reply #4)

Fri Jan 20, 2012, 09:19 PM

5. I don't understand it myself.

 

I sadly can't recommend any other books on the subject.

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Response to laconicsax (Reply #5)

Fri Jan 20, 2012, 11:34 PM

6. On what level are you looking for understanding?

It helps to note that in his QED book, there are really two things Feynman is teaching. One is his path integral formulation of quantum field theory, which is what most of the business with the arrows on paper is about. The other is the specific application of path integrals to electromagnetism - all the optical and other phenomena his formalism explains.

I don't think anyone can do much better than Feynman at explaining the combination, for the lay audience. Feynman does have a technical book on path integrals with some QED material; I've not read it.

Now if you want to dig deep into the mathematical physics at the level of graduate texts, you may start by doing quantum field theory with a different formalism in place of path integrals. I've had just one quantum field theory course, where we started with "toy" systems and worked up to the beginnings of QED as the first "real world" example. Our text was Diagrammatica (probably because when I was at Michigan Veltman was still there, waiting for his Nobel). At the time (mid-'90s), a common standard graduate text on quantum field theory was Bjorken and Drell. Peskin and Schroeder was a new text at the time; I own a copy but can't say I've really read it. I'm intrigued by the title of Anthony Zee's Quantum Field Theory in a Nutshell, which seems to be very popular among Amazon reviewers.

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Response to caraher (Reply #6)

Sun Jan 22, 2012, 02:21 PM

7. Anthony Zee

He wrote the intro to the edition of Feynman's QED that I have and did a good job of promoting it. When I read his intro, I thought I'd try to tackle that next but was waylaid by life. Thanks for the reminder - I have a credit at Amazon I need to use.

Crap - it's $48. Ouch!

http://www.amazon.com/Quantum-Field-Theory-Nutshell-Princeton/dp/0691140340/ref=sr_1_1?ie=UTF8&qid=1327260397&sr=8-1

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Response to laconicsax (Reply #3)

Sun Jan 22, 2012, 06:44 PM

8. QED does not explain everything except gravitation and radiation.

Let's talk about quantum field theory (QFT) in high-energy physics. Four QFTs must be distinguished:

1. Quantum Electrodynamics (QED) is only a theory of electromagnetic phenomena. It has nothing to say about the strong, weak, or gravitational forces.

2. Quantum chromodynamics (QCD) does for the strong force what QED does for electricity and magnetism.

3. The electroweak theory of Weinberg, Salam & Glashow generalizes QED to include the weak force.

4. The standard model combines electroweak theory with QCD. The standard model (not QED) explains everything except gravitation.

These four theories all contain infinities which must be swept under the rug by the formal device of renormalization. Because of this necessity, I wouldn't describe any of these theories as beautiful. They are, however, indispensable theoretical tools for high-energy physicists.

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Response to Lionel Mandrake (Reply #8)

Sun Jan 22, 2012, 09:53 PM

10. I'm just going off of what Feynman wrote.

 

If it's inaccurate, I'm happy to correct myself.

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Response to laconicsax (Reply #10)

Sun Jan 22, 2012, 10:04 PM

11. What, exactly, did Feynman write?

A quotation would help us sort this out.

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Response to Lionel Mandrake (Reply #11)

Sun Jan 22, 2012, 10:26 PM

12. I don't have my copy of QED handy right now...

but by way of introducing his subject, Feynman says something like this: With the exceptions of gravity and radioactive decay, "everyday" interactions between light and matter, and between atoms, are dominated by processes ultimately described by QED.

He does talk about the rest of the Standard Model, briefly, and mainly to contrast QED with other quantum field theories both for the degree of experimentally-verified precision it has achieved (as of when he gave the lectures the book comes from in the early-mid 1980s) and the huge variety of familiar phenomena one can understand through the theory.

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Response to Lionel Mandrake (Reply #11)

Mon Jan 23, 2012, 01:41 AM

13. He writes:

 

I would like to impress you with the vast range of phenomena that the theory of quantum electrodynamics describes: It's easier to say it backwards: the theory describes all the phenomena of the physical world except the gravitational effect, the thing that holds you in your seats (actually, I think that's a combination of gravity and politeness, I think), and radioactive phenomena, which involve nuclei shifting in their energy levels. So if we leave out gravity and radioactivity (more properly, nuclear physics), what have we got left? Gasoline burning in automobiles, foam and bubbles, the hardness of salt or copper, the stiffness of steel. In fact, biologists are trying to interpret as much as they can about life in terms of chemistry, and as I already explained, the theory behind chemistry is quantum electrodynamics.

It seems I misspoke when I said radiation. He said radioactivity, not radiation. Is this an inaccurate description? If so, does that inaccuracy relate to it being published in 1985?

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Response to laconicsax (Reply #13)

Mon Jan 23, 2012, 02:08 AM

14. Feynman's statement was as confusing in 1985 as it is now.

First it was everything but gravity and "radioactive phenomena".

Then it was everything but gravity and nuclear physics. By nuclear physics, in this context, Feynman meant the strong and weak forces.

In other words, QED describes only one of the four known forces of nature. But that's okay, because electromagnetic phenomena are exceedingly rich.

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Response to Lionel Mandrake (Reply #14)

Mon Jan 23, 2012, 02:37 AM

15. I think "exceedingly rich" is a slight understatement. n/t

 

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Response to n2doc (Original post)

Sat Jan 28, 2012, 03:15 PM

16. 2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION? {responses}

http://edge.org/responses/what-is-your-favorite-deep-elegant-or-beautiful-explanation


Father of "Eternal Chaotic Inflation"; Professor of Physics, Stanford University

Why Is Our World Comprehensible?

"The most incomprehensible thing about the world is that it is comprehensible." This is one of the most famous quotes from Albert Einstein. "The fact that it is comprehensible is a miracle." Similarly, Eugene Wigner said that the unreasonable efficiency of mathematics is "a wonderful gift which we neither understand nor deserve." Thus we have a problem that may seem too metaphysical to be addressed in a meaningful way: Why do we live in a comprehensible universe with certain rules, which can be efficiently used for predicting our future?

One could always respond that God created the universe and made it simple enough so that we can comprehend it. This would match the words about a miracle and an undeserved gift. But shall we give up so easily? Let us consider several other questions of a similar type. Why is our universe so large? Why parallel lines do not intersect? Why different parts of the universe look so similar? For a long time such questions looked too metaphysical to be considered seriously. Now we know that inflationary cosmology provides a possible answer to all of these questions. Let us see whether it might help us again.

To understand the issue, consider some examples of an incomprehensible universe where mathematics would be inefficient. Here is the first one: Suppose the universe is in a state with the Planck density r ~ 1094 g/cm3. Quantum fluctuations of space-time in this regime are so large that all rulers are rapidly bending and shrinking in an unpredictable way. This happens faster than one could measure distance. All clocks are destroyed faster than one could measure time. All records about the previous events become erased, so one cannot remember anything and predict the future. The universe is incomprehensible for anybody living there, and the laws of mathematics cannot be efficiently used.

If the huge density example looks a bit extreme, rest assured that it is not. There are three basic types of universes: closed, open and flat. A typical closed universe created in the hot Big Bang would collapse in about 10-43 seconds, in a state with the Planck density. A typical open universe would grow so fast that formation of galaxies would be impossible, and our body would be instantly torn apart. Nobody would be able to live and comprehend the universe in either of these two cases. We can enjoy life in a flat or nearly flat universe, but this requires fine-tuning of initial conditions at the moment of the Big Bang with an incredible accuracy of about 10-60.


*** more responses at link

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Response to n2doc (Original post)

Mon Jan 30, 2012, 11:39 PM

17. I have to say GR

A seriously elegant theory of the force of gravitation though as many have pointed out - just because it is beautiful doesn't mean we accept that it is true. It has however survived every test that I am aware of including the recent Gravity Probe B results.

What is really cool is that modern M-theory (the direct descendent of what was once called "string-theory") includes GR as a "post-diction." Meaning that had Einstein not formulated GR in 1916 and M-theory had developed independently - then GR would have been predicted by it.

I would say M-theory but it is not accepted by the general physics community as established and may not ever be testable so I'll hold that one back and say GR.

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