RoR: Forum

Post 0

Thursday, March 24, 2005 - 10:48pm

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Here's a description of the moment Tesla invented the AC induction motor, from a book I read recently called Empires of Light, by Jill Jonnes.

One chilly February late afternoon in 1882, the athletic Szigety persuaded Tesla to wander forth to a city park as the sun was setting lushly. Tesla, as was his dreamy wont, began reciting poetry, Goethe's Faust, to celebrate the blazing sky before them:

          The glow retreats, done is the day of toil;
          It yonder hastes, new fields of life exploring;
          Ah, that no wing can lift me from the soil,
         Upon its track to follow, follow soaring...

     "As I uttered these inspiring words the idea came like a flash of lightning and in an instant the truth was revealed." Tesla had been swaying and waving his arms gracefully as he declaimed, as if he were about to soar aloft. Now, tall, emaciated from his illness, he stood stock still. Szigety was worried that his friend had been stricken again and tried to steer him to a bench. Instead, Tesla swooped down and snatched a big twig. "I drew with a stick in the sand... The images I saw were wonderfully sharp and clear and had the solidity of metal and stone, so much that I told him, 'See my motor here; watch me reverse it.' I cannot begin to describe my emotions."

Here's another passage from the book:

During high school, Tesla, a prodigy in math and physics, fell even more deeply and irrevocably in thrall to the still nascent science of electricity. He alarmed his professors with his voracious and exhausting appetite for work, especially if it had to do with electricity. "It is impossible for me to convey an adequate idea of the intensity of feeling I experienced in witnessing [my physics teacher's] exhibitions of these mysterious phenomena. Every impression produced a thousand echoes in my mind. I wanted to know more of this wonderful force; I longed for experiment and investigation."

And here's another passage, describing one of Tesla's thoughts at age 3:

But Tesla seemed destined only for electricity. All his life he recalled this formative episode at age three with his beloved cat, Macak. "It was dusk of the evening and I felt impelled to stroke Macak's back. Macack's back was a sheet of light and my hand produced a shower of sparks loud enough to be heard all over the place." What was this? the young boy wondered to his father. " 'Well,' [his father] finally remarked, 'this is nothing but electricity, the same thing you see on the trees in a storm.' My mother seemed alarmed. 'Stop playing with the cat,' she said, 'he might start a fire.' I was thinking abstractedly. Is nature a giant cat? If so, who strokes its back? It can only be God, I concluded... Day after day I asked myself what is electricity and found no answer."

Post 1

Friday, March 25, 2005 - 2:32am

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Daniel,

Thank you. I've added "Empires of Light" to my book list.

Post 2

Friday, March 25, 2005 - 4:45am

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The differences between Edison and Tesla were not a matter of right and wrong or better and worse but only of different. Genius cannot be taught. Each of us finds our own way in the world, of course, and that is all the more true for those who live larger than the rest of us. Edison had the opportunity to live in a civilized time and place. When public education failed him, his mother taught him at home. Tesla benefited from a more formalized, traditional education that included science and mathematics at a European university. Lacking those tools, Edison could only work harder. He quipped about it, claiming that genius is 1% inspiration and 99% perspiration. Of course, Edison was kidding in that without intelligent insight, hard work amounts to nothing. The fact remains that Edison lacked the tools that Tesla possessed.

The DC motor is not greatly different from an AC motor. If anything, it is less elegant. Edison championed direct current because he could understand it. The development of AC transmission required calculus and physics that only were invented in the mid-19th century and which were not completely understood -- if they are now. For instance, E=mc^2 can be derived readily from Maxwell's Equations --- once you know where to find it. Even today engineers still speak of transmitting electricity down a wire when in fact that is as crude as speaking of the Sun traveling about the Earth -- and we never argue about a beautiful "sunset."

Perhaps like direct current, Edison is easier to understand, to relate to. Tesla was quirky, compulsive, obsessive. Edison was large. Tesla was thin. They were different. They shared several passions, not the least of which was showmanship. They did not claim. They proved.

Post 3

Friday, March 25, 2005 - 2:13pm

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I would consider AC motors to be more elegant than DC motors. How could commutator brushes be elegant? They can spark and waste energy. From generators to motors to long-distance transmission, AC is far more elegant than DC.

I haven't read "Empires of Light", but I did read Tesla : Man Out of Time by Margaret Cheney. Quite a good non-technical read. It also mentions other Tesla inventions (bladeless turbines, radio, attempts at wireless power transmission, etc.).

Those who would like to know more about Tesla without the expense may want to download (PDF) his autobiography, The Strange Life of Nikola Tesla. As a teaser; from the very first paragraph of the first chapter:

The progressive development of man is vitally dependent on invention. It is the most important product of his creative brain. Its ultimate purpose is the complete mastery of mind over the material world, the harnessing of the forces of nature to human needs. This is the difficult task of the inventor who is often misunderstood and unrewarded. But he finds ample compensation in the pleasing exercises of his powers and in the knowledge of being one of that exceptionally privileged class without whom the race would have long ago perished in the bitter struggle against pitiless elements. Speaking for myself, I have already had more than my full measure of this exquisite enjoyment; so much, that for many years my life was little short of continuous rapture. I am credited with being one of the hardest workers and perhaps I am, if thought is the equivalent of labour, for I have devoted to it almost all of my waking hours. But if work is interpreted to be a definite performance in a specified time according to a rigid rule, then I may be the worst of idlers.

Sounds like someone named John, doesn't it?

Post 4

Friday, March 25, 2005 - 6:09pm

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Wait a minute - calculus invented in the 19th century? where 'd you get that?
Other than that slight quibble - no question Tesla was much more of genius than any of the others - so farsighted that even today there is exploring of his ideas and possible implications to making more of them reality..

Post 5

Sunday, March 27, 2005 - 12:16am

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How can you derive E=mc^2 from Maxwell's equations? I thought to get E=mc^2 you had to make some dramatic non-classical assumptions that aren't a part of Maxwell's theory of electromagnetism. Bit skeptical of that one.

Post 6

Sunday, March 27, 2005 - 2:39am

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In today's physics curricula, the derivation is done in the opposite direction: magnetism is derived as the relativistic correction to Coulomb's law. Since the whole derivation consists of equations, it also works in the opposite direction. But it would be truer to say that before relativity, magnetism was the paradigm of mystery. Maxwell's equations had no derivation from more fundamental laws until Einstein.

Post 7

Sunday, March 27, 2005 - 8:19am

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Daniel asked:

How can you derive E=mc^2 from Maxwell's equations?

You're right to ask that question because you can't derive E = mc^2 from Maxwell's equations. The four Maxwell equations don't contain mass anywhere in them, so you need something else.

Adam said:

Maxwell's equations had no derivation from more fundamental laws until Einstein.

From what fundamental laws was Einstein able to derive Maxwell's equations? I don't follow this. (You can answer this offline if you don't want to get too technical on this thread.)

Thanks,
Glenn

Post 8

Sunday, March 27, 2005 - 10:04am

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The derivation of magnetism as a relativistic correction to Coulomb's Law can be found in, among others, lecture 28 of The Feynman Lectures on Physics, Feynman, Leighton and Sands (volume 1) Addison-Wesley 1963.

Post 9

Sunday, March 27, 2005 - 10:48am

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Are you saying magnetism is a derivative of gravitative forces? If the universe is itself like a gigantic electromagnetic power grid, an effect of its dynamic nature, wouldn't it be more that the gravitative force stems from that rather than the usually proscribed reverse?

Post 10

Sunday, March 27, 2005 - 11:12am

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No. If you don't understand "Coulomb's Law" and "relativistic correction," you may need to study the foundations of physics before you get to the derivation.

Post 11

Monday, March 28, 2005 - 6:24am

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Robert Malcom asked: "Wait a minute - calculus invented in the 19th century? where 'd you get that?"

I wrote: "The development of AC transmission required calculus and physics that only were invented in the mid-19th century and which were not completely understood."

I did not mean that "The Calculus" was invented in the 19th century. Newton and Leibnitz did this in the late 17th century. Newton's Principia was written in 1686 and published first in 1687 and revised several times and translated into English and so on. I only meant "19th century calculus" in the same sense as "19th century algebra." The first part of Newton's Principia is a geometry book.

(In fact, I happen to have Feynmans's Lost Lecture. He wanted to reproduce Newton's work for his students -- and could not. We have lost a lot of geometry that was known to Newton. Feynman worked out other ways to prove the same things, but he admits that he could not follow Newton's geometry. For myself, I remember the first time I looked at an "advanced geometry" book and found that there were no pictures: it was all equations. That was pretty disappointing.)

Tesla benefited from new ideas in mathematics and physics. That's all.

Post 12

Monday, March 28, 2005 - 6:31am

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MM: "The DC motor is not greatly different from an AC motor. If anything, it is less elegant."

Num ++ wrote : " I would consider AC motors to be more elegant than DC motors."

Yes, that was my point. I apologize for the ambiguous "it." The DC motor is not greatly different from an AC motor. If anything, the DC motor is less elegant. The point is that direct current is easier to understand than alternating current. However, to achieve DC transmission (apart from batteries) requires a contraption that is less elegant than an AC motor. Both involve the moving of magnets relative to coils of copper wire, of course.

Post 13

Monday, March 28, 2005 - 6:39am

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Adam Reed wrote: "The derivation of magnetism as a relativistic correction to Coulomb's Law can be found in, among others, lecture 28 of The Feynman Lectures on Physics, Feynman, Leighton and Sands (volume 1) Addison-Wesley 1963."

Thanks for pulling my chestnuts from the fire. At the end of second term freshman physics, the day before the final, our professor told us to relax and just watch. He did the work. So, I know that E=mc^2 can be derived from Maxwell's Equations. (Unless he was tricking us, you know, dividing by zero in there somewhere or something that even the A students missed.) Then, when looking through Feynman's Lectures in a bookstore, I saw it again and I realized that this must be something that it standard for "real" students of physics, but was just not in the engineering physics we got at midwest community college.

Anyway, thanks, again. I saw this mountain of painful work in front of me, not the least of which was figuring out how to post an essay with a nabla in it.

Post 14

Monday, March 28, 2005 - 6:46am

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Adam said:

The derivation of magnetism as a relativistic correction to Coulomb's Law can be found in, among others, lecture 28 of The Feynman Lectures on Physics, Feynman, Leighton and Sands (volume 1) Addison-Wesley 1963.

Actually, it can't be found there. Any discussion about how magnetism is related to electricity via relativity can be found in Volume 2, but even there they don't discuss how Maxwell's equations can be derived from "more fundamental laws".

If you don't want to discuss this here, that's fine, or if you want to discuss this offline, that's fine too, but please don't blow me off by giving an incorrect reference to a Freshman textbook (excellent though it is).

Thanks,
Glenn

Post 15

Monday, March 28, 2005 - 11:33am

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Glenn,

It was in my freshman physics course at MIT, which used the PANIC (Physics - A New Introductory Course) textbook. If you don't find Feynman's presentation satisfactory, go through the one in PANIC - it was written for freshmen. I don't have a copy of PANIC now, though, so I can't point you to a specific place in the text.

Post 16

Monday, March 28, 2005 - 12:30pm

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Glenn,

A correction to the above: I found the PANIC textbook and checked, and it turns out that the printed textbook does not have the derivation, although it is mentioned at the end of chapter 21. Prof. French must have included the derivation in his lecture on that chapter as an extra - I do remember it clearly from the lecture.

Also, you are correct that the derivation is not completely stated by Feynman in v. I lecture 28. The rest is in volume II, 13-6.

It was not my intention to "blow anyone off," and I apologize for giving that impression. Actually, what was it that you wanted to discuss?

Post 17

Monday, March 28, 2005 - 1:15pm

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Thanks M. Marotta for the clarification.

Daniel O'Connor wrote:
How can you derive E=mc^2 from Maxwell's equations? I thought to get E=mc^2 you had to make some dramatic non-classical assumptions that aren't a part of Maxwell's theory of electromagnetism. Bit skeptical of that one.

Newtonian mechanics and Maxwellian electrodynamics are actually two separate and essentially incompatible physical theories*. The "dramatic non-classical assumption" (DNCA) is from an important implication of Maxwell's equations...

A verbal overview regarding the derivation of E = mc² from Maxwell's Equations:

1. Solve Maxwell's Equations for a complete vacuum in the absence of external magnetic and electrical fields. The result derived describes a set of self-propagating sinusoidal plane waves.

This is about as far as Maxwell got (and here he already got something profound in itself). Hertz later empirically showed that these waves described the entire EM spectrum from radio waves to ultraviolet light.

2. The sinusoidal plane waves travel at a speed of (μ₀ε₀)^-1/2, where the terms are for the permittivity and permeability of free space, respectively. Since the waves describe light, this term is the speed of light, c (from celeritas, Latin for speed).

Now for the DNCA. Solving Maxwell's Equations for any inertial frame of reference (zero or constant velocity), yields the same constant term c, implying that the speed of light is an absolute universal constant for all inertial observers. This is what the brilliant Einstein intuited. It is also the jump-off point for the special theory of relativity.**

3. Since the speed of light has to remain constant for said observers, one cannot simply add and subtract velocities of moving objects as their speeds approach that of light. Time and space themselves have to make way to keep c constant. The manner of these adjustments are described by the Lorentz transformations (these equations always have the (1-v²/c²)^-1/2 term in them, called the Lorentz factor, γ).

Velocities are not simply superimposed. Time and space are now an active part of physical phenomena, not inert backgrounds. These are radical breaks from Newtonian mechanics. Newton's laws of motion have to be relativistically corrected for greater generality.

4. Energy is classically defined as force x distance. Momentum is classically defined as mass x velocity. Since force can be defined as the rate of change of momentum with time (dp/dt), we can get:

dE = F dx = (dp/dt)dx = dp v

in short...
dE = dp v

Now for the last steps...

Introducing the relativistic correction for the classical definition for momentum (p=mv) gives p=mv/γ.
Expand the Lorentz term and get dp.
Apply this to the above equation and we now have...

dE = v m(1-v²/c²)^-3/2 dv

Dividing the equation by dv and integrating, we obtain...

E=mc²(1-v²/c²)^-1/2

Since we are dealing with the energy inherent in matter, not in motion, we get the rest mass (v=0), and voil�!

E=mc²

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Notes:

* They can be used together, of course, but they are "metaphysically" different, as QM and relativity are now.

** for non-inertial frames of reference (accelerating/decelerating systems), special relativity gives way to general relativity. Time and spce are no longer treated as separate entities here. Alas, this requires mathematics beyond my ken.

The 19th century mathematics M. Marotta refers to is Oliver Heaviside's use of vector calculus and operators to shorten calculations in EE and ECE. There's some strange parallels here. Maxwell and Einstein were trained foremost in the sciences and were quite taciturn in nature. Tesla was a dapper eccentric and Heaviside was an English eccentric. Both were trained on a more engineering bent, and got odder and odder with age. Tesla almost certainly had OCD like Howard Hughes (compulsive washing rituals, etc.) while Heaviside probably went schizophrenic like John Nash ("A Beautiful Mind"), obsessing with patterns.

I hope I haven't made any grievous errors here and that this settles matters with the derivation. I have posted here what I remember to be the most succinct. More technical material can be found in the internet of course, along with alternative derivations.

Post 18

Monday, March 28, 2005 - 2:38pm

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Hello, Num++.
That was a nice explanation of some aspects of relativity and electricity and magnetism, but it wasn't a derivation of E = mc^2 from Maxwell's equations. Your derivation actually took place in step 4, where you introduced the Lorentz factor to get the relativistic momentum. You derived E = mc^2 from the relativistic version of Newton's second law and the definition of work.

Thanks,
Glenn

Post 19

Monday, March 28, 2005 - 2:50pm

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Adam said:

It was not my intention to "blow anyone off," and I apologize for giving that impression. Actually, what was it that you wanted to discuss?

Sorry if I overreacted, Adam. What I wanted to discuss was your statement that

Maxwell's equations had no derivation from more fundamental laws until Einstein.

I didn't know what you meant by this. But, based on the reference you gave (Feynman, et al.'s derivation), I take you to mean that Einstein showed that the electric and magnetic fields that enter into Maxwell's equations are different manifestations of the same field depending on the observer's reference frame. If that's what you mean by "more fundamental laws" then I can agree with that.

Thanks,
Glenn