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Archive for March, 2013

Dirac, Heaviside, Physics, and Electrical Engineering

Wednesday, March 27th, 2013

Heaviside and Dirac giants of Electrical Engineering and Quantum Mechanics

Over at Copasetic Flow, I wondered briefly last week whether electrical engineering notation and quantum mechanics notation had shared a common background and if so, which was the progenitor[1].  A few days ago I came across a helpful article by J. D. Jackson, If you’re on the physics side of things, yes, that Jackson, (careful, language in the  subtitles).

Dr. Jackson points out[5] that what most of us call the Dirac delta function was introduced in its modern form 35 years before Dirac’s definition[2] by Oliver Heaviside, first in The Electrician, and then in his Electromagnetic Theory volume I[4].  So, as early as 1895, (before quantum mechanics was invented), the two fields were already intertwined.

If you’ve never read Heaviside’s book, you should, (go ahead, it’s free on Google Books).  He introduces a sizable amount of the notation that we use in EE.  First, there’s the Heaviside step function.  Then, there’s the entire field of operational calculus.

If you vaguely remember a linear systems course in EE  where derivatives suddenly went from being denoted as d/dt to being denoted as multiplication by p, that’s operational calculus and Heaviside invented it.  I remember being awestruck that I could now do differential calculus simply by multiplying by p, (taking the derivative), or dividing by p, (taking the integral).  Consequntly, this is one of the notations that seems to be similar between EE and quantum mechanics.  Reading Heaviside, it seems to have its origin in physics.  p in physics was and is the symbol for momentum which is the time derivative, (d/dt) of position.  Heaviside doesn’t elucidate the point, but on page 232 he starts using the p notation, (“for convenience”), and apparently never goes back.  Later on he’ll realize that Fourier analysis is also kind of fun and start using omega, or frequency, as a derivative and one over omega as an integral.  Both of these really nice notations have never been adopted by the physics texts.  Interestingly though, quantum mechanics will pick up the whole Fourier habit and denote p, (momentum), as the Fourier conjugate of position space.

I only really have one gripe with Heaviside, great hero of engineering though he may be.  He killed the quaternions Man!  I mean dead, for decades.  The text I’ve referenced here is where he did it.  He replaced them with the easier to work with, (he thought), vectors.  They started turning back up in the 1960′s, 70′s, and 80′s when people began to realize that they were very nice for doing efficient rotations, (think computer graphics and games).  It also became apparent that they could be used to provide geometric explanations of quantum mechanics, (more on that later).  On the fringe side of things, they’re of course the reason the Russians got to the moon before us and also how they got ahead in teleportation technology, but I digress.

So, in summary, quantum mechanics and EE do seem to be intertwined, the p notation in operational calculus, and the ‘Dirac’ delta point towards a common heritage, but there’s no smoking gun yet as far as locating a common link between the two in a single person.


1.  Copasetic Flow about the history of EE and QM

2.  Dirac’s Introduction of what will be called the Dirac Delta Function

3.  Heaviside’s introduction of the same function, (the derivative of what will be called the Heaviside step function), 35 years earlier

4.  Heaviside’s Electromagnetic Theory

5.  Jackson on Dirac and Heaviside

Fringe Science and the Science of Meanness

Thursday, March 21st, 2013


It should come as no surprise to readers of this column that I’m a big fan of fringe physics history and literature.  When done well,, it can serve to inform and inspire.  Take for example, the Philadelphia Experiment by William Moore.  Mr. Moore never claims that the story he tells about the purported experiments that allegedly made a naval destroyer disappear during World War II are true.  What he does do is construct a chain of credible research and then let the reader come to their own conclusions.  In doing this, he exposes the reader to narratives about electromagnetism, high voltage engineering, special and general relativity, and Einstein’s attempts to create a unified field theory.  As a kid, this book more than anything else inspired my interest in physics and engineering.  Then, there’s the whole Tesla mythos.  Much of the legend surrounding Tesla is patently scientifically unprovable.  Take for example the Tunguska event[1].  Supposedly Tesla used a large antenna near Shoreham, NY to transmit energy over the north pole and blew a large hole in the Siberian countryside.  While this story almost certainly isn’t true, it serves to inspire interest in the man who actually did invent our power distribution system, induction motors, and radio controlled vehicles.  As an aside, if you like stories along the line of the Philadelphia Experiment, and t the Tunguska event, you should check out Jeff Smith’s RASL[2].

In addition to my fringe physics reading, I also read quite a few science blogs, and I’ve noticed a disturbing trend lately towards what I’ll call fringe-bashing.  The trend may have been inspired by the fervor of the climate change activists, or maybe by the anit-creationists, both of whom have valid reasons for censuring psuedo-scientific theories.  I don’t know it’s origin, but I define fringe-bashing is the practice of singling out an article for being un-scientific in it’s viewpoint or implications and then calling the intelligence of the author into question, taunting, and generally writing in a denigrating manner rather than simply and objectively stating the facts of the scientific matter in a polite and helpful manner.  

To me fringe-bashing comes across as nothing more than high-handed meanness, and then of course, there’s always the matter of stones and glass houses.  Recently, while reading the weekly summary of interesting scientific articles at Cocktail Party Physics[3], a blog published by Scientific American, I came across a link to a post[4] on the proper use of the term ‘dimension’.  Since I’m currently working on exercises involving Lorentz contractions and time dilation,(basically four-dimensional space-time), I happily clicked on through.  What I arrived at was a blistering diatribe written by PhD computer scientist, Mark Chu-Carroll, about a ‘crackpots’ improper use of the word dimension.  Apparently, the ‘crackpot’ had the audacity to write the following, (among other things)

Energy can travel at the speed of light, and as Special Relativity tells us, from the perspective of light speed it takes no time to travel any distance. In this way, energy is not bound by time and space the way matter is. Therefore, it is in a way five-dimensional, or beyond time.

So, this is a rather philosophical use of the term five-dimensional.  I’ll give you that.  The author of the blog, however, went on a five paragraph rant starting with

Bzzt, no.
Energy does not travel. Light travels, and light can transmit energy, but light isn’t energy. Or, from another perspective, light is energy: but so is everything else. Matter and energy are the same thing.
From the perspective of light speed time most certainly does pass, and it does take plenty of time to travel a distance.

and after illustrating the theory of time dilation for awhile ends with,

It’s not that there’s some magic thing about light that makes it move while time stops for it. Light is massless, so it can move at the speed of light. Time dilation doesn’t apply because it has no mass.

Which is all very nice, except for one thing.  Here’s what Brian Greene author of “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” and famed PBS popular scientist has to say about how light experiences time.

A watch worn by a particle of light would not tick at all  Light realizes the dream of Ponce de Leon and the cosmetics industry; it doesn’t age.

Hunh…  so… anyway. Maybe we do need to correct ‘bad’ science when we find it.  Maybe someone does need to protect the internet at large from the dread of crackpottery, but in this case I’m reminded of a quote from one of my favorite scientists, Dr. J. B. Tatum[5],

Phillips opened his article by writing about “deep ignorance and antiscientific attitudes” concerning collecting. I am one of those who-in spite of 20 years of active scientific research (although not in ornithology)-hold to those very views that Phillips criticizes, and I do not feel that he does great credit to his own arguments or to ornithology as a whole by the use of such intemperate language.

In science as in most aspects of life,intemperate language is simply neither necessary or classy.


1.  The Tunguska Event

2.  RASL

3.  Cocktail Party Phyiscs

4.  New Dimensions of Crackpottery

5.  On Killing Birds

The Hodoscope

Wednesday, March 13th, 2013

After writing a post about the hodograph of Sir W. R. Hamilton and how it relates along with a few other rather obscure mathematical theorems to angular momentum and planetary orbits, my wife, a PhD physicist, remarked, “Yes, but what about the hodoscope?”.  A little bit of digging revealed that unbeknownst to me she had actually built a hodoscope.

A hodoscope is a subatomic particle detector that displays the path a particle travels along through a region of space.  It does this by utilizing an array of single particle detectors that each on it’s own can only detect the presence of a particle in its active region.  By tracking the binary events produced by each detector, (logical high for the presence of a particle and logical low for its absence), the hodoscope can reconstruct the track of the particle display it on an array of pixels on your computer screen for example, or on an array of light bulbs, as in the original hodograph discussed below.

The first hodoscope, was designed and built by Dr. Thomas H. Johnson and Dr. E. C. Stevenson of the Bartol Research Foundation of the Franklin Instititue.  In time for the 1933 World’s Fair in Chicago. The Review of Scientific Instruments described it as:

… a hodoscope, designed by Dr. Johnson of the Bartol Institute, will show the paths of individual cosmic rays by means of flashing neon lamps. The astonishing thing about these rays is that they have come to us through our atmosphere, which is equivalent to over two feet of lead, whereas similar radium rays will penetrate only about two inches of lead.

A diagram of the array of detector tubes used in the hodoscope is shown below. All diagrams are taken from the Franklin Institute report on the device.

M1 and M2 are detectors that are used to determine when a single particle has penetrated the entire device as a cosmic ray would, but a lower energy background particle from the laboratory would not.  If M1 and M2 both fire at nearly the same time, then the tubes in the array are allowed to fire and light their constituent bulbs in the devices display.

Why should all of this be interesting to electrical engineers?  Check out the circuit that detects coincident events between M1 and M2 and uses those events to enable the array of tubes to display the cosmic ray’s track.

It’s an early example of a vacuum tube logic circuit!  Notice that they could incorporate a number of gates, (called grids in vacuum tube parlance), denoted by the squiggly lines in each tube.  The operation of the circuit is described in one final excerpt from the Franklin Institute’s report:

In closing, I leave you with a picture of the hodoscope from Electrical Engineering magazine circa 1933 and it’s eerily similar modern counterpart, (in form, but not in function), the Fringe light box.


1.  Franklin Institute Report

2.  IEEE Electrical Engineering Article

3.  Review of Scientific Instruments on the 1933 World’s Fair

4.  hodagraph post

5.  Built a hodoscope