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...continued
Maxwell's equations
(without the equations)


1. Advancing with Time ...

LC circuit
Figure-1
The image in Figure-1 shows a typical LC circuit with its capacitor and inductor. Once stimulated, the energy imparted to the circuit is stored, alternatively, in the capacitor and the inductor by the current (i) circulating to and from the capacitor and through the inductor. The energy stored in the capacitor (C) thaks the form of an electric field (E), whereas the energy stored in the inductor (L) takes the form of magnetic field (B). Since both are alternating, they continuously generate each other in succession. The current -- and therefore the electric and the magnetic fields -- all take the form of a sinusoidal waves: sinusoid.

forward
Figure-2
It is of the outmost consequential importance to note how the two fields relate to each other along the timeline.

"A" in Figure-2 represents part of the magnetic field wave. As the magnetic field collapses (passes through the zero mark), it causes the electric field (acually, electric charge or voltage) to peak in "B". As seen in the "B" part of the wave, the induced wave is projected forward in time a quarter of a wavelength.

Similarly, if "A" represents the current (in essence, a moving electric charge) crossing the zero mark, the induced magnetic field in "B" reaches its peak and likewise leads by a quarter of a wavelength in time.

Time and space are a single continuum known as space-time. The implication is that the entire electromagnetic wave -- the combined electric and magnetic waves -- which is projected forward in time with each regeneration, is equally projected forward in space. In other words, a lead-in time implies projection forward in space.

All that remains now is to see how the energy circulating in the LC circuit in Figure-1 is made to propagate forward through space as an electromagnetic wave. The best way to accomplish this is through Hertz's original experimental setup.

setup
Figure-3
Figure-3 is a schematic diagram of Hertz's experimental setup. The line from point S to point S' constitutes the conductor of a basic dipole antenna. The two segments of the antenna (S to b and S' to b') are each equivalent to quarter of the wavelength.

2-segments

The form of energy circulating in the LC circuit in Figure-1 is fed into the dipole antenna by means of the current (I) through points b and b' in Figure-3. A question may well be asked at this point: how can a current flow through the dipole antenna when it appears to be an open circuit?

The answer to this question is the key to understanding how antenna is fed in general.

right segment
Figure-4
Figure-4 shows the right segment of the dipole antenna as the current (I) is fed at point b' in Figure-3.

The current, while moving very rapidly, does not reach the endpoint of the antenna instantly. Rather, it travels at the speed of light. By the time it traverses the length of the antenna segment, it reaches a quarter of a wavelength, at which point the current ceases to flow (as seen by the curve above the antenna segment in Figure-4). The current -- which is, in fact, a moving electric charge -- deposits the charge at the far end of the antenna, where the current stops flowing at point S' in Figure-4. This creates a point of electrical charge at point S' of the dipole antenna segment in Figure-3.

The same process takes place in the left segment of the dipole antenna, and it occurs simultaneously with the process in the right segment. The only difference is that the current flows in the opposite direction. It therefore creates a point of an electrical charge of the opposite sign at point S of the dipole antenna in Figure-3.

An electric field now exists between points S and S' in Figure-3. This field is alternating, due to the alternating current.

ac

The alternating electric field generates a magnetic field perpendicular to it, which is also alternating and therefore generates a new electric field, and so on with the two fields continuously generating each other in succession. Each new generation is propelled forward in space-time as seen in Figure-2 above.

(All that stems from the briglient idea making each antenna segment attaining quarter of the wavelength long.)

The fields and their resultant waves are shown schematically in Figure-5a and 5b, frozen in space and time.

Perpendicular fields
Figure-5a
90 degrees waves
Figure-5b
The image in Figure-6 is a snapshot of the outcome: electromagnetic wave packet traveling in space at the speed of light (since the current that created it flows at this speed).

It consists of a magnetic wave and an electric wave, that continuously regenerate each other. The two wave are perpendicular in space and are 90 degrees (a quarter wavelength) out of phase.

An electromagnetic wave must possess all these properties to qualify as a real traveling electromagnetic wave.

em wave
Figure-6

For the sake of visualizing the ongoing process, in real-time -- in the unfrozen dynamic state -- it may be best to describe the movement of the waves as "walking" in a straight line from the transmitting antenna to the receiving one, rather than simply traveling or propagating through space.

The two waves move forward continuously regenerating each other for every step.

The little friendly fellow would like to demonstrate how it's done dino walking

left foot, right foot ... The magnetic wave is leading; the electric wave is leading ...

"Inching" forward step by step -- a quarter of the wavelength ahead in space with each step -- is how the waves propagate.

(Well, in realty, it happens somewhat faster than that, but the little fellow is doing his best.)

wave walking

How does the outcome of electromagnetic waves from Maxwell's equations compare in this race?


2. Left in the Dust ...

in phase
Figure-7a
in phase
Figure-7b
in phase



Figure-7c
The outcome of an electromagnetic wave from Maxwell's equations is invariably presented as shown in Figures 7a, 7b or 7c. (These given figures were picked up at random from the myriad of such independent presentations.)

The problem with these images is that the magnetic and the electric waves they portray are in-phase -- that is, their wave crest coincides along the timeline. Such electromagnetic "waves" are in fact STATIC in nature; they are not self-regenerating and therefore can not travel in space in the first place, despite being shown in these presentations as "traveling waves" thtough sophisticated animation:
moving em-wave


in phase
Figure-8a
out of phase
Figure-8b
Figures 8a and 8b are enlarged views of a portion of an electromagnetic wave, intended to clarify this most crucial point.

They present both the wrong and the correct way in which an electromagnetic wave is qualified to become a traveling electromagnetic wave in space, as shown earlier in Figure-6.

The waves in Figure-7a,7b, and 7c imply that Maxwell's equations are lacking. Given the preceding description, they also appear incorrect presentation of space-traveling electromagnetic wave.

But that is not all ...

According to Maxwell, a vector leaving the transmitting antenna is the same vector arriving at the distant receiving antenna. Nothing could be further from reality.

Major radio transmission stations are known to have emited a form of power which is equivalent to hundreds of kilowatts (if not megawatts), while the voltage induced on a distant receiving antenna may amount only to millivolts (if not microvolts).

Evidently, Maxwell's theory proposes vectors without magnitude. Had his theory incorporated additional basic principels -- such as Coulomb's law -- it may have endowed these vectors with magnitude as well, thereby portraying more realistic outcome.

perhaps it could have clarified that light is a quantum packet of energy -- a photon in wave form, thereby avoiding the enduring controversy over whether a light is a wave or a particle and resolving wave-particle duality.

Yet there remains a debt to be paid to Maxwell.


3. Aristotle and his Housefly

Maxwell's equations are often described as intimidating to engineering students due to the mathematics knowledge they command for proper interpretation of their meaning. From my recollection of those days, mathematics itself was not the issue. This sort of mathematics was routinely practiced then.

The difficulty lay in visualizing a space traveling wave, even after formally working through their mathematics. It took a considerable amount of imagination and self-persuasion to convince oneself that indeed one could see a wave emerging.

Failing to to "see" waves moving could be taken as a lack of understanding of the meaning of Maxwell's equations, and that could present a problem.

Aristotle allegedly declared at one point that the housefly has eight legs. The academia of his day, engaged in considerable self-convincing to "confirm" that they too could see eight legs on a fly.

If a freshman happened to claim he saw only six legs, he was promptly expelled because, clearly, anyone unable to see eight legs lacked the capacity for academic study.

I am sorry, Mr. Maxwell -- I see only six legs.

Having cleared my debt to Maxwell for "helping" me realize a speeding electromagnetic wave in space, there is still remains a debt in arrears that history owes to Hertz.


4. Hertz and his Antenna

Whenever there is a need to transfer energy that is circulating in an LC circuit into traveling electromagnetic wave, a designer reachs for an antenna tuned to the circuit's frequency. This is far from being trivial, but it is based on a well-established practice.

Hertz did not have this advantage, as there was no precedence for what he was attempting to accomplish. He had to discover how to divert a wave moving within the confined space of an LC circuit into free space outside the circuit.

It is worthwhile at this point to revist what was said earlier regarding the LC circuit causing a shift forward in time. More precisely, it causes movement forward in space-time.

But does the LC-circuit-generated wave which advances in time, also move through space?

Yes, it does. It moves within the space of the capacitor, though confined between the parallel plates in there. This clarifies the dilemma Hertz faced: How do you release the wave from this confinement?

He "opens up" the capacitor and "spreads" it over his antenna.

It was nothing short of a stroke of genius on Hertz's part to realize that an antenna would accomplish this.

Many wrongly assume that the antenna is merely another form of LC circuit. Hertz's antenna is not an LC circuit, nor is it one of its elements. It constitutes a unique element of its own.

It is tuned into resonance with the supplied frequency, not by changing capacitance or inductance, but by adjusting the conductor length to match a quarter of the wavelength of the frequency.

Hertz's antenna can, however, be viewed as a virtual LC circuit for the sake of understanding its operation. There is no physical capacitor within it, only a virtual one.

The two extreme points of electrical charge on the antenna conductors substitute for the plates of this "capacitor". The entire space surrounding the antenna effctively becomes the space of this virtual capacitor extending outward toward distant receiving antennas.

A traveling electromagnetic wave moving through this "capacitor space" can therefore reach receiving antennas located anywhere across the globe and beyond.

A more direct explanation is simply to regard the antenna as a newly invented device capable of continuously generating and regenerating magnetic and electric waves, as seen in figures 4, 5a and 5b.

These waves are continually advance through space-time. Since nothing prevents them from moving forward through space, they do so -- as demonstrated earlier by the little fellow.

Is it not a remarkable invention?

This should never have been belittled, as these kinds of events -- those that eventually change the world (such as the invention of the wheel, the saddle stirrups, or the printing press) -- occur very seldom. The closest exemple that comes to mind in more modern times is the case of Tesla.

A gifted engineering student named Tesla attends a demonstration of a direct-current motor in operation, where the motor's commutator produces a copious amount of sparks. He instantly perceives a multiphase alternating-current rotating magnetic field, in which motors and generators turn at asynchronous speed with no commutators. This insight eventually materialized into the electrical distribution system the world knows today.

The same Tesla, though much older, concieved the idea idea of applying Hertz's antenna to some esoteric and bizarre development projects with unrealistic prospects ... But this story is for another day (I am allready digressing badly.)

Hertz could not possibly have used Maxwell's equations as an instruction manual to build his experimental setup any more then their prediction could have giuded him toward his discovery. Despite the prevailing version of events, it appears that he carried out his work with no reference at all to Maxwell's equations.

In his own words: "... I based my first interpretations of these experiments [electromagnetic propagation] upon the older views" (that is, on the electromagnetic original basic laws and their mutual interactions, not upon Maxwell's theory); and he adds: "To Maxwell's theory in its pure development such a distinction [the cooperation of electrostatic and electromagnetic forces] is foreign."

He goes on in saying: "... propagation of electrostatic force, which, indeed, is meaningless in Maxwell's theory ... understanding of Maxwell's theory [is] more difficult partly for no other reason than that they really posses no meaning ..."

It appears, in all likelihood, that Hertz's actual findings preceded Maxwell's prediction. In other words, it was probably after Hertz's discovery that people -- and indeed Hertz himself -- went back to see whether Maxwell's equations could be made to establish a moving electromagnetic wave in space. Quoting Hertz: "Hence I now wish to show that the phenomena [electromagnetic waves] can be explained in terms of Maxwell's theory ..."

Not having derived his idea from Maxwell, one may still wonder whether Hertz came upon his discovery through serendipity. However, there is another generally unrecognized point that demonstrates Hertz's full awareness of what he was doing in this work.

Throughout his various experimental setups, Hertz consistently terminated his antenna length with conductive spheres, as seen in Figure-3 S and S'.

What are these spheres doing there? At that time, it was known that conductor's sharp edge causes loss of electrical-charge through bleeding into the surrounding space, particularly in the case of relatively highly charged conductors.

Franklin specified a sharp edge for his lightning arrester in order to readily attract electrical charge from the clouds. It was done similar to Hertz , though for a contrasting purpose. Franklin's sharp edge caused a high concentration of electrical charge (high-voltage) and, consequently, a strong attractive force in the surrounding space.

The opposite to a sharp edge is a very blunt and a smote edge. A conductive sphere fits this role best. It clearly suggests that Hertz, aware of this problem, used these spheres to facilitate and optimized the functioning of his antenna.

Modern transmitting antennas are often fitted with similar extensions (known as top hates) in order to compensate for antennas that are physically too short from a true quarter of wavelength. However, these antennas more often then not possess sharp edges on their extensions, defeating the purpose of maximizing radiation efficiency.
top-hat top-hat top-hat
Should future designers of transmitting antennas return to these roots, they may be amazed by the radiation performance achieved by following Hertz's footsteps and terminating an antenna with a sphere ... (OOPS, digressing again.)

History owes Hertz an apology for relegating him to footnotes as "the person who merely confirmed Maxwell's 'prediction' in practice." The irony is that Hertz himself did not think much of his discovery. (Then again, Hertz should perhaps be remembered primarily as a great inventor, not necessarily as a great visionary.)

It still required a genuine visionary to realize that a mere laboratory curiosity could evolve into what is now known as radio. Enter Marconi.


5. Hertzian's Waves versus Marconigrams

Every book on the history of radio in the Western world asserts that Marconi invented of the radio (the Russians, of couese, have their own "inventor of radio"). Marconi was a visionary and an entrepreneur -- and perhaps also a minor inventor -- who recognized the potential of Hertzian's waves.

(Instead of the cumbersome phrase "electromagnetic waves that travel through space and comprise electric and magnetic components". These waves were, quite appropriately, termed Hertzian's waves at the time, a term that arguably ought to endure.)

Marconi established telegraph stations based essentially on hertz's experimental setup, with only minor modifications and improvements. These stations successfully substituted for the long-haul wired telegraph systems of that era. this represented a major step towrad worldwide wireless telecommunications. Furthermore, it enabled also ships to communicate wirelessly. It might even have averted the Titanic tragedy, if not for human failure... But I am digressing once more.

Marconi's enterprise proved successful. Mssages sent worldwide became knowen as "Marconigrams" (though strangely enough, the term did not survive; eventually, a message came to be called a "cable" even when sent wirelessly).

Marconi initiated the era which the use of radio became a commonplace. But is that a sufficient reason to make him the "inventor of radio"?

Marconi is not the inventor of radio. Hertz is!


6. Hertz's Antenna and Columbus's Egg

The quintessential skeptic may maintain that Maxwell's equations constitute solid mathematics and remain a powerful tool for designers of telecommunications systems. Radio, after all, is more than merely an antenna set up by Hertz. Besides, this antenna is just a piece of wire -- something that could have been done by anybody and indeed was done.

Quite so. These arguments are well taken. The mathematics used in Maxwell's equations is undeniably powerful for calculations involving of all sorts of waves, such as water waves and sound waves, not only for electromagnetic waves that are ... Hum ... Hertzian's waves.

(By the way, these waves were never termed "Maxwellian's waves". Should that not be the case if Maxwell's "prediction" truly came first?)

However, Maxwell did not invent these mathematics. Nor was he the one who formulated the equations in the form in which they are presented today. That was done later by others, based on Maxwell's theory.

Maxwell's equations do not propose any fundamentally new laws of nature. Apart from the prediction they imply (assuming, of course, that this so-called "prediction" can evevn be properly presented), they reveal no direct discovery. All they do is restate in mathematical form several electromagnetics laws that are already well known and thoroughly described.

The design of the Wi-Fi system in your cellphone was not directly facilitated by the use of these equations. It appears that one major use of these equations is to provide engineering students with exercises through which to practice solving theoretical and hypothetical mathematical problems.

The antenna is, in essence, a piece of wire. But it is not barely that. It is also the heart and soul of radio. It is the sole component in which the waves are conceived and launched into space. Certainly, later radios incorporated oscillators, amplifiers, modulators, detectors, filters, mixers, vacuum-tubes and transistors. Yet these, and similar more, are mere accessories intended to improve operation and extend functionality far beyond basic telecommunication. They are not essential to the most fundamental operation. Marconi operated radio systems all over the world using only Hertz's teaching and without any of those accessories.

Indeed, anybody can set up an antenna easily -- but only after having been shown how. It takes somebody little short of a genius to discover how to do it in the first place. It recalls the story of Columbus and his egg ... Oh no, I am not going there! But... I have just remembered the role played by the most influential spark.


7. The Vanishing Spark Everlasting Mojo

The transmitter LC-circuit of that era required an opening gap that was continually switched on and off by means of a spark. At the time, this was the only possible way to stimulate the LC-circuit into operation.

In addition to feeding the antenna, points b and b' in Hertz's experimental setup in Figure-3, also served the dual role of switching the circuit on and off by means of the spark being visible during the transmitter operation.

A space-propagating electromagnetic wave leaving the transmitting antenna eventually arrives at a receiving antenna. But how could one verify that such a wave indeed being received when no practical radio receiver yet existed?

Hertz's solution was to bent the receiving antenna into a circle so that a small gap remained between its ends (as shown at the bottom of Figure-3). Since the circle was positioned close to the transmitting antenna, a sufficiently high voltage was induced in it to ignite a spark across the gap.

sparks

OOPS... Just a demonstration of the idea ... I would avoid holding the ring in bare hands while it is in operation!
(Can you say: "heart defibrillation"?)


The spark in the receiving antenna constituted explicit proof of the existence of space-propagating electromagnetic-waves. Important as it was, however, the spark did not merely end there. It eventually received full credit for the entire process.

It appeared as though the visible spark at the transmitting antenna somehow ended up at the receiving antenna, giving the impression that the two separate sparks were actually one and the same.

People concluded that the spark somehow migrated through space from the transmitting antenna to the receiving one. A kind of a blind belief emerged that the spark itself accomplished the entire "transaction" without outside assistance while the role of the electrical circuit generating the spark went unrecognized and was completely ignored.

Since it was not possible to provide a simple explanation based on basic physics, people resorted to Maxwell's treatise for an explanation.

Eventually, sparks vanished from LC-circuits due to technological progress. It is puzzling -- and somewhat disturbing -- that this belief appears to persists even today, despite the fact that modern transmitting equipment contains no sparks whatsoever (better not!).



With apologies to Maxwell for toppling him from the pedestal upon which he stood for all these years,

Joel Tepper, P.Eng.

telejt[delete_me]@shaw.ca