The Catt Anomaly Confusion
In two different papers written as responses to the Catt Question, two Italian physicists have interpreted the Catt Question as an anomaly or paradox. The response of Ivor Catt to this assertion is simply that the Catt Question is “just a question”. This may seem an unimportant point, but in their paper the Italians attempt to suggest that the Catt Question is merely an apparent paradox, and not an anomaly. This method of answering the Catt Question is a type of obfuscation that avoids providing an answer. It is clear that an actual answer to the Catt Question must make a definitive statement regarding the ambiguity contained in the difference between the velocity of electricity and the flow of electric conduction current. In this essay I will endeavor to make this distinction understandable.
In my essay, The Catt Question Background, the basic problem posed by the Catt Question was discussed. There it was shown that the problem has its roots in two different definitions of electricity that are currently being used. One definition regards electricity as energy in the form of electromagnetic fields and the other regards electricity, and its companion magnetism, as a property of material particles called electrons. In the first definition, electricity travels or moves at the speed of light, since light is a form of electricity. The other view holds that electricity is the result of conduction currents of electrons that move through wires in response to an applied electric field inside the wire. Experiments show conclusively that the velocity of electricity is the speed of light and that the velocity of electrons is very much lower than that. Hence the conclusion must be that electricity is a form of energy consisting of electric and magnet fields and not electrons. The objective of The Catt Question is to bring this point of contradiction to a resolution. That is that since it is impossible for electrons to move at the speed of light then electrons can not be responsible for the conveyance of electricity in wires as is currently the dogma of physics teaching. Hence a new paradigm is needed for the understanding of electricity and its companion magnetism.
The Italian Resolution Of The Anomaly
Here is how the Italians formulate the Catt Question in their first paper: “Now, this is what Catt calls an anomaly: where are these charges coming from? Electrons are the moving charges in metal. If the wave travels at c, electrons, which have a mass, cannot. However, classical electromagnetics requires that the electrons appear on the bottom conductor (and disappear from the top conductor) as if they could.” In the second paper they restate it to read like this: “The so-called Catt’s anomaly is as follows: where is this charge coming from? Electrons are the moving charges in metal, but they have mass and cannot travel at the speed of light in vacuum. How can they follow the electric field?” Here is how Catt himself states the “question”: “The key to grasping the question is to concentrate on the electric charge -q on the bottom conductor. The step advances one foot per nanosecond. Extra negative charge appears on the surface of the bottom conductor to terminate the new lines (tubes) of electric flux D (figure 2) which appear between the top (signal) conductor and the bottom conductor. Since 1982 the question has been: Where does this new charge come from?”
Curiously, although they seem to correctly state the question, the Italian writers seem to think that there is an anomaly involved in the fact that while the electric fields advance at the speed of light for the wires, that it is possible for electrons within the wires to provide the necessary current. Thus, they conclude that the anomaly is in the discrepancy between the speed of the wave front and the magnitude of the electron density required to provide the necessary current. They then proceed to demonstrate that there is no anomaly at all with regard to this problem. Hence there is no anomaly and so they conclude that the Catt Anomaly is merely an apparent paradox. To explain why the answer provided by the Italians is defective, it is necessary that they avoid actually answering the question that was asked. They provide the answer that it is possible for the electron conduction current density inside the wires to be equal to the amount of charge that is being added to the lower wire. This is a simple calculation that involves making the required electron density equal to the differential increase in charge added as the wave advances. However, the question asks where the charge comes form and not if it is possible for a sufficient charge to be provided, as is answered by the Italians. So they don’t really answer the question, but simply dispense with the need for providing an answer by saying the question is not a real problem, or question that requires an answer, because it is merely an apparent paradox and not a real anomaly.
Why The Catt Question Asks: Where does the Charge Come From?
This section discusses a key point of the Catt Question. That is why does the question ask, where does the charge come from, specifically for the bottom wire. It doesn’t ask about the top wire at all and the question should be posed for both wires, why doesn’t it? The answer is that the question is posed with the specific objective of refuting the standard textbook problem solution for electron conduction current in wires. (See Peter G. M. Dawe’s description page 1 and page 2 in his letter to Wireless World in reply to Catt.) That particular theory of current electricity states that when a closed circuit is connected to a battery or power source, there is an electric field produced within the wire that acts to pull the charged particles, in this case the electrons, forward from the negative terminal through and around the complete circuit. Now in the case of the Catt Question, the problem is posed for a completely different hypothesis regarding the creation of electric current. That viewpoint is more properly viewed as a different paradigm about the nature of electricity. In the Catt Question paradigm, the problem setup states that the charge appears in the top wire as the TEM wave front “step” advances at the speed of light. It asks where does the charge come from in the bottom wire? There is a trick in the question, because it has already been stipulated in the problem setup that there is no electric field inside the wire that could urge the electrons to emerge from the negative terminal as an electron conduction current. That is because in the TEM wave the electric field is perpendicular to the wires and external to them rather than the electric field being inside the wires as assumed in the standard textbook problem. This produces the contradiction that, if there is no field inside the bottom wire to urge the electrons forward around the circuit, then where does that new charge come from? However, Catt does not focus on this difficulty, he focuses his attention on the problem that the electrons behind the step can not travel at the speed of light and so can not keep up with the step as it moves forward at light speed. He therefore asks the question, where do the electrons, that constitute the negative charge which terminates the electric field, come from, since they can not keep up with the forward moving wave front.
The Catt Anomaly Defined
This section address a definition of what will be called or referred to as the Catt Anomaly. The definition follows from the interpretation given to it by Italian experts who have attempted to answer the Catt Question by answering the Catt Anomaly instead. In other words, the Catt Anomaly is an interpretation of the Catt Question that views the question as referring to an anomaly. The anomaly is this: How does the electron conduction current carry the power of the electromagnetic signal when electrons can not travel at the speed of light? The reader should note that this definition of the anomaly seeks to answer the question, or is it a paradox, as to how the electromagnetic wave moves forward at the speed of light, while the physical electrons inside the wire can not, because they have mass and can not be accelerated to light speed. This is actually what the Italian writers seek to resolve in their proposed answer to the Catt Question, which they change into an “apparent anomaly”. They interpret that the problem is simply a paradox regarding the velocity of electron conduction current flow versus TEM wave velocity.
Before getting into the details of the proposed answers, the reader should take note that although Catt does not state in his question how the question should be answered, it is assumed from the context, that the answer should be consistent with the concepts of classical electromagnetism and physics. That means that he is not looking for a quantum mechanical explanation of the problem, although he does not specifically rule that out as an answer. Despite that quantum mechanical solutions are not specifically ruled out, the Italians and others provide answers to the anomaly in classical physics terms.
The method used to answer the anomaly, or as the Italians call it, an apparent paradox, is to remove the distinction between the velocity of the transverse electromagnetic (TEM) wave that moves forward at the speed of light and the velocity of the conduction current electrons. The claim is that it is possible for the electrons to follow the TEM wave although they have a velocity that is very much slower than the advancing TEM wave. Here is what they claim: “Although each single electron is not able to travel at the speed of light, a great number of slow electrons are able to produce a current as fast as an electromagnetic wave travelling at the speed of light in the conductor.” The purpose of this statement is to remove the so called Catt anomaly by simply asserting that there is no anomaly at all, because it is possible for there to be two simultaneous actions, the motion of a TEM wave at light speed and the movement of much slower conduction current electrons. However, having made the distinction that there are two different physical processes involved, and hence the anomaly is apparently removed, the Italian writers don’t offer a very good physical analysis that justifies the claim that these two processes can occur concurrently. That is that a TEM wave travels at light speed, while the conduction current electrons move at a much slower pace.
From the viewpoint of the Italian writers, all that is required to remove the anomaly is to solve an equation that relates the amount of electric charge that is required in each forward moving increment of time, to the number of electrons needed to produce the necessary negative charge needed to terminate the additional electric field lines that are being created as the wave front advances. They see the problem as simply one of calculating the required number of electrons needed to produce the electron conduction current flow that is needed, while ignoring the velocity question. They calculate the number of slow moving electrons that are needed, although they are moving slowly, in order to equal an equivalent current of charge moving at light velocity. All that is necessary is, to show that there is a sufficient number of electrons available to satisfy the equation of equality. The question as to how this is physically possible is thereby avoided and dismissed as an apparent paradox and so does not constitute an actual anomaly or paradox. To reiterate, the solution conflates, that is confuses, the conception of the velocity of electricity, that is the question of how fast do the electrons that convey the energy in the form of electricity move, with the problem of the magnitude of an electric conduction current required to convey an equal amount of energy at a much slower speed. They find, not surprisingly, that there is a proportionality factor that allows then to accomplish this slight of hand trick using mathematics.
What Is It That Is Moving at Light Speed?
The solution proposed by the Italians to what they call the Catt Anomaly has three parts. The first part was to redefine the Catt Question into a so called anomaly or paradox, second, show that there is no anomaly, and finally, suggest that it is possible for electricity as electromagnetic energy and as conduction current electrons to be essentially the same thing. Here we will discuss the last part of the puzzle, which is the most obscure and arcane part of the Italian’s Catt Anomaly solution. In the second paper we read this: “A possible analogy is the start of a marathon: the referee shoots the starting gun, the sound of the bang propagates in air, and each athlete begins to run when they hear it. The apparent effect is a wave of running athletes that propagates along the street at the speed of sound, even if obviously no one person can run so fast.” It is not easy to make sense of this statement. A marathon is not the same thing as an electric current and people are not electrons. In this analogy, the roles of the starting gun sound and the runners as they correspond to the wave and the electrons is not made specific.
The first Italian paper provides more detail as follows: “However, current is the product of charge density and speed: where there is a high charge density, the speed could also be very slow. Physically, a current follows the field traveling at the speed c, but this current is due to a great number of slowly moving electrons. A possible analogy is the start of a marathon: the referee shoots the starting pistol, the sound of the bang propagates in the air, and each athlete begins to run when they hear it. The apparent effect is a wave of running athletes that propagates along the street at the speed of sound, even if obviously no one person can run so fast!” This is not physics and it is definitely not clear at all.
Here is what was said by an IOP board member in response to criticism by Stephen Crothers: “It’s quite easy to cite an example of group velocity where something appears to move quickly even though the parts move slowly – a Mexican wave at a rugby match.” A Mexican wave is where people rise up out of their seats vertically and the motion looks like a progressive wave. This however, is not a wave since there is nothing progressively moving with the wave it is an illusion created by the intelligence of the people participating in creating the appearance of a physical wave. That is like the starting gun analogy, there is the assumption that the people are moving voluntarily in response to the starting gun sound. This leaves us with the group velocity claim. In the case of group velocity, there is a difference of velocity with frequency. That is different frequencies travel at different velocities. However, in this case we are dealing with a DC step, which settles into a DC or zero frequency steady state. There is no reason or justification for the group velocity analogy here. Hence the argument that a large number of slow electrons is equivalent to a fast moving electromagnetic wave doesn’t seem to have any valid physical reasoning behind it.