An extremely common mistake of our thinking.

Why?

Because we perceive the world with our senses, and they give us information about a PHENOMENON, that is, a certain consequence of INVISIBLE AND IMPERCEPTIBLE CAUSES! This is already the concern of our brain, to catch the patterns, the secret springs behind the phenomena and, having understood where the cause is and where the effect is, to formulate our guesses in the form of explanations, the correct answer to the eternal question: WHY?

I will immediately move on from abstract philosophical arguments to a specific topic.

We put two identical spoons in a cup of freshly brewed tea, one silver and one steel. Which pen will heat up faster?

Well, of course, silver.

Why?

Because silver is a better conductor of electric current than steel. The wellknown Wiedemann-Franz law, which relates the electrical and thermal conductivity of metals, also states this. For any metal at any temperature, there is a strict proportionality of these two parameters. As the temperature increases, this ratio also increases almost linearly. But again, the most important thing is that thermal conductivity is always directly related to electrical conductivity.

(There are, however, deviations- beryllium and manganese do not obey this law at all)

By the way, what is the reason for the increase in the ratio of thermal conductivity to electrical conductivity with increasing temperature? Most likely, a faster decrease in electrical conductivity with an increase in temperature, with possibly increasing thermal conductivity.

So, the official and generally accepted version is the presence of free electrons. In silver, gold, and copper, the best conductors, the concentration of free electrons is higher than in steel, lead, or the so-called Neusilber (an alloy of copper 60%, nickel 20%, and zinc 20%).

It clearly suggests quite a reasonable idea that it is the concentration of free electrons that determines both heat and electrical conductivity.

One cannot disagree with the electrical conductivity.

And, here, thermal conductivity causes some unpleasant reflections.

The thermal conductivity of metals is generally related ONLY to the concentration of free electrons, NOT THEIR MOBILITY. Mobility is the ratio of the increment of the velocity of a charged particle to the strength of the applied electric field, that is, say, meters per second, divided by volts divided by centimeters. (The units are chosen purely conditionally).

What is the point of this statement? The meaning is simple – it is not the velocity of the electron cloud drift that determines the heat conduction, but only the concentration of free electrons.

Now let’s ask ourselves the following question: what is the speed of propagation of the “wave” of heat? Again, everyone has noticed from daily practice that usually a spoon in hot tea heats up in a few minutes.

So the trouble broke out:

First, the VELOCITY OF FREE ELECTRONS in a metal DOES NOT DEPEND ON TEMPERATURE, ranging from almost Absolute zero -273 degrees Celsius to ten thousand degrees!

Second. The velocity of chaotic motion of free electrons in a metal is from 600 to 2000 km/sec.

This means that if free electrons, hitting each other, would transfer heat (which clearly contradicts the first statement!), then they would have to transfer heat at a TREMENDOUS SPEED in micro-nanoseconds along any conductor with a length of meters and kilometers!

And a spoon 14-16 cm long transmits it billions and trillions of times SLOWER!

The current drift of electrons itself is also extremely slow, as I have written about more than once – thousandths, hundredths, and at most tenths of a millimeter per second! 15 cm of the average length of a spoon is 150 millimeters. Let’s say that the handle of the spoon is heated to the temperature of tea in 3-5 minutes. This means that the speed of the heat wave reaches 0.83 -0.5 mm/sec. Such electron cloud drift velocities can melt a conductor by themselves!

Too fast!

This results in a double contradiction. On the one hand, if the “HEATED” electrons transmitted heat by collisions, it would spread with great speed along the metal. But this contradicts the real facts and the statement about the INDEPENDENCE of their speed from temperature.

If, again, a cloud of “heated” electrons slowly drifts through the metal, then the usual heat transfer occurs too quickly! But, again, the drift of a cloud of “heated” electrons, and the diffusion of heat due to collisions, both of these assumptions contradict the experimental fact that the VELOCITY of FREE ELECTRONS is CONSTANT! ITS INDEPENDENCE FROM TEMPERATURE!

And HOW to explain the propagation of the metal cooling wave? Do “cold” electrons hit their neighbors more weakly, or does the cloud of “cold” electrons crawl more slowly through the metal?

An unsolvable mystery! The paradox. And there are no paradoxes in nature, it’s just a product of our stupid brains, when one dominant in it collides with another dogma!

There’s only one thing left to admit: We’ve confused CAUSE and EFFECT again!

THE REASON lies in the special configuration of the electronic orbits of metal atoms, where their outer orbits OVERLAP and THIS ensures the FREE MOVEMENT OF ELECTRONS.

The so-called free electrons, DUE to the OVERLAP of the external atomic orbits, arise and receive the “FREEDOM” of movement in any direction of a piece of metal.

But not always the same “degree of freedom” of translational motion, because in single crystals there is an asymmetry of physical and chemical properties called ANISOTROPY, that is, an inequality of directions in space.

So, THE REASON FOR THE THERMAL CONDUCTIVITY OF METALS IS NOT RELATED TO free electrons, but they themselves, like thermal conductivity, ARE CAUSED BY THE OVERLAP OF THEIR EXTERNAL ATOMIC ORBITS SPECIFIC TO METALS,

Then how to explain it, this great thermal conductivity?

The thermal DEFORMATION of the electronic orbits from the hot end is gradually transmitted along the metal due to the influence of the modified configuration of the already “heat-deformed orbits” on others that are still UNDEFORMED. And this process is relatively slow and the explanation does not contradict the mentioned fact of the CONSTANCY of the velocity of free electrons.

Good conductors (silver, gold, copper) this OVERLAP is GREATER and therefore more electrons become “free”.

They confused the cause, the specifics of the outer orbits of metal atoms, with the consequence, the presence of a huge number of free electrons due to this specificity.

It is not “heated” electrons that are moving, but a change in configuration, deformation of electronic orbits!

Faciant meliora potentes.

If I’m wrong, let my seniors correct me. .

11 XI 2025