A discussion of one funny and interesting mistake, in my opinion.

A high school student came up to me one day and asked if I could answer a question he was interested in in the theory of electricity.

I readily and quite kindly replied that I would try if I could figure it out myself!

Here’s what he told me:

As you know, electromagnetic waves are, say, sinusoidally varying electric and magnetic field strengths that propagate through space at the speed of light.

The wavelength ranges from thousands of kilometers for industrial AC frequencies and up to angstroms for high-energy gamma rays. I’m taking the infrared range, where the wavelength will be, say, a few microns.

(The student sketched a wave on the blackboard.)

Since the wavelength is one micron, it means that the distance between the maxima of the positive and negative half-waves will be half a micron. The strength can be quite large.

So, the question is, since the positive and negative half-waves are very close in distance to each other, WON’T THEY ATTRACT? After all, according to Coulomb’s law, they should attract, especially at such a small distance from each other. Does this mean that light traveling for millennia, millions and billions years to us from stars and galaxies should SELF-DISTORT, experience some kind of “self-compression”, say, “aging” over time as it travels to us?

I told him that his reasoning was very interesting and entertaining, but the idea was fundamentally wrong.

Why?

Because the electromagnetic field changes not only in space, but also IN TIME. And the spatial arrangement of the crests is precisely due to the fact that the wave propagates in space, constantly changing IN TIME.

This means that no half-waves CAN BE ADJACENT TO EACH OTHER SPATIALLY, because they appear at DIFFERENT TIMES!

They NEVER COEXIST AT THE SAME TIME!

There is ALWAYS ONLY ONE field state defined at a given time.

He asked: And the wavetrain?

My answer: This is also a moving electromagnetic field that continuously changes over time, and not some kind of “frozen” segment of a wave traveling through space at the speed of light.

And the quantum?

Similarly!

And then how can they interfere, that is, overlap each other in phase and out of phase?

In the phenomena of interference and diffraction of waves, amplifying or compensating for each other, different, albeit coherent waves overlap. Half-waves of the SAME WAVE do NOT interact with each other.

The student was obviously upset by my answers, but I praised him for his thoughtfulness and penchant for analytical thinking and recommended that he continue in the same way of thinking, not discouraged by mistakes!

“We are all just mortal people,” I told him, “and we all make mistakes, even the greatest scientists have made mistakes in some of their judgments. This is natural, and you need to keep thinking about solving the problem, even if you are plagued by setbacks! Do not be afraid of failures, but boldly and consistently go on with your thoughts!

From 1916 to 1955, 39 years, Einstein tried to solve the problem of creating a Unified Field Theory, but, unfortunately, he was never able to create it!

Therefore, do not despair and do not give up! An interesting idea comes to mind, in your opinion, feel free to start “playing” with it and consider the results of these mental games “from different angles.” The result may be very interesting and very close to reality, although the initial assumption may have been false!

Think, fantasize, and criticize yourself – this is a very useful and exciting activity!

If you have an idea and you want to know my opinion, I am always ready to listen and give you an honest answer!

31 VII 2026