How J. K. Maxwell Figured Out The Light is an Electromagnetic Wave（原声文稿）

Probably all of you know that light is an electromagnetic wave.

It is one of the first things you learn at physics classes because it is such an important discovery.

But what less people know is how philosophers and physicists of the past slowly came up with this discovery.

And it is such a remarkable journey, which culminated with the connection of three major pieces of physics into a single one.

But of course this wasn't accomplishment of just a single person, this came slowly by discovering the secrets of each pillar individually throughout the history.

And only then, when there was enough knowledge behind all of the pillars, the connections could be made.

This culminated with the James Clark Maxwell, who brought all of them together with a series of four equations.

So, this video is going to be a historical overview of all the steps that led to this discovery. So don't expect too much details. That will come in another videos. So without further ado, let's start.

For a long time in the past, the electricity, magnetism and light were totally separated phenomena.

Apart from electricity and magnetism, light is everywhere.

So it was not about discovering the phenomena but explaining why we see things in the first place.

I don't wanna go very deep into the past but yeah, there were times when people thought that we see things because eyes send some sort of ray that in some sense illuminate the object.

But this would clearly give you the ability to see during the night.

And therefore it was thought that there is some interaction between the light from our eyes and the light from the source, like the sun.

And without this interaction you are not able to see. But that was too far in the past.

At around the year 1000, Islamic scientist, even al -Haytham, I hope I am saying it right, but he was the first to correctly explain the vision, that it's a phenomena that happens in our brain.

And everything we see is a light from a certain source that bounces off of objects to our eyes.

And therefore, light is a physical phenomena that is independent of our eyes.

And now you can start asking scientific questions about it. Why there are different colors? How does it reflect?

Why it changes its direction when entering a different transparent media?

Why it propagates through a certain materials while it just bounces off of others?

What is the speed of propagation or is it instant? And what it is actually made of? The law of reflection was known for a long time.

It tells us that the angle of reflected light is the same as the angle of incident light.

And it's mostly attributed to Euclid who formalized the law.

The law of refraction, though, is more tricky.

It was rediscovered many times throughout the history, but the first correct mathematical description of refraction came from Wilbord Snelius, a Dutch astronomer and mathematician in the early 17th century.

And this is where the real game starts, because Snel didn't use any model of light light that he derived this equation from.

It was just basically a looking at the data and fit an equation to it.

But a question why light obeys this law was still a mystery.

But now at least it wasn't pure philosophy.

Now you can actually test whether your model of light obeys the Snell's law. And if not, then it must be wrong.

For example, Isaac Newton believed that light is made of tiny particles, while Christian Huygens believed that light is made of waves.

But Newton was a big figure, and therefore he had a much bigger support from other physicists from the past.

But the correct model should explain Snell's law, right?

The Huygens theory had a natural explanation for it, provided that the wave slows down in a denser medium.

But how on earth you want to explain this using particles Newton?

Well, Newton found a way and it's actually pretty impressive.

His idea was that each particle of the light is attracted to mediums and if it's in a single medium then the forces are isotropic, since it is the same medium around the particle.

But if you put it on the boundary of a denser media, then the particle will be attracted more strongly in the direction that is perpendicular to the surface of the media.

And this would result in a higher velocity in this direction, which would cause the light to bend. How nice!

But there were other problems that this theory couldn't explain, like diffraction, interference or polarization.

Not to mention that there were many other problems with the model as well.

And I would like to make a separate video about this BAFE versus Particle model of light in a future, so stay tuned.

More and more evidence started to pointing towards the BAFE theory.

But what I personally think was the nail in the coffin was finding that the light might actually travel slower in a denser media.

But now is the good question to ask. What is the speed of light?

The first who tried to measure it was Galileo Galilei in 1638, who had two people with lanterns on a hilltop in a Tuscany.

And the idea was that one person uncovers the lantern, and the moment the other person see it he also uncovers the lantern and by the time delay you can determine the speed of light.

But the speed of light would have to be very slow if you wanted to detect it this way.

Much better measurement was done by Danish astronomer Oli Romer in 1676 observing Jupiter's moon Io.

He noticed that the eclipse time of the moon vary depending on the direction of the Earth.

Knowing the rough distances of the celestial bodies, he could calculate the speed of light to be around 220 ,000 km per second.

And much later, more and more precise measurements have been done.

James Bradley in 1728 measured 301 km per second using stellar aberration.

Fiesau in 1849 using two -thread wheel measured around 313 km per second and a year later Leon Focult repeated this experiment with a higher accuracy getting 298 ,000 km per second which is very close to the today's defined value of 299 ,792 ,458 meters per second.

So now we are pretty sure that light is a wave and it has a finite speed of propagation. But what is actually waving?

To answer this question we need to take a look at the other front of the scientific endeavor.

So this was the light part, but simultaneously people studied the electricity and magnetism.

And people discovered these two phenomena quite far in the past, but only recently they were able to tame their powers.

If you consider for example electricity, for a long time it was just a nice curiosity so that you can create a spark or use a static electricity to impress others.

The first genius way to explain electricity came from Benjamin Franklin.

He imagined that every object has a certain amount of electric fluid around it. Some bodies have more and some have less.

And a fundamental rule of nature is to always balance this amount.

So if there are two bodies with different amount of electricity near each other, the electric fluid starts to flow from one body to another to equalize.

So the electricity we observe is this flow of this fluid from one body to another.

This is quite similar to the model as we know it today.

The lack of fluid can be related to the negative charge and the excess of fluid can be related to the positive charge.

And this could partly explain a big mystery of the time, the functioning of the famous Leidenjar.

In 1785 Coulomb published his work on the relationship between the charge force and distance that it is directly proportional to the amounts of electricity of each body and inversely proportional to the square distance between them.

You see the closer my hand is the more strongly that tracks this piece of plastic but yeah I'm not fully insulated so this effect this actually diminishing a bit with time. So yeah, this is Coulomb's law.

There haven't been any formal units of charge at the time yet.

And in modern Coulomb's law there is this proportionality constant.

Here I'm going to use only modern notation and SI units to avoid any confusion, because historically many different units for electric charge were used and also many different notations.

And this is how the law looks like in modern units, where this is called the permittivity and has these units.

At the time when Coulomb formulated his law, the continuous current hasn't been discovered yet.

This has been done by Alexandro Volta in 1794.

He found out that if you put a zinc and a copper together and put some cardboard soaked in a salt water between them, they produce continuous electricity.

From this discovery, things went forward pretty quickly.

But before I go any further, we also need to look briefly at the history of magnetism, before we bring all the pieces together.

The magnetic material lodestone was discovered by Greeks in around 600 BC.

And apart from electricity, the magnetic properties of the lodestone had pretty good applications.

For example you could pull out a metal arrowhead from the body, but more importantly it led to the discovery of the compass in 11th century which was a device of crucial importance at the time.

But people didn't know anything about how magnets work and they didn't even know how these compasses work.

They thought that maybe North Star is magnetic, or there is some magnetic island on the North.

And that is why these compasses point in this direction all the time.

But in a year 1600, William Gilbert concluded from his experiments that Earth itself is a giant magnet. And this is the reason why compasses work.

But this still doesn't explain anything about what magnetism actually is.

But there was a suspicion that magnetism is somehow linked to the electricity.

Some people thought that it's maybe some sort of static electricity or something.

But at the same time, these magnets behaved differently from electricity.

A big breakthrough came in 1820 from Hans Christian Orstedt, who discovered that a The compass needle deflects from the magnetic north pole of the earth by nearby currents.

There is a nice demonstration of this phenomenon Wikipedia.

This was the first direct evidence of a link between two seemingly separated forces of nature.

Now the task was to formulate this link between these two forces mathematically.

This was done by Ampere between 1820 and 1825, which you today know as Ampere's law.

This law states that if you take a certain curve ds and you evaluate the magnitude of the magnetic field that is parallel to the curve and sum all the contributions, meaning you do a line integral of the b field on a curve ds, then it's equal to the total current that is passing through the surface and closed by the curve ds, multiplied by a certain constant, which we call magnetic permeability.

In 1830, Carl Friedrich Gauss introduced his Gauss law, which is basically the Coulomb's law, but written in a much more fundamental way.

It simply says that electric flux through a certain closed surface S is equal to the total charge inside the volume enclosed by this surface.

You can derive the Gauss law from the Coulomb's law and vice versa, but Gauss law is much easier to use in certain scenarios where you have multiple charges and provide much better physical interpretations of certain absurd phenomena and it ultimately became one of the Maxwell's equations.

I'm sorry that I can't go into too much detail in this video but it's getting much longer than I anticipated and I still have to talk about the famous Michael Faraday.

So we already know that the electricity and magnetism are linked through Amperes law so we know that we can create magnetism from electricity, but Faraday discovered the way how to create electricity from magnetism.

He figured out qualitatively that just having a magnetic flux doesn't produce electricity in a wire, but if the magnetic flux is changing with time, then it produces electricity, which is Faraday's law of induction.

But what is also a very Very important contribution from Faraday in discovering this electromagnetic theory is that he was the first who brought the notion of fields, as we know them today.

He called them lines of force, where positive charges had these lines pointing outwards and negative charges served as a sink, where the lines point inwards.

And by using these lines of force, all the laws of electromagnetism could be explained intuitively.

For example father explained induction in a way that when the conductor cuts the magnetic field lines then the current is induced.

And yes maybe I was talking about electric and magnetic fields with a connection to the amperes or Gauss law but it wasn't used in the same context.

The discussion was more about forces and potentials rather than lines of force that permeate the space.

But Faraday didn't provide any mathematical descriptions for his findings. He only provided qualitative understandings.

And now is the time for the biggest hero of this story.

The James Clark Maxwell. So what did he do?

But before I start, just for the record, I'm not using the equations in the original form as they were derived, but in the modern form as we use them today.

avoid any confusion. But the content of those equations is completely the same.

So at this time we have the Gauss law, which is one piece of the puzzle.

The Max law also introduced the Gauss law for magnetism, which says that if you do this integral for any closed surface, you will always get zero, since we don't have magnetic monopoles.

Then there is the Ampers law. But there was a problem with the Amper's law.

It was inconsistent meaning you could set up an experiment in which the Amper's law would give you two different results.

I will keep the details for another video, but to make this equation consistent he had to introduce another term which is called the displacement current density.

So to make the Amper's law consistent not only current densities produce magnetic field around, but also time varying electric fields produce magnetic fields.

This is sometimes considered to be his biggest contribution to the electromagnetic theory, as now you not only have a relation between field and something physical, like current, but there is also relation between the fields themselves.

Then Maxwell managed to derive mathematical expression for paradise law, which tells us that time -varying magnetic field produces electric field.

Yeah and this electric field then produces the electromotive force and that's why we measure current in a wire.

And what is interesting that this equation is made of just fields and nothing else, as there is nothing like magnetic current.

So without this paradise idea of fields that permeate the space, it would be quite difficult to discover.

But let's get rid of all the physical stuff, like current and charges. And what you are left with are vacuum equations.

These equations are just pure relations between the electric and magnetic fields.

You can also see these equations written in a form of differential operators. Again the same physics but different form.

So changing electric field creates magnetic field and changing magnetic field produces electric field.

And this seems like a nice symbiosis right?

If you create a ripple in electric field then it will create another ripple in magnetic field and this another ripple in magnetic field will again generate an electric field.

And this will go on forever until there is something physical that absorbs the energy.

But how fast these ripples propagate in space?

The good thing is that you can calculate it using these equations. And the number you get is this.

So, all you have to know are these two constants that you can determine from static experiments.

And these constants were known at the Maxwell's time, so he pluged them in and got this number.

And when he compared it to the measurements of the speed of light, he must have been very very satisfied.

Can you imagine how satisfied he must have felt that these ripples in electromagnetic fields travel the same speed as light?

Of course, this doesn't have to necessarily mean that electromagnetic wave is a light. But it's quite a strong evidence for that, right?

Now I'm going to cite Einstein. The precise formulation of the time -space law was the work of Maxwell. Maxwell.

Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves and at the speed of light.

To few men in the world has such experience been vote -saved.

It took physicists some decades to grasp the full significance of the Maxwell's discovery.

So bold was the leap that his genius forced upon the conceptions of his fellow workers.

But to me what is also very interesting that Maxwell discovered the first relativistic theory, a theory that obeys the laws of special relativity, a theory that doesn't even existed yet.

So if somebody asked me who was the first true theoretical physicist I would probably say Maxwell because if we say that the work of theoretical physicists is to unravel the physical reality through mathematics then Maxwell did exactly that.

This video captures this discovery in very shallow manner because the video would have to be very long and I'm very sorry for that but there are many parts of this story that deserve their own video and that's my future plan so if you are interested definitely stay tuned to this channel and also big thanks to my patreon supporters this is very crucial help for me thank you again and see you in another video