Ever wondered, how Einstein conjured up the Theory of Special Relativity?
Why did Einstein fixated on the constancy of velocity of light so much so that he was ready to discard the revered Newton’s theories of motion; theories which were accepted for centuries by scores of mathematicians and physicists?
Can Einstein’stheory of special relativity be all credited to his famous ‘thought experiments’ or was there something else that Einstein took immense inspiration form for his theory?
Well, the answer to all of the above questions lies in the path breaking work done by mathematician and physicist - James Clerk Maxwell - which paved the way for Einstein’s Special Theory of Relativity
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James Clerk Maxwell is not as well known as Newton or Einstein, but his contributions to science are arguably among the greatest. He is the one who laid the foundations of Einstein’s Theory of Special Relativity almost 40 years before Einstein.
Jame Clerk Maxwell
The best way to understand Einstein’s Special Theory of Relativity is through the understanding of seminal work done by Maxwell in the theory of Electromagnetism.
The roots of the Special Theory of Relativity lies in the understanding of Electromagnetism and the realization that the speed of light is universal constant.
Lets take a look…
In the beginning of the 19th century, many experimental and theoretical works had been accomplished in the understanding of electro-magnetics.
In the 1780s, Coulomb's law of electrostatics had been established.
the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects
In 1825, Ampère published his Ampère's law.
allows us to calculate magnetic fields from the relation between the electric currents that generate this magnetic fields.
Michael Faraday discovered the electromagnetic induction through his experiments and conceptually, he emphasized the lines of forces in this electromagnetic induction.
whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced which is called induced current.
In 1834, Lenz solved the problem of the direction of the induction.
the direction of the electric current which is induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.
German physicist Franz Ernst Neumann (a rather unconventional physicist who interrupted his studies when he was 17 to volunteer in the war against Napoleon before he was wounded and returned to studies) wrote down the equation to calculate the induced force by change of magnetic flux.
Oliver Heaviside a British mathematician and physicist brought the study of complex numbers (read more about the history of complex numbers’ in this post) to circuital analysis in the field of electro magnetism in physics and reduced Maxwell’s 12 of the original 20 equations down to 4 equations.
Maxwell’s equations served as the foundation of Einsteins Theory of Special Relativity and yet oddly enough Oliver who reduce Maxwell’s 12 equations to 4 had this to say of Einstein’s theory:
Heaviside was an opponent of Albert Einstein's theory of relativity and "was the only first - rate physicist at the time to impugn Einstein…"
At the simplest level of description I describe below what these four equations tells us:
Gauss’s Law
Gauss’s Law
This law explains how electrical charges create electrical fields.
If you have an electrical charge, there will be an electrical field emanating from it, strength of this electrical field, can be calculated using above equation.
Note that the strength of this electric field is proportional to a constant called Epsilon - known as the vacuum permittivity. This is a property of the vacuum of space. It can be thought of as the resistance of free space against the formation of an electrical field.
Gauss’s Law for Magnetism
Gauss’s Law for Magnetism
It basically says that if you had a magnet, you will never find a configuration where the magnetic lines of force always point outward, or always point inwards.
There is always as much field pointed out as there is pointed in. It will be in loops. In other words, a magnet will always have two poles. There are no magnetic monopoles.
Faraday’s Law of Induction
Faraday’s Law of Induction
This law basically says that if you move a magnet, you will create an electric field.
In other words if you change the magnetic field with time, it creates an electric field. What does it mean to create an electrical field? It just means that if you put a charge there, it will be affected. It will be accelerated. You can take large magnets and rotate them, and if you put a wire near it, as you move the magnet, then electricity will be created in the wire. This is because there are electric charges in the metal wire and as electric field lines are created, these charge will move, creating a current of electricity.
Ampere’s Circuital Law
Ampere’s Circuital Law
The law basically says that if you have a moving charge through a wire, or an electrical current, you generate a magnetic field.
In other words, two wires can be attracted to each other if they have current flowing through it. The equation will tell you how strong the magnetic field would be.
This requires another constant of nature called mu. This is known as the permeability of free space. This can be thought of as the resistance of free space against the formation of magnetic field.
Note: epsilon and mu - both of these constants have to be measured, since they are inherent properties of nature. They are not derived from anything.
We can see that moving electrical charges creates magnetic fields. And that moving electrical fields creates magnetic fields. This idea of magnetic fields being created from electric fields was Maxwell’s addition to Ampere’s law. It was not based on experiment. He figured that there should be some symmetry with Farday’s law. Because if moving magnetic fields could create electric fields, then moving electric fields should also create magnetic fields.
Somewhat like Einstein, Maxwell built on the concepts originated by other scientists, but synthesized them and put them in mathematical terms, that allowed us to see a new kind of relationship, between electricity & magnetism, and light (light?? don’t be confused - light is going to debut shortly in this discussion).
Maxwell showed that Electricity & Magnetism were really manifestations of the same phenomenon. This idea is one of the most important and practical set of idea in all of classical physics.
Not only do these equations describe about every electrical and magnetic phenomenon, but believe it or not, hidden within these equations is a fundamental truth about the nature of light, and why it is the ultimate speed of the universe.
Objects have something called a charge. This is a property of matter like mass is a property of matter.
Know that if you have a static object with a charge, it will affect only other charges.
And if you have a static magnet, it will affect only other magnets. It will not affect charges.
But if you have a moving charge, it will affect a magnet.
And if you have a moving magnet, it will affect a charge.
You might say at this point, well, you’re just talking about electricity and magnets. What does this have to do with light? So here comes the most interesting part.
Let’s take what we have learnt from Maxwell’s equation, and put it to practical use via a thought experiment.
What if I take an electric charge and put it on a rod of iron, and I move it up and down continuously.
What will this cause?
Well, if you did that then, according to Ampere’s law, if an electric field moves or changes with time, it would create a magnetic field perpendicular to that.
And because of the changing movement, of up and down that you're making with the charge, the magnetic field would also be changing with time. And according to Faraday’s law the moving magnetic field lines would create another new set of electric field lines.
Now, since the same thing is happening to these new electric field lines, that is, they are changing over time, they would in turn create new magnetic field lines. And the new moving magnetic field lines would create yet more electric field lines.
So this becomes like an unstoppable positive feedback loop of electric fields creating magnetic fields creating electrical fields, creating magnetic fields, and so on.
Each is produced by the movement of the other.
You have just created a self propagating wave.
But what kind of wave is this? This wave must be occurring in nature because electricity and magnetism exist.
Well, what would this wave look like?
How fast is this wave moving?
Solving the above four equations and you come up with the below velocity of wave:
So what the equation is saying is,
the velocity of this wave is inversely proportional to the permittivity and permeability of free space and this is CONSTANT.
Does this even make any sense?
It does.
Recollect form above what is epsilon and mu - the resistance of free space against the creation of electric and magnetic field.
These are properties of free space that tell us how fast magnetic fields and electric fields can interact with each other. If there is a finite speed with which the electric and magnetic fields can form, influence and interact with each other, then it sets a limit on how fast these fields can propagate through space.
Now we take the measured values of these two constants, and calculated the velocity of moving wave to be about 300,000 km per second. What kind of wave moves this fast?
Back in 1728, English astronomer James Bradley, had calculated the speed of light as about 297,000 km/sec.
And a huge Eureka moment hits Maxwell that this electromagnetic wave must be light and could be a manifestation of electricity and magnetism.
Although, he could not prove it at the time but about 20 years later, Heinrich Hertz, proved experimentally that Maxwell was absolutely right.
And the rest of the story is that about 40 years later another great scientist by the name of Albert Einstein did his own thought experiments, inspired by Maxwell’s equations. And his thought experiment was based on one simple assumption - that he is not allowed to modify the speed of light per Newtonian physics.
After all, if the speed of light is an inherent property of space, why would this speed be any different based on the speed of the observer?
It should not matter whether you measured the speed of light moving on a fast train, or whether you measured it standing still. It should be the same regardless of your reference frame.
And it was from this simple assertion, that Einstein came up with the special theory of relativity in 1905, which changed our ideas about the nature of time.
Later in his life, when people suggested to Einstein that he stood on the shoulders of Newton, he corrected them and said, no I stand on the shoulders of fMaxwell. No wonder, Einstein kept three portraits in his Princeton study - of Newton, Faraday and James Maxwell.
