Tue. Oct 20th, 2020

In the following text, I’m going to tell you a story about the end of classical physics and early development of Quantum Theory of Modern Physics. But before starting that, I would like to acknowledge the major source of my content (so that nobody will accuse me for plagiarism). Majorly, the story is taken from a book “Quantum” written by Manjit Kumar. Then comes wikipedia, and then all those science books that I have read.

After the arrival of human species on Earth, human endeavored to secure its survival and for that it dominated over all species including our own cousin species. But after they insured their survival, they started asking question about their origin, and how nature works, which leads to invention of religion and God. Gods were playing their part very well in life of humans, but many illogical dogmas of religion made Gods more fiction than reality. We can call use term ‘God of the Gaps’. That is to say, when the ancients experienced gaps in their understanding of the world around them, they filled those gaps with God.

As human proceeded with logic in its quest of secret of nature, science started developing. ‘The Scientific Revolution’ begins somewhere in 16thcentury but it’s major event (which is a real revolution, in my opinion) was publication of ‘Principia Mathematica’ by Sir Issac Newton. In it he explained his laws of motion and gravitation, not in words but rather in form of Mathematical equations. The beauty of these equations is that it tells not only ‘why’s and ‘how’s but also ‘how much’. After that, Mathematical equations became most important dogma of Physical Science.

After Newton, many great scientists and experimentalists came and made their contribution to physical science, which is now called Classical Physics. It is fundamentally based on Newton’s law, because motion is the most fundamental aspect of any phenomenon.

As 19th century came to end, the content of Classical Physics became so huge that many started believing that soon, all laws of nature will be discovered. Lord Kelvin once made a statement, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.”

Obviously, he was wrong, but why was he? What made this journey continues, so long, that even today after more than 100 years, there is a huge ocean of knowledge left to be learned.

With development of science, role of God reduced. If I ask any physicist does he/she believe in God, it would be a miracle for me if he/she says YES.

Blackbody Radiation Problem

Near the end of 19th century, Blackbody Radiation Problem was one of the most confusing and most studied problem among Physicists. If you have physics background, then you might know what term of blackbody is. But in case, if you are reading this term for first time, I will try to tell you what a blackbody is and what was the problem with it. Problem of the blackbody and solving it was probably most important part of the early start of quantum phsics.  

First of all, what is a blackbody? The most obvious answer you might have in your head is that it is an object with black color. If you thought so, you are not completely wrong. An ideal blackbody (by saying ‘Ideal’, I mean it does not exists) is an object which can absorb light of all wavelengths (if you don’t understand wavelengths, you can consider it as different colors of light), the seven colors of rainbow, and the UV and Infra-Red light, which we cannot see. (Wavelength is a property of wave, and light has a wavelength, so obviously I am considering wave nature of light)

Blackbody, by nature absorbs every colors of light, that is why it should appear absolutely black, but most black colored object which we see in our daily lives are not absolute black. Also, all blackbodies are not black. WHY? I will explain it in the following text.

Now, a body with certain temperature emits electromagnetic radiation, in simple words, LIGHT. As already mentioned, human eyes cannot see all lights. That is why every object does not appear luminous. According to Stephan-Boltzmann law, the Emissive Power of a body is directly proportional to 4th power of absolute temperature and not on material of body. It means emissive power will increase 16 times on doubling absolute temperature.

Now, one of the important result of Kirchhoff’s law of radiation is that the emissivity of a body is equals to its absorptive power, i.e., a good absorber of light will also be a good emitter of it. So, because a blackbody represents an ideal case of absorber, it is also an ideal emitter of radiation. So a heated blackbody, which is emitting visible light mostly, will not appear black. A good example of such hot blackbody is Sun.

Because blackbody is an ideal emitter, it emits all wavelengths of radiation or light but they all have different intensities (amount of energy in a given wavelength range). Some wavelengths have high intensity, and some have lower intensity.

Kirchhoff developed the idea of this ideal absorber and emitter, somewhere near 1860, to help simplify his analysis of relation between temperature and light. Intensity of certain wavelength emitted by blackbody depends on its temperature, i.e., every wavelength at certain temperature has some intensity. So if you try to write down the intensity of all wavelengths at every temperature, it will be a mission impossible because that will be a infinitely large data.

Gustav Robert Kirchhoff

But physicists were still interested in that data. So in such condition, math came to rescue with a tool called Distribution Equation or Formula, which stores all this data in a single equation.

Kirchhoff set a task for himself and his colleagues, to find this Distribution law for blackbody at given temperature and reproduce it for all temperatures, a problem which came to known as ‘Blackbody Radiation Problem‘. But due to technical obstacles for constructing a real blackbody and precise instrument to measure radiation, there was no sign of progress for many years.

Attempts for solution of Blackbody Problem

In 1880s, when German Companies tried to develop more efficient light bulbs and lamps than their American and British rivals, measuring the blackbody spectrum and finding Kirchhoff’s fable equation became a priority.

In 1887, the German government founded the Physikalisch-Technische Reichsanstalt (PTR), the Imperial Institute of Physics and Technology located on the outskirts of Berlin in Charlottenburg, on the land donated by George Siemen. The PTR was conceived as institute fit for an empire determined to challenge Britain and America.  The construction of entire complex lasted more than a decade, as PTR become the best equipped and most expensive research facility in the world.

Its mission was to give Germany the edge in the appliance of science by developing the standard and testing new products. The need to make a better light bulb was the driving force behind the PTR blackbody research program in 1890s.

In February 1893, Wilhelm Wien, who was working as an assistant in the PTR’s optics laboratory under the leadership of Otto Lummer, discovered a simple mathematical relationship that describes the effect of a change in temperature on the distribution of radiation.

He founded that wavelength with greatest intensity becomes shorter with rise in temperature, a law which became to known as Wien’s Displacement Law. Mathematically it says that product of wavelength with maximum intensity and absolute temperature remains constant. So, if somehow, the wavelength with maximum intensity at particular temperature is measured, then same can be easily calculated for all temperature.

Wilhelm Wien

Wien’s day job was the practical work that was prerequisite for an experimental investigation of blackbody radiation. Lummer’s and his first task was to construct a better photometer, an instrument capable of comparing intensities of light. In autumn of 1895, they devised a new and improved blackbody capable of being heated to a uniform temperature.

While they developed their new blackbody during the day, Wien continued to spend his evenings in search for Kirchhoff’s equation for distribution of blackbody radiation.

In 1896, Wien found a formula that Friedrich Paschen, at University of Hanover, quickly confirmed agreed with the data he collected on the allocation of energy among short wavelengths of Blackbody Radiation. This distribution law published in June that year.

Lummer take this law through a rigorous test. To do so required measurement over greater range of temperature than even before. Lummer along with Ferdinand Kurlbaum and Ernst Pringsheim, through modification and refinement, made a blackbody which is capable of reaching temperature as high as 1773 K.

They found that Wien’s Displacement law was correct, but situation regarding the distribution law was unclear, due to experimental errors. Nothing could be said about it without precise experiment. They reported this result in February 1899.

Paschen announced that his measurement, though conducted at lower temperature compared to Lummer, agreed with Wien’s distribution law. At the beginning of November 1899, after spending 9 months extending the range of their experiment and eliminating all possible sources of technical error, Lummer along with his co-workers found discrepancies of systematic nature between theory and experiment. Although in perfect agreement for shorter wavelengths, they discovered Wien’s Distribution law consistently overestimated the intensity of long wavelength.

However, within weeks Paschen contradicted Lummer. He presented another set of data and claimed that the distribution law ‘appears to be rigorously valid law of nature’. After that many objections arrived from both side, many discussion occurred regarding the status of Wien’s distribution law. At last, Lummer with his latest measurements showed that Wien’s law fails at longer wavelengths. Other scientists also confirmed the failure of Wien’s law with their own measurements.

But, as this problem was very popular at that time, then obviously many others were also looking for answer of it. A British scientist Lord Rayleigh, in 1900, derived a proportionality relation between intensity and wavelength of blackbody radiation. Later in 1905, a more complete derivation with proportionality constants was presented by Rayleigh and Sir James Jeans, which came to as Rayleigh-Jeans law.

John William Strutt or Lord Rayleigh

But unfortunately that formula also failed, this time for shorter wavelengths. For longer wavelengths, it predicted correct intensities. That error which it predicted is called ‘Ultraviolet Catastrophe’ because it hugely overestimated the intensities of UV and other lights.

The Revolutionist

Both Wien’s Distribution law and Rayleigh-Jeans law was based on classical physics, which scientist thought as ultimate reality of nature. But if it is true, then why these laws cannot explain blackbody radiation completely. Obviously there was some mystery hidden in that problem.

As already mentioned, blackbody radiation problem came to known when Kirchhoff was analyzing the relation between light and temperature. So it was a connection bridge between two branches of physics called Thermodynamics and Electromagnetism (Optics). That is why; many scientists were desperately waiting for the solution of this problem because it can check the status of laws of thermodynamics.

Among those many scientists, there was one named Max Planck. He once was the student of Kirchhoff and Rudolf Clausius, another physicist who introduced the concept of entropy and spontaneity of thermodynamical processes.

Planck was also one of those who once told that ‘it is hardly worth entering physics anymore because there was nothing important left to discover’, after studying physics 3 years at Munich University.

Max Planck

When Wien’s distribution law was given, he waited for its confirmation. But when it got discarded, Planck himself started the quest for correct distribution law in 1990. He had 3 crucial pieces of information. First, Wien’s displacement law is correct. Second, Wien’s distribution law was correct for shorter wavelengths. Third, it failed in Infra-red region.

After a few unsuccessful attempts, through a combination of inspired scientific guesswork and intuition, Planck had a formula. It looked promising but nothing can be said without experimental confirmation. Planck hurriedly penned a note to Rubens (the guy who confirmed the failure of Wien’s distribution law in infra-red region) and went out in middle of the night to post it. After a couple of days, Rubens arrived at Planck’s home with answers. He had checked Planck’s formula against data and found an almost perfect match.

Image Source: Wikipedia
A graphical comparison between Wien’s, Rayleigh-Jeans’ and Planck’s distribution law
Here, Bν represent Intensity of light with frequency ν divided by π
(Frequency is another property of wave like wavelength. It is inversely related to wavelength, i.e., higher frequency means shorter wavelength and vice-versa, for constant speed of light in a medium)
     

Planck presented his formula at a meeting of German Physical Society on 19th October, 1900, as ‘An improvement of Wien’s equation of spectrum’. There, after his lecture, he got polite nods of approval from his colleagues. After few days Rubens and Kurlbaum announced that they had compared there measurements with the prediction of 5 different formulas and Planck’s formula proved to be much more accurate than any other.

But having a formula, which was got from an elementary operation performed on previous formula, won’t tell the complete story. What this formula means? Why is it correct? What is the hidden theory behind it? Planck went on further, to work on what this formula means.

Planck was one of those who didn’t believe in existence of atoms. He believed that matter is continuous. But he believed Maxwell’s Theory of Electromagnetism, which was given by James Clark Maxwell. According to Maxwell’s Theory, when an electrical charge undergoes acceleration, it emits electromagnetic radiation or light. Now, a body with certain temperature also emits Electromagnetic radiation.

Planck came up with a model of blackbody. He assumed that the wall of blackbody is made of an array of oscillators (most common example of an oscillator is a pendulum or a body hanging from spring) of charge. When the body is heated, this array of oscillators start oscillating, which is an accelerated motion, and due to this the body emits electromagnetic radiation. All these oscillators oscillate at different frequencies (number of oscillations per second), due to which it emits radiation of all different frequencies.

Now, more oscillators oscillate with same frequency, more intensity that frequency will have. Nobody actually can count the number of oscillators oscillating with certain frequency. So, in desperation he turns to the ideas of Ludwig Boltzmann, an Austrian physicist, who the foremost advocate of Atomic theory. Boltzmann had a great reputation as a physicist for his contribution to Kinetic Theory of Gases and Statistical Mechanics.

Ludwig Boltzmann

In nearly 1860s,  Maxwell, while studying motion of gaseous molecules, used principles of Statistics and Probability to work out most likely distribution of velocities of molecules, which honestly, was one of the boldest moves. Later on, Boltzmann took it to the next level and used same principles to explain second law of thermodynamics by linking entropy (an extensive property of any system) to disorder.

Planck used same principles to find out the most probable distribution of frequencies among oscillators. When he tried to drive his formula like this, he came up to a step when he had to consider that energy of electromagnetic radiation comes in packets and energy of each packets (which is called a quantum) is directly proportional to its frequency. But according to Maxwell’s Theory, Electromagnetic radiation is continuous and its energy depends on amplitude (size of oscillation) of wave.

Mathematically, it says E=hν, where E is energy of each packet, ν is frequency and h is a proportionality constant which Planck called as quantum of action but which later came to known as Planck’s constant. He found that the energy of his oscillators can have the value which are integral multiples of hν (i.e., hν, 2hν, 3hν,…., nhν). It was a strange idea that energy of Electromagnetic radiation was independent of amplitude of oscillation and even stranger was that it comes in packets, like particles (which was a long back discarded idea). It was the way how his oscillators could receive and emit energy.

On 14th December, 1900, at Berlin University’s Physics Institute, he delivered his lecture, ‘Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum’, On the Theory of Energy Distribution Law of Normal Spectrum, to the German Physical Society. There he presented the physics behind his new equation.

At the end of meeting his colleagues roundly congratulate him. Just as Planck regarded the introduction of the quantum, as a ‘purely formal assumption’, to which he ‘really did not give much thought’, so did everyone else that day. Everyone was impressed not from the introduction of quantum, but from accuracy of Planck Distribution Law, and they thought quantum as a mathematical trick.

Planck discovered quantum but even he could not understand its complete significance. He regarded his discovery as an ‘act of desperation’. He tried to get rid of the quantum. He only realized the far-reaching consequences of what he had done much later.

The first person who understood the radical nature of quantum was not Planck but a young man living in Bern, Switzerland. He is an epitome of genius; he was none other than Albert Einstein. Einstein said that in formula E=hν, E is energy of a photon, particle (quantum) which light consists, but the strange thing was that a particle (photon) have a frequency ν, which is a property of wave.

Einstein used Planck’s theory to explain photoelectric effect in 1905. Later on, more unexplained phenomenon was explained using quantum theory and this Revolution went on further, very far.

Quantum theory was a great revolution and although it had a huge success, Planck hopelessly tried to avoid it. It was his revolution against his own will. But later on he stated, “It doesn’t help. We have to live with quantum theory. And believe me, it will expand”. If you read more about quantum theory, you will see it had already expanded too much.

Conclusion

One of the most important events in quantum physics was the research of the phenomen called Blackbody. Every scientist that worked on this problem, contributed to the final solution of Max Planck.

Honestly, I don’t have any technical conclusion regarding this post. I have already covered all technical parts. It was just a story of how the quest for solution of not so big looking problem lead to a revolutionary idea, and later that idea lead to other ideas and theories.

But there is a message. If you want to bring change in your life, the whole world or in anything, never hesitate in doing small thing or taking small steps. Sometimes, it might appear wrong to you, but if it is for the right purpose, then just DO IT. Who knew that such a small step could bring a revolution.

You can draw a conclusion of your own regarding this post.

If you have drawn one, share it in comments. I would like to read it.

Written by: Sara Nadzak and Rohit Verma

9 thoughts on “A Revolution that changed the fate of Physics”
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