**INTRODUCTION**

Classical Physics and General Relativity, both the theories are incompatible with small-scale universe, that is, both the theories are not applicable on small particles. The scale where general relativity seems to predict some ‘strange’ things is below **10 ^{-9} meters**.

On the other hand, the special theory of relativity works well with particles. Actually, the tests conducted to prove special relativity had been done on very small scale.

So, what about small-scale universe?

Special Relativity, alone, isn’t able to explain the small world as it only deals with the effects which can be observed when objects move with a constant speed and it tells us that every motion should be considered relative.

There was a need of something ‘new’. This new type of MECHANICS was ‘QUANTUM MECHANICS’ or ‘QUANTUM PHYSICS’, or, simply ‘QM’.

Actually the story of quantum physics was started some five years before from RELATIVITY. Quantum physics was introduced in 1900.

So, quantum physics is actually older than relativity!

Quantum Physics was introduced by a German physicist, Max Planck, who was also a friend of Einstein, and, Planck is also honored as ‘FATHER OF QUANTUM PHYSICS’. Max Planck also have some contributions in Relativity.

Quantum Physics is the foundation of modern chemistry and modern biology, and, QM has a very important role in the development of modern electronics.

In this article, some basic principles of QM will be discussed.

**1. PLANCK’S QUANTUM THEORY**

It was in the late nineteenth century that it was predicted using the classical physics, that a body at a constant temperature would emit an infinite amount of energy which actually doesn’t (and can’t) happen.

So, to avoid this obviously ridiculous result predicted by classical physics, Max Planck suggested the idea of quantum (plural – quanta) in the year of 1900

According to his quantum theory, energy (like light) can only be radiated in some energy packets which he called quanta, (now, one quantum of light is known as ‘*PHOTON*’), and the energy carried by these packets or quanta is limited for a single frequency and wavelength. F

Frequency is the number of cycles completed by a wave in one second . Wavelength is the distance covered by a wave in one cycle. These two quantities are inversely proportional, that is, when frequency increases, wavelength decreases and vice versa, and, frequency is directly proportional to energy.

There is a minimum and maximum amount of energy carried by these particles (quanta) at a particular frequency.

For example, in the VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red) *spectrum*, Violet has the highest frequency and the shortest wavelength, and Red has least frequency and longest wavelength.

So, the photon (or quantum of light) of red color, with least energy is the minimum possible amount of light energy that can be emitted by a body (as a single photon) and a photon of violet color, with highest energy is the maximum possible amount that can be radiated or emitted by a body as a single quantum.

A wave is illustrated below:

**1.1 PHOTOELECTRIC EFFECT**

Planck’s quantum hypothesis, to become a theory, should be proved with some strong observations, which was done by Einstein himself in a paper published by him in 1905 (the same year when he introduced special relativity).

In the nineteenth century after the physicist James Clerk Maxwell proved that light is an electromagnetic wave, it was believed that light was a wave but not composed of particles or quanta (as Newton had also suggested before), so, this was a difficulty to prove quantum hypothesis.

But Einstein proved the ‘*PHOTOELECTRIC EFFECT*‘ in 1905, which, in turn, was a proof of Planck’s quantum hypothesis.

According to photoelectric effect, when a photon hits a ‘*free electron*‘, the electron can escape the metal and this electron is called a ‘*PHOTO-ELECTRON*‘ (Electron is a particle in an atom and a free electron is an electron which ‘feels’ the least amount of electromagnetic force). This photoelectric effect was introduced by another German physicist ‘Heinrich Rudolf Hertz’ in the nineteenth century.

Einstein (also a German) proved this photoelectric effect.

So, this proved that light is made of particles, but, what about its wave nature.

Actually, both the things are correct, light shows both the natures of particles (as photons) and electromagnetic wave.

So, this proved Planck’s theory.

The photoelectric effect can be understood by the illustration below:

**1.2 EINSTEIN-PLANCK RELATION**

Einstein and Planck also provided a well defined equation which related the energy of a quantum and the frequency of its corresponding wave.

According to ‘*Planck’s law*‘, energy carried by a quantum of light (that is, a photon) is equal to the product of *Planck’s Constant* and the frequency of ‘corresponding light wave’, that is, frequency multiplied by Planck’s constant gives us the energy of one quantum of that frequency.

**Value of Planck’s Constant is 66 × 10**

^{-35}**2. WAVE-PARTICLE DUALITY**

Einstein proved that light showed both wave nature and particle (photon) nature, but, a French physicist Louis de Broglie suggested that not only light showed a duality (of wave and particle) in its nature, but all other particles of matter, like electrons etc., behaves both as a wave and a particle which is true.

**2.1 DE BROGLIE’s WAVELENGTH**

De Broglie also provided a well defined relation between the momentum of a particle of matter and the wavelength of the corresponding matter wave which is —

Value of Planck’s Constant is

**66 × 10**

^{-35}This above formula also works for photons and light.

Because Planck’s Constant is an unchangeable value (that is, a constant value), so it can be concluded that wavelength of a matter wave is inversely proportional to the momentum of corresponding matter particle. This means that greater the momentum, smaller the wavelength.

A question arises now, if matter has both wave and particle nature, why can’t we observe the wave nature of matter in our daily life?

Let us find out the answer with an example.

So, take an example of any bullet of four grams moving with a velocity of **400 meters per second**. Consider its diameter is **five centimeters**.

The mass of bullet in kilograms will be **0.004 kg**.

So, its momentum will be **0.004 kg** multiplied by **400 m/s**, that is, **1.6 kg m/s** (mass × velocity).

Now, the wavelength of the corresponding wave will be only about —

**4 × 10 ^{-34} meters **

And, the diameter of the bullet is five centimeters or **0.05 meters**, which is very larger than the wavelength. So, here, absolutely, particle nature dominates, so for the objects far larger than the size **10 ^{-9} meters**, particle nature dominates due to having large size and very short wavelength.

**3. HEISENBERG’s UNCERTAINTY PRINCIPLE**

In 1814, a French mathematician Marquis de Laplace introduced a principle of *determinism* in which he suggested that if we know the present state of the universe, then, using the correct *laws of physics*, we can find out the future or past state of universe with 100 percent certainty.

It seems to be true because, if we know the present position and momentum (that is, mass × velocity) of Earth, Sun and our Moon, we can find out when will the next solar or lunar eclipse will take place by using Newton’s laws.

Everyone was satisfied by this principle of determinism.

After developing his general theory of relativity and being awarded by the noble prize for the photoelectric effect in 1921, Einstein was researching in quantum theory, but he was interrupted by another German physicist, ‘Werner Heisenberg’ in 1928, when he presented his ‘*UNCERTAINTY PRINCIPLE*‘*.*

It was the most important conclusion of Planck’s theory that was realized in 1928, by Heisenberg.

This principle states that we can’t measure the position and momentum of a particle with 100 percent certainty. If we increase the certainty in one of these two, the certainty in the other quantity decreases.

This is because to measure the position of a particle, we have to emit light on it, and, we know that light is composed of photons, so, when the photons will collide with the particle, the photons will change the particle’s velocity, and, thus, the momentum will also be changed.

So, we can’t measure both position and momentum of a particle with 100 percent certainty, and there is a mathematical relation between uncertainty in position, momentum and Planck’s constant, which is:

**52 × 10**

^{-35}But, this uncertainty is very in large objects, almost equal to zero (because reduced Planck’s constant is a very small value), that is why we can find when the next lunar or solar eclipse will take place.

This principle is the one of the most fundamental principle of physics.

But, Einstein never agreed with this principle, his feelings are represented in his famous statement —

God Never Plays Dice

**Thanks for Reading and Hope You Liked It!**

**REFERENCES**

- Hawking, Stephen (2000).
*A Brief History of Time.*New York: Bantam Books. - Hawking, Stephen (2005).
*A Briefer History of Time.*London: Bantam Press. - Sorout, Madhur (2018, April 7).
*Theory of Relativity in Brief*. Retrieved from Maddyz Physics: https://maddyzphysics.com/2018/04/theory-of-relativity-in-brief/ *Uncertainty Principle*. (n.d.). Retrieved from Wikipedia: https://en.wikipedia.org/wiki/Uncertainty_principle*Wave-particle Duality*. (n.d.). Retrieved from Wikipedia: https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

**About the Author – Madhur Sorout**

Sorout is currently a last third year high school student, living in India. His main fascination lies in Physics mainly in the field of general theory of relativity and topics related to it like Big Bang, Black Holes and Evolution of Universe. He likes to make out the meaning of what he see in this universe. He loves to read books by Stephen Hawking, Neil deGrasse Tyson and other authors (and Physicists). He is an atheist and believes that Physics completely rejects the idea of a god. He likes to play cricket also and he wants to continue down the route of research in Theoretical Astrophysics.

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