All You Need To Know About The Most Relevant Fundamental Physical Constant

In the world of physics– if we exclude all the Fundamental Physical Constant, the whole scientific world will collapse. Physics is narrated in the language of Mathematics, and the Mathematical equations involved in this language uses a broad range of the fundamental physical constants.

In my view, Physics is the King of Science while Mathematics is the Queen. Jokes apart, In physical understanding, the values of these mathematical fundamental physical constant define our day to day life. A fundamental physical constant, occasionally referred to as a physical constant is a physical quantity that is believed principally to be universally constant in nature as well as having a constant value in time.


These fundamental physical constant are generally derived from direct observation, either directly such as (the measurement of the speed of light or charge of an electron) or by characterizing a relationship between measurable quantities and then deriving the value of the constant such as (in the case of gravitational constant).


It should be explicitly noted or kept in mind that these fundamental physical constant are written in different units (as preferable while solving a problem), so if you find different sets of physical value that isn’t indeed same as the previous one, then don’t get confused; it maybe has been converted into another set of units.


Literally, fundamental physical constants can be bifurcated into two categories such as

Dimensioned Fundamental Physical Constants

The term Dimensioned Fundamental Physical Constants is explicitly used to mention those physical constants which are universal in nature. In simple words, those physical constants which are expressed dimensionally as length divided by the time such that it has some units attached; has a numerical value that is precisely dependent on the system of units used. 

1. Speed Of Light (C)

Technically speaking, Ole Christensen Rømer a Danish astronomer was the first one to demarcate the quantitive measurement of the speed of light in 1676. He was able to demonstrate that light travels at a finite speed which was instantaneously opposed by studying the apparent motion of Jupiter’s moon named Io. After Ole Rømer; in 1865, physicist James Clerk Maxwell represented the speed of light in free space in his world celebrated Maxwell’s Equations, proposing that light is an electromagnetic wave and therefore will travel at speed of light emerged in his Theory Of Electromagnetism.

physical-constant-speed-of-light
Nothing Can Travel Faster Than Speed Of Light
Credit: BBC.com
Finally, after James Clerk Maxwell, Albert Einstein restructured the speed of light in his Special Theory Of Relativity. Einstein postulated that the speed of light is constant with respect to any inertial frame and is independent of the motion of the light source. Einstein showed that the parameter c had applicability outside the context of Light and Electromagnetism.
c = 2.99792458 x 108 meters per second 
❋ (C) entangles space and time. It also appears in the world’s most famous Mass-Energy Equivalence E = mc2

2Electric Charge (e)

The electric charge or sometimes referred to as the elementary charge, denoted by (e), is the electric charge carried by a single photon as well as by single-electron too which has a charge e.

physical-constant-electric-charge-oil-drop-experiment
Millikan’s setup for the Oil Drop Experiment for measuring Electric Charge
Credit: Wikipedia


In 1909, Robert A. Millikan was the first one to measure the magnitude of the elementary charge is his notes Oil Drop Experiment. Though, in 1874, the use of the electric charge as a unit was promoted by George Johnstone Stoney; called Stoney Units.


In simple words, as we all know, our modern world basically runs on electricity. Whenever we are talking about the behavior of the electric current or electromagnetism, the elementary charge of an electron is the most fundamental unit 


e = 1.602177 x 10-19 C

3. Electric Constant 0)

The fundamental physical constant ε0 pronounced as (“epsilon naught”) represents the capability of a classical vacuum to permit electric field lines. The physical constant εalso usually called by the name such aselectric constant,vacuum permittivity, orpermittivity of free space that associates the units of electric charge to the mechanical quantities such as length and force.
Its appearance can be seen in representing Columb’s Law
Similarly,  ε(“epsilon naught”) also appears in Maxwell’s Equations, which is used to define the properties of Magnetic and Electric Field and Electromagnetic Radiation.
ε0 = 8.854 x 10-12 C2/N m2

4. Gravitational Constant (G)

The term Gravitational Constant or the Universal Gravitational Constant, also known as Newtons Constant was developed as a law of gravity involved in the calculation of Gravitational Effects in Albert Einstein’s General Theory Of Relativity and Issac Newton’s Law Of Universal Gravitation. 

newton's-laws-of-motion-experimental-values-of-big-G
Error plot showing experimental values for big G.
Credit: Wikipedia
Denoted by the letter G, the Universal Gravitational Constant is very difficult to measure with high accuracy because of their extremely weak Gravitational Force compared to other Fundamental Forces.
According to the Law of Gravitation, the attractive force (F) between two point-like bodies is directly proportional to the product of their masses (m1 and m2), and inversely proportional to the square of their distance (r) between them.
{displaystyle F=G{frac {m_{1}times m_{2}}{r^{2}}},.}
gravitational-interaction
The gravitational constant G is a key quantity in Newton’s law of universal gravitation
Credit: Wikipedia




G = 6.67259 x 10-11 N m2/kg2

5. Planck’s Constant (h)

A German theoretical physicist  Max Karl Ernst Ludwig Planck (known as the Father Of Quantum Physics) commenced the entirely new field in the department of physics named Quantum Physics by his explanations to the solution to the “Ultraviolet Catastrophe” while investigating the Black-Body Radiation problem. While exploring so, he defined a fundamental physical constant, known as Planck’s constant.
While explaining Black-body radiation, Planck derived his famous Plank’s Constant
Credit: Wikipedia


The Planck’s Constant is a fundamental physical constant which was coined for the quantization of Light and Matter. In simple terms, it is an amount of energy in one cycle of the wave from Electromagnetic Radiation, regardless of an associated wavelength.

The Planck’s Constant is the only fundamental physical constant which is known to it’s lowest level of precision. It is seen as the sub-atomic scale constant. In fact, it is one of the smallest physical constant used in the physics. 
 h = 6.6260755 x 10-34 J s
❋  Planck’s Constant appears in Planck-Einstein Relation that connects photon energy E with its associated wave frequency f
                                     E = h f
It also appears in De Broglie Hypothesis that connects the linear momentum of a particle P (for every materialistic elementary particle) to the De Brogie wavelengthλ


Dimensionless Fundamental Physical Constant

The term Dimensionless Fundamental Physical Constant is explicitly used to mention those physical constants universal in nature, just same as dimensioned fundamental physical constant. the dimensionless fundamental physical constant cannot be derived but have to be measured. In simple terms, those physical constants which have no units attached to them and has a mathematical value; but are independent of the unit systems used.

Fine-Structure Constant (α)

In the study of physics, the fine-structure constant or coupling constant, denoted by a Greek letter alpha (α), is a fundamental physical constant used to outline the strength of an Electromagnetic Interaction between elementary particles such as(electrons, muon) and light (photons). Almost 100 years ago in 1916, the fine-structure constant (αwas introduced by a German Theoretical Physicist Arnold Johannes Wilhelm Sommerfeld therefore, being also referred as Somerfield fine-structure constant. For the explanation of fine-structure constant, Somerfield extended the Neil Bohr theory to incorporate elliptical orbits and the relativistic dependence of mass on velocity.

Being a dimensionless physical quantity; currently, the value of the fine-structure constant (α)  having the smallest uncertainty that basically comes from the comparison between the Theoretical Expression ae(theoretical) and the Experimental value ae(experimental) of the inconsistent magnetic moment of an electron. Fine-structure constant is considered as a coupling constant for the electromagnetic force similarly as for the other three known fundamental forces or interaction of nature; (gravitational force, weak nuclear force and strong nuclear force).

list of coupling constant or fine-structure constant 

1. Strong force  (αs =≈1)
2. Weakforce  (αw =  10-6)
3. Electromagnetic force  (α = 1/137)
4. Gravitational force  (αg = 10-39)



At last, I will leave you all my readers with a quote by Albert Einstein regarding Fundamental Physical Constant, and he quote

“… there are no arbitrary constants … nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).” 

           Albert Einstein

On that note, I can say that I have tried enough to give an overview of All You Need To Know About The Most Relevant Fundamental Physical Constant. If there are any suggestions, feel free to comment.
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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my carrier, and therefore I just completed my postgraduate degree in physics. Right now I am a loner (as like ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every part of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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