Constants of the universe - Planck Units of Max Planck :

In 1899, German physicist Max Planck proposed a universal set of units for length, time, mass, temperature and other physical qualities. He was trying to come up with a way to define units that depended only on constants of the universe. Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units.

To determine and measure the fundamental constants. The four most important of these are:

• Speed of light c = 299792458 m s^-1
• Gravitational constant G = 6.673(10) x 10^-11 m^3 kg^-1 s^-2
• Planck’s constant (reduced) h(bar) = h/2π = 1.054571596(82) x 10^-34 kg m^2 s^-1
• Boltzmann constant k = 1.3806503(24) x 10^-23 kg m^2 s^-2K^-1

Note, that these constants in SI units: metres (m), kilograms (kg), seconds (s) and degrees Kelvin (K). The numbers in brackets represent the decimal places where the values are uncertain.

The Planck length, denoted ℓP, is a unit of length in the system of Planck units that was originally proposed by physicist Max Planck, equal to 1.616255(18)×10^−35 m. 

The Planck time tP is the time required for light to travel a distance of 1 Planck length in vacuum, which is a time interval of approximately 5.39×10^−44 s. No current physical theory can describe timescales shorter than the Planck time, such as the earliest events after the Big Bang.

However, according to Planck the velocity of electromagnetic waves, or light, is equal to one Planck length per Planck time; the limit to which photon can travel. 

Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants. Originally proposed by the German physicist Max Planck in 1899, these units are a system of natural units because their definition is based on properties of nature. It may be mentioned here that Einstein first published his special theory of relativity in 1905, which describes his revolutionary ideas about light, time and energy.

The ratio of the Planck length to the Planck time (ℓP/tP) :

• Planck length = ℓP = L ≈ 1.61626 × 10^−35 m; 

• Planck time = tP = T ≈ 5.391247 × 10^−44 s; 

• ℓP/tP is the ratio of the Planck length to the Planck time;

Since, ℓP/tP = (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s);

1. To divide two numbers in scientific notation, we subtract the exponents of the 10 and divide the coefficients:

2. Coefficient: (1.61626) / (5.391247) ≈ 0.299792458

3. Exponent: (10^(-35)) / (10^(-44)) = 10^(-35 - (-44)) = 10^9

4. So the simplified value is approximately:

5. 0.299792458 × 10^9 m/s

6. Now, we recognize that this is the speed of light in a vacuum, which is denoted by 'c':

7. c ≈ 2.99792458 × 10^8 m/s

8. So, the simplified expression is:

9. (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s) ≈ 2.99792458 × 10^8 m/s;

The ratio of the Planck length to the Planck time (ℓP/tP) yields a value to the speed of light in a vacuum, c;

This is a fundamental constant in physics and is denoted by 'c'.

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