# What will happen with your length, if you approach the speed of light?

To answer this question, we need to know Lorentz contraction formula.

$L = L_0 \cdot \sqrt{1-\frac{v^2}{c^2}}.$

L – is the length of an object as a function of its velocity v with respect to an observer

L0 – is the length of the object at rest

c – is the speed of light

Analysis of the function:
• As approaches the speed of light, the relation (v^2)/(c^2) approaches 0.99999999999…  When we subtract this number from 1, we get 0.000…1 . After, we take square root of this number, we get an infinitely small number. Then, this number is multiplied by L0 which gives us, again, an infinitely small number. Therefore, as the object approaches the speed of light his length shrinks to infinitely small value.

Graph of Lorentz contraction formula:

# Why is it impossible to travel with a speed of light?

• m– mass of an object
• c-speed of light
• v-speed of  an object
• E-energy required

Example:

• Speed of object is 99.999999666438906878704733792869% of speed of light.

E= (m*(299 792 458 m/s)^2)/((1-((299 792457.000009m/s)^2)/(299 792 458 m/s)^2))^1/2

E=(m* (8.987551787368176e+16 m/s))/(2.5828824797042237670667301169722e-8)

E= m *3.47965959 × 1024

If we continue to approach speed of light, our mass will be equal to infinity.

If the object continue to approach speed of light, his mass will approach infinite value. Therefore, the energy needed to travel with a speed of light will be infinite (E=m C^2) which means it is impossible to travel with a speed of light.