Lorentz Contraction

If you are taking up your first course in advanced classical mechanics, you will soon be introduced to the special theory of relativity. It is one of the most shocking and paradigm shifting theories that you will be ever introduced to, in physics. The notions of intuitive Newtonian mechanics are shattered as you start learning about the true relative nature of space and time. Lorentz contraction is one of the predicted and experimentally verified consequences of special theory of relativity, which was first proposed as a conjecture to save the ether hypothesis, by Hendrik Antoon Lorentz and George Francis FitzGerald. Einstein showed that length contraction came out as a natural consequence of fundamental postulates of special theory of relativity.

What is Lorentz Contraction?

Lorentz contraction is a phenomenon of shortening of the length dimension of an object, in the direction that is parallel to its velocity of movement, with respect to a stationary frame and observable from it. This shortening of the object is directly proportional to its velocity. This phenomenon was shown to be as a consequence of the postulates of special theory of relativity by Albert Einstein in 1905. The constancy of speed of light and the requirement that all laws of physics be the same in all inertial reference frames inevitably lead to the effect of Lorentz contraction.

Consider a horizontal ruler traveling at speeds substantially close to the speed of light (which is about 3 x 10⁸ m/s) in a parallel direction to its length. For a stationary observer, observing the ruler, it will appear to have shrunk horizontally! This is Lorentz contraction. Now you must be wondering why don't we see Formula 1 cars or buses shrinking as they move at high speeds? The reason is that they do shrink but the shrinking being directly proportional to the speed of the object, it is very very very negligible to be observed. You will require a ruler which can measure changes in length shorter than billionths of a meter!

Formula

No phenomenon can be studied without the establishment of an equation that describes it completely, as it enables quantification and experimental verification. Here is one more addition to your physics formulas list. The Lorentz formula is as follows.

L' = L x √(1 - v²/c²)

where L' is the observed length of the object in the stationary reference frame, L is the proper length of the object (when at rest), 'v' is object velocity and 'c' is the speed of light. The factor - '1 / √(1 - v²/c²)' is called the Lorentz factor. The length contraction can be determined by multiplying the rest length of the object by inverse Lorentz factor.

As you can see, compared to the speed of light which travels about 300 million meters per second, an object traveling at speeds of a few meters per second, the factor which multiplies the rest length, will be almost 1. So the length contraction effects only become prominently observable at very very high speeds, which are comparable to or sizable fractions of the speed of light!

If you closely observe, the Lorentz contraction formula presented above, when v = c, the length become infinite, which is an impossible result! Rather than interpreting it as contraction limit, it restates the fact that no object can reach the speed of light, which is like the most fundamental speed limit imposed by the very structure of space time!

As you can see, Lorentz contraction is one of the most astounding effects that arise as a result of the axioms of special theory of relativity. What is more, this effect is not a figment of imagination or just a hypothesis, it has been experimentally tested. However, as explained before, measurable consequences of this phenomenon are difficult to observe as they are super minuscule. The effect of Lorentz contraction becomes more and more apparent as an object approaches the speed of light! If only light would have traveled at much lower speeds, every time you would speed up, your visage and the tip of your nose, would appear to have shrunk, to any bystander at rest!