Omkar Phatak
Mar 25, 2019

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One of the most intriguing predictions of Einstein's special theory of relativity is Lorenz contraction. Here is a short explanation of the same.

If you take up your course in advanced classical mechanics, you will 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 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 comes about as a natural consequence of the fundamental postulates of special theory of relativity.

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 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 leads to the effect of contraction.

Consider a horizontal ruler traveling at speeds substantially close to the speed of light (which is about 3 x 10^{8} m/s) in a parallel direction to its length. For a stationary observer, 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 it 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 lengths which are shorter than billionths of a meter.

No phenomenon can be studied without the establishment of an equation that describes it completely, as it enables quantification and experimental verification. The formula is as follows.

**L' = L x √(1 - v**^{2}/c^{2})

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. Here, '1 / √(1 - v^{2}/c^{2})' is called the Lorentz factor. The length contraction can be determined by multiplying the rest length of the object by the Lorentz factor.

As you can see, compared to the speed of light which travels at about 300 million meters per second, for 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, when they are comparable to or sizable fractions of the speed of light.

If you closely observe the contraction formula presented here, 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 fundamental speed limit imposed by the very structure of spacetime.

As you can see, the contraction is one of the most astounding effects that arises 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 the contraction becomes more and more apparent as an object approaches the speed of light.

If only, light would have traveled at 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.