Hello everyone! I am Rahul here and in last article I simplified time dilation for you. As I promised, today I will simplify the concept of length contraction for you.
If you are new here and haven't read my previous article about time dilation, click here to check it out. I recommend reading my previous article first because I will be using some terms which I have already explained in it.
Since now you have(I hope) read my previous article, let's start today's journey.
Have you ever tried to measure length of something? Of course I have. You may say. All I have to do is just put it in front of me and use a scale to measure its length. Simple. You may say again. But have you ever thought what will happen if that thing, whose length we are trying to calculate is moving relative to you and now you try to measure its length? Will the results be different now? Does it even matter if it is moving or not?
If you said that results will stay the same whether it moving or not then I am sorry my friend you are wrong. It's not me who is saying that. It's sir Albert Einstein who said that. According to him the length of an object contracts in the same direction it is moving. This phenomenon is known as length contraction. This contraction is also called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George Francis FitzGerald.
But why don't we observe it everyday? Can we measure this length contraction? Is it a reality or just an illusion?You may ask. Today I will be answering all these questions.
But first I want to define some terms which I will be using in the rest of the article.
- Proper Length: It is the length of the object when measured by the observer who is at rest relative to the object.
- Apparent length: Length of the object measured by the observer who is not at rest relative to the object. It is always less than the proper length.
Why don't we observe it everyday?
This effect is only significant when object is traveling with speed comparable to the speed of light. Otherwise it is negligible and we humans with even our current technology can't measure this difference. That's the reason we don't observe it everyday. For us the length of the car or a bus is same whether it is moving or not.
Can we measure this length difference?
Yes we can. Einstein proved this phenomenon of length contraction mathematically. He derived a formula to calculate the apparent length if we already know its proper length or vice versa. This is the formula:
Here L' denotes proper length, L denotes apparent length, v is the speed of the object and c is our speed of light.
Einstein derived this formula by using the very famous Lorentz Transformation.
Illusion or an Reality?
Well it depends on your definition of reality and illusion. What is your minimum criteria for reality? Let's take an example. Assume an object having proper length L is moving with half the speed of light. When it travels past you and you measure its length(say L') your observation will be different according to Einstein. But for someone who is also moving with half the speed of light in the same direction the length will still be L.
For you the object is moving so you are observing length contraction but for him the object is at rest, there is no length contraction for him. Now the question is who is right? You or him? The answer is both of you are correct. But how is that possible? Simultaneously there is length contraction and no length contraction? You may ask. The answer is very simple. Space, time and length are relative and not absolute. Since they are relative observations for you and your friend may differ and still both of you can be right. That's how it is.
That's all for today. I tried to keep it as simple as possible. Any suggestions are welcome.
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Reference:
- Length Contraction - Wikipedia
- Lorentz Transformation - Wikipedia
- Length Contraction - College Physics
- Consequences of Special Relativity | Boundless Physics
- Length contraction explained - Study.com
- Length Contraction: the Real Explanation - Fermilab