Relativity Theory in Actual Formulas

I think a lot of people know some basic elements of Einstein's Relativity Theory. Some things which are not as commonly known are actual equations with numerical examples. Everything is relative, except for the light of speed. That includes space and time, which were always viewed as absolute.

However, what might be interesting, how much do space and time get stretched or compressed? Obviously, most people know that the effects are only important at speeds close to the speed of light. But what does it mean?

Well, just assume a car, which is going really fast. LIKE REALLY FAST. The following table starts with 0.001 of c as the start speed, which is still 29,979 m/s. Here, the car is still (to an unomved observer) 5 m long with an error of 0.0000025 m. That is accurate enough to say that it is negligible. So any car going at regular (even lower) speeds will not be subject to any noticeable space compression.

But we see that around 30% of c, the car will look noticeably shorter, roughly 25 cm. At speeds almost equal to c, for example 99.9999% of c (second-to-last row), the car will only be 7 mm long. You read that right. An observer standing on a road where a car just happens to pass by at that speed will (if he is able to notice any differences due to how fast it will probably be out of sight) estimate the length of the car at 7 mm.

That graph shows the relationship. The length of the car goes down the closer you come to c and reaches 0 at exactly c. It also practically 5 at all speeds which will be encountered. Just to emphasize, if you were sitting in the car, you would not feel compressed. Rather, the surrounding environment would be compressed.