Relativistic effects such as time dilation and length contraction are present for cars and airplanes. Why do these effects seem strange to us?

Time dilation and length contraction are two effects predicted by Einstein's theory of Special Relativity. Time dilation states that time slows down for an object in motion, compared to an object at rest. Mathematically, it is represented as: \[T = T_0 \cdot \gamma\] Where \(T\) is the time experienced by the moving object, \(T_0\) is the time experienced by the stationary object, and \(\gamma\) is the Lorentz factor, defined as: \[\gamma = \frac{1}{\sqrt{(1 - (\frac{v^2}{c^2}))}}\] With \(v\) being the velocity of the object and \(c\) denoting the speed of light. Length contraction states that objects in motion experience a decrease in their length along the direction of motion, as observed by a stationary observer. Mathematically, it is represented as: \[L = L_0 \cdot \sqrt{(1 - (\frac{v^2}{c^2}))}\] Where \(L\) is the length experienced by the stationary observer, \(L_0\) is the proper length (the length as measured in the object's rest frame), and again, \(v\) is the velocity, and \(c\) is the speed of light.

For relatively low velocities, which are typical in everyday life (e.g., cars and airplanes), the fraction \(\frac{v^2}{c^2}\) becomes very small compared to 1. This results in the Lorentz factor, \(\gamma\), being very close to 1. Consequently, time dilation and length contraction effects are minimal in daily life and are thus not significant or noticeable.

Let's take a car traveling at 100 km/h (27.8 m/s) as an example. To calculate the Lorentz factor, we first compute the fraction \(\frac{v^2}{c^2}\): \[\frac{(27.8)^2}{(3\cdot 10^8)^2} \approx 1.02 \cdot 10^{-15}\] Now, we can calculate the Lorentz factor: \[\gamma \approx \frac{1}{\sqrt{1 - 1.02 \cdot 10^{-15}}} \approx 1 + 5.1 \cdot 10^{-16}\] As we can see, the Lorentz factor is very close to 1. Thus, time dilation and length contraction effects are negligible for a car traveling at 100 km/h. In conclusion, relativistic effects such as time dilation and length contraction are present in everyday objects like cars and airplanes. However, these effects seem strange to us because we do not observe them in our daily lives due to the low velocities involved, which result in negligible relativistic effects compared to the speed of light.