|MLA Citation:||Bloomfield, Louis A. "Question 1423"|
How Everything Works 14 Aug 2018. 14 Aug 2018 <http://howeverythingworks.org/print1.php?QNum=1423>.
But suppose that the bus were traveling at 99.999999% of the speed of light and you were to run toward its front at 0.000002% of the speed of light (about 13 mph or just under a 5 minute mile). Now what would happen?
First, the bus speed I quoted is in reference to some outside observer because the seated passengers on the bus can't determine its speed. After all, if the shades are pulled down on the bus and it's moving at a steady velocity, no one can tell that it's moving at all. So let's assume that the bus speed I gave is according to a stationary friend who is watching the bus zoom by from outside.
While you are running toward the front of the bus at 0.000002% of the speed of light, your speed is in reference to the other passengers in the bus, who see you moving forward. The big question is what does you stationary friend see? Actually, your friend sees you running toward the front of the bus, but determines that your personal speed is only barely over 99.999999%. The two speeds haven't added the way you'd expect. Even though you and the bus passengers determine that you are moving quickly toward the front of the bus, your stationary friend determines that you are moving just the tiniest bit faster than the bus. How can that be?
The answer lies in the details of special relativity, but here is a simple, albeit bizarre picture. Your stationary friend sees a deformed bus pass by. Ignoring some peculiar optical effects due to the fact that it takes time for light to travel from the bus to your friend's eyes so that your friend can see the bus, your friend sees a foreshortened bus—a bus that is smashed almost into a pancake as it travels by. While you are in that pancake, running toward the front of the bus, the front is so close to the rear that your speed within the bus is miniscule. Why the bus becomes so short is another issue of special relativity.