Objection: He says my clock slows down and that my distances shrink when I know that it is really his time and space that are changing.
Answer: Actually, there is no contradiction to each of us observing the other's clocks and distances changing. There would only be a contradiction if both of us were making our measurements from the same frame of reference and then arrived at different results. However, in order to be in the same frame of reference, one of us would have to alter his motion in order to bring it in line with the other person's. When this happens, extra forces are brought into play and that person is no longer moving with a constant velocity with respect to us. This destroys the symmetry of the situation, and results in one of us definitely having a slower clock.
Experimental Verification: Several relativistic effects have been confirmed experimentally. For example, highly accurate atomic clocks have been synchronized with one another and then one has been flown at high speeds in a jet for a sufficient length of time, and when compared with each other again, less time is found to have passed on the clock that was moving at high speeds. It has also been observed that atomic particles decay more slowly when moving at high speeds as predicted by relativity. In addition, many other experiments have been performed over the years that provide ample verification of the predictions of relativity.
Final Conclusions: Space and time are stranger than we imagine, and our usual ideas of space and time are just as inaccurate as the belief that people once had that the earth is flat. Much of our confusion results from the assumption that time and space are things that exist independently of objects. However, try to imagine a universe in which no objects exist. In such a universe there would be no points of reference from which to measure the passage of time or distances in space. In such an existence, time and space would only exist as mental constructs. Thus, if we can accept that time is only a measurement that is made of the separation between parts of an observed sequence of events and that distance is only a measurement of the separation between events that are observed to occur at the same time, then it is not so surprising that observers in different frames of reference will measure these things differently. In other words, the universe is relatively . . . interesting!