It follows from Einstein's Theory of
Relativity (which explains the strange observations) that if you keep changing
your speed for some time while your friend doesn't move, then your clock goes
slower than the clock of your friend. This is called time dilation. If you make
a long journey through space in a fast rocket, then your journey will take less
time as measured by your accurate ship's clock than as measured by an
identical clock back at home. This effect is only noticeable when speeds are
reached that are close to the speed of light.
In your daily life, the effect is very
small. For example, if you accelerate from 0 to 100 km/h (62 mph) in 20 seconds
and then slow down to 0 again in another 20 seconds, then you'll have remained
20 femtoseconds (0.000,000,000,000,06 seconds) younger relative to your friend
who didn't move, but both of you have of course aged by about 40 seconds.
Is time dilation true? How big are the effects?
Do clocks at speed really run slower, and do people or things travelling at speed live longer?
One question at a time. Yes, clocks do run more slowly. Planes travel about a million times more slowly than c (so ? is about 1.0000000000005), but atomic clocks are very precise and so this tiny effect effect can actually be measured. In 1971, J. Haefele and R. Keating took atomic clocks on airliners travelling both East (with the Earth rotating underneath them: we could call these "slow frames") and West (these planes have the Earth's rotation speed plus their own, and return to where they came from). Apart from some complications due to the gravitational field variations and their acceleration (which are dealt with by general relativity), this is like the twin paradox, and it gave results in agreement with the relativistic prediction. (See the original paper by J.C. Hafele and R. E. Keating, Science 177, 166 (1972) for details. Also see the diagrams and discussion about this experiment and its complications on the FAQ in high school physics.)
Do people age more slowly? We don't know whether people age more slowly, because even cosmonauts don't travel fast enough for the effect to be statistically observable on their life spans*. However, people's ages are determined by physical and chemical processes in our bodies. Certainly we expect that people would age more slowly at relativistic speeds. Particles certainly do. Particle accelerators generate some short lived particles (eg muons or pions) that travel within a fraction of a percent of c, and (in the laboratory frame) they survive for much longer than their lifetime when at rest in the lab frame. Muons with a half life of 1.5 microseconds are also created several tens of km above the Earth in the upper atmosphere by cosmic rays. Travelling 50 km at c would take 170 microseconds or 110 half lives, so we should expect their numbers to be reduced by a factor of 2110 ~ 1033 (ie effectively none) to reach the surface. In fact they are measured at sea level and at various altitudes, with rates that agree with the relativistic dilation of their half lives. Time dilation happens, however counter-intuitive it may seem at first.
* Low orbits are the fastest, travelling around the Earth in about 90 minutes, which gives ? of about 1.0000000003. Suppose that a cosmonaut spent 2 years in space. Time dilation due to special relativity (neglecting general relativistic effects) would give an expected lifetime increase of 20 milliseconds. Lives, let alone life expectancies, are not measured that precisely!
How big are time dilation effects? Note the shape of the curve above: ? only starts to become large at speeds close to c. At 0.99*c, ? is 7. But in many modern devices, electrons are accelerated to higher speeds than this. In a typical electron accelerator used to treat cancers, the electrons have an energy of 20 MeV (see Module 5). The speed of such electrons is 0.9997*c and ? is 40.
Now of course an electron cannot go much faster than this, but it can have a lot more energy. In the Large Electron-Positron collider in Europe's nuclear research lab CERN, electrons (and positrons, or anti-electrons) were accelerated to energies of 100 GeV. For such particles, v = 0.999 999 999 95*c and ? is 200,000. Yes, time is slowed down by that factor. And the momentum is increased by that factor too: something that is rather important in the design of the collider because these electrons must be turned to go in a circle.
Nature can produce even larger particle energies. Some particles striking the Earth's upper atmosphere have energies that exceed 2*1020 eV. If such particles are protons (with mass of about 1 GeV), their speeds would be 0.999 999 999 999 999 999 999 995 c. For them, ? is 1011. Now the age of the universe is about 13 billion years for us, but for such particles, the age of the universe would be about (13 billion years/1011), ie about a month. Such a particle could cross the visible universe in a matter of months (their time).