TIME DILATION
In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses.
An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself.
When two observers are in relative uniform motion and uninfluenced by
any gravitational mass, the point of view of each will be that the
other's (moving) clock is ticking at a
slower rate than the local
clock. The faster the relative velocity, the greater the magnitude of
time dilation. This case is sometimes called special relativistic time dilation.
For instance, two rocket ships (A and B) speeding past one another in
space would experience time dilation. If they somehow had a clear view
into each other's ships, each crew would see the others' clocks and
movement as going too slowly. That is, inside the
frame of reference of Ship A, everything is moving normally, but everything over on Ship B appears to be moving slower (and vice versa).
From a local perspective, time registered by clocks that are at rest
with respect to the local frame of reference (and far from any
gravitational mass) always appears to pass at the same rate. In other
words, if a new ship, Ship C, travels alongside Ship A, it is "at rest"
relative to Ship A. From the point of view of Ship A, new Ship C's time
would appear normal too.
A question arises: If Ship A and Ship B both think each other's time
is moving slower, who will have aged more if they decided to meet up?
With a more sophisticated understanding of relative velocity time
dilation, this seeming
twin paradox
turns out not to be a paradox at all (the resolution of the paradox
involves a jump in time, as a result of the accelerated observer turning
around). Similarly, understanding the twin paradox would help explain
why astronauts on the ISS age slower (e.g. 0.007 seconds behind for
every 6 months) even though they are experiencing relative velocity time
dilation.
A comparison of
muon
lifetimes at different speeds is possible. In the laboratory, slow
muons are produced, and in the atmosphere very fast moving muons are
introduced by cosmic rays. Taking the muon lifetime at rest as the
laboratory value of 2.22 μs, the lifetime of a cosmic ray produced muon
traveling at 98% of the speed of light is about five times longer, in
agreement with observations.
In this experiment the "clock" is the time taken by processes leading
to muon decay, and these processes take place in the moving muon at its
own "clock rate", which is much slower than the laboratory clock.
People have a strong intuitive notion about what "time" is. It works
very well in every-day use, but unfortunately, it's wrong. And because
it works so well, it's going to be difficult to substitute a different
intuition.
We can, at least, pinpoint exactly where intution fails you. You
have the notion that there's a single "time" that's the same for
everybody, some universal clock ticking away that we can all agree on,
and all actual clocks are their best representation of that real clock.
This is the part that's false. It turns out that in reality, every
"frame of reference" has its own little clock. A "frame of reference"
is a bunch of objects all moving together in space. They all have the
same clock, because they're moving together. Viewed within that
reference frame, all of the laws of physics remain exactly as we expect
them to be, and we all agree about what it means for two things to be
happening "at the same time".
(I need to clarify one thing at this point: I'm talking about
inertial
frames of reference. That is, those that are moving at a constant
speed, or not moving at all, as opposed to one that is accelerating. Or
put another way, one that is experiencing no force. There will be no
force anywhere in this. In physics we need to be very precise in our
terminology, or we'll be led astray. So imagine we're talking about
spaceships in outer space.)
The problem is that what's true
within a reference frame doesn't apply
between
reference frames. That is, if your reference frame is moving, and I
take a look at it, your clock will be moving differently from mine. In
fact, it will appear to be moving slower.
The interesting part is that if you look at my clock, you'll think that
my clock is moving slower.
Which of us is right? Both of us! That's the unintuitive part.
Einstein gave us a way to mathematically determine exactly how much slower the other clock is moving, and it says that
both of us
think that the other clock is slower. But when the difference in speed
is small, the difference in time is small, so you're used to thinking
that the clocks are the same. But when the speed gets very close to the
speed of light (more like 90%; even 25% of the speed of light has only a
very small correction factor) you can notice that the times are
different.
Neither one of us thinks our clock is running fast, or slow. There's
no "force" slowing the clock down. It's just time, running, and it
seems the same to us. Any physics experiment we do within our reference
frame will behave exactly as if we were stopped.
How is it possible that we can BOTH see the clocks going slower in
the other reference frame? What you have to give up is the idea that
there's a universal, "correct" reference frame. You imagine that you
can jump into the other frame and say, "Hey, your clock is going slow!"
but you can only do that by accelerating. And when you accelerate, the
whole thing falls down, because this only applies to inertial reference
frames that aren't accelerating. When you accelerate, now YOU are the
one who's doing something special, and your "reference frame" acts
weird.
And yes, this has been confirmed by experiment. They send atomic
clocks out on airplanes and space ships, and we can see that they do
come back as if they ran slower. Why is it the clocks on the planes
that ran slow, and not the ones on the ground? Because the airplane is
the one that accelerated away, and then decelerated to come back. The
numbers are so small that only the most precise clocks can measure it,
but it's very real.
So... if you want to make this intuitive, the best thing you can do
is to realize that time is always different in somebody else's frame of
reference, and that neither one is wrong, but you can't compare the two
without accelerating to join the other frame. And it's the one who
accelerates who changes to join the other frame of reference.
where Δ
t is the time interval between
two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock), this is known as the
proper time, Δ
t' is the time interval between those same events, as measured by another observer, inertially moving with velocity
v with respect to the former observer,
v is the relative velocity between the observer and the moving clock,
c is the
speed of light, and
is the Lorentz form.
Thus the duration of the clock cycle of a moving clock is found to be
increased: it is measured to be "running slow". The range of such
variances in ordinary life, where
v ≪ c,
even considering space travel, are not great enough to produce easily
detectable time dilation effects and such vanishingly small effects can
be safely ignored. It is only when an object approaches speeds on the
order of 30,000 km/s (1/10 the speed of light) that time dilation becomes important.