͢͡
His argument was simple, based on the equally simple fact that
we cannot be in two places at once.
We are accustomed to feeling that we share the same reality with
those around us because we appear to share the same experiences as
we look about together. But that is an illusion created by the fast
speed of light.
When I observe something happening now, say, a car crash down
the street or two lovers kissing under a lamppost as I walk nearby,
neither of these events happened now, but rather then. The light
that enters my eye was reflected off the car or the people just a little
bit earlier.
Similarly when I take a photo of a beautiful landscape, as I just did
in Northern Ireland where I began writing this chapter, the scene I
captured is not a scene merely spread out in space, but rather in
space and time. The light from the distant pillared cliffs at Giant’s
Causeway perhaps a kilometer away left those cliffs well before
(perhaps thirty-millionths of a second before) the light from the
people in the foreground scrambling over the hexagonal lava pods
left to reach my camera at the same time.
With this realization, Einstein asked himself what two events that
one observer views as happening at the same time in two different
locations would look like for another observer moving with respect
to the first observer while the observations were being made. The
example he considered involved a train, because he lived in
Switzerland at a time when a train was leaving about every five
minutes for somewhere in the country from virtually any other place
in the country.
Imagine the picture shown below in which lightning hits two
points beside either end of a train that are equidistant from observer
A, who is at rest with respect to those points, and observer B on a
͢͢
moving train, who passes by A at the instant A later determines the
lightning bolts struck:
A little while later A will see both lightning flashes reaching him
at the same time. B, however, will have moved during this time.
Therefore the light wave bringing the information that a flash
occurred on the right will already have passed B, and the light
bringing the information about the flash on the left will not yet have
reached him.
B sees the light coming from either end of his train, and indeed
the flash at the front end occurs before the flash at the rear end.
Since he measures the light as traveling toward him at speed c, and
since he is in the middle of his train, he concludes therefore that the
right-hand flash must have occurred before the left-hand flash.
Who is right here? Einstein had the temerity to suggest that both
observers were right. If the speed of light were like other speeds,
then B would of course see one wave before the other, but he would
see them traveling toward him at different speeds (the one he was
moving toward would be faster and the one from which he was
moving away would be slower), and he would therefore infer that
the events happened at the same time. But because both light rays
are measured by B to be traveling toward him at the same speed, c,
the reality he infers is completely different.
As Einstein pointed out, when defining what we mean by
different physical quantities, measurement is everything. Imagining a
reality that is independent of measurement might be an interesting
philosophical exercise, but from a scientific perspective it is a sterile
ͣ͢
line of inquiry. If both A and B are located at the same place at the
same time, they must both measure the same thing at that instant,
but if they are in remote locations, almost all bets are off. Every
measurement that B can make tells him that the event at the forward
end of his train happened before the next, while every measurement
that A makes tells him the events were simultaneous. Since neither A
nor B can be at both places at the same time, their measurement of
time at remote locations depends upon remote observations, and if
those remote observations are built on interpreting what light from
those events reveals, they will differ on their determination of which
remote events are simultaneous, and they will both be correct.
Here and now is only universal for here and now, not there and
then.
• • •
I wrote “almost all” bets are off for a reason. For as strange as the
example I just gave might seem, it can actually be far stranger.
Another observer, C, traveling on a train moving in the opposite
direction from B on a third track beside A and B will infer that the
event on the left side (the forward part of his train) occurred before
the event on the right-hand side. In other words, the order of the
events seen by the two observers B and C will be completely
reversed. One person’s “before” will be the other’s “after.”
This presents a big apparent problem. In the world in which most
of us believe we live, causes happen before effects. But if “before” and
“after” can be observer dependent, then what happens to cause and
effect?
Remarkably, the universe has a sort of built-in catch-22, which
ends up ensuring that while we need to keep an open mind about
reality, we don’t have to keep it so open that our brains fall out, as
the publisher of the New York Times used to say. In this case, Einstein
ͤ͢
demonstrated that a reversal of the time ordering of distant events
brought about by the constancy of light is only possible if the events
are far enough apart so that a light ray will take longer to travel
between them than the inferred time difference between the two
events. Then, if nothing can travel faster than light (which turns out
to be another consequence of Einstein’s effort to coordinate Galileo
and Maxwell), no signal from one event could ever arrive in time to
affect the other, so one event could not be the cause of the other.
But what about two different events that occur some time apart at
the same place. Will different observers disagree about them? To
analyze this situation Einstein imagined an idealized clock on a train.
The ticks of the clock occur each time a light ray sent from a clock
on one side of the train reflects off a mirror located on the other side
and returns to the clock on the original side of the train (see below).
Let us say each round-trip (tick) is a millionth of a second. Now
consider an observer on the ground watching the same round-trip.
Because the train is moving, the light ray travels on the trajectory
shown below, with the clock and mirror having moved between the
time of emission and reception.
Clearly this light ray traverses a greater distance relative to the
observer on the ground than it does relative to the clock on the train.
However, the light ray is measured to be traveling at the same speed,
ͥ͢
c. Thus, the round-trip takes longer. As a result, the one-millionth-
&nbs
p; of-a-second click of the clock on the train is observed on the ground
to take, say, two-millionths of a second. The clock on the train is
therefore ticking at half the rate of a clock on the ground. Time has
slowed down for the clock on the train.
Stranger still, the effect is completely reciprocal. Someone aboard
the train will observe a clock on the ground as ticking at half the rate
of their clock on the train, as the figure would look identical for
someone on the train watching a light travel between mirrors placed
on the ground.
This may make it seem like the slowing of clocks is merely an
illusion, but once again, measurement equals reality, although in this
case a little more subtly than for the case of simultaneity. To
compare clocks later to see which, if any, of the observers’ clocks has
really slowed down, at least one of the observers will have to return
to join the other. That observer will have to change his or her
uniform motion, either by slowing down and reversing, or by
speeding up from (apparent) rest and catching up with the other
observer.
This makes the two observers no longer equivalent. It turns out
that the observer who does the accelerating or the decelerating will
find, when she arrives back at the starting position, that she has
actually aged far less than her counterpart, who has been in uniform
motion during the whole time.
This sounds like science fiction, and indeed it has provided the
fodder for a great deal of science fiction, both good and bad, because
in principle it allows for precisely the kind of space travel around the
galaxy that is envisaged in so many movies. There are a few rather
significant glitches, however. While it does make it possible in
principle for a spacecraft to travel around the galaxy in a single
human lifetime, so that Jean-Luc Picard could have his Star Trek
ͣ͜
adventures, those back at Star Fleet command would have a hard
time exerting command and control over any sort of federation. The
mission of ships such as the USS Enterprise might be five years long
for the crew on board, but each round-trip from Earth to the center
of the galaxy of a ship at near light speed would take sixty thousand
years or so as experienced by society back home. To make matters
worse, it would take more fuel than there is mass in the galaxy to
power a single such voyage, at least using conventional rockets of the
type now in use.
Nevertheless, science fiction woes aside, “time dilation”—as the
relativistic slowing of clocks is called with regard to moving objects
—is very much real, and very much experienced every day here on
Earth. At high-energy particle accelerators such as the Large Hadron
Collider, for example, we regularly accelerate elementary particles to
speeds of 99.9999 percent of the speed of light and rely on the effects
of relativity when exploring what happens.
But even closer to home, relativistic time dilation has an impact.
We on Earth are all bombarded every day by cosmic rays from space.
If you had a Geiger counter and stood out in a field, the counter
would click at a regular rate every few seconds, as it recorded the
impact of high-energy particles called muons. These particles are
produced where high-energy protons in cosmic rays smash into the
atmosphere, producing a shower of other, lighter particles—
including muons—which are unstable, with a lifetime of about one-
millionth of a second, and decay into electrons (and my favorite
particles, neutrinos).
If it weren’t for time dilation, we would never detect these muon
cosmic rays on Earth. Because a muon traveling at close to the speed
of light for a millionth of a second would cover about three hundred
meters before decaying. But the muons raining down on Earth make
it twenty kilometers, or about twelve and a half miles or so, from the
ͣ͝
upper atmosphere, in which they are produced, down to our Geiger
counter. This is possible only if the muons’ internal “clocks” (which
prompt them to decay after one-millionth of a second or so) are
ticking slowly relative to our clocks on Earth, ten to one hundred
times more slowly than they would be if they were produced at rest
here in a laboratory on Earth.
• • •
The last implication of Einstein’s realization that the speed of light
must be constant for all observers appears even more paradoxical
than the others—in part because it involves changing the physical
behavior of objects we can see and touch. But it also will help carry
us back to our beginnings to glimpse a new world beyond the
confines of our normal earthbound imagination.
The result is simply stated, even if the consequences may take
some time to digest. When I am carrying an object such as a ruler,
and moving fast compared to you, my ruler will be measured by you
to be smaller than it is for me. I might measure it to be 10 cm, say:
But to you, it might appear to be merely 6 cm:
Surely, this is an illusion, you might say, because how could the
same object have two different lengths? The atoms can’t be
compressed together for you, but not for me.
Once again, we return to the question of what is “real.” If every
measurement you can perform on my ruler tells you it is 6 cm long,
then it is 6 cm long. “Length” is not an abstract quantity but requires
a measurement. Since measurement is observer dependent, so is
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length. To see this is possible while illuminating another of
relativity’s slippery catch-22s, consider one of my favorite examples.
Say I have a car that is twelve feet long, and you have a garage that
is eight feet deep. My car will clearly not fit in your garage:
But, relativity implies that if I am driving fast, you will measure
my car to be only, say, six feet long, and so it should fit in your
garage, at least while the car is moving:
However, let’s view this from my vantage point. For me, my car is
twelve feet long, and your garage is moving toward me fast, and it
now is measured by me to be not eight feet deep, but rather four feet
deep:
Thus, my car clearly cannot fit in your garage.
So which is true? Clearly my car cannot both be inside the garage
and not inside the garage. Or can it?
Let’s first consider your vantage point, and imagine that you have
fixed big doors on the front of your garage and the back of your
garage. So that I don’t get killed while driving into it, you perform
the following. You have the back door closed but open the front
door so my car can drive in. When it is inside, you close the front
door:
ͣ͟
However, you then quickly open the back door before the front of
my car crashes, letting me safely drive out the back:
Thus, you have demonstrated that my car was inside your garage,
which of course it was, because it is small enough to fit in it.
However, remember that, for me, the time ordering of d
istant
events can be different. Here is what I will observe.
I will see your tiny garage heading toward me, and I will see you
open the front door of the garage in time for the front of my car to
pass through.
I will then see you kindly open the back door before I crash:
After that, and after the back of my car is inside the garage, I will
see you close the front door of your garage:
ͣ͠
As will be clear to me, my car was never inside your garage with
both doors closed at the same time because that is impossible. Your
garage is too small.
“Reality” for each of us is simply based on what we can measure.
In my frame the car is bigger than the garage. In your frame the
garage is bigger than my car. Period. The point is that we can only be
in one place at one time, and reality where we are is unambiguous.
But what we infer about the real world in other places is based on
remote measurements, which are observer dependent.
But the virtue of careful measurement does not stop there.
The new reality that Einstein unveiled, based as it was on the
empirical validity of Galileo’s law, and Maxwell’s remarkable
unification of electricity and magnetism, appears on its face to
replace any last vestige of objective reality with subjective
measurement. As Plato reminds us, however, the job of the natural
philosopher is to probe deeper than this.
It is said that fortune favors the prepared mind. In some sense,
Plato’s cave prepared our minds for Einstein’s relativity, though it
remained for Einstein’s former mathematics professor Hermann
Minkowski to complete the task.
Minkowski was a brilliant mathematician, eventually holding a
chair at the University of Göttingen. But in Zurich, where he was
one of Einstein’s professors, he was a brilliant mathematician whose
classes Einstein skipped, because while he was a student, Einstein
appeared to have a great disdain for the significance of pure
mathematics. Time would change that view.
Recall that the prisoners in Plato’s cave also saw from shadows on
their wall that length apparently had no objective constancy. The
shadow of a ruler might at one time look like this, at 10 cm:
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 7
