Lawrence Krauss - The Greatest Story Ever Told--So Far

by Why Are We Here (pdf)

  ͢͡

  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

  ͣ͞

  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: