Lawrence Krauss - The Greatest Story Ever Told--So Far Page 6

  Everything we see in our daily lives comes to rest. Everything, that

  is, except the Moon and the planets, which is perhaps one reason

  that these were felt to be special in antiquity, guided by angels or

  gods.

  However, every sense that we have that we are at rest is an

  illusion. In the example I gave earlier of throwing a ball up and

  catching it while in a moving plane, you will eventually be able to tell

  that your plane is moving when you feel the bouncing of turbulence.

  But even when the plane is on the tarmac, it is not at rest. The

  airport is moving with the Earth at about 30 km/sec around the Sun,

  and the Sun is moving about 200 km/sec around the galaxy, and so

  on.

  Galileo codified this with his famous assertion that the laws of

  physics are the same for all observers moving in a uniform state of

  motion, i.e., at a constant velocity in a straight line. (Observers at rest

  are simply a special case, when velocity is zero.) By this he meant

  that there is no experiment you can perform on such an object that

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  can tell you it is not at rest. When you look up in the air at an

  airplane, it is easy to see that it is moving relative to you. But, there is

  no experiment you can perform on the ground or on the plane that

  will distinguish whether the ground on which you are standing is

  moving past the plane, or vice versa.

  While it seems remarkable that it took so long for anyone to

  recognize this fundamental fact about the world, it does defy most of

  our experience. Most, but not all. Galileo used examples of balls

  rolling down inclined planes to demonstrate that what previous

  philosophers thought was fundamental about the world—the

  retarding force of friction that makes things eventually settle at rest

  —was not fundamental at all but rather masked an underlying

  reality. When balls roll down one plane and up another, Galileo

  noted, on smooth surfaces the balls would rise back to the same

  height at which they started. But by considering balls rolling up

  planes of ever-decreasing incline, he showed that the balls would

  have to roll farther to reach their same original height. He then

  reasoned that if the second incline disappeared entirely, the balls

  would continue rolling at the same speed forever.

  This realization was profoundly important and fundamentally

  changed much about the way we think about the world. It is often

  simply called the Law of Inertia, and it set up Newton’s law of

  motion, relating the magnitude of an external force to the observed

  acceleration of an object. Once Galileo recognized that it took no

  force to keep something moving at a constant velocity, Newton

  could make the natural leap to propose that it took a force to change

  its velocity.

  The heavens and the Earth were no longer fundamentally

  different. The hidden reality underlying the motion of everyday

  objects also made clear that the unending motion of astronomical

  objects was not supernatural, setting the stage for Newton’s

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  Universal Law of Gravity, further demoting the need for angels or

  other entities to play a role in the cosmos.

  Galileo’s discovery was thus fundamental to establishing physics

  as we know it today. But so was Maxwell’s later brilliant unification

  of electric and magnetic forces, which established the mathematical

  framework on which all of current theoretical physics is built.

  • • •

  As Albert Einstein began his journey in this rich intellectual

  landscape, he quickly spied a deep and irreconcilable chasm running

  through it: both Galileo and Maxwell could not be right at the same

  time.

  More than twenty years ago, when my daughter was an infant, I

  first began to think about how to explain the paradox that young

  Einstein struggled with, and a good example literally hit me on the

  head while driving her in my car.

  Galileo had demonstrated that as long as I am driving safely and

  at a constant speed and not accelerating suddenly, the laws of

  physics in our car should be indistinguishable from the laws of

  physics that would be measured in the laboratories in the physics

  building to which I was driving to work. If my daughter was playing

  with a toy in the backseat, she could throw the toy up in the air and

  expect to catch it without any surprises. The intuition her body had

  built up to play at home would have served her well in the car.

  However, riding in the car did not lull her to sleep like many

  young children, but rather made her anxious and uncomfortable.

  During our trip, she got sick and projectile-vomited, and the vomit

  followed a trajectory well described by Newton, with an initial speed

  of, say, fifteen miles per hour, and a nice parabolic trajectory in the

  air, ending on the back of my head.

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  Say my car was coasting to a red light at this time at a relatively

  slow speed, say, ten miles per hour. Someone on the ground

  watching all of this would see the vomit traveling at 25 miles per

  hour, the speed of the car relative to them (10 mph) plus the speed

  of the vomit (15 mph), and its trajectory would be well described by

  Newton again, with this higher speed (25 mph) as it traveled toward

  my (now moving) head.

  So far so good. Here’s the problem, however. Now that my

  daughter is older, she loves to drive. Say she is driving behind a

  friend’s car and dials him on her cell phone (hands-free, for safety) to

  tell him to turn right to get to the place they are both going. As she

  talks into the phone, electrons in the phone jiggle back and forth

  producing an electromagnetic wave (in the microwave band). That

  wave travels to the cell phone of her friend at the speed of light

  (actually it travels up to a satellite and then gets beamed down to her

  friend, but let’s ignore that complication for the moment) and is

  received in time for him to make the correct turn.

  Now, what would a person on the ground measure? Common

  sense would suggest that the microwave signal would travel from my

  daughter’s car to her friend’s car at a speed equal to the speed of

  light, as might be measured by a detector in my daughter’s car (label

  it with the symbol c), plus the speed of the car.

  But common sense is deceptive precisely because it is based on

  common experience. In everyday life we do not measure the time it

  takes light, or microwaves, to travel from one side of the room to

  another or from one phone to a nearby phone. If common sense

  applied here, that would mean someone on the ground (with a

  sophisticated measuring apparatus) would measure the electrons in

  my daughter’s phone jiggling back and forth and observe the

  emanation of a microwave signal, which would be traveling at a

  speed c plus, say, ten miles per hour.

  ͥ͡

  However, the great triumph of Maxwell was to show that he

  could calculate the speed of electromagnetic waves emanated by an

  oscillating charge purely by measuring the stre
ngth of electricity and

  magnetism. Therefore if the person on the ground observed the

  waves having speed c plus 10 mph, then for that person the strength

  of electricity and magnetism would have to be different from the

  values that my daughter would observe, for whom the waves were

  moving at a speed c.

  But Galileo tells us this is impossible. If the measured strengths of

  electricity and magnetism differed between the two observers, then

  it would be possible to know who was moving and who was not,

  because the laws of physics—in this case electromagnetism—would

  take on different values for each observer.

  So, either Galileo or Maxwell had to be right, but not both of

  them. Perhaps because Galileo had been working when physics was

  more primitive, most physicists came down closer to the side of

  Maxwell. They decided that the universe must have some absolute

  rest frame and that Maxwell’s calculations applied in that frame only.

  All observers moving with respect to that frame would measure

  electromagnetic waves to have a different speed relative to

  themselves than Maxwell had calculated.

  A long scientific tradition gave physical support to this idea. After

  all, if light was an electromagnetic disturbance, what was it a

  disturbance of? For thousands of years, philosophers had speculated

  about an “ether,” some invisible background material filling all of

  space, and it became natural to suspect that electromagnetic waves

  were traveling in this medium, just as sound waves travel in water or

  air. Electromagnetic waves would travel with some fixed,

  characteristic speed in this medium (the speed calculated by

  Maxwell), and observers moving with respect to this background

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  would observe the waves as faster or slower, depending on their

  relative motion.

  While intuitively sensible, this notion was a cop-out, because if

  you think back to Maxwell’s analysis, it would mean that these

  different observers in relative motion would measure the strength of

  electricity and magnetism to be different. Perhaps it was deemed to

  be acceptable because all speeds obtainable at the time were so small

  compared to the speed of light that any such differences would have

  been minute at best and would certainly have escaped detection.

  The actor Alan Alda once turned the tables on conventional

  wisdom at a public event I attended by saying that art requires hard

  work, and science requires creativity. While both require both, what

  I like about his version is that it stresses the creative, artistic side of

  science. I would add to this statement that both endeavors require

  intellectual bravery. Creativity alone amounts to nothing if it is not

  implemented. Novel ideas generally stagnate and die without the

  courage to implement them.

  I bring this up here because perhaps the true mark of Einstein’s

  genius was not his mathematical prowess (although, contrary to

  conventional wisdom, he was mathematically talented), but his

  creativity and his intellectual confidence, which fueled his

  persistence.

  The challenge that faced Einstein was how to accommodate two

  contradictory ideas. Throwing one out is the easy way. Figuring out a

  way to remove the contradiction required creativity.

  Einstein’s solution was not complex, but that does not mean it

  was easy. I am reminded of an apocryphal story about Christopher

  Columbus, who got a free drink in a bar before departing to find the

  New World by claiming he could balance an egg upright on top of

  the bar. After the barman accepted the bet, Columbus broke the tip

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  off the egg and placed it easily upright on the counter. He never

  mentioned not cracking it, after all.

  Einstein’s resolution of the Galileo-Maxwell paradox was not that

  different. Because, if both Maxwell and Galileo were right, then

  something else had to be broken to fix the picture.

  But what could it be? For both Maxwell and Galileo to be right

  required something that was clearly crazy: in the example I gave,

  both observers would have to measure the velocity of the microwave

  emitted by my daughter’s cell phone to be the same relative to them,

  instead of measuring values differing by the speed of the car.

  However, Einstein asked himself an interesting question, What

  does it mean to measure the velocity of light, after all? Velocity is

  determined by measuring the distance something travels in a certain

  time. So Einstein reasoned as follows: it is possible for two observers

  to measure the same speed for the microwave relative to each of

  them, as long as the distance each measures the ray to travel relative

  to themselves during a fixed time interval (e.g., say, one second, as

  measured by each of them in their own frame of reference) is the

  same.

  But this too is a little crazy. Consider the simpler example of the

  projectile vomit. Remember that in my frame it travels from her

  mouth in the backseat to hit my head, say, three feet away, in about

  one-quarter second. But for someone on the ground the car is

  traveling at 10 miles per hour during this period, which is about 14.5

  feet per second. Thus for the person on the ground, in one-quarter

  second the vomit travels about 3.6 feet plus 3 feet, or a total 6.6 feet.

  Hence for the two observers, the distances traveled by the vomit

  in the same time is noticeably different. How could it be that for the

  microwave the distances both observers measure could be the same?

  The first hint that perhaps such craziness is possible is that

  electromagnetic waves travel so fast that in the time it takes the

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  microwaves to get from one car to another, each car has moved

  hardly at all. Thus any possible difference in measured distance

  traveled during this time for the two observers would be essentially

  imperceptible.

  But Einstein turned this argument around. He realized that both

  observers had not actually measured the distances traveled by the

  microwaves over human-scale distances, because the relevant times

  appropriate for light to travel over human-scale distances were so

  short that no one could have measured them at the time. And

  similarly, on human timescales light would travel such large

  distances that no one could measure those distances directly either.

  Thus, who was to say that such crazy behavior couldn’t really

  happen?

  The question then became, What is required for it to actually

  occur? Einstein reasoned that for this seemingly impossible result to

  be possible, the two different observers must measure distances

  and/or times differently from each other in just such a way that light,

  at least, would traverse the same measured distance in the same

  measured time for both observers. Thus, for example, it would be as

  if the observer on the ground in the vomit case were to measure the

  vomit traversing 6.6 feet, but would somehow also infer the time

  interval over which this happened to be larger than I would measure<
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  it inside my car, so that the inferred speed of the vomit would be the

  same relative to him as I measure it to be relative to me.

  Einstein then made the bold assertion that something like this

  does happen, that both Maxwell and Galileo were correct, and that

  all observers, regardless of their relative state of motion, would

  measure any light ray to travel at the same speed, c, relative to them.

  Of course, Einstein was a scientist, not a prophet, so he didn’t just

  claim something outlandish on the basis of authority. He explored

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  the consequences of his claim and made predictions that could be

  tested to verify it.

  In doing so he moved the playing field of our story from the

  domain of light to the domain of intimate human experience. He not

  only forever changed the meaning of space and time, but also the

  very events that govern our lives.

  ͢͠

  C h a p t e r 5

  A S T I T C H I N T I M E

  He stretcheth out the north over the empty place, and hangeth

  the earth upon nothing.

  —JOB 26:7

  The great epic stories of ancient Greece and Rome revolve

  around heroes such as Odysseus and Aeneas, who challenged the

  gods and often outwitted them. Things have not changed that much

  for more modern epic heroes.

  Einstein overcame thousands of years of misplaced human

  perception by showing that even the God of Spinoza could not

  impose his absolute will on space and time, and that each of us

  evades those imaginary shackles every time we look around us and

  view new wonders amid the stars above. Einstein emulated artistic

  geniuses such as Vincent van Gogh and reasoned with the

  parsimony of Ernest Hemingway.

  Van Gogh died fifteen years before Einstein developed his ideas

  on space and time, but his paintings make it clear that our

  perceptions of the world are subjective. Picasso may have had the

  chutzpah to claim that he painted what he saw, even as he produced

  representations of disjointed people with body parts pointing in

  different directions, but van Gogh’s masterpieces demonstrate that

  the world can look very different to different people.

  So too, Einstein explicitly argued, for the first time as far as I know

  in the history of physics, that “here” and “now” are observer-

  dependent concepts and not universal ones.