—PSALMS 104:5
When Galileo Galilei was being tried in 1633 for heresy for “holding as true the false doctrine taught by some that the Sun is the center of the world,” he allegedly muttered under his breath in front of his Church inquisitors, “And yet it moves.” With these words, his revolutionary nature once again sprang forth, in spite of his having been forced to publicly adhere to the archaic position that the Earth was fixed.
While the Vatican eventually capitulated on Earth’s motion, the poor God of the Psalms never got the news. This is somewhat perplexing since, as Galileo showed a year before the trial, a state of absolute rest is impossible to verify experimentally. Any experiment that you perform at rest, such as throwing a ball up in the air and catching it, will have an identical result if performed while moving at a constant speed, as, say, might happen while riding on an airplane in the absence of turbulence. No experiment you can perform on the plane, if its windows are closed, will tell you whether the plane is moving or standing still.
While Galileo started the ball rolling, both literally and metaphorically, in 1632, it took another 273 years to fully lay to rest this issue (issues, unlike objects, can be laid to rest). It would take Albert Einstein to do so.
Einstein was not a revolutionary in the same sense as Galileo, if by this term one describes those who tear down the dictates of the authorities who came before, as Galileo had done for Aristotle. Einstein did just the opposite. He knew that rules that had been established on the basis of experiment could not easily be tossed aside, and it was a mark of his genius that he didn’t.
This is so important I want to repeat it for the benefit of those people who write to me every week or so telling me that they have discovered a new theory that demonstrates everything we now think we know about the universe is wrong—and using Einstein as their exemplar to justify this possibility. Not only is your theory wrong, but you are doing Einstein a huge disservice: rules that have been established on the basis of experiment cannot easily be tossed aside.
• • •
Albert Einstein was born in 1879, the same year that James Clerk Maxwell died. It is tempting to suggest that their combined brilliance was too much for one simple planet to house at the same time. But it was just a coincidence, albeit a fortuitous one. If Maxwell hadn’t preceded him, Einstein couldn’t have been Einstein. He came from the first generation of young scientists who grew up wrestling with the new knowledge about light and electromagnetism that Faraday and Maxwell had generated. This was the true forefront of physics for young Turks such as Einstein near the end of the nineteenth century. Light was on everyone’s mind.
Even as a teenager, Einstein was astute enough to realize that Maxwell’s beautiful results regarding the existence of electromagnetic waves presented a fundamental problem: they were inconsistent with the equally beautiful and well-established results of Galileo regarding the basic properties of motion, produced three centuries earlier.
Even before his epic battle with the Catholic Church over the motion of Earth, Galileo had argued that no experiment exists that can be performed by anyone to determine whether he or she is moving uniformly or standing still. But up until Galileo, a state of absolute rest was considered special. Aristotle had decided that all objects sought out the state of rest, and the Church decided that rest was so special that it should be the state of the center of the universe, namely the planet on which God had placed us.
Like a number of Aristotle’s assertions, although by no means all, this notion that a state of rest is special is quite intuitive. (For those who like to quote Aristotle’s wisdom when appealing to his “Prime Mover” argument for the existence of God, let us remember that he also claimed that women had a different number of teeth than men, presumably without bothering to check.)
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 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 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.
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 strength 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 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 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 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 oc
cur? 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 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 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.
Chapter 5
* * *
A STITCH IN TIME
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.
The Greatest Story Ever Told—So Far Page 5
