by Carlos Calle
You may be confusing the physical flow of time with the psychological passage of time that we all experience. Relativity requires that actual physical time and space change as the observer moves, but this motion must be at speeds much greater than any human being has ever experienced. That’s why these changes don’t appear intuitive to us.
Your final paper was concerned with your E=mc2 equation. You called it a consequence of relativity. How was this a follow-up and what does the equation mean?
I considered the relative motion of an atom emitting light and, by using the equations of relativity, showed that the mass of the atom decreased after the light emission. The E=mc2 equation says that energy and mass are equivalent and that one can change into the other under certain circumstances.
Professor, you’ve whetted my appetite for your explanations of your theories. I’m beginning to get a glimpse of the implications of your astonishing discoveries that took place during a single year. I’d like to come back to these topics later on in our conversation.
It would be my pleasure to talk to you about these matters.
OF TIME AND SPACE: THE THEORY OF RELATIVITY
Einstein’s most celebrated discovery, the theory of relativity, changed forever our understanding of space and time. Published during his year of wonders of 1905, it quickly attracted the attention of the world’s best-known physicists. Later known as the special theory of relativity, it appears to contradict our everyday experiences, and for many years after its publication people found it to be beyond comprehension. The British scientist Arthur Eddington was once asked if it was true that only two people in the world besides Einstein understood the theory. “I am wondering who the other one might be,” was his tongue-in-cheek reply.
Professor Einstein, how did you come to discover the theory of relativity?
It’s difficult to know how one discovers something – the mind is motivated by various complexities with different weights. The special theory took final form in about five weeks in 1905, after ten years of trying to resolve a paradox that I encountered at the age of 16: what would an observer see if he pursued a beam of light with the same velocity as that of the light? The definitive answer to the question required two assumptions, which became the foundation of the special theory: the principle of relativity and the principle of the constant velocity of light.
I have the feeling that I’d need to understand these two principles if I hope to ever understand the theory of relativity. Could you, please, explain them?
I’ll use an easy illustration. If I stand inside the sleeper cabin of a train travelling on very smooth tracks at a steady speed and drop a stone, I see the stone descend in a straight line. If the cabin has the curtains drawn closed so that I can’t look outside, the motion of the stone won’t reveal to me whether the train is moving relative to the Earth or is stationary. Moreover, no experiment I may attempt inside this cabin can ever allow me to discover the motion of the train. Everything behaves in the same way whether the train moves or remains at rest. The laws of physics are the same for all observers in steady motion or at rest. This is the principle of relativity.
And this is true for any speed of the train?
Yes, the principle of relativity applies to any state of motion as long as this motion is at a steady or constant speed, with no accelerations or turns. And a constant speed includes zero speed, or rest. Rest and motion depend on a reference point. You may think that you’re at rest while sitting on that chair. A space traveller will see you spinning with the Earth at 1,500 kilometres per hour. Rest and motion are relative concepts and the laws of physics apply equally to them. Once I understood this, I was able to resolve my paradox, which leads us to the second principle.
I think I’m ready for this now.
The principle of the constant velocity of light was not an easy notion to formulate. Consider again the example of an observer riding alongside a beam of light. Such an observer should see the stationary front edge of the beam. However, a stationary light wave seems to be an impossibility on the basis of scientific experiments and well-established theory. Moreover, on the basis of my principle of relativity, all observers in constant motion or at rest should experience the same phenomena. According to this principle, then, all such observers should measure the same speed of light. That was the resolution of my paradox, for no observer could ever hope to see the front edge of a light beam. Regardless of how fast they move, all observers should see light travelling at the same speed as that measured by an observer who, relative to Earth, is at rest. This insight became known as the principle of the constant velocity of light.
That insight, as you call your great discovery, is perhaps one of the most difficult ideas for people to grasp.
That’s because it’s not an intuitive notion. What is intuitive is that if you are a passenger on a train, for example, and the train is moving at 40 kph and you’re walking from the back to the front of a train car at 5 kph, someone outside the train would say that you’re moving at 45 kph. But it seems different with light. If you shine a beam of light from the back of the moving train, the light, the photons that your lamp sends off, travels at a speed of about a billion kph, a speed that I call c. In this case, a pedestrian outside the train doesn’t measure c plus 40 kph, but only c.
Why is it different with light? Why doesn’t the pedestrian outside the train measure the speed of light to be c plus 40 kph in the same way that he measures the passenger’s speed to be 40 plus 5 kph? I’m confused.
You should be confused. I was in conflict with this idea for a long time, because there’s an apparent contradiction. The solution to this dilemma came to me one night in 1905 after a long discussion with my friend Michele Besso. That night I went home still troubled by the problem, but the next morning I had the solution and told Besso straight away. My solution dealt with the concept of time. I realized that time isn’t absolute – it’s connected to the velocity of light. It was now clear in my mind – the speed of light is fixed when you move, but time and space change. Time is relative and space is relative. That’s the essence of the special theory of relativity.
How do time and space change? That idea seems so removed from everyday experience.
In our everyday experience, everything moves at comparatively small speeds and we don’t notice anything odd about space and time. In reality, the pedestrian measuring the speed of the passenger walking at 5 kph as the train travels at 40 kph doesn’t measure 45 kph. If the pedestrian had access to extremely precise instruments, he would measure a slightly slower speed than 45 kph, about one ten-thousandth of a billionth of 1 per cent less. The reason for the difference is that time slows down when you move, affecting the value of the speed you measure. Since we can’t perceive that tiny difference, we don’t notice and think that it’s exactly 45 kph.
So, not everything is relative, as some people are fond of saying when referring to your theory. Time and space are relative but the speed of light is not relative, it’s constant.
Exactly! Space and time change when you move. They are both linked to the speed of light and change in such a way as to keep this speed always constant. Before relativity we had Newton’s theory. For Newton, space and time were fixed, but all speeds were relative. Relativity turned this around.
I can’t really say that I now understand the theory, but I think I have an appreciation of what it implies.
Understanding comes initially from our perception of the world around us. Our senses aren’t keen enough to experience relativistic effects without attaining the extremely large speeds required for their direct appreciation. Before we leave the topic, here’s yet another application of the principle of relativity for your delight. Today I’m described in Germany as a “German savant”, and in England as a “Swiss Jew”. Should it be my fate to be represented as a bête noire, I should, on the contrary, become a “Swiss Jew” for the Germans and a “German savant” for the English.
ABOUT TIME
According to Einstein’s special theory of relativity, time no longer flows at the same rate for everyone: it changes when you move. However, to be able to notice this change, you would have to be moving at close to the speed of light, and no vehicle comes even close to approaching these extremes. Subatomic particles do, however. Certain particles formed at an altitude of 10,000 metres last only a couple of microseconds – their short lives allow them to travel a mere 600 metres before disintegrating. Yet, they are found near the Earth’s surface. The theory of relativity solved this paradox. From our reference point, time flows more slowly for these particles and, as a consequence, their lives are extended.
Professor Einstein, I’d like to return to the idea that time and space change. I believe you said that time slows down when you move at great speeds. So if I move fast enough, my days would last longer.
Not according to your clock. However, if I look at your clock, I’d see that it has slowed down compared to the clock in my room. I must tell you that this effect is real, it’s not just something in my imagination nor in yours. Now, we’ve all experienced that when we’re happy and content, time seems to pass more slowly. That’s a psychological phenomenon, not a physical one. The relativistic change in the flow of time is a physical phenomenon that can and has been measured.
Would it be possible to understand this effect without complex mathematics or even without any maths at all?
We can try a thought experiment, an experiment that we can carry out in our minds, but making sure we obey the laws of physics. And it won’t require any maths. Imagine that you’re on a super-fast train that can travel at speeds close to the speed of light. If the train moves at a constant speed, everything inside it behaves in the same way as when the train is at rest.
That’s your principle of relativity, correct? You can’t distinguish rest from steady motion.
That’s right. Uniform motion can’t be detected. Let’s continue with our thought experiment. At some point during the night, while the train travels at a relativistic speed, a flashbulb located exactly in the middle of your car is fired. You’ll then see the light from the flashbulb reaching the front and back of the car at the same time.
Yes, that’s clear, Professor. Because the flash is in the middle of the train, the light from the flashbulb travels the same distance in both directions and reaches the two ends at the same time.
Now, try to imagine that I’m standing outside looking at your relativistic train with a telescope. Through a window in your train car, I observe the light travelling away from the flashbulb. Since the train is moving, I see that the back end of the car moves closer to the place where the flashbulb was when it fired. As a result, the light has a shorter distance to travel than the light travelling to the front of the car, which has actually moved farther away.
It appears that we perceive the same phenomenon differently. Is this the case?
Yes, but the important thing to understand is that two events that happened simultaneously for you – the arrival of the light at the front and back of your train car – were seen by me as not happening at the same time.
Is that what you mean when you say that time is relative?
Yes, but it’s more than that. Let me walk you through a simple illustration. Imagine the flashbulb in the train car was actually hanging from the ceiling and I placed a light sensor on the floor of the car, right under the flash, so that when the light from the flashbulb reaches the sensor, it causes it to fire the flash again. If it did that repeatedly, you can see that I could use this setup as a clock – the ticking of your clock is the firing of the flash.
You’d want both observers to measure their own time by counting these cycles, right?
Correct. For you, observing on the train, you simply see the light from the flashbulb on the ceiling travelling straight down to reach the sensor. The length of the path that the light travels is the height of the ceiling. However, I see that by the time the light reaches the sensor, the sensor would have travelled some distance forward. The path of the light that I see is longer than the one you see, so for me the clock takes longer to tick. Notice that we only have one clock, but you see it ticking faster. Time flows faster for you when you move relative to me.
And you say that this is a real phenomenon. It isn’t just your particular clock?
It isn’t just the clock. Your heart beats more slowly, your metabolic processes take longer, and you age at a slower rate.
It’s a kind of time machine. All I have to do is get on a fast spaceship for some time and I’ll return younger.
When you return, your relatives and friends would have aged faster. Yes, you could think of it as a time machine into the future.
MASTERPIECE
The special theory of relativity only applies to motion at a constant speed along a straight line (what Galileo called uniform motion). Soon after the publication of the special theory, Einstein started to try and extend it so that it would include all types of motion, uniform and accelerated. His efforts came to fruition in 1915, after a decade of extremely hard work. Along the way, he had to learn new mathematics, enlisting the help of Marcel Grossmann, one of his college friends – now a professor of mathematics – for that part of the endeavour. The result was the general theory of relativity, which scientists have called the greatest scientific theory ever developed. It is considered to be Einstein’s masterpiece.
Professor Einstein, what would you regard as your greatest achievement?
My general theory of relativity, the generalization of the special theory to include all motion. It is a system of the world.
In what way is it a generalization of the special theory?
When you consider the special theory, you see that it aims at areas beyond its domain. Why should the laws of nature remain unchanged only for the case of uniform motion? The laws of the universe should be fully independent of the type of motion. After I developed the special theory, I set out to do just that – generalize it so that it would include accelerated motion.
Why wasn’t accelerated motion in the special theory?
The special theory is based on the principle that uniform motion is undetectable – you can’t become aware of it unless you refer to an outside reference point. You can, on the other hand, detect accelerated motion. For example, you know right away when your train is starting to move, takes a turn, or stops without having to look outside for a reference point. Thus, accelerated motion is not relative and can’t be included in the special theory. Generalizing the theory to include it turned out to be extremely difficult. I didn’t know where to start.
I can begin to see the difficulty. Accelerated motion needs to be included in relativity, but since it isn’t relative, it can’t be. How did you finally resolve this impasse?
I had to look for another property that would remain undetectable under certain conditions. I had a great motivation to do so because the extension of relativity to include accelerated motion would automatically include gravitation, since motion under gravity is an accelerated motion. In 1907, while preparing a comprehensive paper on the special theory, it suddenly occurred to me that a person falling from the roof of a house wouldn’t feel his own weight – that is, he wouldn’t feel gravity. That was the most fortunate thought of my life – it made me realize that gravity is also relative and that it depends on the state of motion of the observer. This thought propelled me towards the general theory.
I see how gravity could be considered relative, since it exists for someone on the ground but not for someone falling towards the ground, as you’ve explained. Is gravity the property that remains undetectable?
Not just gravity but acceleration in general. I’ll give you an example. A group of scientists are working in a windowless laboratory aboard a spaceship that’s continuously accelerating at one g. In this ship, the scientists aren’t weightless because they feel pushed to the floor with the same force as the gravitational force back on Earth. If one of the scientists lets go of one
or two objects, these float in space until they collide with the floor of the lab, which is accelerating in their direction. From the frame of reference of the scientists, who are moving with the ship, these bodies are accelerating to the floor of the lab exactly at one g, as if the lab were on the ground on Earth. It’s impossible for the scientists to determine experimentally if they are still accelerating at one g or back on the ground on Earth. The laws of physics are the same in both instances. Acceleration and the effects of gravity are the same phenomenon.
Couldn’t you distinguish acceleration if the ship were accelerating at one-third g, for example? You’d know that you weren’t on the ground on Earth, right?
Yes, but you couldn’t distinguish that acceleration from the effects of Martian gravity, which has the value of one-third g. The acceleration due to gravity depends on the mass of the celestial body you are close to.
I see now, Professor. It’s not terrestrial gravity that’s important, but the acceleration due to gravity near any celestial body.
Yes, any value of the acceleration of the ship would be indistinguishable from the gravitational acceleration to a certain body. This insight put me on the path towards general relativity. But the path was thornier than expected, since it required one to move away from Euclidean geometry, where space is flat, to a new geometry where space is curved. The curvature of space implies that light is propagated curvilinearly in a gravitational field. To be able to observe this phenomenon, one needs a strong gravitational field, like the field generated by the Sun. Even so, its detection requires very precise instrumentation.
How did the curvature of space come about in the theory?
