Special relativity
A week ago, I was at the Nazi party rally grounds in Nuremberg, Germany. For some odd reason, I had brought a jacket with me; not a single cloud came to my rescue as the Sun turned the sweat glands in my head into faucets. At least I had my sunglasses. The other Americans and I made our way to the Zeppelinfeld, a large field where hundreds of thousands of Germans historically congregated to hear Adolf Hitler's rally speeches. As I walked the steps to ascend the tribune, my heart began to beat more quickly, for I knew that I would be standing in the exact spot that Adolf Hitler – a name which has become synonymous with pure evil – stood not more than a century ago. A few other tourists were there as well, and they each took their turn standing upon the little balcony that overlooked the entire Zeppelinfeld. When my turn came, I braced myself for whatever paranormal curse that Hitler left on the tribune to hit me like a freight train. Thankfully, it never came.
There's something deeply fascinating about looking at a point of space and remembering everything that ever happened at that point. This is a fascination I've held since early childhood: as a six-year-old I wondered what occupied the space where my house currently is before it existed. A farm? Before the farm, a forest? Did a dinosaur ever walk over the spot where my house now lies? But as I grew older and began to understand that the entire Earth was moving, both along an axis of rotation and in an orbit around the Sun, I had to rethink what it means to be in "the same place as before". I left my house for Germany about four weeks ago. I just got back yesterday. My house is not occupying the exact same position in space as when I left, because the entire Earth had to have moved around the Sun during the time I was in Germany. If mankind is ever able to create a time machine – say, out of a DeLorean – it seems that such a machine would not only need to accomplish temporal displacement (that is, time travel), but also spatial displacement (that is, teleportation), since if I traveled back in time five and a half years to the point in space I'm at right now, I would most likely die in the vacuum of space because the Earth would be located somewhere else. I would have also had to teleport to the spot where I am now relative to the Earth.
For a simplified example, imagine you are sitting on a bus whose speedometer reads a constant 45 miles per hour. If you get up out of your seat and start walking to the front of the bus, from your point of view, you would only move a distance of maybe 10 meters – the distance from your seat to the front of the bus. However, from the point of view of a stationary observer at the bus stop, it would appear you moved 10 meters plus the distance the entire bus traveled during the time you spent walking. If the entire bus moved 100 meters during the time you spent walking, then to the observer at the bus stop, you really moved 110 meters! Which is "right"? 10 meters or 110?
The critical piece of the picture we're missing is a frame of reference. In order for position and speed to have any meaning, we must have a frame of reference. For most practical purposes, our frame of reference is the surface of the Earth. As you drive down the highway, your speedometer tells you that you are traveling at a speed of 87 miles per hour. That 87 miles per hour tells you that if you maintained your current motion for one hour, you would travel 87 miles on the surface of the Earth. However, if the frame of reference is the car, then your body is moving at 0 miles per hour, since your position is not changing relative to your car. On the other hand, if your frame of reference is the center of the Earth, you would have to factor in the speed of the Earth's rotation around its axis. According to this article on the website of Scientific American, a point on the Earth's equator is moving at a speed of about 1000 miles per hour relative to the center of the Earth. Thus, if the highway you are driving on is along the equator, and your frame of reference is the center of the Earth, and you are driving in the direction of the Earth's rotation, then you would be traveling at approximately 1087 miles per hour – more than enough for a speeding ticket! And that's ignoring the speed of the Earth as it orbits the Sun, and the speed of the entire solar system as it orbits the center of the galaxy, and the speed of the galaxy as it travels through the universe!
"Nothing can travel faster than the speed of light." This has become common knowledge to virtually anyone who has been exposed to any form of scientific education. But what does that really mean? We've already established that the concept of "speed" is dependent on a frame of reference: a person sitting could be moving anywhere from 0 miles per hour to many thousands of miles per hour, depending on your point of view. And yet we accept as a universal law that light travels at a finite speed: 299,792,458 meters per second – nothing more, nothing less. It would seem that the law that "nothing can travel faster than the speed of light" can be broken if one changes their frame of reference. For example, if you were to shine a flashlight right now from one end of the room to another, it would appear to you to travel at "the speed of light", but to some imaginary observer from outer space watching the entire Earth move around the Sun, shouldn't it appear to them that the beam of light is actually traveling just a little faster than the "speed of light", since you have to factor in the speed of the Earth too?
I guess we have to analyze how a speed is measured. It's fairly simple: you take the distance an object traveled and divide it by the time it took for the object to travel that distance. (It should be noted that this gives you an object's average speed. We can then use either calculus or kinematics to determine an object's speed at specific instants in time if we know the forces that are acting on it.) But as we saw with the example of walking forward on a bus, the "distance" an object travels is dependent on the frame of reference. To you, you only traveled 10 meters from your seat to the front of the bus, but to the guy at the bus stop, you traveled 10 meters plus the distance the bus traveled during the time you spent walking. The same principle works with light: to you, the distance the light from your flashlight travels is only 10 meters, but to the guy at the bus stop, the light travels 10 meters plus the distance that the entire bus moves in the time the light took to reach the front of the bus. Since light is so fast, the additional distance is probably extremely small (on the scale of nanometers) – but it exists nonetheless. It should follow, then, that the guy at the bus stop would calculate a different speed of light than you, since his measurement of distance is different than yours.
But that isn't what happens. This has been proven experimentally over and over and over again: no matter what your frame of reference is, you will always calculate the speed of light to be the exact same value.
The unspoken assumption which may make this seem illogical at first is the assumption that time is absolute. Going back to the bus example, we assume that the time you measure for the light to reach the front of the bus is the same as the time that the bus stop guy measures. But what a smart German patent office worker named Albert Einstein realized was that the whole situation could be solved if we rid ourselves of the concept of absolute time. What Einstein proposes is that even though the bus stop guy measures a different distance that the light traveled than you, you and he agree on the same speed of light because time moved a little slower for you relative to the bus stop guy. If the bus stop guy's measured distance is x times your measured distance, then his measured time would be x times your measured time. Since speed is just distance over time, the difference then cancels out and you two would then agree on the same speed of light. This is one of the core principles of Albert Einstein's special theory of relativity: that the speed of light must be calculated to be the same in all frames of reference, because neither distance nor time are absolute.
The consequences of special relativity are wide-ranging and fascinating. If time is not absolute, that means that I can slow down time for just me by simply adjusting how fast I am moving. Theoretically, if I were to somehow go into a space ship that lets me travel very close to the speed of light (such as the fictional Millennium Falcon spacecraft in the Star Wars franchise), time would move much, much slower for me than for the people on Earth, because I would still need to calculate the speed of light to be the same as an observer on the Earth. It's the same principle as the bus example, only that the "bus" here is moving much, much faster. If I shine a flashlight on the Millennium Falcon traveling at near light speed, it would shoot forward to the front of the Falcon, and I would calculate it to be the speed of light – about 299,792,458 meters per second – and so would an observer on the Earth. The light would appear to me to only travel forward, say, 10 meters in the cabin of the Falcon, but to the Earth observer, it would travel a much, much greater distance, since the entire Falcon is also moving very close to the speed of light. Despite this difference in distance, we both calculate the same speed of light because to the Earth man, it takes much more time for the light to travel the distance the Earth man measures – in other words, to the Earth observer, time appears to flow much more slowly for me on the Falcon (but from my point of view, time appears to flow much more quickly for the guy on Earth!). When I return to Earth, it would appear that I "time traveled" into the future, since time on Earth moved faster relative to the time I experienced in the Falcon.
The idea of a "position in space" is still meaningless without a frame of reference. When I ascended those steps at the Nazi rally grounds where Hitler once stood, I really did stand in the same position where Hitler once stood if I set my frame of reference to be the surface of the Earth (as I should). Of course, I could make my frame of reference the center of the Earth or the Sun or the center of the galaxy, but there wouldn't be any point in that. The power of special relativity, however, is that we now have a universal standard whereby frames of reference don't matter: the speed of light.
There's something deeply fascinating about looking at a point of space and remembering everything that ever happened at that point. This is a fascination I've held since early childhood: as a six-year-old I wondered what occupied the space where my house currently is before it existed. A farm? Before the farm, a forest? Did a dinosaur ever walk over the spot where my house now lies? But as I grew older and began to understand that the entire Earth was moving, both along an axis of rotation and in an orbit around the Sun, I had to rethink what it means to be in "the same place as before". I left my house for Germany about four weeks ago. I just got back yesterday. My house is not occupying the exact same position in space as when I left, because the entire Earth had to have moved around the Sun during the time I was in Germany. If mankind is ever able to create a time machine – say, out of a DeLorean – it seems that such a machine would not only need to accomplish temporal displacement (that is, time travel), but also spatial displacement (that is, teleportation), since if I traveled back in time five and a half years to the point in space I'm at right now, I would most likely die in the vacuum of space because the Earth would be located somewhere else. I would have also had to teleport to the spot where I am now relative to the Earth.
For a simplified example, imagine you are sitting on a bus whose speedometer reads a constant 45 miles per hour. If you get up out of your seat and start walking to the front of the bus, from your point of view, you would only move a distance of maybe 10 meters – the distance from your seat to the front of the bus. However, from the point of view of a stationary observer at the bus stop, it would appear you moved 10 meters plus the distance the entire bus traveled during the time you spent walking. If the entire bus moved 100 meters during the time you spent walking, then to the observer at the bus stop, you really moved 110 meters! Which is "right"? 10 meters or 110?
The critical piece of the picture we're missing is a frame of reference. In order for position and speed to have any meaning, we must have a frame of reference. For most practical purposes, our frame of reference is the surface of the Earth. As you drive down the highway, your speedometer tells you that you are traveling at a speed of 87 miles per hour. That 87 miles per hour tells you that if you maintained your current motion for one hour, you would travel 87 miles on the surface of the Earth. However, if the frame of reference is the car, then your body is moving at 0 miles per hour, since your position is not changing relative to your car. On the other hand, if your frame of reference is the center of the Earth, you would have to factor in the speed of the Earth's rotation around its axis. According to this article on the website of Scientific American, a point on the Earth's equator is moving at a speed of about 1000 miles per hour relative to the center of the Earth. Thus, if the highway you are driving on is along the equator, and your frame of reference is the center of the Earth, and you are driving in the direction of the Earth's rotation, then you would be traveling at approximately 1087 miles per hour – more than enough for a speeding ticket! And that's ignoring the speed of the Earth as it orbits the Sun, and the speed of the entire solar system as it orbits the center of the galaxy, and the speed of the galaxy as it travels through the universe!
"Nothing can travel faster than the speed of light." This has become common knowledge to virtually anyone who has been exposed to any form of scientific education. But what does that really mean? We've already established that the concept of "speed" is dependent on a frame of reference: a person sitting could be moving anywhere from 0 miles per hour to many thousands of miles per hour, depending on your point of view. And yet we accept as a universal law that light travels at a finite speed: 299,792,458 meters per second – nothing more, nothing less. It would seem that the law that "nothing can travel faster than the speed of light" can be broken if one changes their frame of reference. For example, if you were to shine a flashlight right now from one end of the room to another, it would appear to you to travel at "the speed of light", but to some imaginary observer from outer space watching the entire Earth move around the Sun, shouldn't it appear to them that the beam of light is actually traveling just a little faster than the "speed of light", since you have to factor in the speed of the Earth too?
I guess we have to analyze how a speed is measured. It's fairly simple: you take the distance an object traveled and divide it by the time it took for the object to travel that distance. (It should be noted that this gives you an object's average speed. We can then use either calculus or kinematics to determine an object's speed at specific instants in time if we know the forces that are acting on it.) But as we saw with the example of walking forward on a bus, the "distance" an object travels is dependent on the frame of reference. To you, you only traveled 10 meters from your seat to the front of the bus, but to the guy at the bus stop, you traveled 10 meters plus the distance the bus traveled during the time you spent walking. The same principle works with light: to you, the distance the light from your flashlight travels is only 10 meters, but to the guy at the bus stop, the light travels 10 meters plus the distance that the entire bus moves in the time the light took to reach the front of the bus. Since light is so fast, the additional distance is probably extremely small (on the scale of nanometers) – but it exists nonetheless. It should follow, then, that the guy at the bus stop would calculate a different speed of light than you, since his measurement of distance is different than yours.
But that isn't what happens. This has been proven experimentally over and over and over again: no matter what your frame of reference is, you will always calculate the speed of light to be the exact same value.
The unspoken assumption which may make this seem illogical at first is the assumption that time is absolute. Going back to the bus example, we assume that the time you measure for the light to reach the front of the bus is the same as the time that the bus stop guy measures. But what a smart German patent office worker named Albert Einstein realized was that the whole situation could be solved if we rid ourselves of the concept of absolute time. What Einstein proposes is that even though the bus stop guy measures a different distance that the light traveled than you, you and he agree on the same speed of light because time moved a little slower for you relative to the bus stop guy. If the bus stop guy's measured distance is x times your measured distance, then his measured time would be x times your measured time. Since speed is just distance over time, the difference then cancels out and you two would then agree on the same speed of light. This is one of the core principles of Albert Einstein's special theory of relativity: that the speed of light must be calculated to be the same in all frames of reference, because neither distance nor time are absolute.
The consequences of special relativity are wide-ranging and fascinating. If time is not absolute, that means that I can slow down time for just me by simply adjusting how fast I am moving. Theoretically, if I were to somehow go into a space ship that lets me travel very close to the speed of light (such as the fictional Millennium Falcon spacecraft in the Star Wars franchise), time would move much, much slower for me than for the people on Earth, because I would still need to calculate the speed of light to be the same as an observer on the Earth. It's the same principle as the bus example, only that the "bus" here is moving much, much faster. If I shine a flashlight on the Millennium Falcon traveling at near light speed, it would shoot forward to the front of the Falcon, and I would calculate it to be the speed of light – about 299,792,458 meters per second – and so would an observer on the Earth. The light would appear to me to only travel forward, say, 10 meters in the cabin of the Falcon, but to the Earth observer, it would travel a much, much greater distance, since the entire Falcon is also moving very close to the speed of light. Despite this difference in distance, we both calculate the same speed of light because to the Earth man, it takes much more time for the light to travel the distance the Earth man measures – in other words, to the Earth observer, time appears to flow much more slowly for me on the Falcon (but from my point of view, time appears to flow much more quickly for the guy on Earth!). When I return to Earth, it would appear that I "time traveled" into the future, since time on Earth moved faster relative to the time I experienced in the Falcon.
The idea of a "position in space" is still meaningless without a frame of reference. When I ascended those steps at the Nazi rally grounds where Hitler once stood, I really did stand in the same position where Hitler once stood if I set my frame of reference to be the surface of the Earth (as I should). Of course, I could make my frame of reference the center of the Earth or the Sun or the center of the galaxy, but there wouldn't be any point in that. The power of special relativity, however, is that we now have a universal standard whereby frames of reference don't matter: the speed of light.