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The secrets are being imparted...
Sep. 5th, 2010 02:29 pmAnd by that I, of course, mean the secrets of the universe. I have been told my entire life — well as much of it as people were talking to me about this sort of thing or I could get my hands on books that were comprehensible to me at the time — that the special theory of relativity (1905) came about because the failure of the Michelson-Morley experiment (1881) to detect the “æther” led Einstein to reason that another explanation was needed. In reality, Einstein, to the best of anyone's knowledge, had never even heard of the pivotal experiment, but rather was led to his theory because of Maxwell's equations (1864) which said that light was actually an electromagnetic wave (and which, in one swoop, united the previously separate fields of electricity, magnetism, and optics). The problem with the equations was that if you applied classical Galilean transformations to them you got nonsensical answers. Specifically, if you you measured the speed of light in a “reference frame” moving at a constant velocity (say a person in a car) relative to, and sent from, another reference frame that is considered “at rest” (say a person standing by the road with a flashlight that the car is moving towards), the classical transformations said that the person in the car would measure the speed of light as the speed it left the flashlight (“c”) plus the speed of the car (say “v”). Maxwell's equations said that you should measure the speed of light as “c” in both reference frames, and this clearly did not agree with classical predictions, so something was wrong somewhere. Einstein's success (or genius as people suggest) was in accepting what Maxwell's equations were saying, as well as the Galilei-Newton basic Principle of Relativity that the laws of nature must be the same for all observers, to arrive at two “postulates” that he considered fundamental (note, inertial frames are just two systems moving at constant velocity with respect to one another, like the person in the car relative to the one by the road):
In his own words, “What led me more or less directly to the special theory of relativity was the conviction that the electromagnetic force acting on a body in motion in a magnetic field was nothing else but an electric field”. Whereas I have called his other reasoning his success, this leap of understanding is a true flash of inspiration that can be called genius without any reservation on my part. I don't know that it is possible for me to express how powerful an impact this had on me reading it for the first time last week. Like any great work of art (which I consider it to be), either it speaks to you or it doesn't, and if it does, what it says is utterly individual. The textbook I was reading (2nd year physics) indicated that the math was well beyond what I likely have been exposed to at this point; however, the concepts don't need the math to understand. An electric field is generated when two things have electric charges: if the charge sign (+/−) is the same, they repel; if they are opposite, they attract. Magnetic fields are generated when electric charges move: they generate a flux that permeates space and is perpendicular (90°) to the direction of motion of the charge. So imagine a charged object (say with a positive charge for simplicity's sake) that is moving outside of and along the length of a copper wire. The wire is conducting electricity and thus, because there are moving electric charges in the wire, it is generating a magnetic field. Again, for simplicity's sake, assume the object is moving in the same direction and at the same speed as the negative charges in the wire. Viewed from the reference frame of the wire, the object is moving through its magnetic field and because of its motion will experience a force that will push the object away from the wire — it feels no electric force because the wire is electrically neutral... even though there are moving negative charges generating a magnetic field, the number of negative charges is the same as the number of positive charges and the electric fields cancel each other out (it's just a bunch of copper atoms). Note: this is how electric motors work, it's a pretty important principle in modern life.
Now suppose we jump onto the object and that becomes our new reference frame (we've hopped in the car) and we do the experiment again. Well, once more for simplicity's sake, remember that the object is moving at the same speed as the negative charges moving in the wire and so, from the perspective of the object, it is not moving with respect to the magnetic field generated by the wire and so feels no force from it... but it still “sees” a force that is pushing it away from the wire. The magnetic field that was acting on the object from the perspective of the wire is not acting on it from the perspective of the object itself; but no matter the reference frame, a force is pushing the object away from the wire (observers in both frames would see the object and the wire moving apart because of the force, presuming no other force was acting on it). The answer lies in the Lorentz transformation between the two inertial frames! To the object, the negative charges in the wire appear stationary; however, the positive charges in the wire (that are stationary from the reference frame of the wire) appear to be moving to an observer on the object (at the same speed, but opposite direction, as the negative charges are moving from the reference frame of the wire). But earlier, I said that the positive and negative charges balanced in the wire (and so there was no electric force on the object), but that was from the perspective of the reference frame of the wire. From an observer on the object, the positive charges in the wire are moving and, from the reference frame of the object, will experience a compression of space in the direction of their motion per the Lorentz transformation and will appear to be closer to each other than do the negative charges that are not moving relative to the object. Because, to the object, there are more positive charges per length of wire than negative changes, the wire will appear to have a positive charge and will repel the object due to an electric field!
Again, words can't express how beautiful I find this result. With the publication of his special theory of relativity, Einstein negated the need for there to be an æther for electromagnetic waves to travel through, changed the way we view and experience space and time, and drew a firm line between “classical” physics and “modern” physics (oh, and his simultaneous publications of a paper explaining Brownian motion as an effect of the motion of molecules, and another paper fixing the field of thermodynamics by introducing the quantum nature of light as the source of the photoelectric effect didn't hurt either). His general theory of relativity, fyi, extends the two “postulates” to non-inertial (i.e. accelerating) frames and models gravity as a curvature of spacetime as a result (and was more perspiration than inspiration at that point, but amazing that he accomplished it in his lifetime given he could easily have left the task to others and sat on his laurels).
- The principle of relativity: The laws of physics are the same in all inertial systems. There is no way to detect absolute motion, and no preferred inertial system exists.
- The constancy of the speed of light: Observers in all inertial systems measure the same value for the speed of light in a vacuum.
In his own words, “What led me more or less directly to the special theory of relativity was the conviction that the electromagnetic force acting on a body in motion in a magnetic field was nothing else but an electric field”. Whereas I have called his other reasoning his success, this leap of understanding is a true flash of inspiration that can be called genius without any reservation on my part. I don't know that it is possible for me to express how powerful an impact this had on me reading it for the first time last week. Like any great work of art (which I consider it to be), either it speaks to you or it doesn't, and if it does, what it says is utterly individual. The textbook I was reading (2nd year physics) indicated that the math was well beyond what I likely have been exposed to at this point; however, the concepts don't need the math to understand. An electric field is generated when two things have electric charges: if the charge sign (+/−) is the same, they repel; if they are opposite, they attract. Magnetic fields are generated when electric charges move: they generate a flux that permeates space and is perpendicular (90°) to the direction of motion of the charge. So imagine a charged object (say with a positive charge for simplicity's sake) that is moving outside of and along the length of a copper wire. The wire is conducting electricity and thus, because there are moving electric charges in the wire, it is generating a magnetic field. Again, for simplicity's sake, assume the object is moving in the same direction and at the same speed as the negative charges in the wire. Viewed from the reference frame of the wire, the object is moving through its magnetic field and because of its motion will experience a force that will push the object away from the wire — it feels no electric force because the wire is electrically neutral... even though there are moving negative charges generating a magnetic field, the number of negative charges is the same as the number of positive charges and the electric fields cancel each other out (it's just a bunch of copper atoms). Note: this is how electric motors work, it's a pretty important principle in modern life.
Now suppose we jump onto the object and that becomes our new reference frame (we've hopped in the car) and we do the experiment again. Well, once more for simplicity's sake, remember that the object is moving at the same speed as the negative charges moving in the wire and so, from the perspective of the object, it is not moving with respect to the magnetic field generated by the wire and so feels no force from it... but it still “sees” a force that is pushing it away from the wire. The magnetic field that was acting on the object from the perspective of the wire is not acting on it from the perspective of the object itself; but no matter the reference frame, a force is pushing the object away from the wire (observers in both frames would see the object and the wire moving apart because of the force, presuming no other force was acting on it). The answer lies in the Lorentz transformation between the two inertial frames! To the object, the negative charges in the wire appear stationary; however, the positive charges in the wire (that are stationary from the reference frame of the wire) appear to be moving to an observer on the object (at the same speed, but opposite direction, as the negative charges are moving from the reference frame of the wire). But earlier, I said that the positive and negative charges balanced in the wire (and so there was no electric force on the object), but that was from the perspective of the reference frame of the wire. From an observer on the object, the positive charges in the wire are moving and, from the reference frame of the object, will experience a compression of space in the direction of their motion per the Lorentz transformation and will appear to be closer to each other than do the negative charges that are not moving relative to the object. Because, to the object, there are more positive charges per length of wire than negative changes, the wire will appear to have a positive charge and will repel the object due to an electric field!
Again, words can't express how beautiful I find this result. With the publication of his special theory of relativity, Einstein negated the need for there to be an æther for electromagnetic waves to travel through, changed the way we view and experience space and time, and drew a firm line between “classical” physics and “modern” physics (oh, and his simultaneous publications of a paper explaining Brownian motion as an effect of the motion of molecules, and another paper fixing the field of thermodynamics by introducing the quantum nature of light as the source of the photoelectric effect didn't hurt either). His general theory of relativity, fyi, extends the two “postulates” to non-inertial (i.e. accelerating) frames and models gravity as a curvature of spacetime as a result (and was more perspiration than inspiration at that point, but amazing that he accomplished it in his lifetime given he could easily have left the task to others and sat on his laurels).
