Relativity of Simultaneity Help (page 2)
Relativity of Simultaneity
There are two aspects to relativity theory: the special theory and the general theory . The special theory involves relative motion, and the general theory involves acceleration and gravitation.
Before we get into relativity, let’s find out what follows from the hypotheses that the speed of light is absolute, constant, and finite and that it is the highest speed anything can attain.
When he became interested in light, space, and time, Einstein pondered the results of experiments intended to find out how the Earth moves relative to the supposed medium that carries electromagnetic (EM) waves such as visible light. Einstein decided that such a medium doesn’t exist—EM waves can travel through a perfect vacuum.
Before Einstein’s time, physicists determined that light has wavelike properties and in some ways resembles sound. However, light travels much faster than sound. Also, light can propagate through a vacuum, whereas sound cannot. Sound waves require a material medium such as air, water, or metal to get from one place to another. Many scientists suspected that light also must need some sort of medium to travel through space. What could exist everywhere, even between the stars and galaxies, and even in a jar from which all the air was pumped out? This mysterious medium was called luminiferous ether , or simply ether .
If the ether exists, some scientists wondered, how could it pass right through everything, even the entire Earth, and get inside an evacuated chamber? How could the ether be detected? One idea was to see if the ether “blows” against the Earth as our planet orbits around the Sun, as the Solar System orbits around the center of the Milky Way galaxy, and as our galaxy drifts through the Cosmos. If there is an “ether wind,” then the speed of light ought to be different in different directions. This, it was reasoned, should occur for the same reason that a passenger on a fast-moving truck measures the speed of sound waves coming from the front as faster than the speed of sound waves coming from behind.
In 1887, an experiment was done by two physicists named Albert Michelson and Edward Morley in an attempt to find out how fast the “ether wind” is blowing and from what direction. The Michelson-Morley experiment , as it became known, showed that the speed of light is the same in all directions. This cast doubt on the ether theory. If the ether exists, then according to the results obtained by Michelson and Morley, it must be moving right along with the Earth. This is quite a coincidence; it implies that the Earth is stationary relative to absolute space, and no one believed that in 1887. Attempts were made to explain away this result by suggesting that the Earth drags the ether along with itself. Einstein could not believe this. He decided that the results of the Michelson-Morley experiment had to be taken at face value: The speed of light is constant in every direction. Einstein believed that the Michelson-Morley experiment would have the same outcome for observers on the Moon, on any other planet, on a space ship, or anywhere in the Universe.
The Speed Of Light Is Constant
Einstein rejected the notion of luminiferous ether. Instead, he proposed an axiom, a fundamental rule of the Universe: The speed at which light (and any other EM field) travels in a vacuum is the same no matter what the direction and regardless of the motion of the observer with respect to the EM energy source. Then he set out to deduce what logically follows from this assumption.
Einstein did all his work by using a combination of mathematics and daydreaming that he called “mind journeys.” He wasn’t an experimentalist but a theorist. There is a saying in physics: “One experimentalist can keep a dozen theorists busy.” Einstein turned this inside out. His theories have kept thousands of experimentalists occupied.
There Is No Absolute Time!
One of the first results of Einstein’s speed-of-light axiom is the fact that there can be no such thing as an absolute time standard. It is impossible to synchronize the clocks of two obervers so that they will see both clocks as being in exact agreement unless both observers occupy the exact same point in space.
In recent decades we have built atomic clocks, and we claim that they are accurate to within billionths of a second (where a billionth is 0.000000001 or 10 –9 ). However, this has meaning only when we are right next to such a clock. If we move a little distance away, then the light (or any other signal that we know of) takes some time to get to us, and this throws the clock’s reading off.
The speed of EM-field propagation, the fastest speed known, is approximately 300 million meters per second (3.00 × 10 8 m/s), or 186,000 miles per second (1.86 × 10 5 mi/s). A beam of light therefore travels about 300 m (984 ft) in 0.000001 s (one microsecond or 1 µs). If you move a little more than the length of a football field away from a superaccurate billionth-of-a-second atomic clock, the clock will appear to be in error by a microsecond, or 1,000 billionths of a second. If you go to the other side of the world, where the radio signal from that clock must travel 20,000 km (12,500 mi) to reach you, the time reading will be off by 0.067 s, or 67 thousandths of a second. If you go to the Moon, which is about 400,000 km (250,000 mi) distant, the clock will be off by approximately 1.33 s.
If scientists ever discover an energy field that can travel through space instantaneously regardless of the distance, then the conundrum of absolute time will be resolved. In practical scenarios, however, the speed of light is the fastest possible speed. (Some recent experiments suggest that certain effects can propagate faster than the speed of light over short distances, but no one has demonstrated this on a large scale yet, much less used such effects to transmit any information such as data from an atomic clock.) We can say that the speed of light is the speed of time. Distance and time are inextricably related.
Point Of View
Imagine that there are eight clocks in space arranged at the vertices of a gigantic cube. Each edge of the cube measures 1 light-minute, or approximately 18 million km (11 million mi) long, as shown in Fig. 16-1. We are given a challenge: Synchronize the clocks so that they agree within the limit of visibility, say, to within 1 second of each other. Do you suppose that this will be easy?
Because the clocks are so far apart, the only way we can ascertain what they say is to equip them with radio transmitters that send time signals. Alternatively, if we have a powerful enough telescope, we can observe them and read them directly by sight. In either case, the information that tells us what the clocks say travels to us at the speed of light. We get in our space ship and maneuver ourselves so that we are in the exact center of the cube, equidistant from all eight clocks. Then we proceed to synchronize them using our remote-control, wireless two-way data communications equipment. Thank heaven for computers! The task is accomplished in a just a few minutes. It can’t be done instantaneously, of course, because our command signals take the better part of a minute to reach the clocks from our central location, and then the signals coming back from the clocks take just as long to get to us so that we can see what they say. Soon, however, everything is in agreement. Clocks A through H all tell the same time to within a fraction of a second.
Satisfied with our work, we cruise out of the cube because there’s nothing there of any real interest except a few small meteoroids. We take a look back at the clocks, mainly to admire our work but also because, as technicians, we are instinctively programmed to suspect that something can always go wrong. What do we see? To our dismay, the clocks have already managed to get out of sync. Muttering a curse or two, we take our ship back to the center of the cube to correct the problem. However, when we get there, there is no problem to correct! The clocks are all in agreement again.
You can guess what is happening here. The clock readings depend on how far their signals must travel to reach us. For an observer at the center of the cube, the signals from all eight clocks, A through H, arrive from exactly the same distance. However, this is not true for any other point in space. We have synchronized the clocks for one favored vantage point; if we go somewhere else, we will have to synchronize them all over again. This can be done, but then the clocks will be synchronized only when observed from the new favored vantage point. There is a unique sync point —the spot in space from which all eight clocks read the same—for each coordination of the clocks.
No sync point is more valid than any other from a scientific standpoint. If the cube happens to be stationary relative to some favored reference point such as Earth, we can synchronize the clocks, for convenience, from that reference point. However, if the cube is moving relative to our frame of reference, we will never be able to keep the clocks synchronized. Time depends on where we are and on whether or not we are moving relative to whatever device we use to indicate the time. Time is not absolute, but relative, and there is no getting around it.
Practice problems of this concept can be found at: Special and General Relativity Practice Problems
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