Note that some small Graphics where add for frame of reference.
SPECIAL RELATIVITY
Thus far no special point was raised about how measurements of such physical quantities as length, time. and mass are carried out. It was simply assumed that these quantities could be determined in some way, and that. since standard units have been established for each of them, it doesn't matter who makes a particular determination - everybody ought to get the same figure. There is certainly no question of principle associated with, say, finding the length of an airplane on the ground: all we need do is place one end of a tape measure at the airplane's nose and note the number on the tape at the airplane's tail.
But what if the airplane is in flight and we are on the ground? It is not hard to find the length of a distant object with the help of a surveyor 5 transit to measure angles, a tape measure to establish a base line, and a knowledge of trigonometry. When the object is moving, however, things become more complicated because now we must take into account the fact that light does not travel instantaneously from one place to another but does so at a definite, fixed velocity - and light is the means by which information is carried from a distant object to our measuring instruments. When a careful analysis is made of the problem of measuring physical quantities when there is relative motion between the measuring instruments and whatever is being observed, many surprising results emerge.
When we observe something moving, what we actually detect is that its position relative to something else is changing (Fig. 1-1).
A passenger moves relative to a train; the train moves relative to the earth; the earth moves relative to the sun; the sun moves relative to the galaxy of stars (the "Milky Way") of which it is a member; and soon. In each case a frame of reference is part of the description of the motion: it is meaningless to say that something is moving without specifying with respect to what the motion occurs.
There is no universal frame of reference that can be used everywhere. If we see something changing its position with respect to us at constant velocity, we have no way of knowing whether it is moving or I we are moving. If we were isolated from the rest of' the universe, we would be unable to find out if we were moving at constant velocity or not-indeed, the question would make no sense. All motion is relative to the observer, and there is no such thing as "absolute motion."
The theory of relativity is concerned with the physical consequences of the absence of a universal frame of reference. The special theory of relativity, published in 1905 by Albert Einstein, is confined to problems involving the motion of frames of reference at constant velocity (that is, both constant speed and constant direction) with respect to one another; the general theory of relativity, published 10 years later by Einstein, deals with problems involving frames of reference accelerated with respect to one another. The special theory has had an enormous impact on all of physics, and its chief conclusions will be examined here.
Two principles are fundamental to the special theory of relativity. The principle of relativity states that
The laws of physics are the same in all frames of reference moving at constant velocity with respect to one another.
Principle of relativity
This principle follows directly from the absence of a universal frame of reference. If the laws of physics were different for different observers in relative motion, they could infer from these differences which of them were "stationary" in space and which were "moving." But such a distinction does not exist in nature, and the principle of relativity is an expression of this fact.
Thus experiments of any kind performed, for instance, in an elevator which is ascending at a constant velocity yield exactly the same results as the same experiments performed when the elevator is at rest or is descending at a constant velocity. On the other hand, an isolated observer can detect accelerations, as any elevator passenger can verify.
The second principle states that
The velocity of light in free space has the same value for all observers, regardless of their state of motion.
At first glance the constancy of the velocity of light may not seem so very extraordinary, which is a misleading impression. Let us examine a hypothetical experiment in essence no different from actual experiments that have been performed in a number of ways.
Suppose I turn on a searchlight at the same moment you take off in a spacecraft at a speed of 150,000 mi/s (Fig. 1-2). We both measure the speed of the light waves from the searchlight using identical instruments. From the ground I find their speed to be 186,000 mi/s, as usual. "Common sense 'tells me you ought to find a speed of (186,000 - 150,000) mi/s or only 36,000 mi/s for the same light waves. But you also find their speed to be 186,000 mi/s, even though to me you seem to be moving parallel to the waves at 150,000 mi/s. As so often, common sense is wrong.
There is only one way to account for the apparent discrepancy between the above results without violating the principle of relativity, and that is to conclude that measurements of space and time are not absolute but depend upon the relative motion of the observer and that which is observed. If your clock ticks more slowly than it did on the ground and your meter stick is shorter in the direction of motion of the spacecraft, then you will find 186,000 mi/s for a velocity that I think should be only 36,000 mi/s. To you, your clock and meter stick are the same as they were on the ground before you took off, but to me they are different because of the relative motion. Time intervals and lengths are relative quantities, not absolute ones.
THE RELATIVITY OF TIME
Measurements of time intervals are affected by relative motion between an observer and what he observes. As a result, all moving clocks tick more slowly than clocks at rest do, and all natural processes (including those of life) that involve regular time intervals occur more slowly when they take place in a moving frame of reference.
We begin by considering the operation of the particularly simple clock shown in (Fig. 1-3). In this clock a pulse of light is reflected back and forth between two mirrors. Whenever the light strikes the lower mirror, an electrical signal is produced that is registered as a mark on the recording tape. Each mark corresponds to the tick of an ordinary clock.
Let us consider two of these clocks, one of them at rest in a laboratory and another in a spaceship moving at the velocity v relative to the laboratory. An observer in the laboratory watches both clocks: does he find that they tick at the same rate?
Figure 1-4 shows the laboratory clock in operation. The mirrors are L apart, and the time interval between ticks is to. Hence the time needed for the light pulse to travel the distance L between the mirrors at the velocity.
Figure 1-5 shows the moving clock as seen from the laboratory. The time interval between ticks is t. Because the clock is moving, the pulse of light follows a zigzag path in which it travels the distance ct/2 in going from one mirror to the other in the time t/2. From the Pythagorean theorem.
Because the quantity is always smaller than 1 for a moving object. t is always greater than to. A clock moving with respect to an observer ticks more slowly than a clock that is stationary with respect to the same observer. This effect is referred to as time dilation (to dilate is to become larger).
Now let us turn the situation around and ask what an observer in a spacecraft finds when he compares his clock with one on the ground. The only change needed in the preceding derivation is the direction of motion:
if the man on the ground sees the spacecraft moving to the east, the man in the spacecraft sees the laboratory on the ground moving to the west. To the man in the spacecraft the light pulse of the ground clock follows a zigzag path that requires a total time per round trip of
whereas the light pulse in his own clock takes to for the round trip. Thus to the man in the spacecraft the clock on the ground ticks at a slower rate than his own clock does. A clock moving relative to an observer always is slower than a clock at rest relative to him, regardless of where the observer is located.
A light clock is a rather more exotic timepiece than most of us are accustomed to. What if a stationary cuckoo clock and a moving one are compared: do we again find that the moving clock runs more slowly?
The principle of relativity makes it easy for us to predict the outcome of the experiment. Suppose cuckoo clocks tick at exactly the same rate to all observers. whether there is relative motion or not. We put a cuckoo clock and a light-pulse clock (which does tick more slowly when in motion) on a spacecraft. On the ground they show the same time.
In flight, the two clocks show different times to an observer on the ground, since the light-pulse clock ticks slower whereas the cuckoo clock (by hypothesis) does not. To an observer in the spacecraft. however, the two clocks agree, since to him the clocks are stationary and it is the ground which is moving away from him. Therefore the laws of physics which govern the operation of the clocks must be different on the spacecraft from what they are on the ground-which contradicts the principle of relativity. All moving clocks tick more slowly than clocks at rest.
It is important to keep in mind that the slowing down of a moving clock is significant only at relative velocities not far from the velocity of light. Such velocities are readily attained by elementary particles. and most of the experiments that have confirmed time dilation have employed such particles. Today's spacecraft are far too slow to exhibit time dilation. For instance,. the highest velocity reached by the Apollo 11 spacecraft on its way to the moon was only about 10,840 m/s, or 0.0036 percent of the velocity of light. At this velocity. clocks on the spacecraft differ from those on the earth by less than 1 part in 109.
Next time we will read about,
MUON DECAY
LORENTZ CONTRACTION
ORIGIN OF MAGNETIC FORCES
RELATIVITY OF MASS
This is the text version of my webpage. I hope it shed some light on the subject.