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The third prediction: The demise of Universal Time


Another peculiarand surprising consequence of the Principle of Relativity is that time intervals are no longer universal but depend on the frame of reference. Consider, for example, a clock consisting of a light source and detector. The source emits a light pulse, the pulse goes up and is reflected at a height h by a mirror. It is then detected and this determines one unit of time. See Fig 6.11.


Figure 6.11: A clock at rest with respect to the observer  
\begin{figure} \centerline{ \vbox to 3 truein{\epsfysize=4 truein\epsfbox[0 0 612 792]{6.str/}} }\end{figure}

The time it takes the light pulse to come and go is t0 = 2 h / c. This is precisely the time it would be measured by any observer carrying any other clock as long as this observer is not moving with respect to the above timepiece.

Now let's consider what an observer moving with respect to this simple clock sees. This is shown in Fig. 6.12


Figure 6.12: A clock moving with speed v to the right with respect to the observer 
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It is clear that the distance traveled by the beam is larger than the up-down trip observed by the first person. But since the speed of the light beam is the same for both observers, the time measured by the second observer will be larger. If we have two such clocks one is at rest with respect to us and the other is moving, we find that the moving clock slows down, moreover, the faster it moves the slower it ticks. This is called time dilation: a moving clock ticks slower. You can see this happening in the following Quick-Time movie clip (you can download the player from Apple at )

This argument was based on the simple clock of Fig. 6.11, will it be true for all clocks? To examine this question let's assume we have another clock (a Rollex, for example) which gives ticks same way no matter how it moves. You go on a long trip to a near-by star taking the Rollex with you and also a clock like the one in Fig. 6.11. Your spaceship, you will notice, has no windows (they had to cut the budget somewhere!), but you go anyway. You experience the effects of lift-off but after a while you appear to be at a standstill: you are then moving at a constant speed with respect to Earth. But remember we assumed that the Rollex still ticks the same way as the clocks on Earth, and we have proved that your light-clock does not. So you will see a mismatch between the Rollex and the light-clock: this is an experiment which is done completely inside the spaceship and which determines whether you are moving. If there were such a Rollex the Principle of Relativity would be violated.

If we accept the Principle of Relativity we must conclude that time dilation will occur for any clocks, be it a Rollex, a biological clock or a Cartier. Note that this follows from the Principle of Relativity and the validity of Maxwells' equations, no additional assumptions are required.

If an observer at rest with respect to a clock, finds that she is pregnant and eventually delivers, the whole process taking precisely nine months, another observer moving with respect to her (and the simple clock) will find this claim to be wrong, he will state that she had a longer pregnancy (or a very long delivery) but that in any case the whole thing took longer than nine months.

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So how come we do not see this in ordinary life? The reason is that the effect is very small in everyday occurrences. To be precise it an observer at rest with respect to the clock in Fig. 6.11 measures a time T0 then the observer which sees the clock move at speed v (and sees the situation depicted in Fig. 6.12) will measure a time T, where

$ 1/\sqrt{1-v^2/c^2} $

(see the box above). So the effect reduces to the appearance of the factor

$ 1/\sqrt{1-v^2/c^2} $

which in usual circumstances is very close to one (so that T is almost equal to T0). For example an ordinary man moving at, say 90miles/hr (trying to get his wife to the hospital before she delivers), v / c = 0.0000001 = 10-7 (approximately) so that the above factor is essentially one (up to a few hundredths of a trillionth). This is typical of the magnitude of the new effects predicted by Einstein's theory for everyday situations: they are in general very small since the velocities of things are usually very small compared to c.

There are some instances, however, in which the effects are observable. There are subatomic particles which are unstable and decay (the process by which they decay is irrelevant) in a very small time interval when measured in the laboratory. It has also been found that high intensity radiation coming from space and hitting the upper atmosphere generates these same particles (again the process is immaterial). To the initial surprise of the experimenters, these particles survive the trip down to surface of the earth, which takes longer, as measured on the Earth, than the particle's lifetime! The surprise evaporated when it was noted that the particles are moving very fast with respect to the Earth, almost at the speed of light, so that a time interval which is very short when measured at rest with respect to the particle will be much longer when measured in the laboratory.

So the rate of all clocks depends on their state of motion. In this sense

Time is relative.

And while the effect is small in many cases, it is spectacular in others. This is a surprising consequence of the Principle of Relativity and requires a complete divorce from Newton's concept of time (which he assumed to flow evenly under all circumstances, see Sect. 4.3.1): time intervals depend on the motion of the observer, there is no ``universal'' time.

Time dilation is a prediction of the theory which must not be accepted as dogma but should be verified experimentally. All experiments do agree with this prediction. The fact that the theory of relativity makes predictions which can be tested experimentally, is what makes this an honest theory: it is falsifiable. It has been accpeted not because of its beauty, but because these predictions have been verified.

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Next: Length contraction Up: Enter Einstein Previous: The second murder mystery

Jose Wudka