4.2 Time dilation examples. Verify the results for the four time dilation examples (with results of 52,48, 36, and 8.5 minutes) given on page 34.
4.2 Time dilation examples. Verify the results for the four time dilation examples (with results of 52,48, 36, and 8.5 minutes) given on page 34.
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Transcribed Image Text:4.2 Time dilation examples. Verify the results for the four time dilation examples (with
results of 52,48, 36, and 8.5 minutes) given on page 34.
Transcribed Image Text:time, then focus on the qualitative discovery that T is larger than To-that a
If your brain is reeling because you haven't exercised using algebra for a long
moving clock ticks slowly. The light clock, the symbols, the algebra-these are just
different frames, and time existed (and dilated!) long before humans were around
scaffolding to propel the argument. The result is that time behaves differently in
to build light clocks and write symbols.
Q: Do you expect me to memorize this derivation?
A: No. The derivations in this book are important because they show a logical
connection between experiment and conclusion, but they are not the only way
to make these connections. For example, when Einstein discovered relativity in
1905, he used a very different path from the one that we're taking. Instead of
memorizing derivations, learn how to work with these concepts by doing a few
34
Uncovering Relativity
Q: If a moving clock ticks slowly, why haven't I ever noticed it before?
A: The effect is minute at everyday speeds. For example, the space shuttle orbits
Earth at a speed of about 5 miles/second. A clock moving past us at that speed will
lose time relative to our clocks. But how much time? The time dilation formula
tells us that while our clocks tick off 1 hour (T) the moving shuttle clock will tick
off 1.3 millionth of a second less than an hour (To). It is a rare clock that can
measure time with this sort of accuracy!
As the speed of the clock increases, the effect becomes more noticeable. While
our clocks tick off 1 hour,
a clock moving at half the speed of light ticks off 52 minutes,
clock moving at 3/5 the speed of light ticks off 48 minutes,
a clock moving at 4/5 the speed of light ticks off 36 minutes,
a clock moving at 99% the speed of light ticks off 8.5 minutes.
Q: Why stop there? What if the clock moves at the speed of light? At twice the
speed of light?
A: The time dilation formula is T = To/√1- (V/c)². If V = c, then √/1-(V/c)² = 0,
so this formula involves division by zero. It's hard to understand how to interpret
this. If V = 2c, then √/1 - (V/c)² =√√-3, so the formula involves taking the square
root of a negative number. It's even harder to understand how to interpret this!
*Why don't I guide you along Einstein's path? Because it uses even more symbols and algebra!
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We are given a clock. We know that for a clock on earth which is at rest, time ticks of 1 hour or 60 minutes. We are given clock moving with various speeds. We use concept of time dilation to find what time clock ticks off for 6 minutes.
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