6 Special Relativity
113
When physicists explore the domain of cosmic rays, they encounter particles that are moving at speeds approaching that of light, when time dilation
effects are much more pronounced. The muon is such a particle. In Chap. 9
we shall discuss muons, and other subatomic particles, in some detail. Here
we need only note that the muon’s average lifetime, when it is at rest, is 2.2
millionths of a second. In this time, if we disregard the time dilation of Relativity, even if the muon were travelling at the velocity of light, it would only
travel 660 m. However, time dilation cannot be disregarded: thanks to it,
physics students in their laboratories today routinely observe the arrivals of
thousands of muons from the upper atmosphere, i.e. from distances of 15 km
to more than 100 km. 6
6.7 Lorentz Contraction
Suppose now that we manage to hitch a ride on a muon on its way from
the upper atmosphere to the earth’s surface below. We have done the calculations and are aware that with the muon’s average lifetime of 2.2 µs, we
will only have travelled an average of about 660 m before the muon decays
beneath us. And yet when we were back on earth, we had observed most of
the muons arriving safely, having travelled much further. It might seem that
the outcome depends on which frame of reference we choose for our calculations. Doesn’t this violate Einstein’s edict that the results of experiments
should be independent of the frame of reference?
No, because the Lorentz transformations contain another surprise: not
only does the rate of passage of time vary with the speed, but so also does
the length. An observer travelling at a certain velocity relative to an object
will notice a decrease in the length of the object in the direction of motion.
There is a reciprocity between time dilation, and what is now called the
Lorentz contraction of distance. Observer A in the laboratory on earth observes
a long-lived (due to time dilation) muon travelling several kilometres to the
earth; Observer B on the muon sees a short-lived muon travelling a much
shorter distance (due to Lorentz contraction) to the earth’s surface. Thus
both observers see the muon arriving safely at the laboratory before the muon
decays.
These concepts have now been taught in physics classes for the best part of
a century. However, when first published by Einstein, they puzzled not only
lay people, but specialists as well. Shortly after the publication of Einstein’s
6 In doing so, they are replicating a version of an experiment first performed by Bruno Rossi and
David B. Hall in 1941.
113
When physicists explore the domain of cosmic rays, they encounter particles that are moving at speeds approaching that of light, when time dilation
effects are much more pronounced. The muon is such a particle. In Chap. 9
we shall discuss muons, and other subatomic particles, in some detail. Here
we need only note that the muon’s average lifetime, when it is at rest, is 2.2
millionths of a second. In this time, if we disregard the time dilation of Relativity, even if the muon were travelling at the velocity of light, it would only
travel 660 m. However, time dilation cannot be disregarded: thanks to it,
physics students in their laboratories today routinely observe the arrivals of
thousands of muons from the upper atmosphere, i.e. from distances of 15 km
to more than 100 km. 6
6.7 Lorentz Contraction
Suppose now that we manage to hitch a ride on a muon on its way from
the upper atmosphere to the earth’s surface below. We have done the calculations and are aware that with the muon’s average lifetime of 2.2 µs, we
will only have travelled an average of about 660 m before the muon decays
beneath us. And yet when we were back on earth, we had observed most of
the muons arriving safely, having travelled much further. It might seem that
the outcome depends on which frame of reference we choose for our calculations. Doesn’t this violate Einstein’s edict that the results of experiments
should be independent of the frame of reference?
No, because the Lorentz transformations contain another surprise: not
only does the rate of passage of time vary with the speed, but so also does
the length. An observer travelling at a certain velocity relative to an object
will notice a decrease in the length of the object in the direction of motion.
There is a reciprocity between time dilation, and what is now called the
Lorentz contraction of distance. Observer A in the laboratory on earth observes
a long-lived (due to time dilation) muon travelling several kilometres to the
earth; Observer B on the muon sees a short-lived muon travelling a much
shorter distance (due to Lorentz contraction) to the earth’s surface. Thus
both observers see the muon arriving safely at the laboratory before the muon
decays.
These concepts have now been taught in physics classes for the best part of
a century. However, when first published by Einstein, they puzzled not only
lay people, but specialists as well. Shortly after the publication of Einstein’s
6 In doing so, they are replicating a version of an experiment first performed by Bruno Rossi and
David B. Hall in 1941.