Transcript Consequences of Special relativity

Relativity
H4: Some consequences of special
relativity
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Twin paradox
 An interesting and amusing result
predicted by relativity theory is often
called the twins "paradox".
 If one of a pair of twins goes on a long,
fast journey and then returns home, it will
be found that the twins have aged
differently
 the "stay-at-home" twin is always the
older
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Twin paradox
 The special theory of relativity deals only
with inertial frames of reference, the
astronaut twin would have undergone
huge accelerations, thus his frame is
not inertial
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Hafele-Keating experiment
 This was an experiment to demonstration
the twin paradox.
 Two atomic clocks were flown around the
world in opposite directions.
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Hafele-Keating experiment
 The clocks were compare with a
stationary clock.
Eastward Journey Westward
Journey
Predicted -40 +/- 23 ns
Measured -59 +/- 10 ns
+ 275 +/- 21 ns
+ 273 +/- 7 ns
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Hafele-Keating experiment
 This experiment showed that the clocks
had experienced time dilation, compare
to the stationary clock.
 One clock had slowed down and one
clock had sped up
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Vector addition
 At normal speeds,
you just add the
velocities, at
relativistic speeds
the correct formula is
 if ‘u’ is in the same
direction as ‘v’
vu
u
'
vu
1 2
c
'
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Mass and energy
 The mass of a body is a relative concept.
 The mass of a body measured by an observer
at rest relative to the body is called (not
surprisingly) the rest mass of the body.
 The mass (sometimes called the relativistic
mass) of the body measured by other
observers depends on the velocity of the
observer relative to the body.
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Mass and energy
 As the variation of mass
is basically due to the
time dilation effect, you
should not be surprised
to find that, if the rest
mass of a body is mo,
then its mass, m, as
measured by an
observer moving with
speed v relative to the
body is given by
m0
m
2
 v 
1  2 
 c 
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Mass and energy
 The Einstein relationships are:
 E = mc2 (total energy)
 E = m0c2
(rest energy)
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Mass and energy
 If a force causes body B to accelerate
away from observer A (as in the example
above) then work is done by that force.
 As usual we can define the kinetic energy
possessed by body B (as measured by
A) by saying that
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Mass and energy
 K.E. of B = Work Done causing it to
accelerate
 It can be shown that if the relative speed
of body B is such that its mass (as
measured by A) is m, then
 K.E. = mc2 - moc2 or K.E. = (change in
mass)c2
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Mass and energy
 Here we are seeing the equivalence of
mass and energy. Some of the work done
by the force is converted into mass and if
we define the total energy, E, possessed
by a body to be the sum of its rest energy
(moc2) and its K.E. we have the famous
result
DE = Dmc2
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Mass and energy
 It is easy to show that if the velocity of the body
relative to the observer is small compared with
the velocity of light, then the relativistic formula
reduces to the Newtonian expression (½mv2)
 If the velocity of the body relative to the
observer is very close to the velocity of light,
virtually all the work done by the force is
converted to mass.
 Experiments involving high speed particles
(protons, electrons etc.) in particle accelerators
give evidence to support the idea that mass
varies with velocity.
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Units of Mass/Energy
 The S.I. unit for mass is the kg and for energy,
the Joule. However, on the scale of subatomic
particles, we often use MeV for energy (1MeV
= 1·6×10-13J). So, a possible unit for the
quantity "mc2" is MeV.
 For this reason, the masses of subatomic
particles are often expressed in MeV/c2.
 For example the rest energy of an electron is
about 511MeV and its mass is therefore said to
be 511MeV/c2.
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