Special Relativity (4.1)
Special relativity
• describe an example of natural phenomena that cannot be explained by Newtonian
physics, such as the presence of muons in the atmosphere - answer Problems that had
resisted explanation using the Newtonian approach:
- light appeared to be a wave, but the medium for its propagation (the 'aether') was
undetectable
- the equations describing electricity and magnetism were inconsistent with Newton's
descriptions of space and time
Additionally, the problem of accounting for the lifetime of muons at different altitudes
could not be explained by Newtonian physics. Scientists measured the amount of
muons present in the atmosphere at the top of a mountain, compared to the bottom.
From 563/hr at the top, Newtonian calculations predicted 27/hr at sea level. 407/hr were
counted; aligning with the theory of special relativity.
It was found that to the observers, the distance was 1910 m. To the muons, it was 183
m. This is called 'length contraction'.
The mean lifetime in the muon's frame of reference is 2.2us, but in the observers it was
23us, so to the scientists they took longer to decay: known as 'time dilation'.
Special relativity
• define the terms frame of reference and inertial frame of reference - answerWhen you
describe the motion of an object, you need something to compare it against. The frame
of reference is an arbitrary set of axes with reference to which the position or motion of
something is described, or physical laws are formulated. It defines the location of the
observer.
In general, a frame of reference that is stationary or moving at constant velocity is an
inertial frame. However, in a frame of reference that is accelerating, results are different.
The surface of Earth is considered inertial even though undergoing centripetal
acceleration (small enough to be disregarded).
Special relativity
• recall the two postulates of special relativity - answerTwo assumptions or 'postulates'
of special relativity:
1. the laws of physics are the same in all inertial (uniformly moving) frames of reference
, 2. the speed of light in a vacuum has the same value, c, in all inertial frames of
reference
The second postulate can be said to be redundant, as it is a logical consequence of the
first
Special relativity
• recall that motion can only be measured relative to an observer - answer(On a train)
You are moving relative to the stationary observer outside the train, but the stationary
observer is moving relative to you. There is no way of working out who is really moving:
any experiments inside the train would give the same results as on the platform. Both
inertial frames are equally valid. There is one frame in which the train is moving, another
in which the observer is moving, and another in which both frames are moving. The one
thing all observers agree on is the relative speed.
Special relativity
• explain the concept of simultaneity - answerSimultaneity is the relation between two
events assumed to be happening at the same time in a frame of reference. If light
signals from two events reach an observer who is midway between them at the same
time, they are simultaneous in that given reference frame. If an observer is standing
closer to one of the events, and the lights still reach them at the same time, the further
event must have occurred first, as the light had to travel further to their eyes.
Events that are simultaneous i one frame of reference are not necessarily simultaneous
in another frame of reference, even if both frames are inertial. Take above for example.
In the latter scenario, if EB had to occur before EA for the observer (standing closer to
EA) to observe them simultaneously, an observer standing mid-way would have
observed EB before EA; non-simultaneously.
Special relativity
• recall the consequences of the constant speed of light in a vacuum, e.g. time dilation
and length contraction - answerNo matter what frame of reference you're in/how you're
moving through the Universe, you'll always measure the speed of light in a vacuum to
be ~ 300,000 km/s (e.g. if a spaceship travelling at 0.8c fires a laser beam at a piece of
debris, the laser beam still only travels at 1.0c, not 1.8c). In his case, for the value to
remain constant, Einstein proposed that either the distance must be smaller than
expected, or the time taken must be greater than expected, or both. In measuring c,
different observer's frames of reference for time and space have to shift to keep the
speed constant.
The time dilation and length contraction effects are necessary to keep the speed of light
constant.
Special relativity
• define the terms time dilation, proper time interval, relativistic time interval, length
contraction, proper length, relativistic length, rest mass and relativistic momentum -
answerTime dilation is the difference in the time interval between two events as
Special relativity
• describe an example of natural phenomena that cannot be explained by Newtonian
physics, such as the presence of muons in the atmosphere - answer Problems that had
resisted explanation using the Newtonian approach:
- light appeared to be a wave, but the medium for its propagation (the 'aether') was
undetectable
- the equations describing electricity and magnetism were inconsistent with Newton's
descriptions of space and time
Additionally, the problem of accounting for the lifetime of muons at different altitudes
could not be explained by Newtonian physics. Scientists measured the amount of
muons present in the atmosphere at the top of a mountain, compared to the bottom.
From 563/hr at the top, Newtonian calculations predicted 27/hr at sea level. 407/hr were
counted; aligning with the theory of special relativity.
It was found that to the observers, the distance was 1910 m. To the muons, it was 183
m. This is called 'length contraction'.
The mean lifetime in the muon's frame of reference is 2.2us, but in the observers it was
23us, so to the scientists they took longer to decay: known as 'time dilation'.
Special relativity
• define the terms frame of reference and inertial frame of reference - answerWhen you
describe the motion of an object, you need something to compare it against. The frame
of reference is an arbitrary set of axes with reference to which the position or motion of
something is described, or physical laws are formulated. It defines the location of the
observer.
In general, a frame of reference that is stationary or moving at constant velocity is an
inertial frame. However, in a frame of reference that is accelerating, results are different.
The surface of Earth is considered inertial even though undergoing centripetal
acceleration (small enough to be disregarded).
Special relativity
• recall the two postulates of special relativity - answerTwo assumptions or 'postulates'
of special relativity:
1. the laws of physics are the same in all inertial (uniformly moving) frames of reference
, 2. the speed of light in a vacuum has the same value, c, in all inertial frames of
reference
The second postulate can be said to be redundant, as it is a logical consequence of the
first
Special relativity
• recall that motion can only be measured relative to an observer - answer(On a train)
You are moving relative to the stationary observer outside the train, but the stationary
observer is moving relative to you. There is no way of working out who is really moving:
any experiments inside the train would give the same results as on the platform. Both
inertial frames are equally valid. There is one frame in which the train is moving, another
in which the observer is moving, and another in which both frames are moving. The one
thing all observers agree on is the relative speed.
Special relativity
• explain the concept of simultaneity - answerSimultaneity is the relation between two
events assumed to be happening at the same time in a frame of reference. If light
signals from two events reach an observer who is midway between them at the same
time, they are simultaneous in that given reference frame. If an observer is standing
closer to one of the events, and the lights still reach them at the same time, the further
event must have occurred first, as the light had to travel further to their eyes.
Events that are simultaneous i one frame of reference are not necessarily simultaneous
in another frame of reference, even if both frames are inertial. Take above for example.
In the latter scenario, if EB had to occur before EA for the observer (standing closer to
EA) to observe them simultaneously, an observer standing mid-way would have
observed EB before EA; non-simultaneously.
Special relativity
• recall the consequences of the constant speed of light in a vacuum, e.g. time dilation
and length contraction - answerNo matter what frame of reference you're in/how you're
moving through the Universe, you'll always measure the speed of light in a vacuum to
be ~ 300,000 km/s (e.g. if a spaceship travelling at 0.8c fires a laser beam at a piece of
debris, the laser beam still only travels at 1.0c, not 1.8c). In his case, for the value to
remain constant, Einstein proposed that either the distance must be smaller than
expected, or the time taken must be greater than expected, or both. In measuring c,
different observer's frames of reference for time and space have to shift to keep the
speed constant.
The time dilation and length contraction effects are necessary to keep the speed of light
constant.
Special relativity
• define the terms time dilation, proper time interval, relativistic time interval, length
contraction, proper length, relativistic length, rest mass and relativistic momentum -
answerTime dilation is the difference in the time interval between two events as
