Turning Points - Special Relativity Flashcards
Physicists suggested that light needs a medium to travel through, what was this medium?
The ether
Explain why a shift in the interference pattern was expected as the inferometer was rotated?
It was expected that the beam travelling parallel to the Earth’s motion would take longer time to reach the observer. This time difference meant that the two waves would be out of phase once they met by 180º. As the set up was rotated the phase difference changed and so did the interference pattern.
No change in the interference pattern was observed. What was the conclusion of the experiment?
- Either there was no Ether, absolute motion does not exist
- The speed of light is independent of the speed of the observer
What is the purpose of semi-silvered glass block?
To split the light into two beams, one going up and one going through the block
What was the purpose of the plane glass block?
So the light rays travel the same distance through glass
What are the two postulates of special relativity?
- The laws of physics are the same in all inertial frames of reference
- The speed of light is invariant in free space
What is proper time, t0?
How long it took for an event to occur in the frame in which the event was “at rest”
What is the observer time, t?
The time taken from an event to occur from the frame of an observer who sees the event occurring at a velocity, v
What is length contraction?
When the width of an object becomes narrower in the direction it is moving in
What is l0, proper length?
The length of an object in the frame of reference in which the object is stationary
What is l, the observed length?
The length of a moving object in the direction of motion according to someone who sees the object moving at velocity v
What is evidence for time dilation/length contraction?
Muons are subatomic particles with a relatively short lifetime. When muons are created in high-energy particle collisions in Earth’s upper atmosphere, they travel at speeds close to the speed of light. According to classical physics, these muons should decay before reaching the Earth’s surface, as their average lifetime is only around 2.2 microseconds in their rest frame.
However, many muons do reach the Earth’s surface, which suggests that their lifetimes appear to be longer when observed from the reference frame of an observer on the Earth. This phenomenon can be explained by time dilation.
From the perspective of a stationary observer on Earth, the muons experience time dilation due to their high speeds. According to special relativity, time runs slower for objects moving relative to an observer. Therefore, the muons’ internal clocks appear to tick more slowly, and their lifetimes are effectively extended as observed from Earth.
The evidence for time dilation comes from comparing the predicted number of muons that should reach the Earth’s surface based on their average lifetime in their rest frame, with the actual number of muons observed. The observed number of muons is significantly higher than what would be expected if time dilation were not occurring.
Muon decay can also be used to provide experimental evidence for length contraction as well as
time dilation. As the muons are travelling at such a high speed the distance they travel will
appear shorter than the distance as viewed by an external observer.
How can muon decay and time dilation be shown?
Two detectors detect count rate at high altitude and low altitude, distance between detectors is measured. Find time taken for particles to pass between detectors, find number of half lives by dividing total time by half life and do 0.5 to power of number of half lives to find expected count rate.
Repeat for dilated time except multiply half life time by lorenz factor.
Compare expected count rate and actual count rate
what is kinetic energy?
relativistic Ek - total energy (moc^2)
Describe Bertozzi’s experiment
Bertozzi’s experiment provides experimental evidence for the increase in mass of an object with speed.
It involved a particle accelerator which could emit electrons at varying kinetic
energies, two detectors, A and B, connected to an oscilloscope, and an aluminium plate connected
to a temperature sensor:
- The electrons were released in pulses, and the time taken for them to travel between A and B could be calculated using the oscilloscope by measuring the distance between
peaks on the display (and multiplying by the time base). - Next, the distance between A and B is measured and the speed of the electrons was calculated.
- The electrons are directed at the aluminium target and when they collide with it, their
kinetic energy is transferred to the target in the form of heat. The change in temperature of the target is measured using the temperature sensor, meaning the kinetic
energy of the electrons could be directly measured.
Kinetic energy of one electron =
mcΔθ/n
Derived from: Q = mcΔθ
Where m is the mass of the target, c is its specific heat capacity, Δθ is the change in
temperature and n is the number of electrons in that pulse.
What did bertozzi discover?
When Bertozzi plotted his results as a graph of kinetic energy against speed, he found that his values were very close to those predicted by Einstein’s theory of special relativity, meaning
that his experiment provided evidence to support it.
What does it mean when “the speed of light is invariant in free space” ?
It means the speed of light is independent of the motion of the source or observer
