Turning points 3 Flashcards
What was absolute motion
All motion is relative to a fixed point
e.g. if you are on a train travelling 20m/s and throw a ball forward 3m/s from your point of view, then an observer would see the ball moving at 23m/s
What was the ether
Fixed background that all motion could be measured relative to
What was the purpose of the Michelson - Morley experiment
To measure the effect of the Earth’s motion through the ether on the speed of light
What was the method for the Michelson-Morley experiment
- This apparatus is called an interferometer:
- Light passes through a partially reflective surface so some travels vertically up and some passes horizontally through
- There are mirrors at the end of each path so each beam reflects back and recombines as it passes through the partially reflective surface, with now both travelling vertically down
- They will form an interference pattern
What was the prediction for the Michelson-Morley experiment
Light travelling parallel to the Earth’s motion would be slower and light travelling perpendicular to the Earth’s motion would be unaffected
e.g. if the Earth was a train and light is a ball, when the light is parallel, it’s like throwing a ball backwards while on the train so the ball is slower to someone on the platform
Therefore, as you rotate the apparatus 90 degrees, the interference pattern would shift as the other beam light is now slower instead
What were the actual results of the Michelson Morley experiment
The interference pattern did not change showing that the time taken for light to travel was unaffected by rotating the apparatus
What were the conclusions of the result from the Michelson Morley experiment
- The ether doesn’t exist or the Earth drags the ether along with it as it moves
- The speed of light is invariant i.e. independent of the motion of the source or the observer
What are inertial reference frames
A frame which is moving at a constant velocity so a = 0
i.e. object is either stationary or moving at constant velocity
What are the assumptions in Einstein’s theory of special relativity
- Speed of light is invariant i.e. independent of motion of source or observer
- Only applies to inertial reference frames where the laws of physics act the same way in all inertial frames
What is time dilation
Consequence of special relativity causing time to pass at different speeds depending on the motion of observer
What is the formula for time dilation
t = t0 / sqrt (1 - v^2 / c^2)
where
t is the time for the external observer relative to event
t0 is the time for the stationary observer relative to event
v is velocity at which the stationary observer is travelling
Which is greater, t or t0
proper time (t0) is always shorter than the time measured by an external observer
How does Muon decay provide evidence for special relativity
- Muons travel very fast so experience time dilation
- Place 2 detectors and measure the count rate at each and distance between them
- time for muon to go from detec1 to detec2 = distance / speed but this time is t not the time which is experienced by the muon (t0)
- Using t instead of t0 affects half life so expected count rate, meaning the value is much lower than the actual measured count rate at detector 2
What is length contraction
Consequence of special relativity causing the length of objects to appear shorter to an external observer when they are travelling at higher speeds
What is the formula for length contraction
l = l0 / sqrt(1 - v^2 / c^2)
where
l0 is the length of the object measured by an observer at rest relative to the object
v is the velocity at which the object is travelling
Which is greater l0 or l
The proper length (l0) is always greater than the length to external observer (l)
How does length contraction affect width of the object
It has no affect on width, only length
How can muon decay provide evidence for length contraction
- Muons travel fast so the distance they travelled seems shorter to external observer
- This time we can measure first proper length as the scientists are stationary relative to the stationary detectors but muons are moving
- Use the proper length value to measure length for muons using length contraction formula
- Use this to find the actual time taken which can be used to measure half life and actual count rate
Why does mass increase as energy increases at high speeds
If speed is close to speed of light, applying energy (1/2 mv^2) cannot increase speed as cannot travel past speed of light so instead mass increases
How can you calculate the relativistic mass
m = m0 / sqrt (1 - v^2 / c^2)
where m is the new mass when the object is travelling fast (relativistic)
m0 is the rest mass
v is the speed the object is travelling
How can you calculate the total energy of an object travelling very fast
for slow object, E = m0c^2 where m0 is rest mass
so for fast object, E = m0c^2 / sqrt(1 - v^2 / c^2)
How can you find the kinetic energy of the object using the total energy and rest energy
Total energy = kinetic energy + rest energy
Ek = m0c^2 / sqrt (1 - v^2/c^2) - m0c^2
How did Bertozzi’s experiment prove the increase of mass of an object with speed
- Release electrons in pulses using a particle accelerator
- Measure the time taken for electrons to travel between 2 detectors using time x axis of oscilliscope
- Measure distance between 2 detectors and work out speed of electrons
- Place aluminium plate with temperature sensor at second detector so electrons transfer their kinetic energy to plate and calculate this Ek
- Plot a graph of kinetic energy against speed and as Ek tends to infinity speed tends to c meaning c is the max speed and as Ek is increasing mass must be increasing instead
How did Bertozzi calculate the Ek of 1 electron
Measure change in temperature of aluminium plate when electron pulse collides
Ek of 1 electron = mcΔθ / n
where m is mass of plate, c is specific heat capacity of plate and n is number of electron in that pulse
