turning points - special relativity

absolute motion

the belief that everything moves in relative motion to the ether, a substance that they believed permeated the entire universe

michelson-morley experiment (interferometer)

to measure the absolute speed of the earth through the ether

formed of a partially reflective surface/beam splitter, glass block (compensating plate), and two mirrors (same distance from beam splitter)

the partially reflective surface reflects some light, and allows some to pass through

this creates two beams of light that move perpendicular to each other and travel towards the mirrors

after being reflected on the mirrors the two beams return to a detector and the interference pattern can be recorded

purpose of the glass block in the michelson-morley experiment

to make sure the two beams of light pass through the same amount of glass

what they thought would happen in the michelson-morley experiment

speed of the light travelling parallel to the motion of earth would be affected

speed of light travelling perpendicular to the motion of earth would not be affected

light moving parallel to earth’s motion would take longer to travel, so rotating apparatus by 90 would cause a shift in the interference pattern

results and significance of michelson-morley experiment

interference pattern experienced no shift

time taken for light to travel was unaffected by rotating the apparatus

• ether doesn’t exist or the earth drags ether along with it as it moves

• speed of light is invariant in free space, speed of light is independent of the motion of the source or observer

einstein’s two postulates

1. the speed of light in free space is invariant (indpendent of the motion of the source or the observer)

2. the laws of physics have the same form in all inertial frames (intertial frame means acceleration = 0)

proper time t_o

amount of time experienced by a stationary observer

which is bigger, t_o or t

t

experimental evidence for time dilation

muon decay

proper length l_o

length of an object measured by an observer who is at rest relative to the object

what happens to width in length contraction

remains constant

only length changes

experimental evidence for length contraction

muon decay

distance they travel will appear shorter than the distance as viewed by an external observer

when does ke = ½ mv² not apply

when objects are moving at relativistic speeds of light (over 1/10 speed of light) because the mass of the object changes significantly

total energy =

kinetic energy + rest energy

ke =

(γ-1)m_oc²

m =

γm_o

bertozzi’s experiment

experimental evidence for the increase of an object’s mass with speed

particle accelerator which can emit electrons at varying ke

detectors a and b connected to an oscilloscope

aluminium plate connected to a temperature setup

how does bertozzi’s experiment work

1. electrons released in pulses and time taken for them to travel between a and b calculated using oscilloscope by measuring distance between peaks and multiplying by time base

2. distance between a and b measured and speed of electrons calculated

3. electrons directed with aluminium target

4. when they collide with target, ke is transferred to target in the form of heat

5. change in temperature of the target measured using the temperature sensor, so ke of electrons can be measured

ke of one electron from bertozzi’s experiment

(mcΔθ)/n where m is mass of target

how is Bertozzi’s experiment evidence for special relativity

plotted graph of ke against speed

values were very close to those predicted by Einstein’s theory of special relativity

according to special relativity, why can an object not reach the speed of light

as v approaches c, mass approaches infinity so energy approaches infinity, which is impossible