The Michelson Morley Experiment (2 pages)
Find out the reasons why this experiment was carried out, the details of the experiment itself and how the scientific community interpreted the results
Aim: To determine the velocity of the Earth through the Aether.
– A direct method for detecting this is to measure its influence on the speed of light relative to a frame of reference of the Earth
– A measurement of the speed through the aether would provide evidence for the existence of the aether
Hypothesis:
Light would be travelling at different speeds in each arm, and so there would be a difference in arrival time for the light to reach the detector. If the entire inferometer rotates, the light would travel at different angles relative to the aether in each arm and hence, at different speeds in each time.
In 1887, Michelson and Morley attempted to measure the relative velocity of the Earth through the aether, since the aether is stationary.
Why was this experiment carried out?
The aim of the Michelson –Morley experiment was to determine the velocity of the earth through the aether, a substance believed to fill all empty space. This idea was brought about as a result of a discovery made by Thomas Young in the 19th century in which it was discovered light is a wave. At the time, it was believed all waves required a medium by which to propagate and travel through and thus assumed light also required a medium to travel through, however, light was able to travel through a vacuum and thus they developed the theory of the aether.
Properties of the Aether
The aether was believed to have certain properties, these are:
– The aether is stationary in space
Light travels in straight lines, if the aether was in motion, its movement would change the path of light
– Permeates all matter
Must fill all matter as light can travel through all things with the exception of a black hole
– Permeable by all matter
As light can travel anywhere, the aether must be everywhere to facilitate this
– Low density
The aether must have low density because planets do not slow down to a stop
– High Elasticity
High elasticity is required because there is no loss of energy when transferring energy from one object to another
– Transparent
The aether cannot be seen
Details of the Experiment:
(monochromatic) Light was directed at an angle of 45˚ to a half-silvered, half transparent mirror (beam splitter). It splits the beam in half, allowing half through and reflecting the other half. The two beams with a path difference recombine at the half-silvered mirror, interfering constructively and destructively to produce an interference pattern. This recombined beam is reflected to the detector where it can be observed. The interferometer apparatus was rotated as it was mounted on a concrete slab which floated on mercury, this allowed the interferometer to be easily moved from its original position. This was hypothesised to change the velocity of light relative to the aether wind. This experiment was also repeated over different times of the year and in different conditions.
Results:
– When Michelson and Morley repeated their experiment by rotating the apparatus at different angles and at different times of the year, they found the interference pattern did not change:
o The interference pattern did not shift by anywhere near the amount predicted by the theory // the speeds of beams were not affected by their orientation relative to the aether wind
o There was no fringe shift of the magnitude required was ever observed.
o “It appears, from all that precedes, reasonably certain that if there by any relative motion between the earth and luminiferous ether. It must be quite small.”
– This indicated a null result as it did not prove or disprove the aether
Interpretation of Results:
– The null result was unexpected and thus made it more difficult for the aether model to be accepted as correct
– The null result of the aether model theory led support to competing scientific theories which did not require the existence of the aether, such as Einstein’s theory of Special relativity
– Einstein’s theory predicted the constancy of the speed of light in all inertial frame of reference, it did not require the aether model, successfully accounted for the null result of the Michelson-Morley experiment and its predictions were tested to be true
– The rejection of the aether model and acceptance of Einstein’s relativity contributed to a shift in scientific thinking from classic theory to relativity
Interpretation of the results by Einstein:
– Einstein hypothesised that light did not need the aether to propagate, as a result, the idea of having the aether in which these waves could travel became unnecessary
– Einstein also asserted that light travelled at the same speed for all observers, this led Einstein to form his special theory of relativity thus causing the aether model to become unnecessary and obsolete
Einstein and the Theory of Special Relativity (3 pages)
Find out how Einstein came up with his theory of relativity. Outline the major postulates (ideas)
Galilean model of relativity
“The mechanical laws of physics are the same for every observer moving uniformly with constant speed in a straight line”
The principle of relativity takes that there is no physical way to differentiate between a body moving at a constant speed and a body at rest. This explained that it is not possible to perform an experiment to distinguish between inertial frames of reference without another frame of reference to compare it to.
Principle of Relativity Laws of Physics are identical in inertial frames of reference Results of a physical experiment conducted in inertial frames of reference are the same.
The existence of the aether model violated the principle of relativity as an observer could detect motion relative to the speed of light in an inertial frame of reference. This influenced how Einstein attempted to theorise the nature of light and its impact on other concepts.
Thomas Young
Thomas Young of the 19th Century showed how light behaved like a wave in his double slit experiment in which light rays diffracted and interfered with each other to produce an interference pattern. He demonstrated how light could diffract and interfere with itself which is a property only possessed by waves.
Michelson-Morley Experiment
The null result gave experimental support to Einstein’s theory of special relativity, once there was a rejection of the aether model and an acceptance of Einstein’s relativity contributed to a shift in scientific thinking from classic theory to relativity.
As a result of the null result, Einstein was compelled to test for how the Michelson-Morley results made sense and applied to a theory.
James Clerk Maxwell
Maxwell
Inertial and Non-Inertial Frames of Reference
An inertial frame of reference is a non-accelerating frame of reference which is thus moving at constant velocity or at rest. A person will be unable to tell if they are moving at constant velocity or at rest, this is because the laws of physics are identical in all inertial frames of reference, thus the results of the physical experiments are the same, which are the expected results as at rest.
A non-inertial frame of reference is an accelerating frame of reference which refers to an accelerating frame of reference which varies between each frame of reference and their acceleration. The laws of physics take on different forms which depend on the acceleration of the frame. Therefore, experiments give different results for differing accelerations.
Einstein’s First Though Experiment
“Suppose I am sitting in a train travelling at the speed of light. If I hold a mirror in front of me, will I see my reflection?”
Einstein decided there were 2 possible answers to his question:
Answer 1: No
– If the train is travelling at the speed of light, light from his face would not reach the mirror in order to be reflected back
– Since he cannot see his own reflection in the mirror, he would know that the train was moving at the speed of light with having to compare to another inertial frame of reference, this breaks the principle of relativity as the observer would be able to detect their motion despite being in an inertial frame of reference.
Answer 2: Yes
– The light would travel at its normal speed relative to the train. This does not violate the principle of relativity, however, based on the addition of the velocity, it means that the light inside the train would be travelling at twice its usual speed relative to a stationary observer outside the train. However, this would contradict Maxwell’s theory of the constancy of light.
Einstein proposed his theory of special relativity which postulated:
– The laws of physics are invariant in all inertial frames of reference (this extends of the Galilean model of the theory of special relativity)
– The speed of light is constant in all inertial frames of reference (Continues with Maxwell’s theory of the constancy the speed of light)
This accounted for the null result of the aether model as the constancy of the speed of light in all reference frames meant it does not need a medium to propagate through. This led to the relativity of space and time since the speed of light is a constant.
Implications of the Constancy of Light:
– Einstein’s Theory of Special Relativity which proposed the constancy of the speed of light, led to the relativity of space and time for observers in different inertial reference frames. This contradicted classical laws of Physics where time, mass and length were absolute quantities.
o This is a shift in the scientific community from classical to relativity
– The original metre standard was defined as 1/10,000,000 of the distance between the equator and the North Pole, along the meridian travelling through Paris, which was set by a platinum iridium bar. However, the definition has to be changed to be defined after Einstein’s theory of Special Relativity which proposed the constancy of the speed of light as length is no longer an absolute quantity. Length is now defined as the distance light travels in 1/3×10^8 seconds, as the speed of light is constant and absolute for all observers in an inertial frame of reference.
–
Evidence for Relativity Real Experiments vs Thought Experiments (4 pages)
Outline the thought experiments that Einstein used to support his theory. (Time dilation, length contraction and simultaneity)
Find out three examples for special relativity that go beyond thought experiments to physical measurements. Be able to explain the experiments conducted and the results achieved.
Discuss the importance of the evidence to the theory of special relativity
Relativity of Simultaneity
“An event which appears simultaneous to an observer in an inertial reference frame is not simultaneous to a different observer moving at a relative velocity in another inertial reference frame”
Thought Experiment
A train is moving a a constant velocity to the right with two light sensor doors (door A and door B) and a light bulb and observer in the middle of the train. There is another observer outside the train aligned with the observer inside the train.
When the light bulb is switched on:
– The observer in the same inertial reference frame as the rain observes light travel at constant speed c and the same distance d to either doors, hence they open simultaneously
– The observer outside the train is moving at a relative velocity and observers the light travelling at a constant speed c. However, as the train is moving to the right a v, door A has moved closer while door B has moved further away. Hence, an observer outside the train observer’s door A open before door B as light has travelled a greater distance.
Hence, the relativity of simultaneity suggests that observers moving at a relative velocity in inertial reference frames observe events differently
Time dilation
“The slowing down of time for observers in different inertial reference frames moving at a relative velocity”
Thought experiment:
A train is moving to the right at v with a lightbulb and a mirror on the floor with a velocity of v with a light bulb and a mirror on the floor with an observer inside the train and another outside the train. Let the distance from the light bulb to the mirror be d. At some instant, the laser emits a pulse of light which is directed towards the mirror, and at some time after reflecting from the mirror, the pulse arrives back at the laser.
– An observer inside the train with no relative velocity to the lights will see the light travel the distance d to the mirror with constant speed c in time to.
The time interval measured by the observer on the train requires only 1 clock located at the same place in the frame
– An observer outside the train moving at relative velocity v will see the mirror moving to the right, away from the light. The distance from the original position of the mirror to the new position after the light strikes it is given . The observer outside the train concludes that, because of the motion of the vehicle, if the light is to hit the mirror, it must leave the laser at an angle with respect to the vertical direction.
Result:
Light must travel further for the observer outside than for the observer inside the same frame of reference as the event. According to Einstein’s 2nd idea, of special relativity, the speed of light must be measured by both observers as c.
Since the light travels further for the observer on the train, it follows that the time interval measure by the person outside the train is larger than the time interval measure by the observer on the train.
Thus, the time for the observer on the train is slower than the time for the observer outside of the train.
Length contraction
Length contraction is when the length of an object contracts in the direction of motion for observers in a different inertial reference frame moving at a relative velocity.
Length contraction takes place only long the direction of motion. Length contraction is a symmetrical effect, if an object was at rest on Earth, an observer in a moving frame of reference would also measure its length to be shorter by the same factor of .
Thought Experiment
Consider a light clock arranged so that its pulse travels the length of the train. The light bulb and the sensor are located on the back wall and the mirror located on the front wall:
Event 1: The light clock emits a light pulse which travels to the front wall
Event 2: The light is reflected by the mirror and returns to the sensor.
For the observer:
– On the train, Lo = proper length = length of the train perceived by the observer on a train. Therefore, the length of the journey travelled as seen by the observer on the train is 2Lo. Corresponding with the equation .
– Outside of the train sees the path of the light differently, this is because the train is moving at the same time as the light beam and the forward part of the journey has been lengthened.
On the return path for the light,
Since the train is moving at the same speed as the light beam, the return part of the journey has been shortened.
Derivation of length contraction:
Experimental Proof:
Muons (Evidence for time dilation and length contraction)
Muons are unstable elementary particles which have an equal charge to an electron and a mass 207 times greater. Muons can be produced through the absorption of cosmic radiation high in the atmosphere.
Muons have a lifetime of 2.2 microseconds when measured in their frame of reference. Their speed is close to the speed of light (0.998c), by finding their distance travelled in their lifetime, they can only travel about 600m before decaying into another form. Therefore, it would be impossible for them to reach the surface of the Earth if time, length and mass were absolute. However, by the results of some experiments, some muons do reach the Earth. This is explained by time dilation, as in the muons’ frame of reference, they only live for 2.2 microseconds, but the time taken for muons to reach the Earth’s surface from an observer on Earth is 16 microseconds.
In the muons frame of reference, there is no time dilation, but the distance travelled is observed to be shorter when measured in this frame. Similaraly, from the perspective of an Earth observer, there is time dilation, but the distance of travel is measure to be the proper amplitude of the muon away from the Earth. Thus, when calculations on the muons are performed in both frames, one sees the effect of ‘offsetting penalties” and the outcome of the experiment is the same. In one frame, the distance is shorter (length contraction) but the time is also shorter (proper time). In the other frame, the distance is longer, (proper length) but the time is also longer (time dilation). Therefore, the proper length and proper time do need to be measured by the same observer.
Frame of Reference
Time taken for the muon to fall
Length of the fall
Muon
Proper Time
Contracted Length
Observer on Earth
Dilated Time
Proper Length
Haefe Keating Experiment:
Space Travel (1 page)
Research implications of mass increase, time dilation and length contraction for space travel
The consequences of Einstein's theory of special relativity: mass dilation, time dilation and length contraction has both negative and positive implications on long distance space travel.
Mass expansion
• At relativistic speeds, energy is converted to mass (E=mc2)
• An increased mass required a greater thrust force to accelerate (F=ma), This required more fuel costs, hence limiting the possibility of long distance space travel
• As the velocity of an object increases towards the speed of light, its mass expands approached infinity. By Newton's second law, F=ma, the force required to accelerate the object also approaches infinity. Hence, an object with mass cannot travel at the speed of light.
Time Dilation
• At relativistic speeds, time dilates for an astronaut, this makes it possible for astronauts to travel long distances within their lifetime which increases the potential for long distance space travel
Length Contraction
• At relativistic speeds, length contracts, hence, long distances required for space travel will be shorter, increasing the potential for space travel
As you approach relativistic speeds (where relativity effects occur), kinetic energy will be transformed into mass via E=mc2 and thus there is mass dilation. As a result, as mass increases, it is more difficult to accelerate an object as a result of Newton's 2nd Law F=ma, as the kinetic energy will be transformed into mass and thus, as the force exerted is increased, the amount of acceleration decreases as the mass increases. And thus, objects with mass are unable to reach the speed of light.
Acceleration is always the most energy consuming phases of a space missions, in addition to the accumulation of mass at relativistic speeds, means that the force and energy requirements of even small sustained accelerations become greater and greater.
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