Relativity and the Speed of Light

Outline the features of the aether model for the transmission of light

The concept that the aether is a stationary or absolute rest frame requires an understanding of frames of reference and relative motion. Scientists today agree that there is no absolute reference frame and the motion of objects can only be measured relative to other objects. In turn these other objects may be moving relative to still other objects. For example, a person on a train throws a ball. Relative to the train, the ball is travelling north at 5m/s. However, the train is travelling south at 20m/s, and so relative to a person on the Earth’s surface next to the train the ball is travelling south at 15m/s. A person on an aircraft travelling north at 40m/s observes this same event, and sees that the ball is travelling south at 55m/s relative to him. An observer outside the solar system will see the ball’s motion in light of the orbital motion of the Earth, and an observer outside the galaxy will see the ball’s motion in light not only of the orbital motion of the Earth, but the motion of the Sun as it orbits around the centre of the galaxy. In this way it is impossible to “truly” determine an object’s velocity in absolute terms- there is no one “correct” answer for the ball’s velocity, and each of the observations made (in the train, outside the train, in the aircraft etc.) is equally valid. Previously, scientists thought that motion could be determined in absolute terms by measuring motion relative to the aether. Under such a model, the ball may be travelling west at 30m/s relative to the aether (an arbitrary figure) and this would be its true velocity. This is what is meant by the aether being a stationary frame, with all objects moving relative to it. This explanation is not part of the dotpoint and so is not necessary for an exam response. It exists only to clarify the meaning of “absolute rest frame”.

According to the aether model for transmission of light, light was a wave that propagated through a material called the “aether”. According to the model, aether had no mass, could not be seen, heard or felt, and was distributed evenly throughout the universe residing between the particles that make up matter. Further, it was considered to be an absolute rest frame, meaning that the absolute motion of all objects in the universe could be measured relative to the aether.

Remember- The aether was invisible, without mass, existed at all points in the universe, is an abso- lute rest frame, and was the medium for light.

Describe and evaluate the Michelson-Morley attempt to measure the relative velocity through the aether

Be aware that the failure of the Michelson-Morley experiment to observe a changing interference pattern does not disprove the existence of the aether. All it does is question the theory and prove that either the theory or the experiment is flawed. Einstein subsequently interpreted this experiment as disproving the aether, but the experiment itself did not disprove the aether.

If the aether is stationary and the Earth is moving through the aether, then it follows that there is an aether “wind” that will affect the apparent speed of light to an observer on the Earth. The Michelson-Morley experiment was designed to analyse the aether wind, and thus calculate the velocity of Earth through space. A beam of light was split and sent into two directions at 90 degrees to each other horizontally by a half-silvered mirror. They were then reflected back and combined, such that both rays had travelled the same distance. This recombining process resulted in an interference pattern. The device was floated on liquid mercury, which enabled smooth rotation of the entire experiment. As the device was rotated, the aether wind was expected to cause the light to travel at different speeds in each direction, thus causing the interference pattern to change. The velocity of the Earth would be calculated by analysing the changing interference pattern. However, despite extensive testing, no change in the interference pattern was observed. This led to the conclusion that the aether model was flawed, which subsequently led to the conclusion that the aether did not exist. In terms of calculating the velocity of the Earth, the Michelson-Morley experiment was a failure, but its conclusion, based on results that were both valid and reliable changed scientific theory dramatically, making it one of history’s most important experiments.

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Remember- The Michelson-Morley experiment failed in its goal to determine the speed of the Earth through the aether.

Gather and process information to interpret the results of the Michelson- Morley experiment

The Michelson-Morley experiment was designed to calculate the velocity of the Earth through the aether, on the grounds that light would travel faster in certain directions and slower in others, due to the relative motion between the Earth and the aether. The Michelson-Morley experiment split a light beam, creating two beams at right-angles to each other, and after letting them travel for a short distance, recombined them. As the differences between the speed of light change when the device rotates, the interference pattern formed also changes as the phase difference between the two beams change. However, despite much repetition the experiment showed that light seemed to travel at the same speed in all directions, because the interference pattern formed never changed even when the orientation of the experiment was changed by rotating the apparatus. The experiment therefore provided a null result, neither disproving nor proving the existence of the aether. However, the results of the experiment could be taken in two ways- that the Earth wasn’t moving through the aether, or that the aether model was flawed. Since the Earth was known to move, the Michelson- Morley experiment provided the final evidence that debunked the aether model for light transmission. Einstein interpreted the results of the experiment as confirming his theories as to the constancy of the speed of light, as well as the non-existence of the aether.

Remember- The Michelson-Morley experiment demonstrated that the speed of light on Earth was constant in all directions, significant evidence towards disproving the aether model.

Discuss the role of the Michelson-Morley experiments in making determina- tions about competing theories

The Michelson-Morley experiment produced startling results that in the end disproved the aether model for transmission of light and instead supported Einstein’s model of light. At the time of the experiment there were two competing theories- the aether model in which light propagated through a stationary aether through which the Earth moved, and Einstein’s model, part of which specifying that light travelled at a constant speed under all circumstances. The Michelson-Morley experiment showed that light travelled at a constant speed in all directions, and challenged the aether theory by showing that there was no aether wind. So the Michelson-Morley experiment provided pivotal evidence that determined the survival of competing theories as to the transmission of light.

Remember- The Michelson-Morley experiment helped prove Einstein’s theory while debunking the aether theory.

Outline the nature of inertial frames of reference

In terms of Newton’s laws holding true, an inertial reference frame is one in which fictitious forces are not required to account for motion. For example, consider the rotating ride “Rotor” at Luna Park (Sydney), a ride where people are placed inside a rapidly spinning cylinder so that they are pinned to the sides of the cylinder. To an observer on the deck above, it is quite clear that the people inside the ride travel in a circular path because the walls of the ride exert centripetal force. However, an observer in the ride feels a force pressing them into the walls of the ride. To the person outside, this is simply their inertia pushing them against the wall. But to the observer inside, they may not even be moving- all the objects inside “Rotor” are stationary relative to them (as they are spinning along with the ride). Therefore, the fictitious force centrifugal force is pressing them against the wall of the ride. This force is fictitious because it does not exist as an “action” force in all inertial frames of reference- it exists in the frame inside Rotor but in the frame outside it is observed as a reaction force. Fictitious forces only exist in non-inertial reference frames, and so it can be concluded from this that the rotating cylinder in “Rotor” is non-inertial (which is true, as it is constantly accelerating because it rotates). Further, if the rider threw a ball straight into the middle of the ride, they would find that the ball would not travel in a straight line, disobeying Newton’s laws, again showing that the laws only hold directly true in an inertial frame. This needn’t be detailed in an answer- however, it is an important concept to understand. This answer has focussed on the use of the fictitious centrifugal force to show the difference between inertial and non-inertial frames of reference. For a more in-depth examination of centrifugal force itself, see the Extra Content chapter at the end of the Guide.

A frame of reference is essentially the environment from which measurements are taken by an ob- server. It can be a stationary room or a moving train. An inertial frame of reference is one in which no net force is acting, and in which all of Newton’s laws hold true. No mechanical experiment or observation from within the frame can reveal if the frame is moving with constant velocity or at rest.

Remember- An inertial frame of reference is any frame that isn’t accelerating.

Perform an investigation to help distinguish between non-inertial and inertial frames of reference

The experiment we carried out distinguished between non-inertial and inertial frames of reference by considering the definition of an inertial frame- one where all the laws of physics hold directly true and one which is indistinguishable from another inertial frame. In our experiment, we had a pulley with a string attached to a spring balance, holding a 100g weight. We took the apparatus as being an inertial reference frame when stationary- at that point the spring balance registered 100g. When we pulled the rope to cause the balance and weight to rise at a constant velocity, the spring balance still indicated 100g, showing that the constant-velocity frame was inertial. However, when we pulled the rope increasingly faster to cause the spring to accelerate upwards, it registered more than 100g, because according to F = ma, it was exerting extra force on the weight to cause it to accelerate upwards. Because this accelerating frame indicated a different value from the stationary 100g, we identified it as a non-inertial frame where the laws of physics do not directly hold true (in this case, because the 100g weight was indicated as weighing more by the spring balance while accelerating).

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Remember- Spring balance with a pulley experiment, pulling the rope changed the reading on the balance.

Discuss the principle of relativity

Although some interpret this dotpoint as only covering classical Galilean relativity, it is useful at this point to consider Einstein’s special relativity as well.

The classical principle of relativity was first explored by Galileo, and then developed upon by New- ton, and states that no measurement made from within an inertial reference frame can be used to determine the velocity of that frame. This means that when within an inertial frame of reference, it is impossible to determine whether the frame is moving or not, unless measurements are taken involving observations outside the frame. For example, consider a train that is travelling at a con- stant velocity. From within the train, there is no observation that can be made to determine whether the train is stopped at a station (with a constant velocity of 0) or travelling at a constant velocity. This is because the train is an inertial frame of reference (so long as it is travelling at a constant velocity). The only way to determine the motion of the train is to make observations of other frames from within the train- for example, looking out of the window to the frame outside the train to see whether the train is moving or not. Effectively, this means that all inertial frames of reference are equal and equally correct- there is no such thing as an absolute rest frame against which all motion can be measured since all inertial reference frames are equal.

In 1905 Einstein devised his theory of special relativity. It was based on two key postulates- firstly, that the laws of physics are the same for all inertial reference frames (and by that it is meant that all inertial frames are equal and cannot be distinguished from another- there is no absolute rest frame) and secondly that the speed of light is constant for all observers. The idea that the speed of light is constant for all observers was extremely revolutionary because of its implications. Thought experiments, and subsequently physical experiments, showed that as observed velocity increases, time dilates, length contacts, and mass increases. Essentially, the principle of relativity states that nothing in the universe is constant except for the speed of light, and everything else is dependant on the relative movement between frames of reference. Although it was able to explain evidence (such as the Michelson-Morley experiment) and make predictions about the behaviour of light, this extremely revolutionary idea had little evidence to directly prove it when it was formulated. As a result, it took many years for the principle of relativity to become part of mainstream science.

Remember- No measurement from within an inertial reference frame can determine anything about the movement of that frame, all motion occurs relative to something else, and the speed of light is constant for all observers.

Describe the significance of Einstein’s assumption of the constancy of the speed of light

Einstein’s key postulate was that the speed of light is constant for all observers. This means that whenever an observer takes measurements to determine the speed of light, the value calculated is always the same. However, in many cases Newtonian vector addition will increase the distance travelled by light as observed by a stationary observer. Under traditional vector addition, calculating

the velocity by dividing distance by time would break Einstein’s postulate resulting in a value greater than 3 × 108. The consequence and significance of the speed of light being constant is that mass, length and time change so that the speed of light can never be exceeded. This is extremely significant to predicting how objects behave at relativistic velocities.

Remember- The speed of light being constant is significant because it means mass, time and length all become variable.

Analyse and interpret some of Einstein’s thought experiment involving mirrors and trains and discuss the relationship between thought and reality

Make sure you understand everything in this dotpoint, and practice writing a response to this dotpoint. If you are not clear and concise, it’s easy to not fully answer the question or to end up with an extremely long answer that wastes time in a test.

Einstein had two main thought experiments- looking at himself in a mirror on a train moving at the speed of light, and bouncing light from the roof to the floor and back in a moving train. Both these experiments showed that with conventional models such as vector addition, it would be possible for a stationary observer looking to the train to see light travelling faster than c. However, this ran against his principle of the speed of light being constant.

In the mirror thought experiment, Einstein wondered whether he would be able to see his face normally in a mirror held in front of him if the train was travelling constantly at the speed of light. He decided that he would be able to, because he was in an inertial frame and should have no way to determine he was moving at c. But with vector addition, a stationary observer would see light travelling away from Einstein’s face at c, but as the train was moving at c as well, the observer would see light travel twice the distance in the same amount of time. Einstein’s interpretation of this was that the time observed for light to travel that distance changed, so that a stationary observer would still see light travelling at c.

In the light bouncing experiment, light was seen to travel a longer path by an observer. Again, the interpretation was that time changes so that c remains constant. In terms of discussing the relationship between thought and reality, thought experiments can be valuable tools to “perform” experiments that cannot be performed in reality, such as a train moving at relativistic speeds, and to make meaningful conclusions as Einstein did. This makes them extremely useful tools. On the other hand, it is very easy to misinterpret thought experiments, either through flawed logic or failing to take account of other factors, possibly unknown to science that would affect an experiment in reality. So while they are very useful tools, they need to be used carefully when drawing conclusions.

figure 12

Remember- The thought experiments were Einstein looking at a mirror on a train, and bouncing light from the roof of a train to the floor and back as observed by a stationary observer.

Identify that if c is constant then space and time become relative

This is an identify dotpoint, and so requires very little detail. It would be better to study the previous dotpoint as it goes into more detail about the impacts of the speed of light being constant.

In traditional physics, the behaviour of light had to adapt to the motion of the observer. With the speed of light being a constant under Einstein’s theory, the dimensions involved in motion have to adapt to light. This means that space and time become relative to velocity so that c is always a constant.

Remember- When the speed of light is constant, space and time become relative.

Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard

Originally, a metre was defined as /frac {1}{10,000,000}th of the circumference of the Earth, and then later as the distance between two lines on a platinum-iridium bar, which provided the standard measure of a metre. However, today the metre is defined as the distance light travels in /frac {1}{299792458} seconds. This means that distance is calculated based on time- a unit of distance is measured in terms of how much distance light travels in a period of time. A light-year is another distance measured by time, and it is the distance light travels in one year.

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Analyse information to discuss the relationship between theory and the evidence supporting it, using Einstein’s predictions based on relativity that were made many years before evidence was available to support it

Ensure you memorise the evidence, and also make sure you can link it back to Einstein’s theory clearly showing how the evidence supported the theory.

Einstein’s key prediction that was made before available evidence was that space and time are relative to observed movement, and that the speed of light is constant. The consequences of this were that observed time could vary, so time is not constant. In 1971, the Hafele-Keating experiment took 4 synchronised atomic clocks, placed 2 of them on commercial airline flights, and flew them in opposite directions around the world. When later compared after circumnavigating the world, both the clocks showed less time had passed than the clocks on the ground, with differences of around 50 nanoseconds in an easterly direction, and around 270 nanoseconds in a westerly direction, which almost exactly matched up with Einstein’s predictions.

Other experiments using muons found similar effects. The muon is a particle similar to an electron, but heavier. When stationary it has a half-life of around 2 microseconds, but when accelerated in a particle accelerator to speeds up to 0.9994c, it was found their observed half-life was around 60 microseconds- confirmation of Einstein’s theory. There is a distinct link between theory and evidence supporting it. No hypothesis can be considered a theory until there is evidence confirming that the hypothesis is correct. Therefore, Einstein’s conclusions were merely predictions of what would happen at relativistic speeds and nothing more at the time he devised them, and his ideas only became theory later after evidence confirmed his ideas.

Remember- Longer muon decay in accelerators, and atomic clocks in aircraft circumnavigating the Earth.

Explain qualitatively and quantitatively the consequences of special relativity in relation to the relativity of simultaneity, the equivalence between mass and energy, length contraction, time dilation, and mass dilation

See the Formulae chapter for a comprehensive guide to quantitatively determining the effect of relative motion.

Relativity has many consequences. Among the most counter-intuitive ideas is the relativity of simultaneity- meaning that because of special relativity, events observed to be simultaneous in one frame may not be observed as simultaneous in another. Consider a train moving at a relativistic velocity (i.e. an appreciable portion of the speed of light, perhaps 0.5c or more). In the middle of a carriage is a light, and at either end of the carriage are doors with light sensors. When the light in the middle of the carriage is turned on, light travels to the doors, and the doors open as soon as their light sensors detect the light. To the person inside the train, both doors open at the same time because the distance to each door from the light source is equal. However, a person outside the train sees the doors opening as non-simultaneous. When the light turns on, the distance to each door is equal. However the observer from outside sees the train moving. This means that the light reaches the rear door faster than it reaches the front door (since the train is moving forwards, the front door is moving away from the point where the light was originally turned on). This illustrates the idea that simultaneity is dependant on the frame from which events are observed.

Mass and energy are linked by the formula E = mc2, which shows the “rest energy” of an object and also the amount of energy released if matter is destroyed and converted to pure energy. There are several equations that together govern the mathematics of simple relativistic effects:

L_v=L_0 \sqrt {1- \frac {v^2}{c^2} }

T_v= \frac {T_0}{ \sqrt {1- \frac {v^2}{c^2}} }

M_v= \frac {M_0}{ \sqrt {1- \frac {v^2}{c^2}} }

Length contraction means that as observed velocity increases, length appears to contract in the direction of movement according to (1.1). Time dilation means moving clocks appear to run slower as observed velocity increases, according to (1.2). Mass appears to increase as observed velocity increases according to (1.3). All of these observations are true only when the frame being observed and the frame of observation are both inertial reference frames. Note also that these changes are actual changes in the properties of space-time. Moving clocks appear to run slower because in the moving frame, time is actually elapsing at a different rate to time in the frame from which the observation is being made.

Discuss the implications of mass increase, time dilation and length contraction for space travel

Be very careful regarding the implications of time dilation. According to the twin paradox outlined by Einstein, the paradox exists because the other twin will appear younger for each of the twins. However, according to Einstein’s theory of general relativity the non-accelerated frame takes precedence, and so the twin on the spacecraft will actually be younger.

Relativistic effects have several implications for space travel. Mass increase shows that as speed increases towards c, mass increases up to infinity. What this means is that as a spacecraft gets faster, its mass increases and its acceleration progressively decreases. While acceleration never gets to zero, because mass increases a spacecraft can never travel at the speed of light. Time dilation means that astronauts in a relativistic spacecraft will age slower than people back on Earth, which means that they can effectively live longer during relativistic flight compared to a stationary observer, who will pass away well before the astronaut. Finally, length contraction means that as a spacecraft speeds up, the apparent distance to objects ahead of it decreases. This means that trips on a relativistic spacecraft will appear to cover less distance to observers in the spacecraft.

Remember- Conventional spacecraft can never travel at the speed of light, astronauts will age more slowly, and trips will appear to cover less distance from within the spacecraft.